Assessing the Quality of Asian Stock Market Indices - Corps ...

An EDHEC-Risk Institute Publication 

Assessing the Quality of Asian 

Stock Market Indices 

February 2013 

Institute

2 Printed in France, February 2013. Copyright© EDHEC 2013 

The opinions expressed in this study are those of the author and do not necessarily reflect those of EDHEC Business School. 

The author can be contacted at research@edhec-risk.com.

Assessing the Quality of Asian Stock Market Indices - February 2013 

Table of Contents 

Executive Summary..................................................................................................5 

1. Introduction...........................................................................................................17 

2. Literature Review...............................................................................................21 

3. Efficiency Analysis ............................................................................................31 

4. Stability Analysis ...............................................................................................67 

5. Conclusion...........................................................................................................93 

References................................................................................................................97 

About EDHEC-Risk Institute.............................................................................. 103 

EDHEC-Risk Institute Publications and Position Papers (2010-2013).......107 


3


About the Authors 

Narasimhan Padmanaban contributed to this report during his tenure as 

a Research Assistant at EDHEC Risk Institute—Asia in Singapore. He has 

a Master's degree in Financial Engineering from the Anderson School of 

Management, University of California, Los Angeles and a Bachelor's degree 

in Technology, Computer Science and engineering from the International 

Institute of Information Technology, Hyderabad. 

Masayoshi Mukai was an Analyst at EDHEC-Risk Institute at the time this 

report was written. He attended college at the University of California, 

Berkeley, where he graduated with high honors and was a Regents’ and 

Chancellor’s scholar. He also holds an MPhil in Management from the 

University of Cambridge, Judge Business School and is a member of Girton 

College. His research interests are in the area of equity and fixed income 

indexing innovation. 

Lin Tang was a Senior Researcher Engineer at EDHEC Risk Institute— 

Asia in Singapore when this study was prepared. She has contributed 

to industry surveys on ETFs, green investing and private wealth 

management and to a publication on dynamic asset allocation 

with ETFs. She has a Master’s degree in Risk and Asset Management 

from EDHEC Business School. Prior to joining EDHEC, Lin worked as a 

product engineer for one year after receiving her Bachelor’s degree in 

Engineering, with first-class honours, from Nanyang Technological University, 

Singapore. 

Véronique Le Sourd has a Master’s degree in Applied Mathematics from the 

Pierre and Marie Curie University in Paris. From 1992 to 1996, she worked 

as a research assistant in the finance and economics department of the 

French business school, HEC, and then joined the research department of 

Misys Asset Management Systems in Sophia Antipolis. She is currently a 

Senior Research Engineer at EDHEC-Risk Institute. 

4 An EDHEC-Risk Institute Publication

Executive Summary 


5



1 - Cf. Deutsche Bank 

Research Report (7 July 2011): 

http://www.dasinvestment. 

com/fileadmin/images/ 

Euro/11-07-15_Studie_ 

ueber_Einkommensstroeme_ 

von_ETFs.pdf 

Indexation continues to play an important 

role in global asset allocation. Total 

worldwide assets under internal indexed 

management rose to $5.994 trillion as of 

June 30, 2011, a 25% increase over $4.781 

trillion as of one year earlier (Olsen 2011). 

In addition, the market for exchange-traded 

funds (ETFs), which are liquid tracking 

vehicles for standard indices, has grown 

at an annual rate of 30% over the last three 

years globally, and is currently estimated 

to be around $1.4 trillion worldwide 

according to Deutsche Bank 1 . In Asia, total 

ETF assets increased by 20-30% annually 

post 2008 and the number of products have 

gone up by more than 200%. Currently 

the total ETF assets in the Asia-Pacific 

region are estimated at approximately 

$81 billion (Blackrock 2010). All of these 

factors point to an increasing interest 

in indexing management and investing 

directly in tracking products for standard 

market indices, both globally and in Asia. 

In the century-old history of indices, 

capitalisation-weighted indices have 

proven to be the most popular for the 

equity markets. Such indices are supposed 

to represent the market’s average returns 

and – due to their representativity – often 

serve as sources of information and as a 

bellwether for the economy. Beyond this 

informational role, standard cap-weighted 

(CW) indices are tools which have become 

an integral part of the investment process, 

used by a variety of investors, including 

pension funds, endowments and insurance 

companies. They are, however, used for many 

kinds of investment objectives, users and 

markets without any question of suitability. 

Even recently, there have been criticisms 

from both academics and practitioners 

who have questioned the efficiency, 

stability and representativity of 

cap-weighted indices (Haugen and Baker 

1991; Grinold 1992; Amenc et al. 2006; 

Arnott et al. 2005). Such studies often 

show evidence based on US and European 

markets. Though indices are widely accepted 

in Asia, either when assessing performance 

of active managers or when implementing 

passive strategies, relatively little analysis 

is done from an Asian perspective. This 

study will serve the purpose of assessing 

the properties of a range of popular Asian 

equity indices. 

We focus on the indices that are the most 

popular in terms of volume invested in 

related index products and analyse several 

indices for stock markets in Japan (Nikkei 

225 and Topix 100), China (FTSE China 25 

and CSI 300), Hong Kong (Hang Seng), 

Korea (KOSPI 200), India (Nifty 50), Taiwan 

(FTSE TWSE 50), Singapore (FTSE Straits 

Times Index) and for the ASEAN region 

(FTSE ASEAN Index, which is built from 

stocks from Singapore, Malaysia, Thailand, 

Indonesia and the Philippines). It should 

be noted that while most of these indices 

follow the standard cap-weighting scheme, 

the FTSE China 25 Index actually uses 

capping rules to limit the concentration in 

large cap stocks and the Nikkei index is price 

weighted rather than cap-weighted. In this 

study, we have examined whether the main 

issues with indices that have been outlined 

in the literature – often on the basis of 

analysing North American and European 

stock market indices – are also relevant 

for the major Asian market indices. First, 

we will present an analysis of efficiency. 

Whether indices are used as benchmarks in 

performance measurement or as underlying 

components for investment products, an 

efficient risk-reward profile of such indices 




is crucial to avoid using a poor starting 

point in the investment process (Amenc 

et al. 2006). Second, we will turn our focus 

towards stability, as investors typically 

perceive the benchmark to be a neutral 

choice of long-term risk factor exposures. 

However, some studies have suggested 

that the currently available market indices 

display unstable risk exposures over time 

(Amenc et al. 2006, Goltz and Sahoo 2011). 

We will summarise our key results in the 

following parts of this summary. 

I. Lack of Efficiency and 

Concentration Issues 

In this efficiency test, we have analysed 

the risk-return efficiency of current market 

indices and furthermore we have conducted 

a concentration analysis on our indices 

to investigate whether the concentration 

issue would be a possible explanation of the 

results we have found in our efficiency test. 

I.I. Lack of Risk-Return Efficiency 

If an index is risk-return efficient, this 

means that – per unit of risk – investors are 

reaping optimal reward from their equity 

investments. While Asian indices are not 

designed to offer any alpha opportunities 

related to Asian equity investments, indices 

should clearly provide investors with the 

normal return of Asian stock markets, and 

a relevant question is whether currently 

available indices are able to extract the 

equity risk premium in an efficient way. 

The risk-reward efficiency of standard 

stock market indices corresponds to a 

claim typically made by providers of 

such indices, often justified through the 

CAPM. Many index and passive investment 

product providers have emphasised that 

the CAPM provides a theoretical basis 

for standard market indices and for their 

market capitalisation scheme. However, 

Haugen and Baker (1991) as well as Goltz 

and Le Sourd (2010) have both reviewed 

the theoretical literature on the efficiency 

of the cap-weighted market portfolio and 

point out that there are few theoretical 

reasons to believe in the efficiency of 

cap-weighted equity indices, giving 

several arguments; firstly, the CAPM, 

which makes the theoretical prediction of 

an efficient market portfolio, is based on a 

number of highly unrealistic assumptions 

and even the academics, whose work has 

led to the development of model, recognise 

that under more realistic assumptions, 

cap-weighted market portfolios cannot 

be expected to be efficient (Markowitz 

2005 and Sharpe 1991). In particular, if 

investors do not have identical beliefs 

on risk and return parameters or if the 

market has frictions such as short sales 

constraints, the market portfolio in general 

is no longer risk-reward efficient. Also, 

the market portfolio under CAPM refers 

to a portfolio that holds all assets in the 

economy. The market portfolio is thus a 

theoretical construct that includes not 

only publicly listed stocks, but also other 

assets which in practice are either very 

illiquid or cannot be traded at all, such as 

housing and human capital. Clearly, the 

standard cap-weighted equity indices only 

include a small fraction of assets available 

in an economy and therefore would be very 

poor proxies for the true market portfolio. 

Empirically, Haugen and Baker (1991) 

and Grinold (1992) have shown that 

cap-weighted indices do not generate 

efficient risk-reward ratios. Such empirical 

findings support the theoretical arguments 

suggesting that cap-weighted stock market 


7



indices cannot be expected to provide 

efficient risk-reward. 

The present report conducts an analysis of 

efficiency of popular Asian equity indices, 

to complement the existing evidence for 

indices for other global equity markets. In 

this efficiency analysis, we test the validity 

of the claim that standard cap-weighted 

equity indices are efficient investments 

by measuring the distance in terms of 

efficiency between a given Asian stock 

market index and its alternatives on a mean 

variance plane. The alternative portfolios 

we test are based on portfolios made up of 

the same set of stocks as the cap-weighted 

index but use a different weighting scheme, 

notably equal-weighting, Global Minimum 

Variance (GMV) and Maximum Sharpe Ratio 

(MSR) weighting. There are several reasons 

for choosing these three portfolios: (i) 

Equal-weighted portfolios – which are even 

simpler than the cap-weighting – have been 

proven to consistently beat cap-weighted 

indices in terms of performance (Sharpe 

ratios or average returns) because they 

are less concentrated than cap-weighted 

indices (DeMiguel et al. 2009); (ii) The 

GMV and MSR portfolios lie on the 

efficient frontier and thus provide natural 

alternatives to a cap-weighted portfolios 

if one seeks risk-return efficiency as an 

objective. The aim of the MSR approach is 

to be the most similar to a cap-weighted 

index in term of constituents, but with a 

weighting scheme that allows for improved 

risk-return efficiency. Thus, MSR index 

weights are computed subject to several 

constraints, including no negative weights 

(no short sales are allowed) and upper and 

lower bounds constraints, depending on 

the index number of constituents. These 

latter constraints ensure that an MSR 

index includes all cap-weighted index 

constituent stocks (cf. Amenc et al. 2010). 

Likewise, a GMV index is also subject to 

such constraints. In this study, we use an 

in-sample construction for the efficient 

frontier portfolios in order to assess 

whether in principle, moving away from the 

cap-weighted scheme of standard indices 

allows risk-reward properties to be improved, 

and if so, to what degree there may be room 

for improvement. Our conclusion is that 

the existing Asian stock market indices 

are highly inefficient compared to either 

in-sample mean variance optimisation (the 

standard indices lie well inside the efficient 

frontier) or equal-weighting of the same 

stocks. 

We can summarise the results obtained 

from our analysis in the following two 

tables. Table 1 shows the improvements in 

Sharpe Ratio through an equal-weighted 

portfolio which is rebalanced daily, as well 

as for mean variance optimal portfolios 

(MSR and GMV) which are rebalanced 

annually. The results suggest that 

considerable improvements in terms of 

risk-reward efficiency (i.e. Sharpe ratio) 

are achieved by our stylised alternatively 

weighted portfolios. In fact, all alternative 

portfolios lead to a considerable increase in 

Sharpe ratio over the cap-weighted indices, 

except for the GMV weighted portfolio of 

FTSE China 25 stocks, which ends up with a 

lower Sharpe ratio than the cap-weighted 

index. 

These results suggest that standard stock 

market indices do not constitute an efficient 

portfolio in the sense of mean-variance 

efficiency. For an investor, this conclusion 

has strong implications when such stock 

market indices are used in the investment 




Table 1: Improvements in Sharpe Ratio through Equal-Weighted, Maximum Sharpe Ratio and Minimum Variance Indices compared 

to Standard Index 

Market Index Time Period Market Index 

Sharpe Ratio 

Difference in 

Sharpe Ratio of 

EW portfolio and 

mkt index 

Difference in 

Sharpe Ratio 

of Max Sharpe 

Portfolio and mkt 

index 

Difference in 

Sharpe Ratio of 

Min VaR portfolio 

and mkt index 

Hang Seng Jan 2002 - Dec 2010 0.53 0.11 1.38 0.47 

NIKKEI 225 Jan 1996 - Dec 2010 N/A 2 N/A N/A N/A 

TOPIX 100 Feb 1999 - Dec 2010 0.05 0.25 1.62 0.23 

FTSE STI Sep 2001 - Dec 2010 0.65 0.30 1.47 0.33 

KOSPI 200 Jun 2001 - Dec 2010 0.48 0.23 2.21 0.27 

TWSE 50 Jan 2003- Dec 2010 0.51 0.10 1.54 0.31 

CSI 300 Jan 2006 - Dec 2010 0.83 0.51 1.79 0.64 

FTSE China 25 Jan 2003 - Dec 2010 0.73 0.15 1.08 -0.19 

NIFTY 50 Jan 2003 - Dec 2010 0.82 0.25 1.64 0.40 

FTSE ASEAN Jan 2001 - Dec 2010 0.79 0.16 2.25 0.19 

2 - The Sharpe ratios for the 

Nikkei are invalid due to the 

negative aggregate return 

over the period. In fact, a 

negative Sharpe ratio is not 

meaningful as increases in 

volatility would increase 

the Sharpe ratio when 

excess returns are negative. 

Therefore we prefer not to 

report the results for indices 

where the Sharpe ratio is 

negative and hence indicate 

these cases as N/A. 

process. Prior to portfolio construction, 

investors conduct asset allocation 

studies to decide on the asset mix. Such 

studies are based on information on risk 

and returns for various asset classes or 

asset class segments, which in general is 

obtained by looking at standard indices. 

When using standard indices, it should be 

recognised that asset allocation decisions 

will in the end be based on an inefficient 

representation of investment opportunities 

in equity markets. Likewise, monitoring of 

managers and performance analysis will 

depend on the selection of the index as it is 

commonly used as a reference. Using indices 

which provide an inefficient risk-return 

profile may obviously not constitute a 

good starting point for such performance 

assessments. 

The implication of the inefficiency of 

cap-weighted indices is however not 

necessarily that such indices should 

be discarded as useful references. 

Cap-weighted indices do reflect the 

average behaviour on the market, and thus 

constitute a natural choice of a peer group 

for investors. However, what such indices 

may not sufficiently achieve is attractive 

risk-adjusted performance. This implies that 

investors could be better off by moving 

away from such peer group references. Any 

alternative will however introduce a relative 

risk of deviating from the peer group. 

Therefore, other than analysing practical 

alternatives for improving efficiency, an 

interesting question of further research is 

to analyse how relative risk can be properly 

managed. 

We would like to present some comments to 

provide context for further understanding 

of our results. 

Firstly, it should be noted that due to 

differences in the historical data available 

for index constituents and constituent 

returns, the starting time of the analysis 

is different for each index, so that 

comparisons across indices are not possible. 

Rather, the analysis provides a comparison 

of standard cap-weighted indexation 

against possible alternatives for a set 

of different datasets that span different 


9



3 - It should be noted that 

the time period of analysis is, 

however, not the same across 

the various indices. This 

conclusion is thus very broad 

and differences in distance 

from optimality may occur 

when comparing indices over 

identical and shorter time 

periods. 

geographies as well as different time 

periods. 

Secondly, one should note that the analysis 

for GMV and MSR portfolios here has been 

conducted on an ex-post basis, meaning 

that we have computed optimal weightings 

for each year, based on perfect knowledge of 

optimisation inputs, namely the covariance 

matrix of stock returns and expected stock 

returns. In practice, such information is 

not available and parameters have to 

be estimated using past data and such 

estimates will be subject to estimation error. 

Though both optimised portfolios used in 

this study are not realistic in the sense 

that they require perfect knowledge of 

certain input parameters, the comparison 

with in sample optimisation based 

strategies provides some information 

about the magnitude of the inefficiency of 

cap-weighted indices. Indeed, although the 

optimisation based indices require perfect 

knowledge on risk-return parameters, they 

are based on the exact same universe of 

stocks as the standard indices and thus 

do not include the possibility to select 

stocks that lie outside the universe. 

In addition, such in-sample optimisation 

strategies can provide information about 

how much more efficient a portfolio could 

be in the ideal case of perfect knowledge 

of input parameters. To get an assessment 

of efficiency that does not rely on any 

input parameters, we also test an equalweighted 

strategy in all of these universes. 

Even with such a naïve alternative, which 

weights all stocks equally, Table 1 shows a 

clear outperformance of equal-weighted 

portfolios in terms of Sharpe ratio compared 

to the standard market indices. 

Overall, our results are comparable with 

earlier studies on major indices in developed 

markets (Amenc et al. 2006), which were 

found to be highly risk-return inefficient 

compared to in-sample optimal portfolios 

and even equal-weighted portfolios. The 

comparison of distances in terms of Sharpe 

ratio between market indices and test 

portfolios made of the same components, 

but lying on the in-sample efficient frontier 

(Max Sharpe Portfolio, Min Var Portfolio) 

has shown comparable magnitudes for 

Asian indices and European and US indices 

showing that the level of inefficiency 

between Asian indices and European and 

US indices are quite comparable 3 . However, 

such findings may not be surprising given 

that cap-weighting automatically gives 

very high weights to large companies and 

leads to highly concentrated portfolios, 

whereas equal-weighted portfolios 

provide some form of de-concentration, 

and the optimal portfolios by definition 

provide the best diversified portfolios that 

lead to efficient risk-reward. In order to 

further develop the analysis of standard 

indices in Asia, it is appropriate to directly 

analyse how concentrated these indices 

are, as concentration could be a potential 

explanation for the inefficiency reported 

above. 

I.II. Concentration in standard indices 

Cap-weighted indices are often blamed 

for their concentration in a few large 

stocks. Tabner (2007) found considerable 

concentration in the top 10 firms and 

industries for the FTSE 100 Index in 1984 and 

2005. This concentration issue is however 

not unique to the index Tabner studied. 

In fact, Malevergne et al. (2009) argue 

that cap-weighted indices are in general 

heavily concentrated in a few large firms, 




4 - FTSE China Factsheet 

http://www.xfn.com/ 

uploadedFiles/products-andservices/indices/xinhua-ftseindex/FXIbrochure2004.pdf. 

The constituent weights are 

capped at 10% of the total 

index. 

and attribute this to the general shape of 

the distribution of firm size in the economy, 

where a few large firms dominate and are 

followed by firms which rapidly decrease in 

size. However, since these studies all focus 

on the developed market, we would like 

to find out how Asian indices behave with 

regard to the concentration issue. 

There are several ways of measuring 

concentration in an equity portfolio. We 

present the summary of our findings in 

the following table. Table 2 first reports the 

nominal number of stocks that were to be 

found in the respective index on average 

over the time period we studied (see 

Column 3). However, this nominal number 

of stocks may not give a good indication 

of the number of stocks that are effectively 

held in the index, if the index gives most 

weight to a small fraction of the index 

constituents. For example, if an index of 100 

stocks invests 99% of the weight in a single 

stock, the effective number of stocks held 

is close to one while the nominal number 

of stocks is 100. The effective number of 

stocks (presented in Column 4), which is 

computed as , is a formal measure 

of de-concentration. It corresponds to 

the number of constituents in an equalweighted 

portfolio that leads to the same 

concentration as the cap-weighted market 

index. The smaller the difference between 

the nominal number and the effective 

number, the less concentrated the index. 

Hence, we also present the ratio between 

the effective number of stocks and the 

nominal number of stocks for each index. 

The last column provides a simpler measure 

of concentration by reporting the weight in 

the standard index occupied by the largest 

20% of the index constituents. 

Our findings show that most market indices 

in Asia are highly concentrated. For all 

but two indices, the effective number of 

stocks held in the index is less than 50% 

of the actual number of stocks. This is 

equivalent to saying that most of the 

cap-weighted indices are as concentrated 

as an equal-weighted index which holds 

less than half of their constituent stocks. 

Concentration is also clearly visible from 

the weight made up by the largest fifth 

of constituents. Except for the FTSE China 

25 Index 4 , the largest fifth of constituents 

Table 2: Concentration in standard indices 

This table is the summary of the results from the concentration analysis. Column 4 represents the effective number of stocks which 

is calculated by the formula - Effective number of stocks = . In column 5 we calculate the ratio of Effective number of 

stocks/Number of constituents in the index. 

Index Time Period Average nominal 

number of 

constituents 

Average effective 

number of stocks 

(Effective number 

of stocks)/(nominal 

number of stocks) 

Weight 

concentration in top 

fifth of constituents 

Hang Seng Jan 2002 to Dec 2010 45 11.7 29.3% 63.3% 

Nikkei 225 Feb 2001 to Dec 2010 225 82.6 36.7% 61.2% 

Topix 100 Jan 2001 to Dec 2010 100 49.0 49.0% 49.7% 

FTSE STI Feb 2008 to Dec 2010 30 16.9 56.2% 50.3% 

KOSPI 200 Feb 2002 to Dec 2010 200 20.9 10.4% 80.0% 

TWSE 50 Jul 2003 to Dec 2010 50 20.6 41.2% 52.3% 

CSI 300 Sep 2005 to Dec 2010 300 91.1 30.3% 59.5% 

FTSE China 25 Mar 2004 to Dec 2010 25 18.6 74.4% 40.2% 

Nifty 50 Feb 2002 to Dec 2010 50 21.6 43.2% 56.7% 

FTSE ASEAN Jan 2001 to Dec 2010 163 49.2 30.2% 63.3% 


11



5 - Samsung occupied close 

to 15% weight of KOSPI 200 

index in Dec 2010. This was 

followed by POSCO (5.5%) 

and Hyundai (4.5%). 

have all roughly taken up at least a half of 

the share in the index. Based on Table 2, the 

KOSPI 200 Index is the most concentrated 

index 5 , with an effective number of stocks 

of 21 compared to the nominal number of 

200 stocks. And the weights of top fifth of 

constituents account for 80% of the entire 

index. Clearly, an investor who chooses the 

KOSPI index should take into account this 

heavy concentration, which is unlikely to 

lead to a well-diversified portfolio. 

Comparing results obtained in Table 1 and 

Table 2, it appears that indices for which we 

observe the maximum difference in Sharpe 

ratio between the MSR portfolio and the CW 

portfolio are also the ones exhibiting the 

highest concentration, i.e. the lowest ratio 

of effective number of stocks to nominal 

number of stocks. For example, Table 1 

shows that the Sharpe ratio of the MSR 

portfolio obtained with the components 

of the KOSPI 200 index exhibits a highly 

pronounced increase with a Sharpe ratio of 

2.21 compared to the Sharpe ratio of the 

standard CW index. This index is precisely 

the most concentrated of our sample as its 

effective number of stocks represents only 

about 10% of its nominal number of stocks. 

On the other end of the spectrum, the FTSE 

China 25 index is the one for which we 

observe the minimum difference in Sharpe 

ratio between the MSR portfolio and the CW 

portfolio (1.08), and also the one exhibiting 

the lowest concentration, as its effective 

number of stocks amounts to about 74% 

of its nominal number of stocks. Thus, it 

appears that the observed inefficiency of 

standard market indices can be seen as an 

opportunity cost of concentration. 

Overall, our results on the inefficiency 

of standard indices relative to equalweighted 

portfolios of the same stocks or 

relative to in-sample optimal portfolios 

show that there is considerable room for 

improvement when one tries to construct 

well-diversified portfolios in standard 

equity universes for Asia. While the 

alternatively weighted portfolios we use for 

the assessment of standard indices ignore 

practical constraints and are not meant to 

be practical alternatives, they provide an 

estimate of the order of magnitude by which 

standard indices fall short of the efficiency 

that could in principle be obtained within 

an identical universe of stocks, and thus 

without any stock selection ability. More 

importantly, we analyse a common issue 

across all different standard Asian indices, 

which is their high concentration in a small 

number of stocks. Most indices allocate 

as much as 60% of the index weight to 

only one fifth of the stocks in the universe. 

With these tendencies it is not surprising 

that such indices are not well diversified 

portfolios. To be sure, such concentration 

and inefficiencies do not mean that the 

indices analysed in this study fall short 

of representing the average behaviour of 

investors on the respective market, and 

in this sense, they can be an indicator of 

peer group performance. However, for 

investors who are interested in holding 

well-diversified equity portfolios, one can 

see these results as a motivation to explore 

whether more appropriate alternatives can 

be developed in practice. 

II. Lack of Stability 

In order to test whether the major Asian 

indices offer a stable exposure to sectors 

and styles over time, we conducted the 

following two analyses. 




6 - We used the GICS 

classification. 

7 - The average sector drift 

scores for FTSE All Share 

Index 700, DJ Euro Stoxx 300, 

DJ Stoxx 600, Topix 1666 and 

S&P 500 are about 6.5 to 

7.5%, except Germany Prime 

All Share Index 380, which 

is 10.4%. 

For the sector analysis, we obtained 

monthly constituent weights for 10 years 

from 2001 (or from the earliest possible 

starting data if this is later) until December 

2010. We then drew on the classification of 

constituent stocks into ten sectors, which 

are Energy, Materials, Industrials, Consumer 

Staples, Consumer Discretionary, Health 

Care, Financials, Information Technology, 

Telecommunication Services, and Utilities 6 

to obtain the time series of monthly sector 

weights in each index. 

For the style stability test, we use Sharpe’s 

(1992) Return Based Style Analysis (RBSA) 

which consists of a constrained regression 

of the daily return of each index on the 

returns of MSCI country value and growth 

indices. A 250-day rolling window was used 

in order to generate the time series for the 

estimated style exposures. 

Table 3 reports the drift scores for both 

style and sector stability tests. The drift 

score, which is defined as , 

where denotes the variance of the time 

series of the respective style exposure, 

is initially proposed by Idzorek and Bertsch 

(2004). It allows the variability of the style 

exposures across different indices to be 

assessed. 

Our results show that all indices exhibit 

considerable variations in the both sector 

and style exposures during the test period. 

If we look at the sector exposure stability 

in detail, we find that market indices in 

more developed countries (Hong Kong, 

Japan, Singapore, South Korea and Taiwan) 

demonstrate relatively more stability, 

whereas market indices in less developed 

countries (China and India) display higher 

variability over time in terms of sector 

allocation. However, such a clear pattern 

does not exist for the style drift scores. 

We also compare our results with the study 

done by Amenc et al. (2006), which looked 

at equity indices for various developed 

markets – in particular Europe, Japan and 

US markets. We find that the sector drift 

scores for indices in developing countries, 

such as China and India, are much higher 

than the indices in Europe, Japan and US 7 , 

but scores for indices in Asia developed 

markets, such as Hong Kong, Japan, 

Singapore, South Korea and Taiwan, are 

quite comparable with results reported in 

Amenc et al. (2006). In addition, the style 

exposure for Asian market indices seems to 

be less stable than that of European market 

indices. This finding implies that investing in 

Asian markets, especially in less developed 

markets, such as China and India, requires 

even more attention to the variation of risk 

factor exposures. 


13



Table 3: Summary of the sector/style stability of Asian indices 

This table is the summary of the results from the style and sector stability tests. Column 3 and 5 represent the period of the results. 

And column 4 and 6 present the style drift score calculated based on the Idzorek and Bertsch (2004) for both style and sector 

variations over the test periods. 

Geographical zone Index Sector stability test Style stability test 

Period Style drift score Period Style drift score 

Hong Kong Hang Seng Index Jan 2001 to Dec 

2010 

8.89% Jan 2002 to Dec 

2010 

11.77% 

Japan NIKKEI 225 Index Jan 2001 to Dec 

2010 

TOPIX 100 Index Jan 2001 to Dec 

2010 

Singapore 

FTSE Strait Times 

Index 

Feb 2008 to Dec 

2010 

South Korea KOSPI 200 Index Feb 2002 to Dec 

2010 

Taiwan 

FTSE TWSE Taiwan 

50 Index 

Jul 2003 to Dec 

2010 

China CSI 300 Index May 2005 to Dec 

2010 

FTSE China 25 

Index 

May 2005 to Dec 

2010 

India NIFTY Index Jan 2002 to Dec 

2010 

ASEAN FTSE ASEAN Index Jan 2001 to Dec 

2010 

4.83% Jan 2002 to Dec 

2010 

20.59% 

6.81% Jan 2002 to Dec 12.79% 

2010 

4.39% Jan 2002 to Dec 6.39% 

2010 

8.44% Jan 2002 to Dec 8.48% 

2010 

6.51% Jan 2002 to Dec 5.80% 

2010 

11.44% Jan 2003 to Dec 8.96% 

2010 

11.11% Mar 2002 to Dec 19.53% 

2010 

11.51% Jan 2002 to Dec 6.64% 

2010 

5.02% N.A. N.A. 

Our stability analysis shows that Asian 

indices suffer from pronounced fluctuations 

of their risk factor exposures. These 

findings imply that investors are exposed 

to implicit choices on risk factor exposures 

when tracking a market index. In other 

words, investments which passively hold 

the market index do not correspond to an 

absence of preferences in sectors or styles, 

but instead follow the exposures of the 

market index which fluctuate considerably 

over time. For investors, such variation 

over time leads to a clear implementation 

risk of their asset allocation choices as the 

implicit choices the index makes over time 

may not correspond to investors’ original 

choices. 

III. Concluding Remarks 

The present study analyses a set of popular 

equity indices for different Asian markets. 

For such indices to be relevant starting 

points in investment decision making, a 

key requirement is that they provide an 

efficient risk-reward trade-off. While our 

study does not provide implementable 

alternatives to standard equity indices, 

our analysis shows that the standard 

indices are located far from the in-sample 

efficient frontier, and also underperform 

equal-weighted portfolios drawing on the 

same set of constituents. We also assess 

whether the standard indices for Asian 

markets are “passive” references in the sense 

that they provide stable style and sector 

exposures. Our results show that all indices 

exhibit considerable variability of exposures 

over time, leading to a pronounced 

implementation risk for investors who 




have made the decision to allocate assets 

based on current exposures, and who will 

bear the indices’ implicit shifts in style 

and sector exposures over time. Overall, 

our analysis suggests that for investors 

looking for stability of risk exposure, or 

pure economic exposures, simply holding 

a standard cap-weighted market index 

may fall short of fully addressing their 

concerns. On the other hand, there is 

little to argue about other important 

qualities of such indices. In particular, they 

represent highly liquid portfolios. Thus, such 

standard cap-weighted indices are suitable 

underlying components for derivatives and 

useful as peer group benchmarks. However, 

if investors are seeking to address efficiency 

or stability issues, our results suggest 

that there is room for improvement over 

standard indices. 

This improvement of standard indices is 

a first order issue when trying to capture 

the risk premium of equity markets in an 

efficient way. Indeed, when turning to Asian 

equity markets as opposed to European and 

North American equity markets, investors 

often do so out of a concern over improving 

risk adjusted performance. Arguably, 

Asian equity markets with the higher 

growth of the underlying economy may 

be able to provide such outperformance. 

However, when trying to capture such 

outperformance, investors need to address 

the crucial question of how to capture it 

in the most efficient way. 

Indeed, one can make the case, that rather 

than investing in Asian markets, investors 

could improve their performance by 

improving the way in which they capture 

the equity premium in European or US 

equity markets. An interesting question is to 

compare the performance differences due 

to geographic choices of equity exposure 

to the performance differences obtained 

by improving the weighting scheme. 

We now turn to an illustration on these 

performance differences. In this illustration, 

as a starting point we take a US investor 

who captures the equity risk premium 

through a domestic investment where he 

stays with the cap-weighted index. We 

then assess the risk-adjusted performance 

benefits of improving the weighting 

scheme (here we use a minimum volatility 

strategy and compare it to the performance 

improvement which comes from changing 

the geographic exposure from the US to 

Asia. The choice of investing in the US 

minimum volatility index, rather than in 

the S&P 500 index produces higher Sharpe 

ratios, whatever the period considered 

(see table 4). Investing in an Asian index, 

represented here by the MSCI Developed 

Asia-Pacific ex-Japan (free-float weighted) 

index, rather than in a US cap-weighted 

index, also allows investors to obtain higher 

performance, but not so consistently over 

time, compared to the use of a US index 

built with an improved weighting-scheme. 

Indeed, the MSCI Asian index outperforms 

the S&P 500 over the one-year and the 

10-year period, it underperformed the S&P 

500 index over the 3-year and the 5-year 

period. These results suggest that selecting 

the right weighting scheme is at least as 

important as selecting the right geographic 

exposure. 

Moreover, if the investor in this illustration 

had selected the better performing 

geographic exposure (i.e. Asian exposure 

rather than US exposure), they would have 

been able to potentially further improve 

performance by also selecting the better 


15



weighting scheme. In fact, the minimum 

volatility weighting of Asian stocks would 

have led to a consistently higher Sharpe ratio 

than its cap-weighted counterpart. Over the 

full history analysed in this illustration, 

moving from the US cap-weighted index to 

the Asian cap-weighted index would have 

increased the Sharpe ratio from 0.19 to 0.52. 

Improving the weighting scheme would 

have led to a further increase in the Sharpe 

ratio from 0.52 to 0.78. Thus, investors 

who want to capture the Asian market 

premium will do it even better if they use 

indices designed with an efficient weighting 

scheme. In addition to carefully considering 

their geographic exposure, investors clearly 

need to consider the weighting scheme 

that will allow them to extract the equity 

risk premium for a given geography in the 

best possible way. 

Table 4. Comparison of the Sharpe ratio of Minimum Volatility index and Cap-weighted index for US and Asian indices 

S&P500 US Min Volatility MSCI Developed 

Asia-Pacific ex-Japan 

Cap-weighted 

Developed Asia-Pacific 

ex-Japan Min Volatility* 

1Y 1.25 1.32 1.54 1.72 

3Y 0.58 0.78 0.36 0.56 

5Y 0.05 0.15 0.01 0.11 

History** 0.19 0.33 0.52 0.78 

* We calculated out of sample returns of a norm constrained minimum volatility strategy applied to the 400 largest stocks in the 

Developed Asia-Pacific ex Japan universe. 

** The history period refers to the inception of the Min Volatility indices and begins on June, 21st, 2002. All the computations were 

done with data up to December 31st, 2012. 


1. Introduction 


17



Equity indices are widely used in 

investment management. An index is a 

portfolio representative of one or more 

risk factors of which the investor wishes to 

take exposure. For example, a geographic 

index aims to be representative of the 

risk of the stock market of the country 

under consideration, while a style index 

and a sector index are representative of 

the risks of a particular investment style 

or industry sector. The standard way of 

constructing equity indices is to attribute 

weights to individual stocks in proportion 

to the stock’s market capitalisation. 

We speak of indexed management when 

the index is the benchmark of the portfolio. 

However, it is useful to draw a distinction 

between an investor’s inter- or intra-class 

allocation choices, also called a custom 

benchmark or strategy benchmark, and 

an investor’s choice of indices, also called 

reference indices. This is essential because 

these two terminologies are often used 

indiscriminately in practice even though 

they are two different concepts: 

• A reference index is a portfolio that 

should represent the performance of a 

given segment of the market, so the focus 

is on representativeness; 

• A custom benchmark is a portfolio that 

should represent the fair reward expected 

in exchange for risk exposures that an 

investor is willing to accept, so the focus 

is on efficiency. 

Given that the main aim of indices is to 

represent a segment, and thus provide a 

proxy for a “peer group” or the average 

performance of all investors in the market, 

it is perhaps not surprising that investors, 

who are first and foremost interested in 

the financial performance and the risk and 

return properties of their portfolios, may 

wish to deviate from such market indices 

and define custom benchmarks which 

better reflect their investment strategy. 

Such a custom benchmark will however be 

judged not only on its capacity to enable 

investors to achieve their diversification 

objectives and financial performance, but 

also on the relative risk that it includes 

relative to the cap-weighted index. 

The focus of the present study is on the 

properties of the widely used reference 

indices in Asian equity markets. Such 

standard indices available in the market 

are widely used in the investment 

management process by investors. Total 

worldwide assets under internal indexed 

management rose to $5.994 trillion as 

of June 30, 2011 – a 25% increase over 

$4.781 trillion as of one year earlier 

(Olsen 2011). In addition, the growth in 

index products can also be seen through 

a particular market segment, such as 

the market for exchange-traded funds, 

as these funds constitute liquid tracking 

vehicles for standard indices. The total 

global ETF assets have grown tenfold 

from 2000 to the end of 2007. Though 

the financial crisis 2008 stopped the step 

of growing, the global ETF market quickly 

recovered from the crisis and grew to 

about US$1.4 trillion at the end of 2011 

(BlackRock 2011a). In the Asia-Pacific 

region (including Japan), total ETF assets 

increased by 50% to about US$ 91 billion 

between the 2nd quarter of 2010 and 

the 2nd quarter of 2011 (Deutsche Bank 

2011); and the number of products had 

gone up from 280 at the end of 2010 to 

451 in May 2011 (BlackRock 2011b). All 

of these factors point to an increasing 

interest in investing directly into tracking 




products for standard market indices both 

globally and in Asia. Given the general 

relevance of indices in the investment 

process, and the recent growth in index 

tracking products in Asia, it seems useful 

to analyse the properties of the standard 

market indices in detail. 

This document is organised as follows. 

We begin by providing a detailed review 

of academic research on major issues 

with cap-weighted indices in Section 

2. In Section 3, we provide a detailed 

methodology, and the results from the 

efficiency analysis and the concentration 

analysis for the same set of indices. 

Finally, in Section 4, we will present the 

sector and style stability tests for Asian 

market indices. 


19




2. Literature Review 


21



8 - This difference between 

the investability and the 

liquidity requirement perhaps 

needs to be explained in more 

detail and this is best done 

using a simple example. For 

instance, in China, there are 

two classes of shares for a 

company: A shares and B 

shares. Domestic investors 

can trade A shares but 

foreign investors are only 

able to access to B shares. In 

principle, these two classes of 

shares are identical with their 

payoffs and voting rights, but 

research has shown that A 

shares are traded much more 

heavily than B shares (Mei 

et al. 2009). Hence, an index 

comprising China A shares 

would be very liquid but 

not investible for investors 

outside China, as investors 

could not access those shares, 

and as a result they are not 

able to replicate the index. 

The importance of the indexing industry has 

grown tremendously. From the supply side, 

while historically there tended to be one 

dominating index provider for each market, 

both index providers and investment banks 

now offer indices and compete on a global 

scale. This growing competition has also 

lead to more innovative indices coming 

to the markets, and as a result, from the 

demand side, index users face an increasing 

array of choices. 

In fact, indices have played an important 

role in performance measurement as well 

as in investment decision making, i.e., in 

the investment processes and portfolio 

selection models. Given the variety of 

available indices and the crucial importance 

on the investment outcome that choosing 

an index has, a natural question is “what 

makes a good index?” In the literature, 

there are some commonly held rules for 

selecting and assessing an index. Arnott 

et al. (2008, 64) argue that an index should 

be representative, replicable, transparent 

and rule-based, as well as having low 

turnover. Kamp (2008) also points out that 

“an index should be transparent, broad and 

‘investable’”. Although different terms are 

used by different authors for index quality 

criteria, overall, we can summarise them 

into four main qualities: representativity, 

transparency, liquidity and investability. 

• Representativity is an oft-cited quality 

for an index. It refers to the belief that an 

index must represent market activity in 

e.g. a market segment or region. However, 

it should be noted that representativity is 

rarely clearly defined, and the appropriate 

method of measuring the representativity 

of an index is still an outstanding question. 

It is the reason why we do not include tests 

on Asian index representativity in this study. 

• Transparency focuses on the availability of 

the documents describing the concepts and 

methodology used to compute the index, as 

well as availability to current and historical 

data on index values and composition. This 

is critical for investors as transparency 

helps them fully understand what indices 

are doing. In Arnott et al. (2008, 64)’s 

definition, transparency also includes the 

use of consistent and systematic rules in 

the construction methodology. 

• Liquidity ensures that an index can be 

traded by many investors without any price 

impact. 

• Investability guarantees that the 

underlying securities of an index are 

accessible and tradable so that the index 

can be reconstructed. 8 

Besides the above characteristics, 

investment managers explicitly or implicitly 

seek efficiency from an index. When indices 

are used as investment benchmarks, the 

focus on representativity may be of little 

relevance, as achieving the highest possible 

risk-reward ratio is crucial if one does not 

want to have an inefficient starting point 

for the investment process (Amenc et al. 

2006). So a benchmark should represent 

the best investment choice the investor 

can make in the absence of privileged 

information or bets on specific securities. 

In addition to risk-reward efficiency, 

investors typically perceive the benchmark 

to be a neutral choice of long-term risk 

factor exposures. However, some studies 

have suggested that the currently available 

market indices (both equity and bonds) 

display a lack of stable risk exposure (Amenc 

et al. 2006, Campani and Goltz 2011). 

It has been argued that the risk factor 

stability of a benchmark is an important 




consideration when assessing an index. 

In fact, an index with unstable implicit 

exposures over time could potentially 

compromise the explicit risk factor 

allocation decisions that investors have 

taken when defining their global asset 

allocation choices. 

After establishing the key attributes of 

indices, the next question which concerns 

investors is whether or not current market 

indices exhibit these characteristics. From 

the history of equity indices, we find that 

other than the price-weighted index, which 

was the inaugural index, the standard 

approach of capitalisation-weighted 

indices, which are often perceived as a 

bellwether for the economy, was initially 

designed by stock exchanges to measure 

the state of the market is and not meant as 

a tool for long-term investors. To achieve 

the target of representing the markets, the 

index will simply reflect how the market 

behaves. But risk-return qualities, such 

as the diversification of the portfolio and 

stable risk exposures or efficient risk-reward 

ratios, play a critical role for long-term 

investments as the index is used to reflect 

how one could invest systematically in the 

market to achieve desirable risk-return 

properties. Therefore, in this section, we 

will present the main issues associated with 

the cap-weighted (CW) indices for long 

term investors. But before the discussion 

on these issues, we would like to briefly 

introduce the theoretical justification for 

cap-weighted indices. 

2.1 The Theoretical Basis of 

Cap-Weighting 

In academic theory, the use of cap-weighted 

indices is often derived from the central 

conclusion of modern portfolio theory – 

which uses the Markowitz (1959) rendition 

of efficiency. By this definition, every 

investor’s “efficient” strategy would be 

to hold an optimal portfolio that is mean 

variance efficient. According to the CAPM 

(Capital Asset Pricing Model), a pioneering 

development in financial theory (Markowitz 

1952; Sharpe 1964; Lintner 1965), finally 

formulated by Sharpe 1964), all investors 

desire to hold the same optimal portfolio 

made up of all existing risky assets, 

weighted by their market capitalisation. 

This so-called “market portfolio” 

theoretically offers an efficient risk-return 

trade-off. In other words, under the theory, 

no other combination of risky assets can 

obtain a better return for the same degree 

of risk, or a lower risk for the same expected 

return. If we believe this theory (CAPM) 

reflects the real world, any investor should 

indeed hold the market portfolio. But even 

assuming the CAPM to be a valid strategy, 

stock market indices appear to be very 

poor proxies for the market portfolio. 

Roll (1977) had famously noted that the 

true market portfolio cannot be observed, 

because it must include all risky assets – 

not just traded financial assets, but also 

consumer durables, real estate and human 

capital. But stock market indices include 

only a small fraction of listed assets. Thus, 

even if investors believe in the efficiency 

of the market portfolios, they should not 

reasonably expect the cap-weighted equity 

indices to be efficient. 

Since it is clear that the CAPM theory does 

not reflect the real world, the failure to 

hold off any one of the assumptions made 

by the CAPM may mean that theory does 

not predict an efficient market portfolio. 

The theory assumes investors are identical 


23



in terms of preferences and all have the 

same investment horizon. It also assumes 

unlimited borrowing or short selling, 

tradability of all existing assets and absence 

of any taxes or transaction costs. It is 

unreasonable to assume these assumptions 

hold in practice. After all, investors are 

unlikely to have the same preferences and 

the same investment horizons, while the 

existence of taxes and transaction costs 

is quite real. Nor is unlimited borrowing 

feasible for most investors. In fact, Sharpe 

(1991) and Markowitz (2005) themselves 

have emphasised that the market portfolio 

may not be efficient in a more realistic 

setting. 

After a detailed review of the literature, 

Goltz and Le Sourd (2010) conclude that, 

as soon as one of the CAPM assumptions 

no longer holds, financial theory does not 

predict that the market portfolio is efficient. 

2.2 Inefficient Risk-Reward Ratios 

From these concepts, we understand that 

market indices are imperfect proxies for 

the true market portfolio even if CAPM is 

true. There is also a large body of empirical 

studies dedicated to support this argument. 

Haugen and Baker (1991) test the efficiency 

of the Wilshire 5000 index, which is the 

most comprehensive cap-weighted index 

in U.S. Their results suggest that it is 

possible to construct equity portfolios with 

higher risk-reward efficiency than their 

cap-weighted counterparts. Another paper, 

by Sinclair (1998), also shows that equity 

market indices do not generate efficient 

risk-reward ratios. Such empirical finding 

supports the previous theoretical arguments 

that investment opportunities existed to 

build equity portfolios that exhibit better 

risk-reward ratios than cap-weighted 

indices. Similarly, Grinold (1992) adopted a 

Gibbons, Ross and Shanken (GRS 1989) test 

to examine if the five equity benchmarks 

in the US, the UK, Australia, Japan and 

Germany are efficient. The findings showed 

that out of these five countries, the first 

four indices are not efficient which implies 

that other portfolios could be constructed 

to outperform the benchmarks. 

Rather than directly testing the efficiency 

of the market portfolio, additional 

literature has looked at the efficiency of 

cap-weighted portfolios by comparing the 

performance of the cap-weighted portfolios 

to other portfolios constructed with same 

set of constituents but with a different 

weighting scheme applied to them. 

Establishing that portfolios constructed 

from other weighting schemes have better 

risk adjusted returns would clearly mean 

that the cap-weighted portfolios are not 

mean variance efficient. In a recent study, 

Amenc et al. (2011), comparing alternative 

weighted indices including the fundamental 

index, equal-weighted index, efficient 

index, and minimum volatility index, find 

that all these indices show, on average, 

returns superior to those of cap-weighted 

equity indices. Platen and Rendek (2010) 

observe that the equal-weighted portfolios 

constructed from country indices in each 

country had higher Sharpe ratios than the 

corresponding Cap-weighted indices in all 

53 countries tested. Tamura & Shimuzu 

(2005) compare the performance between 

the cap-weighted indices and indices that 

weight stocks by firm characteristics and 

find that the characteristics based portfolios 

produce positive excess returns over the 

cap-weighted indices in their data sample 

of more than 15 years. Chou et al. (2006) 




document that investors who maximise 

the Sharpe ratio of their portfolio based 

on the expected returns generated from a 

multifactor model using firm characteristics 

(see Daniel and Titman (1997) or Daniel 

et al. (2001)) have significantly higher risk 

adjusted returns. They perform this analysis 

on Japanese stocks composing the Nikkei 

index. 

2.3 Concentration in Large Stocks 

Besides the efficient risk-return trade-off, 

CAPM also predicts that the market portfolio 

should be well-diversified – there would be 

only systemic risks as all idiosyncratic risks 

have been diversified. However, literature 

shows that cap-weighted indices are in 

general very concentrated in some large 

stocks. For instance, Strongin et al. (2000) 

find that due to heavy weighting of the 

large capitalisation stocks, the S&P 500 

index actually consists of 86 effective stocks 

and the Russell 1000 index of 118 effective 

stocks. According to Bernstein (2003), 

the S&P 500 index cannot be considered 

a diversified portfolio because the 10 

largest companies in the index account 

for 25% of the market value, and the top 

25 companies account for 40%. Tabner 

(2007) has compared the concentration 

of the top 10 firms and industries in the 

FTSE 100 Index in 1984 and 2005. He 

finds that there is a dramatic increase 

in the concentration of the top 10 firm/ 

sector holdings. This concentration issue 

is however not unique to the index Tabner 

studied. In fact, Malevergne et al. (2009) 

argue that cap-weighted indices are in 

general heavily concentrated in a few large 

firms. In addition, since cap-weighted 

indices assign weights to stocks by their 

market capitalisations, which is the product 

of the price of one share of the stock and 

the total amount of shares, if there is no 

new share offered (or bought back), the 

weight of any stocks depends on the share 

price. Whenever share price goes up (down), 

the market capitalisation of that company 

goes up (down). As a result, the weight 

will increase (decrease). Accordingly, the 

concentration in large stocks may become 

higher over time. 

A different argument about the problems 

with concentrated portfolios is provided by 

Malevergne and Sornette (2007), followed 

by Malvergne et al. (2009). They argue that 

there is a new source of risk that should be 

priced into the assets when the portfolios 

are highly concentrated in few stocks. 

They show that even for economies with 

an ample number of securities, when the 

companies exhibit a fat tailed distribution 

of sizes, the total risk of the portfolio does 

not reduce relative to its market risk. Both 

of these arguments essentially imply that 

index performance is often dictated by 

performance of a few big stocks in the 

index and do not provide investors with 

the risk reduction through diversification, 

as is generally perceived to be the case. 

Goltz and Sahoo (2011) present simplified 

examples of the negative effects of 

concentration on performance, and 

how it produces a significant drag in 

market portfolio returns due to relative 

underperformance of a single large stock 

in the index. These results are reproduced 

in Table 2.1. 


25



Table 2.1: Impact of Single Stock Behaviour on Cap-weighted Indices 

The following table presents cases showing the impact of stock-specific events on the cap-weighted index. The index used for 

comparison is the index which holds all relative weights proportional to the market cap but only changes the weight of the stock 

discussed here to 1/N where N is the number of index constituents. The returns and volatility are calculated based on the period 

examined and are not annualised. 

Time Cap-weighted 

Index 

Single Stock 

Name Return Volatility Name Return Volatility Weight 

at the 

peak 

2010Q2 -2010Q3 FTSE100 -6.70% 20.20% British 

Petroleum 

Index with relevant 

stock down 

weighted to a 1/N 

weight 

Return Volatility 

-74.80% 47.10% 8.00% -0.30% 20.80% 

10/29/2008 DAX -0.30% N.A. Volkswagen -45.00% N.A. 27.00% 15.90% N.A. 

2000Q3 - 2001Q3 EURO -34.20% 23.60% Nokia -83.90% 73.00% 10.50% -30.30% 21.90% 

STOXX 

50 

Goltz and Sahoo (2011) 

2.4 Presence of Factor Exposure in the 

Market Indices 

Other than the inefficient risk-reward ratios 

and concentration in large stocks, Cochrane 

(1999) shows that in the presence of such 

additional priced risk factors, the mean 

variance optimal portfolio is no longer a 

cap-weighted market portfolio. Therefore, 

if the standard market indices chosen were 

mean variance efficient, then the market 

risk should be the only source of priced risk 

and should be able to completely explain 

the cross sectional variation in stock returns. 

However, it has been widely recognised that 

there are priced risk factors other than the 

market factor (as proposed by the CAPM), 

which influence differences in expected 

returns of stocks. This fact is corroborated 

by empirical studies in both academia and 

industry that document a set of facts about 

the cross-section of returns that cannot 

be explained within the traditional CAPM. 

Academic literature notes that stocks sorted 

by size, book to market ratio (Fama and 

French 1992) and momentum (Jagdeesh 

and Titman 1993) have returns that 

cannot be explained by their covariance 

with the index portfolios chosen as a proxy 

for the market. Factor exposures have been 

recognised in practitioners’ finance, (e.g. by 

Barra, who maintains a factor model that 

utilises 65 factors spread across industry 

categories), firm size and earnings are used 

to explain the cross sectional returns of 

American stocks. Such deviations from the 

perennial theme – neutral exposure to the 

risk factors – have been widely documented 

in a range of academic literature, as well 

as on the Asia–Pacific region (see insert 

“Evidence of factor exposure in the Asian 

stock returns” for the literature review). 




Evidence of factor exposure in the Asian stock returns 

A large body of empirical evidence exists on the presence of multiple risk factors in 

Asia-Pacific stock markets. The most common approach for analysing the risk factors 

is the Fama and French (1992) model. Since the 1990s, there have been observed size 

and value effects in the Asian market. For example, Wong and Lye (1990) document 

significant size effects in the Singaporean stock market. Mukherji et al. (1997) find 

that annual returns on the Korean stocks are significantly related to size and bookto-market 

ratio. Chui and Wei (1998) provide evidence that book-to-market (B/M) 

can explain the cross-sectional variation of expected returns in Hong Kong, Korea, 

and Malaysia, while the size effect is significant in all the markets examined except 

Taiwan. 

9 - Chiao and Hueng (2004) 

support the Fama and 

French model during period 

1980-1994 based on GRS 

test of the joint hypothesis 

of zero intercepts for a set 

of ten Tokyo Stock Exchange 

prior-return-based portfolios. 

Pham (2007) analyses the 33 

industry returns based on 

the Fama and French model 

with a Generalised method 

of moment (GMM) test from 

1984 to 2004. 

10 - In China’s domestic stock 

markets, two types of shares 

could be traded: A share and 

B share. A-shares are traded 

in local currency and can 

only be bought and sold by 

Chinese citizens. B-shares 

are traded in US dollars that 

can be bought and sold 

by both Chinese citizens 

and foreigners (including 

residents of Hong Kong, 

Macao and Taiwan). The 

A-shares include state shares, 

legal entity shares, employee 

shares and public shares. Only 

public shares are allowed to 

trade (about 30% of the total 

amount of shares) (Wong 

et al. 2006). Since A-shares 

are more liquid, there are 

price discrepancies between 

A-shares and B-shares from 

the same company. 

There is more evidence from the recent studies on the size and style effects on the 

stock returns in the Asian markets. Lam (2002) and Nartea et al. (2008) both find 

significant size and value premium in the Hong Kong stock market. Daniel et al. 

(2001) find a strong value premium in Japanese stocks for the period of 1975 to 

1987, while Chiao and Hueng (2004) and Pham (2007) build different models 9 but 

reach the same conclusion that the explanation power of the size and book-tomarket 

ratio is significant in Japanese stock returns. Dash and Sumanjeet (2008) find 

that both a firm’s book to market ratio and market capitalisation have significant 

explanatory power on the cross section stock returns in India, confirming Fama and 

French (1992) findings for the Indian market. Similar results on the size and value 

premia are also found in Malaysia, Korea, the Philippines, Singapore and Taiwan 

markets (Drew and Veeraraghavan 2001, 2003; Shum and Tang 2010; Lau et al. 

2002). Because of the distinct characteristics for China’s stock market 10 , the findings 

on the style and size effects in the literature are controversial. Drew et al. (2003) 

target the Shanghai Stock Exchange A-share market from 1993 to 2000 and find 

significant size factor exposure, as well as growth effects, which is contradictory to 

what is found in other countries, where there is a value premium in stock returns. 

On the other hand, Wong et al. (2006) use data from Shanghai Stock Exchange for 

both A- and B- shares from 1995 to 2002 and argue that size and value effects only 

exist in the “up” period, while during the “down” period, all factors have adverse 

effects. Wang and Di Iorio (2007) test both the Shanghai and Shenzhen A-share 

markets from 1995 to 2002 and conclude that size and B/M could explain the crosssectional 

stock returns but such effects are not persistent. In the end, Malkiel and 

Jun (2009) focus on the FTSE China 25 Index (H share and Red chip), which is traded 

on the Hong Kong Stock Exchange and find that value tilted portfolios with the 25 

H share stocks could outperform the capitalisation-weighted index for the period 

of 2000 to 2008. 

Additionally, there is some literature which focuses on the role of momentum 

strategies in the Asian markets. A momentum effect is built according to the underreaction 

hypothesis, which suggests that the stock price cannot immediately and 


27



11 - The data for Indonesia is 

from 1985 to 1995. 

completely adjust to new information. Therefore, a stock price movement is merely 

an extension of the prior period and investors should buy a "winner" portfolio and 

sell a "loser" portfolio to earn an abnormal profit. Jegadeesh and Titman (1993) first 

observed such effect from the New York Stock Exchange (NYSE) and the American 

Stock Exchange (AMEX) between 1965 and 1989. However, the momentum effects 

in Asian markets are not consistently observed. Chan et al. (2000) found a significant 

momentum premium for a 26 week holding period for Hong Kong, Indonesia and 

South Korea (but not Japan, Singapore and Malaysia) from 1980 to 1995 11 . Chui et 

al. (2000) construct momentum portfolios based on 6-month past performance and 

hold them for 6 months. They find significant momentum profits for Hong Kong 

from the 1970s to 2000 and significant results for Hong Kong, Malaysia, Singapore, 

and Thailand for the pre-Asian crisis period. Further, Hameed and Yuanto (2002) 

look into the momentum effects across equity markets in Hong Kong, Malaysia, 

Singapore, South Korea, Taiwan and Thailand and observe insignificant momentum 

premia for individual country momentum portfolios but significant momentum 

effects for country-neutral portfolios over the period from 1981 to 1994. In more 

recent studies, Naughton et al. (2008) find evidence of substantial momentum profits 

during the period 1995 to 2005 for China Shanghai stock exchange A-share market. 

Lam et al. (2010) add one momentum factor to the Fama and French (1993) 3-factor 

model and test the Hong Kong market from 1981 to 2001. They find significant 

explanatory power for all factors. Wang et al. (2009) test the Taiwan market with 

the data from 1997 to 2006 and observe significantly positive momentum profits 

following market gains in the formation period but a negative profit following 

market losses in the formation period. On the other hand, Fu and Wood (2010) find 

that strong momentum effects are restricted to the months following the deadline 

for annual statements in Taiwan. 

There are other market observations that establish the presence of other factors 

apart from the market that explain the cross sectional returns of stocks in some 

Asian countries. Drew and Veeraraghavan (2002) draw on the Malkiel and Xu (1997, 

2000) analysis that states that the idiosyncratic volatility is useful in explaining 

the cross-sectional expected returns in the market and verify the results on a set 

of equity markets in Asia including Hong Kong, India, Malaysia and the Philippines 

from 1995 to 1999. Their findings suggest that the idiosyncratic volatility premia 

are real, positive and pervasive across all markets, and generate superior returns – 

hence firms with high idiosyncratic volatility carry with them a risk premia. Drew 

et al. (2004) apply a similar technique to test the China A-share market from 1995 

to 2000 and they confirm that idiosyncratic volatility is priced in the China market. 

Gan et al. (2010) confirm a significant positive idiosyncratic volatility effect in the 

Hong Kong stock market during the study period from 1980 to 2007. Nartea et al. 

(2011) extend the study to the Singaporean, Malaysian, Thai and Indonesian markets 

and corroborate the existence of the idiosyncratic volatility effects. 




Overall, the literature clearly indicates that the returns of Asian stocks are explained 

by multiple factors other than the value weighted market portfolio or market indices 

alone, and hence these index portfolios cannot be expected to be mean variance 

efficient. 

12 - See Amenc et al. (2010) 

for the methodology to 

construct efficient-weighted 

indices. 

2.5 Instability of Risk Factor 

Exposure 

The presence of risk factor exposures and 

their lack of stability over time contribute 

to the main issues of cap-weighted 

indices. Investors typically construct their 

investment universe from simpler building 

blocks made of style, sector or size indices. 

Once this breakdown is made, an index 

is chosen to replicate the performance 

of each of these smaller building blocks 

which represents a risk factor exposure. A 

market index chosen from this perspective 

is ideally perceived to be neutral to the risk 

factor exposures represented by smaller 

building blocks. These requirements 

mean that the existing indices may be 

of good or bad quality depending on the 

degree to which they fulfil this neutrality 

requirement, and the variability of their 

factor exposures to these smaller building 

blocks. 

Bahri and Leger (2001) have studied the 

stability of risk factors in the UK stock 

market over time by running a multi-period 

Principle Component Analysis (PCA) on 550 

stocks from January 1972 to December 

1993. They find that the explanatory 

sources for all components change 

over time and in addition, only the first 

component – the so called “superfactor” 

– is persistent over multiple periods. They 

argue that it is not reasonable to assume 

constant risk factor exposure for the stock 

market. 

Amenc, Goltz and Le Sourd (2006) have 

studied the stability of major stock indices 

in terms of exposure to both investment 

styles and industry sectors and concluded 

that the relative weight of the different 

sub-indices varies drastically over time. 

For instance, for a given sample period 

from October 1995 to September 2005, 

they show that the Stoxx Europe 600 

index has a variation on the technology 

sector exposure from 5% at the beginning 

of the sample period to approximately 

20% during the tech bubble around 2000; 

similarly, the exposure to the technology 

sector for the S&P 500 jumped to 30% 

around 2000 from 10% in 1995. Moreover, 

the exposure to growth varies from 33% to 

4% for the Nikkei 225 from 1998 to 2005 

and the index itself has a clear value tilt 

throughout the entire period analysed. 

Such variation of sector/style weights in 

the broad market index leads to problems 

for investors, and illustrates the fact that 

the sector/style allocation becomes an 

implicit decision induced by the choice of 

an index, as opposed to an explicit choice 

knowingly made by the investor. 

In a more recent study by Goltz and Sahoo 

(2011), which compares the evolution of 

sector weights between cap-weighted 

indices S&P500 and the efficientweighted 

12 S&P 500 over a long horizon, 

which is from January 1959 to December 

2008, the results show that in the capweighted 

portfolio, there is a shift from 

a manufacturing industry base towards 


29



information technology and the financial 

services industry over a long horizon. 

The weights are heavily concentrated 

in energy in the 1980s and in business 

equipment (technology) in the late 1990s. 

In addition, there is an overweight of 

financial stocks since 2000. On the other 

hand, the efficient-weighted index does 

not exhibit these characteristics. 

The empirical studies suggest that the 

broad market indices constitute specific 

choices of risk factors rather than a 

“neutral” risk exposure. This means that 

investors who passively hold an index or 

managers who select a market index as a 

benchmark can see their risk exposure to 

styles or sectors being modified through 

time (Amenc et al. 2006). As a possible 

consequence their risk exposure may no 

longer correspond to the initial asset 

allocation and their initial choice of risks. 

Having discussed some of the issues 

with the standard market indices, we 

understand that the current market 

indices are not necessarily a good proxy 

as either the reference index or the 

strategy benchmark. To our knowledge, 

most comprehensive studies are done 

for developed markets, such as Europe, 

Japan or the US. There is no exhaustive 

study assessing such issues for a complete 

set of Asian market indices. The present 

document aims to fill this gap by analysing 

the efficiency and stability for a set of 

Asian indices to gain a better perspective 

on the qualities of current market indices 

in Asia and to shed some light on the 

possible asset allocation strategies and 

performance measurements based on 

these indices. 


3. Efficiency Analysis 


31



We begin our study with an efficiency 

analysis. As previously discussed, both 

passive index trackers and active managers 

would value the efficiency of an index, 

since investors above all about the index 

reflecting a fair investment opportunity 

for them (see Amenc et al. 2011). 

Therefore, we shall start our analysis 

with the efficiency test of current market 

indices in the Asian region. We will then 

test the concentration of the current 

indices to see if concentration of these 

indices is consistent with the findings in 

the efficiency tests. 

3.1 Risk-Return Efficiency Analysis 

3.1.1 Data 

In this analysis, we use market indices 

in different countries (major Asian 

equity markets) and regions that are 

most popularly used in indexing and 

benchmarking of funds. In most cases, we 

selected one of the most popular indices in 

the respective country, with the popularity 

measured by the amount of assets under 

management (AUM) tied to ETFs listed on 

such indices. Based on this measure we 

have the Nikkei 225, the Topix 100 (as 

a substitute for Topix index), the Hang 

Seng and the FTSE China indices, which 

are the top four indices by AUM linked to 

ETFs in the Asia-Pacific region (Deutsche 

Bank 2010). A similar report by Blackrock 

cites just the list of top three indices 

by AUM in ETFs and it includes Nikkei, Topix 

and Hong Kong (Blackrock 2010). KOSPI 

200 index is clearly the most actively 

traded index from Korea, and is the only 

index to have futures and options trading 

on US stock exchanges. The remaining 

indices, chosen from Singapore, India, and 

Taiwan, were each clearly one of the most 

prominent indices of the region, and were 

offered by the most established stock 

exchange in each of those countries. 

We collect the daily stock closing prices 

from Bloomberg for all these indices and 

their constituents, except for the FTSE 

ASEAN Index. All the stock prices obtained 

are adjusted for normal dividends, 

abnormal dividends, spinoffs, stock 

splits and stock bonuses (total returns). 

Dividends are reinvested into the index, or 

into the same stock at close if they are 

paid out on a trading day. If a security/ 

index does not trade on its ex-dividend 

date, then the dividends associated with 

that security/index are reinvested at the 

close of trading on the first subsequent 

day that the security trades. For the FTSE 

ASEAN index, the adjusted stock prices 

for the index and the components are 

obtained from DataStream. We use the 

daily series to calculate the returns as 

follows: 

The data availability varied between 

different market indices in the region in 

terms of the information on the historical 

changes to the index constituents. This 

restricted us to perform our analysis 

on each index with varying amounts of 

historical data. In Table 3.1 we presented 

the time frame for which the historical 

index changes were available for each 

index, and the source of this change list. 

3.1.2 Methodology 

3.1.2.1 Building efficient portfolios 

The concept of portfolio efficiency was 

introduced by Markowitz (1952), who was 

the first to quantify the link that exists 




Table 3.1: The table provides the list of data sources for each index. Column 3 contains the description of the sources for the prices 

of the index constituents and the market index (for all the indices) in each country. Column 4 contains the time period for which 

the data is collected and the analysis done for each index. 

Data Source for Efficiency Analysis 

Index Country Data Source Period 

Hang Seng Index Hong Kong 1 - Daily Total returns of the index and adjusted stock prices of Jan 2002 to Dec 2010 

individual constituents obtained from Bloomberg 

2 - The historic list of changes to the constituents in the index was 

obtained from Hang Seng Index Website 

Nikkei 225 Index Japan 1 - Daily Total returns of the index and adjusted stock prices of Jan 1996 to Dec 2010 



obtained from Nikkei Website 

Topix 100 Index Japan 1 - Daily Total returns of the index and adjusted stock prices of Feb 1999 to Dec 2010 


2 - The historic list of changes to the constituents in the index till 

2006 was obtained from Topix website. Changes prior to 2006 were 

obtained from Bloomberg. 

FTSE STI Index Singapore 1 - Daily Total returns of the index and adjusted stock prices of Sep 2001 to Dec 2010 



obtained from FTSE 

KOSPI 200 Index Korea 1 - Daily Total returns of the index and adjusted stock prices of Jun 2001 to Dec 2010 



obtained from KRX Exchange Website 

FTSE TWSE 50 Taiwan 1 - Daily Total returns of the index and adjusted stock prices of Jan 2003 to Dec 2010 

Index 



obtained from FTSE Website 

CSI 300 Index China 1 - Daily Total returns of the index and adjusted stock prices of 



obtained from CSI Index Website 

Jan 2006 to Dec 2010 

FTSE China 25 

Index 

China 1 

1 - Daily Total returns of the index and adjusted stock prices of 



obtained from FTSE Website 

Nifty 50 Index India 1 - Daily Total returns of the index and adjusted stock prices of 

individual constituents obtained from Bloomberg. 

2 - The historic list of changes to the constituents in the index till 

2006 was obtained from NSE Website. Changes prior to 2006 were 

obtained from Bloomberg 

FTSE ASEAN Index 

ASEAN 

Region 2 

1 - Daily adjusted stock prices of individual constituents obtained 

from DataStream, and the Total returns of the index were obtained 

from Bloomberg 

2 - The historic list of changes to the constituents in the index 

obtained from FTSE 

Jan 2003 to Dec 2010 

Jan 2003 to Dec 2010 

Jan 2001 to Dec 2010 

1 - The index consists of the largest 25 Chinese stocks listed and trading in Hong Kong Stock Exchange. Hence the index base 

trading currency is Hong Kong Dollar. 

2 FTSE ASEAN Index consists of stocks from Singapore, Malaysia, Indonesia, Thailand and the Philippines which are a part of the 

ASEAN block of countries. 

between the risk and return of a portfolio. 

An efficient (or optimal) portfolio is 

defined as a portfolio with minimal risk 

for a given return, or, equivalently, as 

the portfolio with the highest return for 

a given level of risk, with the risk being 

measured by the volatility of asset returns. 

The complete set of these portfolios 


33



forms the mean variance frontier, which 

constitutes the convex envelope of all 

the portfolios that can be produced. The 

portfolios located on the mean variance 

frontier are said to be mean-variance 

efficient as they are derived on the basis 

of the first two moments of the asset 

return distribution, i.e., the mean return 

and the variance of the returns. 

To achieve optimal diversification, 

Markowitz developed a mathematical 

portfolio selection model. This model 

enabled him to find the composition of 

all the portfolios that corresponded to 

the efficiency criterion he had defined 

for a given set of securities, and thereby 

construct the corresponding mean 

variance frontier. Taking the definition 

of portfolio return and portfolio risk into 

account, this involves minimising the 

variance for a given return or maximising 

the return for a given variance. In its 

simplest version, the model is written as 

follows: 

Minimise 

Under the condition that 

and 

and 

for all 

Here x i denotes the weight of the asset i in 

the portfolio. E(R i ) denotes the expected 

return on the asset i, and cov(R i ,R j ) 

denotes the covariance between asset i 

and asset j. 

The variance expression reveals the 

usefulness of diversification in reducing 

risk thanks to the correlation that exists 

between asset returns. The mean variance 

frontier calculation involves finding the 

weightings of the assets that make up 

each portfolio. Tracing mean variance 

frontiers of portfolios that are composed 

of the index components and plotting 

the capitalisation weighted index in the 

mean-variance plane will allow us to 

assess the relative efficiency of the index. 

If the claim of efficiency for the index 

holds, it should lie on the mean variance 

frontier. Being located far inside from this 

frontier would in turn result in a lack of 

efficiency. This comparison with the mean 

variance frontier, however, is faced with 

an important limitation. 

The Markowitz method involves obtaining 

an optimal portfolio as a function 

of estimates of return parameters 

(mean) and risk parameters (variance 

and covariance) for the assets being 

considered. It has been shown that the 

portfolio optimisation programme is very 

sensitive to the parameters (Chopra and 

Ziemba; 1993, Jessop 2007). As the mean 

variance frontier for the composition of 

the index is derived from historical data, 

there is no guarantee that the data will be 

representative of long-term trends. So it 

is possible that the optimal weights found 

within the sample will not remain the 

optimal weights outside of the sample. 

This also means that the dominance in 

risk return terms may not hold for the 

portfolios obtained in the optimisation. 

In view of this problem, the MSR 

portfolio can be seen as the portfolio 

that is obtainable for an investor with 




perfect foresight of the assets’ expected 

returns, as well as the covariance matrix 

of asset returns, which might seem quite 

unreasonable. The analysis is nevertheless 

useful as the MSR portfolio has the same 

set of constituents, is computed using 

realistic constraints, and the distance 

of CW from the MSR provides a useful 

measure of the extent of inefficiency 

of the index. Further, in order to obtain 

results with more practical relevance, 

we also focus on equally-weighted (EW) 

portfolios as an alternative to standard 

value-weighted market indices, the 

former being more diversified than the 

latter. 

Moreover, equally-weighted indices, 

which can be regarded as optimal 

portfolios for an investor with overly 

simple and quite extreme ‘priors’ on asset 

return parameters (i.e., mean returns, 

variances and covariances are identical 

for all assets), are very easy to compute 

and do not include any hindsight bias. 

It should be noted that constructing 

and using equally-weighted indices as 

benchmarks is a very easy and low cost 

form of portfolio management. Therefore, 

if these portfolios are more efficient 

than their respective market indices, this 

would be a very clear result in favour 

of the hypothesis of the inefficiency of 

capitalisation weighted indices. 

In performing the analysis, we start by 

plotting the efficient frontier, beginning 

with the minimum variance portfolio 

and stretching it to the maximum return 

portfolio without additional borrowing. 

We also plot the performance of the 

equally-weighted portfolio relative to 

the market index in the mean-variance 

plane. By visually comparing the position 

of the market index within the mean 

variance efficient frontier, one can get a 

fair understanding of the efficiency of the 

index. The conclusion on the efficiency of 

the index will therefore depend on how 

close the index lies from the mean variance 

frontier. In order to compare the market 

index to portfolios obtained through a 

different allocation between the index 

components, we also plot another four 

portfolios on the mean variance plane. 

The portfolios consist of the following: 

i) The efficient portfolio with minimum 

risk given that it has the same return as 

the index; 

ii) The efficient portfolio with the 

maximum return given that it has the 

same risk as the index; 

iii) The efficient portfolio with the 

maximum Sharpe ratio; 

iv) The efficient portfolio with global 

minimum variance. 

We call them the four efficient portfolios. 

Comparing the distance to the first two 

portfolios allows us to assess the gain an 

investor can obtain in terms of the riskreturn 

trade-off by deviating from the 

index using the same stocks. 

For each market index, in addition to a 

plot on the efficiency of that index (cf. 

Figures 3.2.a to 3.2.j), we also provide a 

table (cf. Tables 3.2.a to 3.2.j) summing 

up the main characteristics of the index 

and its comparable portfolios. This table 

presents the risk return performance 

measure of the index and its comparable 

portfolios. In addition, the table also 

includes information on skewness, 

kurtosis, the turnover of these portfolios 


35



13 - The specific dates 

of reconstitution being 

15/6/2001, 14/6/2002, 

13/6/2003, 11/6/2004, 

10/6/2005, 9/6/2006, 

15/6/2007, 13/6/2008, 

12/6/2009 and 11/6/2010. 

and their worst performance against the 

cap-weighted index in a one year and a 

three year period. 

3.1.2.2 Construct the Efficient Frontier 

The efficient frontier is constructed with 

matching constituents as the index for 

each year. These are in-sample frontiers 

that invest in a set of index constituents 

that were present at the start of the index 

reconstitution year. This start is necessarily 

not the start of the calendar year (1st 

January) and is chosen such that for each 

index it coincides with the occurrence of 

the index reconstitution. This is adopted 

for KOSPI 200 index 13 , specifically 

where the major reconstitution to the 

index happens every June. By virtue of 

this method we can see that the index 

rebalancing is done annually. 

To handle the case for a major multiple 

reconstitution over the year, we adopt 

the following procedure for computing 

the efficient frontier. As a first step, we 

identify all the stocks that exist in the 

index throughout a particular year. We 

compute the efficient frontier for these 

sets of stocks using the mean variance 

optimisation technique discussed above. 

We assign equal weights to those 

constituents that do not have the full 

year of data available. For example, when 

a stock first enters the index, we simply 

assign an equal weight without any reoptimisation 

of the index. We prorate 

the rest of the weights to the efficient 

portfolios calculated for the rest of the 

stocks from step one. In other words, an 

assumption is made on the hindsight of 

the risk return parameters of all the stocks 

that exist throughout the year but not on 

the constituents that change. Using this 

approach, we build out the return series 

and the efficient frontier by computing 

the annualised mean and the standard 

deviation. Here we have to note that 

the efficient portfolios constructed by 

this method are only optimal in sample 

for that year. When a new year starts, 

we again perform a similar procedure as 

described earlier in this paragraph to build 

out the efficient frontier for that year. 

To obtain optimal weights in the mean 

variance optimisation process, we use the 

covariance matrix and vector of means 

using the realised return time series 

over each twelve month time period, but 

impose a reasonable weight constraint 

using a flexibility parameter λ. The λ can 

be construed as a constraint around an 

EW portfolio, and a higher λ allows for 

more distance from an EW portfolio. We 

conduct the analysis with two sets of 

weight constraints, a looser level of weight 

constraints (i.e. λ = 10) and a tighter level 

of weight constraints (λ = 5). These λ help 

define the lower bound (1/ (λ *N)) and the 

upper bound (λ /N) weights for the stocks 

where N is the total number of stocks in 

the index. These constraints help ensure 

that we include all the index constituent 

stocks and we do not get any negative 

weights from the optimiser which would 

lead to short sales. It also avoids excessive 

concentration and liquidity problems. 

Overall these portfolio constraints ensure 

that portfolios are quite realistic in terms 

of weights/concentration. For example, 

with an index of 100 constituents, our 

specification of tight constraints means 

that weights in the in-sample optimal 

portfolio will be allowed to take on values 

between 0.1% and 10% and weights in 

the more tightly constrained portfolio will 




be allowed to take on values from 0.2% 

to 5%. 

Once the efficient frontier is built out 

in each year, we average the frontier 

portfolios across years to build a final 

consolidated efficient frontier. This is 

followed by plotting the index and equalweighted 

portfolios whose returns are also 

averaged across time. That is, we calculate 

each year’s index and equal-weighted 

portfolio’s return from the daily data and 

average these annual returns across time 

(years) to calculate the average portfolio 

return for the period analysed. The plot 

of these consolidated efficiency analysis 

results are presented in the following 

sections (cf. Section 3.1.3). 

In the calculation of the performance 

of the equal-weighted portfolios each 

year, we note that these are portfolios 

that invest in the same constituents as 

the index but with equal weights and 

at each rebalancing date are set back 

again to equal weights. The rebalancing 

period of equal-weighted portfolios is 

chosen set to daily in order to maintain 

the same constitution of the market 

index and match the changes in the 

index constituents as they happen. As 

mentioned above, the performance of 

the EW portfolios is evaluated annually 

to make them comparable to the index 

portfolio for each year. 

We also present the efficiency plots for 

each index year by year in an Appendix 

section, which we do not include in 

this report for brevity. The unpublished 

Appendix is available from the authors 

upon request. The yearly plots help to see 

how the market index fared against the 

equal-weighted portfolio and the efficient 

frontier portfolios in the different years 

over which the analysis was conducted. 

A particular point of interest might be 

the year 2008 when the market crash 

occurred and subsequent strong returns 

in equity in late 2009. 

Thus overall, in this analysis we have 

strived to apply the exact constitution 

of the stocks that are present in the 

market index at any point of time, 

in the creation of the comparable 

portfolios. Thus this analysis presents 

a fair comparison between the market 

index, equal-weighted portfolio and 

other efficient portfolios. Note that this 

procedure may not only produce strong 

evidence for the practical inefficiency of 

cap weighting, but also an assessment 

of the potential for improvement simply 

through a reweighting of the stocks 

without any exclusions or inclusions of 

new stocks. Note, however, that EWs may 

also face practical hurdles due to the daily 

rebalancing, although as it is purely out 

of sample, it requires no hindsight. While 

neither the daily rebalanced EW portfolios 

nor the in sample optimised portfolios are 

practical alternatives to cap-weighted 

indices, they clearly illustrate the 

weaknesses of conventional methods. It is 

not the objective of the present research 

to come up with practical alternatives 

to cap weighting, but rather we simply 

assess efficiency against two alternatives 

to give a sense of the relative efficiency. 

3.1.3 Results 

3.1.3.1 Lack of efficiency 

In this section we present the results of 

the efficiency analysis by each index. The 


37



14 - Government bond one 

year constant maturity rate. In 

case this is not available, we 

use the 1 year interbank offer 

rate in the local country. For 

the ASEAN index, we use the 

Singapore interbank offer rate. 

results presented include the efficient 

frontier of the indices over the sample 

period, the relative position of the market 

index portfolio and the equal-weighted 

portfolio. Also shown are the special 

portfolios that lie on the efficient frontier 

that include the minimum volatility 

portfolio (efficient portfolio with lowest 

portfolio volatility), maximum Sharpe 

ratio portfolio (with an assumption 14 

made for the market risk free rate in each 

country), and the two optimal portfolios 

– one representing the efficient portfolio 

with the same volatility as the market 

index and another representing the same 

return as the market index. In our analysis 

we also compute the annual efficiency 

plots for each index and the relative 

position of capital weighted and equalweighted 

portfolios. However, in interest 

of space we push out these plots to the 

Appendix which is available upon request. 

Some of the plots in the Appendix might 

be interesting to observe on how the capweighted 

index performed relative to the 

efficient frontier and the equal-weighted 

portfolio in different market conditions, 

particularly the 2002-2006 run up in 

the equity markets and the downturn 

following the economic crisis of 2008- 

2009. Finally, here we also note that in 

some cases we observe that the return on 

the market index portfolio is lower than 

the minimum volatility portfolio, which 

implies that in this case there are no 

efficient portfolios with the same return 

as the market index portfolio. Following 

the plots are tables that present the key 

risk return properties, turnover and other 

market statistics of these portfolios. 

Hong Kong: Hang Seng Index 

The Hang Seng is a cap-weighted (CW) 

index made of the 45 largest stocks in the 

Hong Kong Stock Exchange (HKSE) and 

represents about 60% of the total market 

capitalisation of all the stocks listed on 

the HKSE. 

Fig 3.2.a: This figure is the plot for Hang Seng’s in sample Efficiency for the period 2002 to 2010 with lambda values equal to 5 and 

10. The interior efficient frontier is built using lambda = 5. The figure also plots EW portfolio (red dot), GMV portfolio (pink dot), 

MSR portfolio and the two efficient portfolios (orange dot) relative to the market index (black dot) in this period. The risk free rate 

is assumed to be 2.4% (average Hong Kong Interbank offer rate over the period). 




The index is located far inside from the 

mean variance frontier during the period 

of analysis (2002-2010) in both the 

plots (λ = 5 and λ =10). The span of the 

efficient frontier is slightly shrunk in the 

second plot as the weight constraints 

applied are more stringent. Even with 

these weight constraints applied to the 

efficient frontier it is apparent that 

the cap-weighted portfolios are very 

inefficient. The improvement brought 

about by calculating the optimised 

portfolio with the same risk is far superior 

to the realised return (4 times more in 

the conservative case where lambda = 5). 

It is also interesting to note that the 

equal-weighted portfolio clearly performs 

better than the cap-weighted portfolio. In 

the period analysed, the equal-weighted 

(EW) portfolio delivers approximately 260 

basis points excess return on an annual 

basis, adjusted for the risk as measured 

by volatility. Thus, the equal-weighted 

portfolio has done remarkably better than 

the cap-weighted portfolio during this 

sample period. 

Table 3.2.a: The table lists the results of Hang Seng in sample Efficiency Analysis for period 2002 to 2010 with Panel 1 representing 

the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with λ = 10. The columns 3rd, 7th, 

9th, 10th represent the first four moments of each portfolio. The annual return for each year for all the portfolios are calculated 

from the arithmetic returns of daily stock prices. Annual returns are then averaged across time (each year) to produce the results 

in column 3 for each portfolio. Volatility is calculated from daily returns and then annualised. The annualised volatility is averaged 

across time (each year) to produce the results in column 7 for each portfolio. The skewness and kurtosis are calculated from the daily 

returns of the whole data sample. The Max Sharpe Portfolio is evaluated using a risk free rate of 2.4%, which is the average HIBOR 

for this time period. Columns 4 and 5 represent the greatest underperformance of each portfolio when compared to the market 

index over a 1 and 3 year period, respectively. So, a positive value in these columns would represent the lowest outperformance of 

those portfolios compared to the market index. A negative value in this column represents the greatest underperformance of these 

portfolios against the market index. The number inside the brackets in these columns represents the market index return during that 

period. The turnover reported is the average annual one way turnover of each portfolio across time. 

Hang Seng Index Jan 2002 - Dec 2010 

Portfolio 

Total return 

over the 

Sample 

Period 

Returns 

(Ann) 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 

Market Index 131.04% 14.56% 0.00% 0.00% 4.76% 22.81% 0.53 .38 13.00 

Equal-weighted 

Index 154.08% 17.12% 

-3.51% 

(-48.91%) 

Using tight constraints for optimal portfolios (λ = 5) 

Efficient Portfolio 

(Same Return) 131.04% 14.56% 


(Same Volatility) 377.01% 41.89% 

Min Variance 

Portfolio 124.65% 13.85% 

Max Sharpe 

Portfolio 341.91% 37.99% 

-15.97% 

(39.1%) 

19.41% 

(8.97%) 

-17.14% 

(39.1%) 

16.44% 

(39.1%) 

Using loose constraints for optimal portfolios (λ = 10) 


(Same Return) 131.04% 14.56% 



Min Variance 

Portfolio 102.51% 11.39% 

Max Sharpe 

Portfolio 394.56% 43.84% 

-21.59% 

(39.1%) 

23.45% 

(36.4%) 

-26.71% 

(39.1%) 

19.12% 

(36.4%) 

Sharpe Ratio 

Skewness 

Kurtosis 

6.11% 

(18.75%) 148.76% 22.83% 0.64 .22 11.56 

-29.58% 

(81.67%) 28.21% 13.84% 1.05 .01 11.93 

85.63% 

(95.97%) 72.97% 22.81% 1.84 .29 6.57 

-32.4% 

(81.67%) 28.43% 13.81% 1.00 .01 11.97 

51.09% 

(95.97%) 72.33% 19.91% 1.91 .22 7.16 

-36.46% 

(39.1%) 41.04% 12.43% 1.17 -.09 12.46 

101.8% 

(95.97%) 80.47% 22.81% 2.11 .41 6.46 

47.88% 

(81.67%) 42.95% 12.24% 0.93 -.12 12.84 

64.91% 

(95.97%) 80.35% 20.20% 2.17 .32 6.30 

Note- The number in the 4th and the 5th column represent the worst outperformance of the specified portfolio over capweighted 

index. The number in brackets in the 4th and the 5th column represent the returns of CW during the specified 

portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is just rebalanced once in a year. However, 

the equal-weighted portfolio is so constructed that it is rebalanced daily. Hence the sum of the turnover in a year exceeds 100% 


39



Japan: NIKKEI 225 Index 

Fig 3.2.b: This figure is the plot Nikkei 225’s in sample Efficiency for the period 1996 to 2010 with lambda values equal to 5 and 10. 

The interior efficient frontier is built using lambda = 5. The figure also plots EW portfolio (red dot), GMV portfolio (pink dot), MSR 

portfolio and the two efficient portfolios (orange dot) relative to the market index (black dot) in this period. The risk free rate is 

assumed to be 0.3% (average Japanese government 1 year constant maturity treasury rate). 

The Nikkei 225 index is a price weighted 

index, that is, it is computed as a mean 

average of the price of the constituents 

in the index. The value of the index is 

generated by adding the prices of each of 

the stocks in the index and dividing them 

by the total number of stocks. Stocks 

with a higher price will be given more 

weight and, therefore, will have a greater 

influence over the performance of the 

index. This is different from capitalisation 

weighted indices where individual 

components are weighted according to 

their market capitalisation. 

The Nikkei 225 index is also located far 

inside from the efficient frontier. The 

efficient frontier produced in the case 

of the NIKKEI is similar to Hang Seng 

but pushed down a bit due to relatively 

flat performance of the index during the 

sample period. Here again we see that it 

is possible to construct portfolios using 

the same index constituents such that 

the portfolio has the same risk as the 

index but a higher return (the efficient 

portfolio with the same volatility). The 

outperformance of the equal-weighted 

portfolio is not apparent from the plot; 

however, the equal-weighted portfolio 

also has had a significant positive 

performance over the period and has 

outperformed the market index by close 

to 480 basis points adjusted for volatility. 

An interesting point to note is that the 

most significant underperformance of the 

index over the equal-weighted portfolio 

happened during the post dot com bubble 

in 2000 and 2001. This could be clearly 

seen from the yearly plots presented in the 

Appendix, which is available upon request. 

Comparing the performance of Nikkei 

over the same period as that of the Hang 

Seng index (post dotcom crash) would 

have produced an underperformance 

of the order of 200 to 300 basis points 

annually. 




Table 3.2.b: The table lists the results of Nikkei 225’s in sample Efficiency Analysis for period 1996 to 2010 with Panel 1 representing 

the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with λ = 10. The columns 3rd, 7th, 

9th, 10th represent the first four moments of each portfolio. The annual return for each year for all the portfolios are calculated 

from the arithmetic returns of daily stock prices. Annual returns are then averaged across time (each year) to produce the results 

in column 3 for each portfolio. Volatility is calculated from daily returns and then annualised. The annualised volatility is averaged 

across time (each year) to produce the results in column 7 for each portfolio. The skewness and kurtosis are calculated from the 

daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using the risk free rate as 0.3% which is the average 

Japanese Government 1 yr constant maturity rate for this time period. Column 4 and 5 represent the greatest underperformance of 

each portfolio when compared to the market index over a 1 year and over a 3 year period respectively. So, a positive value in these 

columns would represent the lowest outperformance of those portfolios compared to the market index. A negative value in this 

column represents the greatest underperformance of these portfolios against the market index. The number inside the brackets in 

these columns represents the market index return during that period. The turnover reported is the average annual one way turnover 

of each portfolio across time. 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

NIKKEI 225 Index - Jan'96 - Dec'10 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 

Market Index -9.30% -0.62% 0.00% 0.00% 4.93% 23.47% N/A .04 6.03 


Index 68.25% 4.55% 

-22.5% 

(23.3%) 


Sharpe Ratio 

Skewness 

Kurtosis 

-8.4% 

(1.1%) 186.71% 25.61% 0.16 .06 9.30 


(Same Return) N/A N/A N/A N/A N/A N/A N/A N/A N/A 



Min Variance 

Portfolio 60.90% 4.06% 

Max Sharpe 

Portfolio 578.55% 38.57% 

19.39% 

(-1.34%) 

-22.06% 

(22.03%) 

18.26% 

(-1.34%) 

34.75% 

(-15.1%) 68.50% 23.47% 1.72 .07 7.89 

-2.97% 

(22.3%) 33.84% 15.97% 0.23 .10 11.91 

32.93% 

(17.58%) 65.94% 22.22% 1.72 .06 8.10 






Min Variance 

Portfolio 53.55% 3.57% 

Max Sharpe 

Portfolio 773.40% 51.57% 

28.03% 

(-1.34%) 

-28.98% 

(22.03%) 

27.14% 

(-1.34%) 

45.19% 

(-15.1%) 79.33% 23.47% 2.25 .03 7.25 

-7.97% 

22.3%) 44.09% 13.88% 0.23 .25 13.61 

44.1% 

(17.58%) 79.03% 22.76% 2.25 .04 7.28 

Note- Elements in the first row of Panel 1 and Panel 2 are N/A as there is no portfolio on the efficient frontier whose returns 

match that of the market index. The number in the 4th and the 5th column represent the worst outperformance of the specified 

portfolio over cap-weighted index. The number in brackets in the 4th and the 5th column represent the returns of CW during 

the specified portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is just rebalanced once a year. 

However, the equal-weighted portfolio is constructed so that it is rebalanced daily. Hence the sum of the turnover in a year 

exceeds 100% 


41



Japan: Topix 100 Index 

Fig 3.2.c: This figure is the plot for TOPIX 100 in sample Efficiency for the period 1999 to 2010 with lambda values equal to 5 and 

10. The interior efficient frontier is built using lambda = 5. The figure also plots EW portfolio (red dot), GMV portfolio (pink dot), 


as 0.23% which is the average Japanese Govt Bond CMM rate during this period. 

TOPIX 100 is a Cap-weighted market index 

in Japan, and belongs to the Topix series 

of indices and represents the performance 

of the top 100 stocks in Japan. The index 

has had an average return of slightly 

above zero in the twelve year period of 

the study. As with other indices, the CW 

TOPIX 100 index is well inside the efficient 

frontier. The value weighted portfolio also 

performs clearly worse than the equalweighted 

portfolio for the consolidated 

period (Feb 1999 – Dec 2010), however, it 

is important to note that some of the high 

outperformance in the equal-weighted 

portfolio is influenced by our choice 

of analysis period. During the dot com 

bubble crash of 2000, the equal-weighted 

portfolio outperformed the cap-weighted 

portfolio by 30%. This could be clearly 

seen in the efficiency plot for the year 

2000 in the Appendix, which is available 

upon request. Excluding this we see that 

the equal-weighted portfolio would 

have still, on average, outperformed 

the cap-weighted index by 300 basis 

points with lower market volatility. 




Table 3.2.c: The table lists the results of TOPIX 100 Index in a sample Efficiency Analysis for period Feb 1999 to Dec 2010 with Panel 

1 representing the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with λ = 10. The columns 

3rd, 7th, 9th, 10th represent the first four moments of each portfolio. The annual return for each year for all the portfolios are 

calculated from the arithmetic returns of daily stock prices. Annual returns are then averaged across time (each year) to produce 

the results in column 3 for each portfolio. Volatility is calculated from daily returns and then annualised. The annualised volatility 

is averaged across time (each year) to produce the results in column 7 for each portfolio. The skewness and kurtosis are calculated 

from the daily returns of the whole data sample. Then these returns are averaged across time to produce results in column 3 

for each portfolio. The Max Sharpe Portfolio is evaluated using a risk free rate of 0.23%, which is the average Japanese Govt 

Bond CMM rate during this period. Column 4 and 5 represent the greatest underperformance of each portfolio when compared 

to the market index over a 1 year and over a 3 year period respectively. So, a positive value in these columns would represent 

the lowest outperformance of those portfolios compared to the market index. A negative value in this column represents the 

greatest underperformance of these portfolios against the market index. The number inside the brackets in these columns represents 

the market index return during that period. The turnover reported is the average annual one way turnover of each portfolio across 

time. 

Topix 100 Index Feb 1999 - Dec 2010 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 

Market Index 16.03% 1.34% 0.00% 0.00% 5.62% 23.15% 0.05 -.04 8.25 


Index 82.08% 6.84% 

-9.08% 

(60.17%) 


Sharpe Ratio 

Skewness 

Kurtosis 

3.64% 

(52.84%) 176.40% 22.18% 0.30 -.02 9.49 





Min Variance 

Portfolio 53.52% 4.46% 

Max Sharpe 

Portfolio 435.48% 36.29% 

20.52% 

(2.58%) 

-35.07% 

(60.17%) 

19.88% 

(-2.58%) 

67.96% 

(52.84%) 69.34% 22.18% 1.67 .07 6.25 

-13.81% 

(54.75%) 39.86% 14.86% 0.28 -.02 12.20 

66.07% 

(52.84%) 69.30% 21.61% 1.67 .05 6.62 






Min Variance 

Portfolio 51.96% 4.33% 

Max Sharpe 

Portfolio 531.12% 44.26% 

25.93% 

(11.58%) 

-42.2% 

(60.17%) 

25.04% 

(35.3%) 

87.28 % 

( 45.64%) 81.58% 22.21% 1.67 .11 5.86 

-21.49% 

(61.95%) 51.28% 13.52% 0.30 .04 11.13 

84.53% 

(52.84%) 81.41% 21.61% 1.67 .10 5.96 



portfolio over the cap-weighted index. The number in brackets in the 4th and the 5th column represent the returns of CW during 

the specified portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is rebalanced only once a year. 

However, the equal-weighted portfolio is so constructed that it is rebalanced daily. Hence the sum of the turnover in a year 

exceeds 100%. 


43



Singapore: FTSE STI Index 

Fig 3.2.d: This figure is the plot for Strait Times index in sample Efficiency for the period 2001 Sep to 2010 with lambda values equal 

to 5 and 10. The interior efficient frontier is built using lambda = 5. The figure also plots EW portfolio (red dot), GMV portfolio (pink 

dot), MSR portfolio and the two efficient portfolios (orange dot) relative to the market index (black dot) in this period. The risk free 

rate is assumed to be 2.88% (average risk free rate for the period). 

The FTSE STI is the largest index in 

Singapore, and was operating as the 

Strait Times Index with around 50 

stocks in its portfolio until it was partly 

taken over by FTSE in 2008 January, at 

which time it underwent a significant 

constituent change with its number 

of constituents brought down to 30. 

Hence we performed separate empirical 

analysis on the data between 2001- 

2007 and 2008- 2010. However given 

the uniformity of results over the two 

periods we have combined the results into 

one consolidated chart in Figure 3.2.d. 

As we see from this plot the CW portfolio is 

well inside from the efficient frontier. Also 

apparent is the significant outperformance 

of the EW portfolio over the CW index. 

This outperformance is consistently high 

over the period of analysis. We also see 

that the index just matches the returns 

of the minimum variance portfolio but 

bears a significantly higher volatility. 




Table 3.2.d: The table lists the results of Strait Times Index in sample Efficiency Analysis for period Sep 2001 to Dec 2010 with 

Panel 1 representing the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with λ = 10. 

The columns 3rd, 7th, 9th, 10th represent the first four moments of each portfolio. The annual return for each year for all the 

portfolios are calculated from the arithmetic returns of daily stock prices. Annual returns are then averaged across time (each 

year) to produce the results in column 3 for each portfolio. Volatility is calculated from daily returns and then annualised. The 

annualised volatility is averaged across time (each year) to produce the results in column 7 for each portfolio. The skewness and 

kurtosis are calculated from the daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using a risk free 

rate of 2.88%, the average Singapore interbank offer rate for the period. Column 4 and 5 represent the greatest underperformance 

of each portfolio when compared to the market index over a 1 and 3 year period, respectively. Therefore, a positive value in these 

columns would represent the lowest outperformance of those portfolios compared to the market index. A negative value in this 

column represents the greatest underperformance of these portfolios against the market index. The number inside the brackets in 

these columns represents the market index return during that period. The turnover reported is the average annual one way turnover 

of each portfolio across time. 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

FTSE STI Index Sep 2001 - Dec 2010 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 



Index 194.31% 21.59% 

-2.53% 

(28.96%) 


Sharpe Ratio 

Skewness 

Kurtosis 

3.89% 

(-5.61%) 176.14% 19.77% 0.95 .12 10.18 





Min Variance 

Portfolio 143.64% 15.96% 

Max Sharpe 

Portfolio 398.61% 43.29% 

21.97% 

(28.96%) 

-10.07% 

(56.62%) 

19.99% 

(28.96%) 



(Same Return) 138.96% 15.44% 



Min Variance 

Portfolio 132.57% 14.73% 

Max Sharpe 

Portfolio 386.55% 42.95% 

-14.35% 

(56.62%) 

24.73% 

(28.96%) 

-14.35% 

(56.62%) 

19.43% 

(28.96%) 

83.07% 

(63.48%) 57.35% 20.16% 2.10 .32 9.60 

-14.04% 

(69.09%) 39.74% 13.32% 0.98 -.34 11.75 

77.73% 

(63.48%) 55.11% 19.05% 2.12 .21 8.72 

-16.28% 

(69.09%) 46.52% 12.39% 1.01 -.44 11.51 

91.07% 

(63.48%) 65.93% 20.16% 2.23 .92 18.36 

-20.47% 

(69.09%) 45.83% 12.38% 0.96 -.45 11.51 

77.88% 

(63.48%) 62.87% 17.78% 2.25 .35 10.07 

Note- Elements in the first row of Panel 1 is N/A as there is no portfolio on the efficient frontier whose returns match that of 

the market index. The number in the 4th and the 5th column represent the worst outperformance of the specified portfolio over 

the cap-weighted index. The number in brackets in the 4th and the 5th column represent the returns of the CW index during 

the specified portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is only rebalanced once a year. 

However, the equal-weighted portfolio is so constructed that it is rebalanced daily. Hence the sum of the turnover in a year 

exceeds 100% 


45



South Korea: KOSPI 200 Index 

Fig 3.2.e: This figure is the plot KOSPI 200’s in sample Efficiency for the period Jun-2001 to Dec-2010 with lambda values equal to 5 

and 10. The interior efficient frontier is built using lambda = 5. The figure also plots the EW portfolio (red dot), GMV portfolio (pink 


rate is assumed to be 4.5% (average KORIBOR rate over the period). 

KOSPI 200 index constituents include the 

largest 200 stocks in Korea and occupies 

close to 70% market capital of the broader 

KOSPI index. The index is highly popular 

because of its listing in the futures and 

options market and is one of the mostly 

highly traded indices in the world. 

As with other indices, the cap-weighted 

KOSPI 200 index is well inside the efficient 

frontier. Further, the index portfolio clearly 

performs poorly compared to the equalweighted 

portfolio for the consolidated 

period (Jun 2001 – Dec 2010), as can be 

seen both in the returns and the volatility 

dimension. Looking at this information 

another way, the equal-weighted portfolio 

outperforms the cap-weighted index by 

more than 500 basis points year on year, 

adjusted for risk. Furthermore, the efficient 

portfolio constructed with the same 

volatility as the cap-weighted portfolio 

(with λ = 5) produces approximately 

4.5 times excess return over the index 

portfolio on an annualised basis. Another 

interesting point to note is the significant 

outperformance of the equal-weighted 

portfolio during the market crash between 

Jun 2008 and Jun 2009. On a technical 

note we see that the divergence between 

the portfolios with λ = 5 and λ = 10 is 

large with the higher levels of volatility 

implying that the portfolios coming out of 

the optimiser have extreme weights. 




Table 3.2.e: The table lists the results of KOSPI 200’s in sample efficiency Analysis for period Jun - 2001 to Dec- 2010 with Panel 1 

representing the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with λ = 10. The columns 





from the daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using the risk free rate as 4.5% which is 

the average KORIBOR rate during this period. Column 4 and 5 represent the greatest underperformance of each portfolio when 

compared to the market index over a 1 year and over a 3 year period respectively. Therefore, a positive value in these columns 

would represent the lowest outperformance of those portfolios compared to the market index. A negative value in this column 

represents the greatest underperformance of these portfolios against the market index. The number inside the brackets in these 

columns represents the market index return during that period. The turnover reported is the average annual one way turnover of 

each portfolio across time. 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

KOSPI 200 Index Jun 2001 – Dec 2010 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 



Index 211.7% 21.11% 

-11.88% 

(19.1%) 



(Same Return) 160.03% 16.03% 



Min Variance 

Portfolio 157.3% 15.73% 

Max Sharpe 

Portfolio 594.0% 59.40% 

-10.1% 

(21.2%) 

32.86% 

(19.1%) 

-10.1% 

(21.2%) 

29.62% 

(19.1%) 



(Same Return) 160.03% 16.03% 



Min Variance 

Portfolio 138.6% 13.86% 

Max Sharpe 

Portfolio 705.8% 70.58% 

-13.94% 

(21.2%) 

47.22% 

(19.1%) 

-14.11% 

(21.2%) 

36.7% 

(19.1%) 

Sharpe Ratio 

Skewness 

Kurtosis 

0.01% 

(14.17%) 237.13% 23.28% 0.71 -.75 10.5 

-6.15% 

(20.8%) 44.55% 15.06% .77 -.75 10.93 

45.44% 

(3.3%) 68.46% 24.18% 2.52 -.72 9.90 

-6.15% 

(20.8%) 44.55% 15.06% .75 -.75 10.93 

41.47% 

(3.3%) 65.41% 20.39% 2.69 -.74 9.83 

-6.95% 

(20.8%) 56.55% 13.23% .87 -.74 8.83 

62.29% 

(3.3%) 82.55% 24.18% 3.24 -.66 9.01 

-8.27% 

(20.8%) 56.41% 13.21% .70 -.72 8.61 

50.38% 

(3.3%) 80.30% 19.37% 3.41 -.58 8.88 

Note - The numbers in the 4th and the 5th column represent the worst outperformance of the specified portfolio over the capweighted 

index. The number in brackets in the 4th and the 5th column represent the returns of the CW index during the specified 

portfolio’s worst outperformance. In this analysis we assumed the period from June 12th 2010 to Dec 31st 2010 as a separate 

period, whose results are aggregated with annual results from previous period to derive the mean returns and the other moment 

values for the index. Finally, the turnover cannot exceed 100% if the portfolio is just rebalanced once in a year. However, the 

equal-weighted portfolio is so constructed that it is rebalanced daily. Hence the sum of the turnover in a year exceeds 100. 


47



Taiwan: FTSE TWSE 50 Index 

Fig 3.2.f: This figure is the plot for Taiwan TWSE’s in sample Efficiency for the period 2003 to 2010 with lambda values equal to 5 

and 10. The interior efficient frontier is built using lambda = 5. The figure also plots EW portfolio (red dot), GMV portfolio (pink dot), 


is assumed to be 2.4% (average risk free rate for the period). 

The TWSE 50 index is the most popular 

narrow market index in Taiwan (the other 

popular index being the Taiwan Taiex index 

which is a broad market composite index). 

The index represents the performance 

of the top 50 Taiwanese companies 

by market capitalisation that occupy 

more than 70% of the market value of 

the stocks in Taiwan stock exchange. 

From the plot it is apparent that the 

TWSE 50 index portfolio is inefficient and 

well inside the efficient frontier. Further, 

we can see the neat outperformance 

of the EW portfolio over the CW index. 

On a risk adjusted basis, similar to the 

Hang Seng index, the EW portfolio 

outperforms the CW index by more than 

200 basis points. The outperformance 

of the efficient portfolio, with same 

standard deviation, is more than 4.5 times 

the market index. Another interesting 

fact is that the returns produced by 

the CW index portfolio are lower than 

the minimum variance portfolio (the 

lowest point on the efficient frontier – 

the efficient portfolio with the lowest 

volatility). Overall the results are similar 

to what is observed with other indices. 




Table 3.2.f: The table lists the results of TWSE 50’s in sample efficiency Analysis for period Jan - 2003 to Dec 2010 with Panel 1 






from the daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using the risk free rate as 2.4%. This is 

average HIBOR during this period and is used as a substitute due to lack of comparable market rate in Taiwan for the whole time 

period. Column 4 and 5 represent the greatest underperformance of each portfolio when compared to the market index over a 1 

and 3 year period, respectively. Therefore, a positive value in these columns would represent the lowest outperformance of those 

portfolios compared to the market index. A negative value in this column represents the greatest underperformance of these 

portfolios against the market index. The number inside the brackets in these columns represents the market index return during 

that period. The turnover reported is the average annual one way turnover of each portfolio across time. 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

TWSE 50 Index Jan 2003 - Dec 2010 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 



Index 126.32% 15.79% 

-1.68% 

(13.35%) 


Sharpe Ratio 

Skewness 

Kurtosis 

2.75% 

(-15.95%) 165.51% 22.06% 0.61 -.20 5.58 





Min Variance 

Portfolio 121.52% 15.19% 

Max Sharpe 

Portfolio 351.84% 44.28% 

22.37% 

(35.97%) 

-13.53% 

(58.62%) 

19.07% 

(35.97%) 

87.47% 

(-15.95%) 72.80% 22.51% 2.01 -.17 4.79 

-9.13% 

(44.39%) 37.53% 15.61% 0.82 -.18 6.76 

78.82% 

(-15.95%) 65.63% 20.24% 2.05 -.16 7.08 






Min Variance 

Portfolio 124.80% 15.60% 

Max Sharpe 

Portfolio 459.60% 57.45% 

26.87% 

(35.97%) 

-23.5% 

(58.62%) 

25.79% 

(35.97%) 

109.22% 

(-15.95%) 84.59% 22.51% 2.50 -.07 4.46 

-6.79% 

(44.39%) 40.80% 13.99% 0.94 -.20 6.62 

106.69% 

(-15.95%) 83.92% 21.94% 2.51 -.08 4.51 



portfolio over the cap-weighted index. The number in brackets in the 4th and the 5th column represent the returns of the CW 

index during the specified portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is rebalanced only 

once a year. However, the equal-weighted portfolio is so constructed that it is rebalanced daily, hence the sum of the turnover 

in a year exceeds 100%. 


49



China: CSI 300 Index 

Fig 3.2.g: This figure is the plot for CSI 300 Index in sample Efficiency Analysis for the period 2006 to 2010 with lambda values equal 

to 5 and 10. The interior efficient frontier is built using lambda = 5. The figure also plots the EW portfolio (red dot), GMV portfolio 

(pink dot), the MSR portfolio and the two efficient portfolios (orange dot) relative to the market index (black dot) in this period. Here 

the risk free rate is assumed to be 3.7% (average risk free rate for the period). 

The CSI 300 Index is a cap-weighted 

index that consists of 300 stocks with the 

largest market capitalisation and highest 

liquidity from the entire universe of listed 

A share companies in China. Launched on 

April 8, 2005, the index aims to measure 

the performance of all the A shares traded 

on the Shanghai and Shenzhen stock 

exchanges. 

Given the recent launch of the index, 

our analysis has been restricted to the 

last five years of data. (2006 to 2010). 

During this period the index has been 

highly volatile, largely affected by 

external market conditions. However, 

we still see that the index performance 

has been highly inefficient and has 

also significantly underperformed the 

equal-weighted portfolio. Given that the 

period was reflected by high returns and 

volatility we see that the efficient frontier 

is prominently shifted to the top right 

corner of the plot. 




Table 3.2.g: The table lists the results of CSI 300 Index in sample efficiency Analysis for period Jan 2006 to Dec 2010 with Panel 1 






from the daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using the risk free rate as 3.7%. Column 4 

and 5 represent the greatest underperformance of each portfolio when compared to the market index over a 1 and 3 year period, 

respectively. So, a positive value in these columns would represent the lowest outperformance of those portfolios compared to the 

market index. A negative value in this column represents the greatest underperformance of these portfolios against the market 

index. The number inside the brackets in these columns represents the market index return during that period. The turnover reported 

is the average annual one way turnover of each portfolio across time. 

CSI 300 Index Jan 2006 - Dec 2010 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 

Sharpe Ratio 

Skewness 

Kurtosis 



Index 218.95% 43.79% 

-8.85% 

(78.52%) 


41.18% 

(-33.15%) 250.90% 30.03% 1.34 -.52 4.93 





Min Variance 

Portfolio 186.55% 37.31% 

Max Sharpe 

Portfolio 396.00% 79.20% 

28.3% 

(78.52%) 

-13.09% 

(72.50%) 

23.76% 

(78.52%) 

162.05% 

(90.93%) 90.80% 32.40% 2.49 -.36 5.30 

27.84% 

(-33.15%) 48.74% 23.01% 1.47 -.34 6.56 

148.62% 

(90.93%) 66.82% 28.87% 2.62 -.39 4.97 






Min Variance 

Portfolio 173.35% 34.67% 

Max Sharpe 

Portfolio 460.20% 92.04% 

42.64% 

(78.52%) 

-20.44% 

(72.5%) 

36.36% 

(78.52%) 

205.69% 

(90.93%) 80.26% 32.40% 2.94 -.03 5.79 

18.12% 

(-33.15%) 63.26% 21.06% 1.48 -.28 6.60 

204.69% 

(90.93%) 78.10% 29.17% 3.04 -.31 4.69 




index during the specified portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is just rebalanced 

once in a year. However, the equal-weighted portfolio is so constructed that it is rebalanced daily. Hence the sum of the turnover 



51



China: FTSE China 25 Index 

Fig 3.2.h: This figure is the plot for FTSE China 25 Index in sample Efficiency for the period 2003 to 2010 with lambda values equal 

to 5 and 10. The interior efficient frontier is built using lambda = 5. The figure also plots EW portfolio (red dot), GMV portfolio (pink 


rate is assumed to be 3.43% (average risk free rate for the period). 

The FTSE China 25 Index consists of 25 

largest and most liquid Chinese stocks 

(Red Chip and H shares) listed and trading 

on the Hong Kong Stock Exchange (HKSE). 

This index represents the performance 

of the Chinese market that is open to 

international investors by the virtue of 

trading in the HKSE. 

As evident from the plot above (cf. Figure 

3.2.h), the cap-weighted portfolio is well 

within the efficient frontier. We again see 

the neat outperformance of the equalweighted 

portfolio over the cap-weighted, 

a result also strengthened by the content 

of Table 3.2.h. 




Table 3.2.h: The table lists the results of the FTSE China 25 Index in sample efficiency Analysis for the period of Jan 2003 to Dec 

2010 with Panel 1 representing the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with 

λ = 10. The columns 3rd, 7th, 9th, 10th represent the first four moments of each portfolio. The annual return for each year for all 

the portfolios are calculated from the arithmetic returns of daily stock prices. Annual returns are then averaged across time (each 

year) to produce the results in column 3 for each portfolio. Volatility is calculated from daily returns and then annualised. The 

annualised volatility is averaged across time (each year) to produce the results in column 7 for each portfolio. The skewness and 

kurtosis are calculated from the daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using the risk free 

rate as 3.43%. Column 4 and 5 represent the greatest underperformance of each portfolio when compared to the market index 

over a 1 and 3 year period, respectively. Therefore, a positive value in these columns would represent the lowest outperformance of 

those portfolios compared to the market index. A negative value in this column represents the greatest underperformance of these 

portfolios against the market index. The number inside the brackets in these columns represents the market index return during that 

period. The turnover reported is the average annual one way turnover of each portfolio across time. 

FTSE China 25 Index Jan 2003 - Dec 2010 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 

Sharpe Ratio 

Skewness 

Kurtosis 



Index 217.20% 27.15% 

-8.27% 

(5.09%) 



(Same Return) 202.40% 25.30% 



Min Variance 

Portfolio 117.36% 14.67% 

Max Sharpe 

Portfolio 460.72% 57.59% 

-11.8% 

(-52.1%) 

16.52% 

(14.54%) 

-27.05% 

(68.96%) 

16.72% 

(14.54%) 



(Same Return) 202.40% 25.30% 



Min Variance 

Portfolio 108.16% 13.52% 

Max Sharpe 

Portfolio 514.64% 64.33% 

-14.11% 

(-52.1%) 

19.18% 

(5.09%) 

-28.73% 

(68.96%) 

20.34% 

(5.09%) 

-11.51% 

(83.7%) 182.07% 27.10% 0.88 .07 11.04 

-20.64% 

(83.7%) 47.33% 21.38% 1.02 -.20 10.72 

75.65% 

(83.7%) 68.04% 29.85% 1.81 .19 11.00 

-57.15% 

(87.59%) 45.20% 20.72% 0.54 -.37 11.02 

76.25% 

(83.7%) 68.04% 29.48% 1.84 .19 11.00 

-17.82% 

(83.7%) 54.63% 20.51% 1.07 -.20 10.08 

87.00% 

(83.7%) 73.34% 29.85% 1.99 .18 9.05 

-58.44% 

(87.59%) 49.09% 19.76% 0.51 -.33 10.31 

91.2% 

(83.7%) 74.91% 30.32% 2.01 .23 9.07 

Note- The number in the 4th and the 5th column represent the worst outperformance of the specified portfolio over capweighted 


portfolio’s worst outperformance. 

The turnover cannot exceed 100% if the portfolio is rebalanced only once in a year. However, the equal-weighted portfolio is so 

constructed that it is rebalanced daily. Hence the sum of the turnover in a year exceeds 100%. 


53



India: NIFTY 50 Index 

Fig 3.2.i: This figure is the plot for NSE NIFTY 50 Index in sample Efficiency analysis for the period 2003 to 2010 with lambda values 

equal to 5 and 10. The interior efficient frontier is built using lambda = 5. The figure also plots EW portfolio (red dot), GMV portfolio 

(pink dot), MSR portfolio and the two efficient portfolios (orange dot) relative to the market index (black dot) in this period. The risk 

free rate is assumed to be 5.5% (average Mumbai interbank offer rate for the period). 

15 - http://www. 

standardandpoors.com/servlet/ 

BlobServer?blobheadername3=MDT- 

Type&blobcol=urldata&blobtable=Mung 

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ilename%3DFactsheet_SP_CNX_Nifty_ 

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Disposition&blobheadervalue1 

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d&blobheadername1=contenttype&blobwhere=1243869097312&blobheadervalue3=UTF-8 

Nifty 50 Index is the largest market index 

in India representing the performance 

of the top 50 stocks in the country and 

covering about 60% of the total market 

capitalisation of all the stocks in the 

National Stock Exchange in India. (cf. S&P 

Nifty 50 Index Factsheet 15 ). 

During this period of analysis, the index 

has had overall high returns in general. 

This is the reason why we see the efficient 

frontier shifted higher and more towards 

the right than the similar plots for other 

indices. As evident from the plot, the 

equal-weighted portfolio is closer to the 

efficient frontier than the market index, 

clearly making it a more efficient portfolio 

than the market index. Further, a look at 

the year by year plot in the Appendix, 

which is available upon request, reveals 

that the equal-weighted portfolio has 

performed nearly as well as or better than 

the market index on risk adjusted terms 

in each year. One interesting positive 

fact about the NSE Nifty Index is that 

the index turnover is one of the lowest in 

comparison to other major market indices 

in Asia. 




Table 3.2.i: The table lists the results of NSE NIFTY 50 Index in sample efficiency Analysis for the period Jan 2003 to Dec 2010 

with Panel 1 representing the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with λ = 

10. The columns 3rd, 7th, 9th, 10th represent the first four moments of each portfolio. The annual return for each year for all the 

portfolios are calculated from the arithmetic returns of daily stock prices. Annual returns are then averaged across time (each year) 

to produce the results in column 3 for each portfolio. Volatility is calculated from daily returns and then annualised. The annualised 

volatility is averaged across time (each year) to produce the results in column 7 for each portfolio. The skewness and kurtosis are 

calculated from the daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using the risk free rate as 5.5% 

(Average Mumbai interbank offer rate for the period). Column 4 and 5 represent the greatest underperformance of each portfolio 

when compared to the market index over a 1 and 3 year period, respectively. Therefore, a positive value in these columns would 

represent the lowest outperformance of those portfolios compared to the market index. A negative value in this column represents 

the greatest underperformance of these portfolios against the market index. The number inside the brackets in these columns 

represents the market index return during that period. The turnover reported is the average annual one way turnover of each 

portfolio across time. 

NSE NIFTY 50 Index Jan 2003 - Dec 2010 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 



Index 262.00% 32.75% 

-3.46% 

(39.04%) 


Sharpe Ratio 

Skewness 

Kurtosis 

-2.49% 

(118.03%) 190.02% 25.96% 1.07 -.07 12.10 





Min Variance 

Portfolio 220.56% 27.57% 

Max Sharpe 

Portfolio 500.40% 62.55% 

18.8% 

(19.29%) 

-23.82% 

(47.1%) 

18.22% 

(19.04%) 

93.35% 

(85.15%) 65.05% 26.28% 2.43 .09 10.06 

-29.92% 

(118.03%) 39.58% 19.30% 1.22 -.05 12.21 

88.06% 

(85.15%) 65.06% 24.97% 2.46 .08 9.78 






Min Variance 

Portfolio 220.24% 27.53% 

Max Sharpe 

Portfolio 563.36% 70.42% 

24.89% 

(19.04%) 

-26.75% 

(47.1%) 

24.1% 

(19.04%) 

114.5% 

(85.15%) 76.22% 26.28% 2.78 .16 8.81 

-30.66% 

(118.03%) 51.30% 18.39% 1.27 -.14 10.51 

110.4% 

(85.15%) 76.33% 25.42% 2.82 .10 8.44 




index during the specified portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is rebalanced only 

once a year. However, the equal-weighted portfolio is so constructed that it is rebalanced daily. Hence the sum of the turnover 



55




Fig 3.2.j: This figure is the plot for the FTSE ASEAN Index in sample Efficiency Analysis for the period 2001 to 2010, with lambda 

values equal to 5 and 10. The interior efficient frontier is built using lambda = 5. The figure also plots the EW portfolio (red dot), 

GMV portfolio (pink dot), MSR portfolio and the two efficient portfolios (orange dot) relative to the market index (black dot) in this 

period. Here the risk free rate is assumed to be 2.8% (average risk free rate for the period). 

The FTSE ASEAN Index Series is the 

first to be designed specifically for a 

combination of five stock exchanges 

within the Association of South East 

Asian Nations (ASEAN) group of countries. 

Stocks are selected and weighted by 

market capitalisation from five South 

East Asian financial markets – Indonesia, 

the Philippines, Singapore, Malaysia and 

Thailand – and they cover 90-95% of the 

investable market capitalisation. 

The plot of the performance of FTSE ASEAN 

index is comparable to the performance 

of the other market indices earlier 

considered. The market index is well inside 

the efficient frontier and clearly less 

efficient than the equal-weighted indices. 

As is apparent from the next table (cf. 

Table 3.2.j), the EW portfolio outperforms 

the CW index by approximately 250 basis 

points, adjusted for risk. 




Table 3.2.j: The table lists the results of FTSE ASEAN index in sample efficiency analysis for the period Jan 2001 to Dec 2010 with 

Panel 1 representing the results for optimisation with λ = 5 and Panel 2 representing the results for optimisation with λ = 10. The 

columns 3rd, 7th, 9th, 10th represent the first four moments of each portfolio. The annual return each year for all the portfolios are 




from the daily returns of the whole data sample. The Max Sharpe Portfolio is evaluated using the risk free rate as 2.8%. Column 4 

and 5 represent the greatest underperformance of each portfolio when compared to the market index over a 1 and 3 year period, 

respectively. Therefore, a positive value in these columns would represent the lowest outperformance of those portfolios compared 

to the market index. A negative value in this column represents the greatest underperformance of these portfolios against the 

market index. The number inside the brackets in these columns represents the market index return during that period. The turnover 

reported is the average annual one way turnover of each portfolio across time. 

FTSE ASEAN Index Jan 2001 - Dec 2010 

Portfolio 

Total return 


Sample 

Period 

Returns 

(Ann) 

Worst 

Performance 

against CW 

over a 1year 

period 

Worst 

Performance 

against CW 

over a 3 year 

period 

Average 

Turnover 

(one way) 

Volatility 

(Ann) 

Sharpe Ratio 

Skewness 

Kurtosis 



Index 184.30% 18.43% 

-21.79% 

(-11.75%) 



(Same Return) 162.00% 16.20% 



Min Variance 

Portfolio 126.50% 12.65% 

Max Sharpe 

Portfolio 489.50% 48.95% 

-4.9% 

(37.57%) 

17.29% 

(18.46%) 

-26.55% 

(59.3%) 

14.07% 

(18.46%) 



(Same Return) 162.00% 16.20% 



Min Variance 

Portfolio 108.20% 10.82% 

Max Sharpe 

Portfolio 583.30% 58.33% 

-23.74% 

(59.3%) 

24.85% 

(18.46%) 

-32.98% 

(59.35%) 

20.66% 

(18.46%) 

-49.36% 

(31.84%) 192.51% 16.50% 0.95 -.41 7.17 

3.78% 

(84.07%) 45.56% 10.11% 1.33 -.60 7.91 

66.37% 

(67.96%) 67.28% 17.06% 2.99 -.11 6.76 

-38.01% 

(87.01%) 44.82% 10.06% 0.98 -.58 7.81 

55.32% 

(67.96%) 66.22% 15.17% 3.04 -.27 6.70 

-28.16% 

(84.07%) 58.68% 8.98% 1.49 -.64 7.41 

93.23% 

(67.96%) 79.50% 17.06% 3.65 -.12 6.39 

-46.09% 

(87.01%) 57.99% 8.90% 0.90 -.63 7.52 

77.85% 

(67.96%) 79.17% 14.91% 3.72 -.27 6.36 

Note: The number in the 4th and the 5th column represent the worst outperformance of the specified portfolio over the capweighted 


portfolio’s worst outperformance. The turnover cannot exceed 100% if the portfolio is rebalanced only once in a year. However, 

the equal-weighted portfolio is constructed so that it is rebalanced daily, hence the sum of the turnover in a year exceeds 100%. 


57



16 - Value at Risk measure 

calculated are the Cornish 

Fisher VaR of daily portfolio 

returns at 1% level of 

significance (99% VaR). 

3.1.3.2 Value at Risk 

We also look at the Value at risk 16 (VaR) 

measures for the market index, the equalweighted 

portfolio and the efficient 

portfolios. As we know, VaR is a widely 

used risk measure of the risk of loss on a 

portfolio. For a given portfolio, probability 

and time horizon, Value at Risk (VaR) is 

the maximum loss not exceeded in that 

probability, over that period of time. We 

calculate this to observe the downside 

risk measures of these portfolios, as only 

analysing pure volatility might not provide 

a complete picture of the extreme negative 

risks the portfolios bear. Further, investors 

might reason that if the VaR of the market 

index is lower than other portfolios it 

could be perceived as a premium paid to 

protect against the extreme negative risk, 

which could explain the mean variance 

inefficiency of the index portfolio. 

As we see from the Table 3.3, VaR measures 

are comparable between the market index 

portfolio and the equal-weighted portfolio. 

Further, we notice that the max Sharpe 

and the minimum variance portfolio have 

consistently lower VaR than the market 

index portfolio. This clearly shows that the 

reason of the mean variance efficiency 

cannot be attributed to extreme downside 

risks. 

Overall we observe that all the popular 

market indices commonly used by investors 

for benchmarking of funds in Asia are 

inefficient. The level of inefficiency varies 

between indices; however we find that 

with each of these indices a simple equalweighted 

portfolio outperforms the capweighted 

market index. We can estimate 

the distance in terms of efficiency between 

the markets indices and the in-sample 

efficient frontier using two portfolios of 

the efficient frontier for each index, the 

Max Sharpe Portfolio and the Min Var 

Portfolio. 

The difference between the Sharpe ratio of 

each market index and the Sharpe ratio of 

an efficient index, obtained with the same 

components, is a measure of the distance 

in terms of efficiency between the markets 

indices and the efficient frontier. The higher 

the distance, the less efficient the index 

is. The results presented in Tables 3.2.a to 

Table 3.3: Table contains the VAR measures on the daily returns of different portfolios for each of the index. The VaR measures 

provided are the Cornish Fisher 99% VAR. 

Market Index 

Time Period 

Value at Risk of 

Market Index 

Portfolio 

Value at Risk of 

EW Portfolio 

Value at Risk 

of Max Sharpe 

Portfolio 

Value at Risk 

of Min VaR 

Portfolio 

Value at Risk 

of efficient 

portfolio with 

the market 

index volatility 

Hang Seng Jan 2002 - Dec 2010 3.67% 3.77% 2.68% 1.82% 3.05% 

NIKKEI 225 Jan 1996 - Dec 2010 3.34% 3.34% 3.12% 2.14% 3.12% 

TOPIX 100 Feb 1999 - Dec 2010 3.16% 3.11% 2.67% 1.80% 2.83% 

FTSE STI Sep 2001 - Dec 2010 2.70% 2.77% 2.43% 1.72% 2.55% 

KOSPI 200 Jun 2001 - Dec 2010 3.59% 3.52% 3.09% 2.24% 3.52% 

TWSE 50 Jan 2003- Dec 2010 3.48% 3.24% 2.68% 1.99% 2.97% 

CSI 300 Jan 2006 - Dec 2010 5.15% 4.89% 3.96% 3.06% 4.30% 

FTSE China 25 Jan 2003 - Dec 2010 4.20% 4.35% 4.16% 2.72% 4.16% 

NIFTY 50 Jan 2003 - Dec 2010 3.74% 3.84% 3.24% 2.46% 3.45% 

FTSE ASEAN Jan 2001 - Dec 2010 2.46% 2.44% 2.05% 1.24% 2.33% 




3.2.j. confirm that, by construction, the 

maximum distance between a market 

index and one of its in-sample efficient 

alternatives is with the in-sample Max 

Sharpe portfolio. The FTSE ASEAN index 

is the one for which the distance is the 

biggest, with a difference of 2.25 between 

the two Sharpe ratios, while the minimum 

value is obtained with the FTSE China 25 

index, with a difference of 1.08 between 

the two Sharpe ratios – still a rather high 

value. A median value of 1.62 is obtained 

with the TOPIX 100 index. 

Similar computations of Sharpe ratios 

were performed in Amenc et al. (2006) for 

European and US indices on a different 

time period. However, having a look at 

the differences between the efficient and 

inefficient indices Sharpe ratios, it appears 

to us that values were in a comparable 

range (see Table 3.4). For example, over 

the period of October 1995 to September 

2000 (Period 1), the maximum difference 

between Max Sharpe portfolio and market 

index Sharpe ratios of US and European 

indices was of 2.90 (compared to the 

2.25 of Asian indices), and the minimum 

difference was 0.30 (compared to the 1.08 

of Asian indices). A median value of 1.41 

was obtained for US and European Indices 

(compared to the 1.62 of Asian indices). 

We thus observe that the two median 

values were quite comparable, but that 

the range of values is slightly wider for 

European and US indices than for Asian 

indices. 

These results are confirmed by those 

obtained with European and US indices 

over the period from October 2000 to 

September 2005 (Period 2). For example, 

the min value for the difference is quite 

the same for Asian indices (1.08) and for 

European and US indices (1.05), while 

max and median values are higher for 

European and US indices over this period. 

Similar comparisons were also made 

based on the in-sample Min Var Portfolio 

as the efficient reference. Here again 

the distance between efficient portfolios 

and market indices appears to be quite 

comparable for Asian indices and 

European and US indices, especially over 

Period 1. For example, the median value 

for Asian indices is of 0.31, compared to 

0.20 for European and US indices, and 

the minimum value is of -0.19 for Asian 

indices, compared to -0.24 for European 

and US indices. Here again, the maximum 

value is higher for European and US 

indices (1.31) than for Asian indices (0.64), 

showing a wider range of values for 

European and US indices than for Asian 

indices. 

Table 3.4: Comparison of the distribution of the differences in Sharpe ratios between in-sample efficient portfolios and market 

index obtained for Asian indices (in the present study) and European and US indices (in Amenc et al., 2006). 

Difference in Sharpe Ratio of Max Sharpe Portfolio 

and mkt index 

Asian indices 

European and 

US indices 

Period 1 

European and 

US indices 

Period 2 

Difference in Sharpe Ratio of Min VaR portfolio 

and mkt index 

Asian indices 

European and 

US indices 

Period 1 

European and 

US indices 

Period 2 

MAXIMUM 2.25 2.90 4.92 0.64 1.31 3.56 

MEDIAN 1.62 1.41 2.35 0.31 0.20 1.26 

MINIMUM 1.08 0.30 1.05 -0.19 -0.24 0.30 


59



Though the observation periods of Asian 

indices and European and US indices 

were not the same, this comparison tends 

to show that the level of inefficiency of 

Asian market indices is quite comparable 

to that of European and US indices, with 

a lower dispersion of values for Asian 

indices than for European and US indices. 

As discussed in the literature review 

section (Section 2.3) of the report 

reviewing issues with cap weighting, one 

of the key reasons for this inefficiency 

is the effect of concentration in such 

indices. High concentration in an index 

leads to poor diversification, and hence 

poor risk adjusted performance in 

returns, therefore, we will follow up with 

an analysis of the concentration effect in 

these indices. 

3.2 Concentration analysis 

3.2.1Data 

We collect the weights of all the stocks in 

the index at the start of every month from 

Bloomberg. This is adopted for the Hang 

Seng, KOSPI 200, Nikkei 225, TWSE 50, 

Nifty 50, Topix 100, FTSE STI and CSI 300 

indices. For the FTSE China 25 index, we 

get the monthly weights from FTSE. And 

the monthly constituent weights of the 

FTSE ASEAN Index are from DataStream. 

The historical data availability of the 

weights varied from one index to another, 

which restricted us to performing the 

concentration analysis on each index 

with varying amounts of historical data. 

We have presented in Table 3.5 with the 

source of data and the time frame over 

which the analysis was performed for 

each index. 


One of the biggest concerns for investors 

in using cap-weighted indices has 

been that it could lead to concentrated 

portfolios in a few sets of stocks (refer 

to part on issues with cap-weighted 

indices under Section 2). Academic 

research points out that concentration 

in portfolios could be one of the factors 

that drive inefficiency in the indices; e.g. 

Table 3.5: Table below provides a summary of the data sources for the concentration analysis. Column 2 contains the source for 

the historic data on weights of the index constituents. Column 3 represents the time period for which the data is collected and the 

analysis performed. 

Data Sources for Concentration Analysis 

Index Data Source Period 

Hang Seng Index Bloomberg Jan 2002 to Dec 2010 

Nikkei 225 Index Bloomberg Feb 2001 to Dec 2010 

Topix 100 Index Bloomberg Jan 2001 to Dec 2010 

FTSE STI Index Bloomberg Jan 2008 to Dec 2010 

KOSPI 200 Index Bloomberg Feb 2002 to Dec 2010 

FTSE TWSE 50 Index Bloomberg Jul 2003 to Dec 2010 

CSI 300 Index Bloomberg Sep 2005 to Dec 2010 

FTSE China 25 Index FTSE Mar 2004 to Dec 2010 

Nifty 50 Index Bloomberg Feb 2002 to Dec 2010 

FTSE ASEAN Index DataStream Jan 2001 to Dec 2010 1 

Note- 1- From DataStream we get the market cap value adjusted for free float for the individual constituents in the index. We use 

this to compute the individual weights of the component stocks in the index . 




Malvergne et al. (2009) point out that 

heavy tails in the distribution of firm sizes 

in an index results in an additional risk 

factor generically appearing, making the 

cap-weighted portfolios inefficient. We 

try to analyse the extent of concentration 

in an index using the Herfindahl measure. 

The advantage of using the Herfindahl 

measure is that its reciprocal provides the 

“effective number” of stocks in the index, 

allowing for an easy, yet meaningful 

measurement of concentration. Highly 

concentrated indices would have a 

lower effective number of stocks as a 

percentage of total stocks in the index. 

On the other extreme, an equal-weighted 

portfolio would have an effective number 

of stocks equal to the number of stocks in 

the portfolio. 

The formula for the effective number of 

stocks is defined as below: 

Effective Number of Stocks = 

where w i is the weight of the ith stock in 

the index, and N is the total number of 

stocks in the index. In addition, we also 

provide the percentage weight occupied 

by the largest 20% of the constituents in 

the index. 

3.2.3 Results 

As we did with the efficiency analysis, we 

present the results of the concentration 

analysis by each index. The results 

presented include the Herfindahl index 

score, the effective number of stocks, 

and the weight occupied by the top 

20% of the largest constituents by 

weight. We also compute the ratio of 

the effective number of stocks to the 

total number of stocks in the index. 

This gives a clear picture of the level of 

concentration in the index, and makes it 

comparable across indices. Further, for 

each of these measures we provide the 

dispersion measures – minimum value 

in the sample period, average value over 

the period, and maximum value in the 

period. These dispersion measures help 

provide a better picture of the stability 

of the concentration measures over 

Hang Seng Index 

Table 3.6.a: Table below lists the results of the concentration analysis for the Hang Seng HSI INDEX for the period from Jan 2002 to 

2010. The figures reported are the Herfindahl index, the effective number of stocks and % weight occupied by the top 20 percent 

of the constituents. Weights are identified at the start of every month. The Herfindahl index is computed using the formula 

for each month t. The reciprocal of this number is the Effective number of stocks for that month. We also 

compute the following ratio - Effective number of stocks/ the number of stocks in the index. For each of these measures the 

maximum, minimum and the average recorded value over the time series is reported. 

Hang Seng (HSI) Index 

Total Stocks 

in Index = 45 

Metrics Considered 

Minimum Value 

in the Period 

Average over the Period 

Maximum Value 


Herfindahl Index 0.05 0.10 0.14 

Effective number of stocks 6.95 11.71 20.02 

Percentage weight of largest 

20 percent constituents 

52.7% 63.3% 73.7% 

Effective number of stocks/ 

17.4% 29.3% 50.1% 

Total stocks in the index 

Note- In the calculation of the ratio in the row 3, we use the total number of stocks in the index as 40, as it is the average of the 

total number of stocks in the index over the analysis period. The number of stocks in the Hang Seng index increased steadily from 

33 to 45 from 2002 to 2010. The minimum is taken as the minimum value of monthly observations, while the maximum is the 

maximum value of monthly observations. 


61



time, and identify how concentrated the 

portfolios become during extreme market 

conditions. 

As we see from Table 3.6.a, the effective 

number of stocks is, on average, around 

30% of the total number of stocks in the 

portfolio. These results are in line with 

other cap-weighted indices in Europe 

and the U.S. Further we notice that there 

is significant dispersion in the effective 

number of stocks implying that there are 

periods in the market when the index 

becomes highly concentrated. 

The Nikkei 225 is a price weighted index, 

hence the weighting is distinct from a 

standard market cap-weighted index. 

Nevertheless, we again observe some 

concentration in the index. However, we 

note that the ratio of effective number of 

stocks to the total number of stocks in the 

index is on average higher than that for 

the Hang Seng index, and the dispersion 

of this measure is also within a relatively 

narrow band. 

The Topix 100 index is similar to TWSE 

50 index and is one of the most well 

diversified indices in the region with a 

Nikkei 225 Index 

Table 3.6.b: Table below lists the results of the concentration analysis for the NIKKEI 225 index for the period from Feb 2001 to 

2010. The figures reported are the Herfindahl index, effective number of stocks and % by weight occupied by the top 20 percent 





Nikkei 225 Index 


in Index = 45 

Topix 100 Index 


Minimum Value 



Maximum Value 




Percentage weight of largest 56.4% 61.2% 69.3% 




25.4% 36.7% 43.2% 

Table 3.6.c: Table below lists the results of the concentration analysis for the TOPIX 100 Index for the period from Jan 2001 

to Dec 2010. The figures reported are the Herfindahl index, effective number of stocks and % by weight occupied by top 20 

percent of the constituents. Weights are identified at start of every month. The Herfindahl index is computed using the formula 




Topix 100 Index 


in Index = 45 


Minimum Value 



Maximum Value 








37.0% 49.0% 60.2% 




higher ratio of effective number of stocks 

to the total number of stocks in the index, 

and lower percentage weight in the top 20 

constituents, relative to the other indices 

analysed. We observe that the dispersion 

is slightly larger than that of the TWSE 50 

index, but still within a relatively narrow 

band. 

We observe that, post reconstitution of 

this index in Jan 2008, the ratio of effective 

number of stocks to the total number 

of stocks in the index has been on the 

high side and percentage concentration 

in top 20 constituents low, implying a 

better diversified and less concentrated 

index. This is in contrast to the level of 

concentration prior to the reconstitution 

period (pre Jan 2008) when the STI index 

was observed to be highly concentrated 

with just the top 5 stocks occupying 

more than 50% of the index (Dresdner 

Kleinwort Wasserstein Research 2005). 

The KOSPI 200 index is one of the most 

concentrated indices amongst the 

FTSE Strait Times Index 

Table 3.6.d: Table below lists the results of the concentration analysis for the FTSE Strait Times Index for the period of Jan 2008 

to Dec 2010. . The figures reported are the Herfindahl index, effective number of stocks and % by weight occupied by top 20 





Strait Times Index 


in Index = 45 


Minimum Value 



Maximum Value 







47.7% 56.2% 65.9% 


Note: This analysis is done with limited amount of time series data on constituent weights – Feb 2008 to Dec 2010 after the major 

reconstitution of the index in Jan 2008. 

KOSPI 200 Index 

Table 3.6.e: Table below lists the results of the concentration analysis for the KOSPI 200 index for the period of Feb 2002 to 

Dec 2010. The figures reported are the Herfindahl index, effective number of stocks and % by weight occupied by the top 20 





KOSPI 200 Index 


in Index = 45 


Minimum Value 



Maximum Value 








5.7% 10.4% 18.4% 


63



other Asian Indices. These results clearly 

indicate that the KOSPI 200 index is a 

highly concentrated index. Samsung 

alone occupies close to 18% weight of 

the index over the analysis period. This 

analysis clearly brings to light this fact, 

which is also documented in Dresdner 

(2005). Because of the high concentration, 

the ratio of the effective number of stocks 

to the total number of stocks is one of 

the lowest amongst Asian indices, and 

the percentage weight occupied by the 

largest 20 constituents is the highest in 

the region. 

In contrast to the KOSPI 200 index, 

the TWSE 50 index is one of the most 

well diversified indices with one of the 

highest ratios for effective number of 

stocks to the total number of stocks, and 

lowest percentage weight in the top 20 

constituents in the Asia-Pacific region. 

We also observe that the dispersion of the 

effective number of stocks is in a relatively 

narrow band indicating relatively greater 

stability in constituent weights during the 


TWSE 50 Index 

Table 3.6.f: Table below lists the results of the concentration analysis for the TWSE Taiwan 50 Index for the period from July 2003 

to Dec 2010. The figures reported are the Herfindahl index, the effective number of stocks and % by weight occupied by the top 

20 percent of the constituents. Weights are identified at the start of every month. The Herfindahl index is computed using the 

formula 

for each month t. The reciprocal of this number is the Effective number of stocks for that month. 

We also compute the following ratio - Effective number of stocks/ the number of stocks in the index. For each of these measures 

the maximum, minimum and the average recorded value over the time series is reported. 

TWSE 50 Index 


in Index = 45 

CSI 300 Index 


Minimum Value 



Maximum Value 








33.6% 41.2% 52.0% 

Table 3.6.g: Table below lists the results of the concentration analysis for the CSI 300 Index for the period from Sep 2005 to 

Dec 2010. The figures reported are the Herfindahl index, effective number of stocks and % weight occupied by top 20 percent 

of the constituents. Weights are identified at start of every month. The Herfindahl index is computed using the formula 

for each month t. The reciprocal of this number is the Effective number of stocks for that month. We 

also compute the following ratio - Effective number of stocks/ the number of stocks in the index. For each of these measures the 


CSI 300 Index 


in Index = 45 


Minimum Value 



Maximum Value 








10.3% 30.3% 43.3% 




As we see from Table 3.6.g, the CSI 300 

index is quite concentrated with the 

percentage weight occupied by the top 

20% constituents indicating this. Also 

interesting to note is the huge dispersion in 

range of market concentration values over 

the sample period as observed by the ratio 

of effective number of stocks to the total 

number of stocks in the index, indicating 

periods of high concentration in the index. 

This is evident from the lowest value in the 

ratio of effective number of stocks to the 

total number of stocks in the index is just 

10% at the lowest. 

Here we note that in the case of FTSE China 

25 index, by the nature of construction, 

this index is capped to ensure that no 

individual company is excessively weighted 

within the index (FTSE Index Factsheet 17 ). 

This ensures the high measures of effective 

stocks and lower percentage weight in 

the top 20% constituent observed for the 

index. We also find that the dispersion of 

the ratio of effective number of stocks to 

the total number of stocks in the index 

is in a relatively narrow band indicating 

the stability of the weights of the stocks 

within the index. 

17 - http://www.ftse.com/ 

Indices/FTSE_China_Index_ 

Series/Downloads/XIN0.pdf. 

FTSE China 25 Index 

Table 3.6.h: Table below lists the results of the concentration analysis for the FTSE China 25 Index for the period from Mar 2004 

to Dec 2010. The figures reported are the Herfindahl index, effective number of stocks and % weight occupied by top 20 percent 


for each month t. The reciprocal of this number is the Effective number of stocks for that month. We 

also compute the following ratio - Effective number of stocks/ the number of stocks in the index. For each of these measures the 


FTSE China 25 Index 


in Index = 45 


Minimum Value 



Maximum Value 








68.8% 74.4% 78.7% 

NIFTY 50 Index 

Table 3.6.i: Table below lists the results of the concentration analysis for the NIFTY 50 Index for the period of Feb 2002 to Dec 

2010. The figures reported are the Herfindahl index, effective number of stocks and % by weight occupied by top 20 percent 



compute the ratio - Effective number of stocks/ the number of stocks in the index. For each of these measures the maximum, 

minimum and the average recorded value over the time series is reported. 

NIFTY 50 Index 


in Index = 45 


Minimum Value 



Maximum Value 








31.5% 43.2% 49.9% 


65



Compared to the other indices, the Nifty 

50 index is moderately diversified with 

a better score on the ratio of effective 

number of stocks to the total number of 

stocks in the index, when compared to 

other indices. We also observe that the 

dispersion in concentration is also better 

than the average when compared to other 

peer indices. 

the level of concentration is highly variant 

for some of the indices, with periods 

where they exhibit significantly higher 

concentration than what is observed on 

average. As we noted in the literature 

review (cf. Section 2), concentration in 

indices leads to less diversified portfolios 

and performance drag. 

As we see from the results, the FTSE 

ASEAN index is quite concentrated 

with heavily weighted stocks. In terms 

of concentration, the index is overall 

comparable to other indices in Asia. 

Although it is not apparent from the table 

(cf. Table 3.6.j), we observe in our analysis 

that the concentration of the index has 

been steadily growing over time with 

the minimal values recorded occurring 

around the beginning of the sample (Jan 

2001) and the maximum values recorded 

occurring around the end of the sample 

period (Dec 2010). 

Overall we find that most of the indices 

in Asia-Pacific are highly concentrated. 

Further, we also note that the dispersion in 


Table 3.6.j: Table below lists the results of the concentration analysis for the FTSE ASEAN Index for the period of Jan 2001 to 

Dec 2010. The figures reported are the Herfindahl index, the effective number of stocks and % by weight occupied by top 20 







in Index = 45 


Minimum Value 



Maximum Value 








16.6% 30.2% 39.7% 


4. Stability Analysis 


67



18 - The GICS structure 

consists of 10 sectors, 24 

industry groups, 68 industries 

and 154 sub-industries into 

which S&P has categorised 

all major public companies. 

The 10 sectors we used 

for this analysis include 

Energy, Materials, Industrials, 

Consumer Discretionary, 

Consumer Staples, 

Health Care, Financials, 

Information Technology, 

Telecommunication Services 

and Utilities. 

The purpose of this section is to perform 

a similar study done by Amenc et al. 

(2006) on the stability of the sector and 

style exposure for each index, as investors 

are typically interested in the allocation 

between the different sub-categories of 

their equity portfolio. The most relevant 

sub-categories for equity investors are 

investment styles (growth and value) 

and industry sectors. This stems from 

the fact that style (growth, value) have 

been shown to explain a significant 

portion of the cross-sectional difference 

in expected stock returns (see Section 

2.4). Likewise, sectors of the industry are 

useful building blocks in the construction 

of equity portfolios, as different sectors of 

the economy have different exposure to 

the business cycle (Badorf and Jacobsen 

2010; Hofschire 2012). As the portfolio 

composition by style and by sector directly 

impacts the risk and return properties 

of the portfolio, this decision requires 

considerable attention from investors. 

Amenc et al. (2006) tested a wide range of 

broad market indices from the US, Europe 

and Japan and reveal that all indices have 

different levels of instability in terms of 

sector or style exposure over a 10-year 

test horizon. In this section, we apply 

their methodology and test the stability 

of existing indices in Asia. 

4.1 Sector stability test 

We start our analysis by investigating the 

evolution of sector weights in an index. An 

understanding of the implicit dynamics of 

sector exposure of an index is crucial for 

investors who want to monitor the risk 

and return properties of their portfolios. 

4.1.1 Data 

The indices used in these studies are the 

same used for the preceding efficiency 

and concentration studies. They represent 

the broad market in a country or in a 

region within Asia. We have indices 

from developed countries in Asia (Hong 

Kong, Japan, Singapore, South Korea and 

Taiwan) and developing countries (China 

and India) as well as a regional index 

(ASEAN). In addition, we choose a 10-year 

period for our empirical tests. This period 

runs from January 2001 to December 

2010, subject to data availability (see Table 

4.1). In general, the historical changes in 

composition of an Asian index are not 

completely available since the inception 

of the index values with data providers. 

Therefore, the test period of each index 

would be either over 10 years or over a 

shorter period starting with the beginning 

of data availability. We use data with 

monthly frequency in this analysis. For the 

sector classification of each component, 

we use the Global Industry Classification 

Standard (GICS) 18 provided by Bloomberg. 


Instead of calculating the sector weights 

by dividing the market value of each 

sector index over the market value of the 

broad market index (Amenc et al. 2006), 

we look at the composition of the index 

by individual component securities. We 

obtain the historical composition of each 

index and classify each component by the 

GICS provided by Bloomberg. In the end, 

by adding up the weights of securities 

from the same sector, we can obtain the 

sector weights for each month. This way, 

we actually observe (based on actual 

holdings) rather than estimate (based 

on return data) the sector exposures of 




Table 4.1: Table below provides a summary of the data sources for the sector stability analysis. Column 3 contains the source for 

the historic data on weights of the index constituents. Column 4 represents the time period for which the data is collected and the 

analysis is done. 

Data Source for Sector Stability Analysis 


Developed countries 

Hang Seng Index Hong Kong Historical weights of each constituent from Bloomberg Jan 2001 to Dec 2010 

Nikkei 225 Index Japan Historical weights of each constituent from Bloomberg Jan 2001 to Dec 2010 

Topix 100 Index Japan Historical weights of each constituent from Bloomberg Jan 2001 to Dec 2010 

FTSE STI Index Singapore Historical weights of each constituent from Bloomberg Feb 2008 to Dec 2010 

KOSPI 200 Index South Korea Historical weights of each constituent from Bloomberg Feb 2002 to Dec 2010 

FTSE TWSE 50 Index Taiwan Historical weights of each constituent from Bloomberg Jul 2003 to Dec 2010 

Developing countries 

CSI 300 Index China Historical weights of each constituent from Bloomberg May 2005 to Dec 2010 

FTSE China 25 Index China 19 Historical weights of each constituent from Bloomberg May 2005 to Dec 2010 

Nifty Index India Historical weights of each constituent from Bloomberg Jan 2002 to Dec 2010 

Regions 

FTSE ASEAN Index ASEAN Region Historical weights of each constituent from DataStream Jan 2001 to Dec 2010 

19 - All constituents of FTSE 

China 25 Index are traded 

on the Hong Kong Stock 

Exchange. 

20 - The period considered in 

Amenc et al. (2006) is from 

Oct 1995 to Oct 2005. 

the indices for the entire test period. The 

period considered is, either the 10-year 

period from January 2001 to December 

2010, or from the starting date of the 

available data to December 2010. 20 


69



4.1.3 Developed countries 

Hong Kong 

Hong Kong’s Hang Seng Index (HSI), 

listed on the Hong Kong Stock Exchange, 

was comprised of 33 stocks in 2001 and 

gradually increased to 45 stocks in late 

2010. In the beginning of the sample 

period, the index constituents only came 

from seven out of 10 sectors, which are 

defined by the GICS. The index did not 

include any stocks from the Energy, 

Materials and Health Care sectors. Since 

August 2001, the Hang Seng Index started 

to include stocks from the Energy sector, 

and gradually grew the weights to about 

7.5% at the end of 2007. In December 

2007, HSI included two energy giants – 

PetroChina and China Shenhua Energy 

– to boost the total share of the Energy 

sector to above 13%. Around the same 

period from 2001 to 2007, the index 

reduced the allocation to the Industrials 

sector from 15% to about 6%. The Hang 

Seng Index began including Materials 

sector stocks from July 2008 onwards, 

but the allocation to this sector was still 

negligible until the end of study period 

(about 0.5%). 

The most significant variation in 

the sector weight occurred with the 

Telecommunication Services sector. The 

weight reached about 27% in 2001. Then 

it went down to about 14% and bounced 

back to about 25% before the financial 

crisis in 2007-2008. At the end of the 

analysis period, the Telecoms sector only 

takes up less than 10% of weights in the 

index. Moreover, the Financials sector also 

shows considerable variation in the sector 

weights during the sample period, ranging 

from 47% to 64%, while it consistently 

constituted the sector with the highest 

weight in the Hang Seng Index. 

Figure 4.1.a. Evolution of sector weights in the Hang Seng Index from 2001 to 2010 

This figure presents the sector weight evolution for Hang Seng Index from January 2001 to December 2010. The classification of 

sectors is based on the GICS. The weights are calculated by adding up all constituents’ weights within each sector at each month. 




Japan 

The Nikkei 225 is a price-weighted average 

index of stocks listed on the Tokyo Stock 

Exchange in Japan. It comprises 225 

components. 

Compared to the Hang Seng Index, the 

variation in weights for each sector 

appears smoother. The sector distribution 

is also more equal, unlike the Hang Seng 

Index, in which the Financials sector 

makes up more than half of the entire 

index. The variation of the Information 

Technology sector is the most significant, 

which reduced from above 30% in the 

beginning of 2001 to below 20% at the 

end of 2010. The large drop in this sector 

exposure after 2001 corresponds to the 

burst of the tech-bubble. Another sector 

showing considerable changes in weights 

is the Industrials sector. The sector weight 

increased from 17% to 24% in the 10- 

year period from 2001 to 2010. 

The Topix 100, also known as the Tokyo 

Stock Price Index, is another important 

index listed on the Tokyo Stock Exchange, 

comprised of the 100 most liquid stocks 

with the largest market capitalisation 

in Japan. These stocks are classified by 

10 sector categories by GICS. Again, 

we can see that the sector weights are 

not constant over time, with the most 

pronounced variation occurring during 

2008 to 2009. The largest variation in 

weights throughout the period is with 

the Financials sector, with the lowest 

(12%) in 2003 to the highest (29%) in 

2006, followed by the Telecommunication 

Service sector, which has variation in 

sector weights ranging from 4.6% to 15%. 

Figure 4.1.b Evolution of sector weights of Nikkei 225 Index from 2001 to 2010 

This figure presents the sector weight evolution for Nikkei 225 Index from January 2001 to December 2010. The classification of 



71



Figure 4.1.c Evolution of sector weights of Topix 100 Index from 2001 to 2010 

This figure presents the sector weight evolution for the Topix 100 Index from January 2001 to December 2010. The classification of 


Singapore 

The FTSE STI Index is a market capweighted 

index, intended to represent 

the market performance in Singapore. 

It was launched in 2008 and is jointly 

calculated by FTSE, SPH (Singapore Press 

Holdings) and SGX (Singapore Exchange). 

The STI, which was constructed by SPH, 

replaced the Straits Times Industrials 

Index in 1998. The FTSE STI Index includes 

30 stocks, which can be categorised into 

five sectors (under the GICS definition). 

Financials and Industrials sectors make up 

most of the weight (about 70-80%) of the 

entire index. 

Though the analysis for this index only 

lasts for two years, the sector weight of 

Financials varies from 43% to 53%. The 

allocations to the remaining four sectors 

also change by about 4 – 6% within two 

years. 

Figure 4.1.d Evolution of sector weights of FTSE STI Index from 2008 to 2010 

This figure presents the sector weight evolution for the FTSE STI Index from February 2008 to December 2010. The classification of 





South Korea 

The KOSPI 200 (Korea Composite Stock 

Price Index) Index is a market capweighted 

index, which contains the 200 

biggest companies in South Korea. The 

weights of constituents are only available 

going back to February 2002 in Bloomberg. 

The 200 constituents could be subdivided 

into 10 sectors, while, in general, the 

KOSPI 200 is exposed to more exportoriented 

sectors – Industrials, Materials, 

Information Technology and Consumer 

Discretionary (Goldman Sachs 2011). 

During the analysis period, the sector 

weights fluctuate significantly, especially 

during 2007 to 2008. For instance, the 

Industrials sector expands it weights from 

about 8% in 2001 to 28% at the end of 

2007. On the other hand, Financials sector 

has contracted from about 28% in 2001 to 

13% after the financial crisis 2007-2008. 

Information Technology sector went 

down from above 30% in the beginning 

of the analysis period to about 15% in 

2007, and went up again to about 25% in 

2009 and 2010. 

Figure 4.1.e.Evolution of sector weights of KOSPI 200 Index from 2002 to 2010 

This figure presents the sector weight evolution for the KOSPI 200 Index from February 2002 to December 2010. The classification 

of sectors is based on the GICS. The weights are calculated by adding up all constituents’ weights within each sector at each 

month. 


73



Taiwan 

The FTSE TWSE Taiwan 50 Index was 

started in 2002 by TWSE (Taiwan Stock 

Exchange Corporation) and FTSE and was 

the first tradable index for the Taiwan 

stock market. It keeps track of the top 50 

companies by total market capitalisation. 

The available data went back to July 2003, 

while the constituents come from eight 

out of 10 sectors defined by the GICS. 

About 60% of stocks come from the 

Information Technology sector, which is 

expected as Taiwan is one of the global 

centres for electronics products. An 

additional 30% of the stocks are from the 

Financials and Materials sectors. 

These three largest sectors also contribute 

to the largest variation in the sector 

weights during the analysis period. The 

Information Technology sector got hit at 

the end of 2004 (46%) and at the same 

time, the Financials sector grew close to 

30% from 23%. Then the Information 

Technology sector recovered after 2004 

(about 55%), while the Financials sector 

dropped to 23% again, and continued 

decreasing to about 15% at the end of the 

analysis period. 

In summary, all indices in developed 

countries in Asia exhibit instability of 

sector exposure during the analysis 

period. The maximum variation in weight 

of a sector was above 10%, and even 

achieved 20% in the Industrials sector 

for KOSPI 200 Index. The variations in 

sector exposure across indices do not 

occur synchronously, but in general, they 

become more volatile after 2007. Now 

we move to the indices from developing 

countries in Asia. 

Figure 4.1.f.Evolution of sector weights of FTSE TWSE Taiwan 50 Index from 2003 to 2010 

This figure presents the sector weight evolution for FTSE TWSE Taiwan 50 Index from July 2003 to December 2010. The classification 

of sectors is based on the GICS. The weights are calculated by adding up all constituents’ weights within each sector at each month. 




4.1.4 Developing countries 

China 

The CSI 300 is a capitalisation-weighted 

stock market index designed to replicate 

the performance of 300 largest and most 

liquid stocks (A share) traded on the 

Shanghai and Shenzhen stock exchanges. 

The index has been compiled by the China 

Securities Index Company since 2005. 

Therefore, our data also started from May 

2005. 

Again, the Financials sector has increased 

its weight significantly since 2006 from 

14% and peaked at 44% at the beginning 

of 2010. Such expansion in the Financials 

sector may be attributed to the economic 

structural change – from manufacturing 

to consumer services – in China during 

this period. The financial services sector 

experienced a fast annual growth of 30% 

in value from 2000 to 2009 (Ehmer 2011). 

Such growth in financial services sector 

reflects the rise of financial services 

companies and concomitantly alters the 

sector exposure of the index, as the index 

is based on market capitalisation of the 

companies. Other than the significant 

change in the Financials sector, the 

variations in weights of Energy, Materials 

and Industrials are also about 10% in this 

five-year period. The remaining sector 

allocations change considerably by about 

3-8%. 

The FTSE/Xinhua China 25 Index consists 

25 of the largest (based on market 

capitalisation) and most liquid Chinese 

stocks (Red Chips and H shares) listed 

and trading on the Hong Kong Stock 

Exchange. The index was launched in 

2001. However, the historical composition 

of constituents is only available from 

May 2005 in Bloomberg. The 25 stocks 

represent maximum eight sectors defined 

by the GICS at each time of period. 

The sector weight distribution varies 

significantly throughout the entire 

period. For example, the Financials sector 

gradually increased from 17% in the 

beginning of the period analysed to about 

50% at the end of 2010. Again, such an 

increase in the exposure to Financials 

sector reflects the industry’s growth 

Figure 4.1.g.Evolution of sector weights of CSI 300 Index from 2005 to 2010 

This figure presents the sector weight evolution for CSI 300 Index from May 2005 to December 2010. The classification of sectors is 

based on the GICS. The weights are calculated by adding up all constituents’ weights within each sector at each month. 


75



Figure 4.1.h.Evolution of sector weights of the FTSE China 25 Index from 2005 to 2010 

This figure presents the sector weight evolution for FTSE China 25 Index from May 2005 to December 2010. The classification of 


in China after 2000. The Consumer 

Discretionary sector disappears at the end 

of 2005 and re-entered in the index at the 

end of 2009. Consumer Staples only ran 

from the beginning of the analysis period 

to the end of 2007. 




India 

The S&P CNX Nifty is a free float market 

capitalisation index, listed on the National 

Stock Exchange of India. It consists of 50 

companies representing 10 sectors of the 

economy defined by the GICS. 

Similar to the two Chinese indices, the 

sector weights here are also extremely 

volatile during the analysis period. 

However, the main changes occur in 

different sectors. For instance, the sector 

weight of Consumer Staples started 

at 27% in the beginning of 2002 and 

dropped sharply to about 3% at the 

end of 2007. And the variation of the 

Information Technology sector seems 

to follow the global economic cycle – 

the exposure drops after the 2001-2002 

tech bubble and gradually increases 

afterwards, and then ceases again after 

the financial crisis in 2007-2008. This may 

stem from the fact that about 40% of 

the IT service revenue are from financial 

services (Deloitte 2009). There is a sudden 

jump in the allocation to Energy sector 

in 2004, which is due to the inclusion of 

energy giant Oil & Natural Gas Corp Ltd. 

In addition, the change from full market 

capitalisation to free-float basis in the 

construction of the index in June 2009 

also has had an impact on the variations 

in sector exposure (Thunuguntla 2009). 

In summary, we find that market indices in 

developing countries are, in general, more 

volatile in their sector exposure than the 

indices in developed countries. Possible 

explanation may be economic structural 

shift, the inclusion of giant companies, 

and the change of the calculation 

methodology in the index construction. 

Figure 4.1.i.Evolution of sector weights of the Nifty Index from 2002 to 2010 

This figure presents the sector weight evolution for the Nifty Index from January 2002 to December 2010. The classification of 



77



4.1.5 Regions 

Finally, we look at one regional index – the 

FTSE ASEAN Index. This index comprises 

of about 147 companies located from 

Singapore, Malaysia, Indonesia, Thailand 

and the Philippines. These constituents 

could be classified into 10 sectors as 

defined by the GICS. 

Overall, the fluctuation of the sector 

weights over time is similar to those we 

have seen for developed countries. The 

Financials and Energy sectors have also 

been observed with high variations of 

about 9% in sector exposure over the 

entire testing period, while the variation 

is more pronounced during 2008. 

4.1.6 Summary of results 

From our analysis, it can be seen that 

exposures to sector factors show 

considerable variation over time, especially 

for developing country market indices. 

In addition to comparing the intensity 

of the sector drift score (the sector 

instability) of the different indices, we 

calculate the sector drift score proposed 

by Idzorek and Bertsch (2004), defined as: 

where denotes the variance of the 

sector exposure w k over time, and n 

represents the number of sectors. This 

approach allows us to rank the different 

indices by the variability of the sector 

weights over time. From Table 4.2, it can be 

seen that the developing country indices, 

mainly CSI 300 Index, FTSE China 25 Index, 

and NIFTY Index, are the least stable. The 

NIKKEI 225 Index, FTSE Strait Times Index 

and FTSE ASEAN Index are the most stable 

indices. Generally speaking, the table 

re-affirms the findings previously 

observed in the figures in Sections 4.1.3 

to 4.1.5. 


Figure 4.1.j.Evolution of sector weights of the FTSE ASEAN Index from 2001 to 2010 

This figure presents the sector weight evolution for the FTSE ASEAN Index from January 2001 to December 2010. The classification 

of sectors is based on the GICS. The weights are calculated by adding up all constituents’ weights within each sector at each 

month. 




21 - The average sector drift 

scores for FTSE All Share 

Index 700, DJ Euro Stoxx 300, 

DJ Stoxx 600, Topix 1666 and 

S&P 500 are about 6.5 to 

7.5%, except Germany Prime 

All Share Index 380, which 

is 10.4%. 

Comparing our results with the study 

done by Amenc et al. (2006), which targets 

world developed markets – Europe, Japan 

and US markets, we find that the sector 

drift scores for indices in developing 

countries, such as China and India, are 

much higher than the indices in Europe, 

Japan and US. 21 But scores for indices in 

Asia developed markets, such as Hong 

Kong, Japan, Singapore, South Korea and 

Taiwan, are quite comparable with their 

study results. The differences between the 

two studies may come from the different 

sample periods and methodologies (see 

Section 4.1.2 for detail). 

One thing worth noting in our results is 

that the financial crisis from the end of 

2007 to 2009 also contributes to sector 

weight variations. However, even during 

the relative calm periods, the variation 

in sector weights occurs for all indices. 

There are many potential sources of the 

variation in the sector exposure, including 

the inclusion of certain large companies, 

which would result in a sudden jump 

in the sector weights, and the change 

of construction methodology – Nifty 

switched from full market capitalisation 

to free-flow basis in June 2009 – which 

leads to the shift in the allocation to 

each sector. The variation could also 

reflect the structural change of the 

economy in which the index resides. Also, 

more fundamentally, the sector weights 

change with the price even if there are no 

constituent changes, as the index weights 

stocks by their market capitalisation or 

price. 

Such findings imply that investors are 

exposed to implicit sector exposure 

chosen by the market index and such 

exposure varies over time. In other 

Table 4.2: Table below provides a summary of the style drift score based on sector exposure. The style drift score is calculated 

according to the method of Idzorek and Bertsch (2004) described in the text. 

Geographical 

zone 

Hong Kong Hang Seng 

Index 

Japan NIKKEI 225 

Index 

TOPIX 100 Index 

Singapore 

Index Period Max Weight Change Sector drift 

score 

Sector Max. Weight Min. Weight 

FTSE Strait 

Times Index 

Jan 2001 to Dec 

2010 


2010 


2010 

Feb 2008 to Dec 

2010 

South Korea KOSPI 200 Index Feb 2002 to Dec 

2010 

Taiwan 

FTSE TWSE 

Taiwan 50 Index 

Jul 2003 to Dec 

2010 

China CSI 300 Index May 2005 to 

Dec 2010 

FTSE China 25 

Index 

May 2005 to 

Dec 2010 

India NIFTY Index Jan 2002 to Dec 

2010 

ASEAN 

FTSE ASEAN 

Index 


2010 

Telecommunication 

Services 

27.68% 8.56% 8.89% 

Information 33.15% 17.40% 4.83% 

Technologies 

Financials 29.57% 12.38% 6.81% 

Financials 53.61% 43.44% 4.39% 

Industrials 28.57% 7.91% 8.44% 

Information 62.38% 46.65% 6.51% 

Technologies 

Financials 44.12% 13.43% 11.44% 

Financials 51.07% 17.19% 11.11% 

Consumer Staples 27.54% 3.08% 11.51% 

Financials 45.83% 36.18% 4.94% 


79



words, passively holding the market 

index does not correspond to an absence 

of choices in terms of sector exposures, 

but rather corresponds to a dynamic 

sector rotation strategy based on the 

implicit view that the market index holds. 

Moreover, investors who are unaware 

about such sector variation over time 

may be exposed to deviations of their 

desired risk exposures. In particular, when 

implementing asset allocation choices 

using such cap-weighted indices, the 

results obtained in implementation may 

no longer correspond to the original 

choices, as the indices’ sector exposure 

changes with time. 

4.2 Style stability test 

In addition to a sector stability test, we also 

identify the evolution of style weights in 

an index. Similar to the previous analysis, 

by understanding the implicit dynamics of 

the style exposure of an index, investors 

could better manage the risk and return 

properties of their portfolios. Note that 

the analysis of style exposures is based on 

a returns-based analysis, contrary to the 

analysis of sector exposures above which 

is based on a holdings-based analysis. In 

particular, we employ a Sharpe (1992) 

returns-based style analysis which consists 

of a constrained regression of the index 

returns on the returns of corresponding 

style indices so as to identify the exposure 

to the different styles. 

4.2.1 Data 

In this section, we use the same indices 

for the analysis except the FTSE ASEAN 

Index since there is no relevant regional 

style index available. In the style stability 

test, we also choose a 10-year period and 

obtain the daily price of each index from 

Bloomberg. This period runs from January 

2001 to December 2010, subject to data 

availability (see Table 4.3). Therefore, the 

test period of each index would be either 

10 years, or since the beginning of the 

available data. In addition, we use the 

daily price of MSCI Value and Growth 

Indices that correspond to the regional 

coverage of the chosen index from the 

Bloomberg as well. The daily frequency 

of the data facilitates our process for 

running regressions. 


In this part, we followed the returnsbased 

style analysis (RBSA) demonstrated 

in Amenc et al. (2006). Such a method 

stipulates that a manager’s investment 

style can be determined by comparing the 

returns on his portfolio with those of a 

certain number of selected indices. Since 

its introduction in 1992 (cf. Sharpe 1992), 

it has been widely used to identify the 

style exposures of mutual fund managers 

when the investor has information on the 

past returns of the fund but does not have 

full information on the fund’s holdings. 

In the industry, the method is often used 

to identify whether the fund manager has 

deviated from his investment style over 

time. Though our objective is somewhat 

different, we can still use the RBSA to 

observe the evolution of style exposure 

over time. Since holding a broad market 

index is typically understood to amount 

to holding a neutral exposure to different 

investment styles, we would like to check 

whether the exposure implicit in the 

indices is stable over time and balanced 

at any given point in time. 




Table 4.3: Table below provides a summary of the data sources for the style stability analysis. Column 3 contains the source for the 

historic data on both market index and MSCI style index. Column 4 represents the time period for which the data is collected and 

the analysis is done. 

22 -All constituents of the 

FTSE China 25 Index are 

traded on the Hong Kong 

Stock Exchange. 

23 - For the Chinese market, 

since there are different share 

classes which are traded in 

different countries, we use 

different MSCI style indices 

as the regressors. The CSI 

300 Index includes 300 

stocks (A-share) traded on 

the Shanghai and Shenzhen 

exchanges, therefore we 

choose MSCI China A Value 

and A Growth Indices which 

are exposed to the China 

A share market. On the 

other hand, the FTSE China 

25 Index comprises of 25 

stocks – both H share and 

Red chip shares – traded on 

the Hong Kong Exchange, we 

use MSCI China Value and 

Growth Indices which include 

non-domestic shares (B, H, 

Red chip and P shares). 

Data Source for Sector Stability Analysis 


Developed countries 

Hang Seng Index Hong Kong 1. Historical price of the index from the Bloomberg Jan 2001 to Dec 2010 

2. Historical prices of MSCI Hong Kong Value and Growth 

Indices from the Bloomberg 

Nikkei 225 Index Japan 1. Historical price of the index from the Bloomberg Jan 2001 to Dec 2010 

2. Historical prices of MSCI Japan Value and Growth Indices 

from the Bloomberg 

Topix 100 Index Japan 1. Historical price of the index from the Bloomberg Jan 2001 to Dec 2010 

2. Historical prices of MSCI Japan Value and Growth Indices 


FTSE STI Index Singapore 1. Historical price of the index from the Bloomberg Jan 2001 to Dec 2010 

2. Historical prices of MSCI Singapore Value and Growth 


KOSPI 200 Index South Korea 1. Historical price of the index from the Bloomberg Jan 2001 to Dec 2010 

2. Historical prices of MSCI South Korea Value and Growth 


FTSE TWSE 50 Index Taiwan 1. Historical price of the index from the Bloomberg Jan 2001 to Dec 2010 

2. Historical prices of MSCI Taiwan Value and Growth Indices 


Developing countries 

CSI 300 Index China 1. Historical price of the index from the Bloomberg Jan 2002 to Dec 2010 

2. Historical prices of MSCI China A Value and A Growth 


FTSE China 25 Index China 22 1. Historical price of the index from the Bloomberg Mar 2001 to Dec 2010 

2. Historical prices of MSCI China Value and Growth Indices 


Nifty Index India 1. Historical price of the index from the Bloomberg 

2. Historical prices of MSCI India Value and Growth Indices 


Jan 2001 to Dec 2010 

Le Sourd (2007) mentioned that the 

success of RBSA relies heavily on 

the correct specification of the style 

benchmark indices used as regressors. 

However, inconsistency existed in the 

classification of securities into different 

styles by different providers. In order to 

deliver cross-country comparable results, 

we carefully choose MSCI Regional Value 

and Growth Indices as our independent 

variables in our analysis. MSCI style 

indices are available for all countries we 

choose as our analysis targets. 23 We do 

not include the MSCI small-cap indices 

because most of our indices chosen 

comprise of only large-cap stocks. In 

addition, MSCI country small-cap indices 

are not available until 31 May 2007 for 

Asian countries except Hong Kong, Japan 

and Singapore. Due to these two reasons, 

we decided to exclude the analysis of 

small-cap exposure. 

In our analysis, we use a 1-year (250 

daily return observations) rolling-window 

RBSA to obtain the time-varying style 

exposure. 


81



For each window, to estimate the β in the 

following equation, 

we have to minimise the sum of square of 

by satisfying two constraints. 

Then we move to the next window until 

the end of the analysing period. In the 

end, we could obtain the time series of 

the β and then we can plot the evolution 

of style exposures. Now we start to discuss 

our results. We shall begin with the market 

indices in the developed countries in Asia. 

4.2.3 Developed countries 

Hong Kong 

Figure 4.2.a shows clearly that the Hong 

Kong Hang Seng Index has a bias towards 

growth stocks. The growth exposure is 

above 50% in most of the time during 

the analysis horizon. The variation in 

the style exposure is also considerably 

high. There is a clear peak in terms of the 

growth exposure around the middle of 

2004, which results in the composition 

of growth/value reaching 78%/22% from 

about 55%/45% the beginning of the 

2002. After the peak, the index quickly 

goes back to neutral exposure (growth/ 

value is 50%/50%) but then gradually 

evolves to again a significant growth 

tilt – 83%/17%, for the composition of 

growth/value at the end of 2010. Such 

substantial change in the style exposure 

over time imposes concerns towards 

long-term investors who passively 

hold the index, as they may be exposed 

to unanticipated biases in their asset 

allocation strategies. 

Figure 4.2.a.Evolution of style exposure for Hang Seng Index from 2002 to 2010 

This figure presents the style exposure for the Hang Seng Index from January 2002 to December 2010. The time series of the style 

exposure is obtained by using a 250-day-rolling window return based style analysis. The exposure to value and growth at each 

point is obtained by regressing the daily index return on a constant and MSCI Hong Kong Value and Growth Index returns subject 

to two constraints: the sum of the factor exposures should be 1 and the factor exposure should be above zero. 




Japan 

The style exposure of the NIKKEI 225 

Index over time varies even more 

extremely than the Hang Seng Index with 

also a clear growth bias for the index. 

The minimum exposure to growth style is 

42.3% in the middle of 2009, while the 

maximum exposure is 100%, which occurs 

after 2010 and remaining until the end of 

period analysed. In addition to the huge 

difference between the minimum and 

the maximum exposure to the growth 

style, the variation in the composition 

of growth/value fluctuates considerably 

over the whole period analysed. In 

addition, it is interesting to note that 

there seems to be a cyclical effect in the 

composition of growth/value; the cycle is 

about two to two and half years over our 


of the period analysed. The exposure to 

growth (value) varies from 64.4% to 29% 

(35.6% to 71%). Figure 4.2.c also shows 

a change of pattern in the evolution of 

growth/value composition after 2007 – it 

is apparently more volatile compared to 

the period before 2007. Though the TOPIX 

100 seems to be more stable in terms of 

style exposure compared to NIKKEI 225, 

the considerably high variation in the 

composition still poses serious problems 

for investors seeking a stable style 

exposure, as its growth/value composition 

evolves from a small growth bias to a 

sharp value bias. 

In contrast to the NIKKEI 225 Index, the 

TOPIX 100 exhibits relatively more balanced 

and less volatile exposure to the growth/ 

value exposure, at least in the first half 

Figure 4.2.b.Evolution of style exposure for Nikkei 225 Index from 2002 to 2010 

This figure presents the style exposure for the Nikkei 225 Index from January 2002 to December 2010. The time series of the style 


point is obtained by regressing the daily index return on a constant and MSCI Japan Value and Growth Index returns subject to two 

constraints: the sum of the factor exposures should be 1 and the factor exposure should be above zero. 


83



Figure 4.2.c.Evolution of style exposure for the Topix 100 Index from 2002 to 2010 

This figure presents the style exposure for the Topix 100 Index from January 2002 to December 2010. The time series of the style 


point is obtained by regressing the daily index return on a constant and the MSCI Japan Value and Growth Index returns subject to 

two constraints: the sum of the factor exposures should be 1 and the factor exposure should be above zero. 




Singapore 

Compared to the three previous indices, the 

FTSE STI Index exhibits much more stable 

exposure to the growth/value style over 

time. The composition of growth/value stays 

about 50%/50% until the middle of 2009 

and changes to about 60%/40% after that. 

We have observed a relatively stable style 

exposure before 2008 and a more volatile 

exposure after 2008. As with the TOPIX 

100 index, one of the possible explanations 

could be that the volatility stemming from 

the financial crisis of 2008, may have led 

to changes in style exposures. Another 

possible explanation would be that the 

FTSE STI Index has been re-calculated and 

re-launched since January 2008, and the 

composition of the index has been reduced 

from 50 constituents to 30 constituents. 

The different construction methodology 

may also result in such changes in the 

characteristics of the style exposure. 

Figure 4.2.d.Evolution of style exposure for the FTSE STI Index from 2002 to 2010 

This figure presents the style exposure for the FTSE STI Index from January 2002 to December 2010. The time series of the style 


point is obtained by regressing the daily index return on a constant and the MSCI Singapore Value and Growth Index returns subject 



85



South Korea 

Unlike the indices we have previously 

discussed, the KOSPI 200 Index has an 

obvious bias towards value stocks during 

the period analysed, however, the style 

exposure over time is also more stable 

than the indices in Japan and Hong Kong. 

The growth/value composition was about 

40%/60% at the beginning of the analysis 

period. The composition slowly evolved to 

about 30%/70% at the beginning of 2005 

and then gradually changed to 52%/48% 

in 2007. After 2008, the composition of 

the style exposure roughly stabilised at 

45%/55%. 

Figure 4.2.e.Evolution of style exposure for the KOSPI 200 Index from 2002 to 2010 

This figure presents the style exposure for the KOSPI 200 Index from January 2002 to December 2010. The time series of the style 


point is obtained by regressing the daily index return on a constant and the MSCI South Korea Value and Growth Index returns 

subject to two constraints: the sum of the factor exposures should be 1 and the factor exposure should be above zero. 




Taiwan 

Figure 4.2.f shows that the FTSE TWSE 50 

Index has a larger bias towards value than 

the KOSPI 200 Index over the whole period 

of analysis. The exposure to growth stocks is 

reduced from about 42% at the beginning 

of 2002 to about 27% in 2005 and then 

stabilised to about 35% after. The overall 

fluctuation of the style exposure is less 

significant than indices in Japan and Hong 

Kong and comparable with the indices from 

Singapore and South Korea. 

In summary, we have seen that indices in 

Japan and Hong Kong have a clear growth 

tilt and are much more volatile in terms 

of style exposure over time compared 

to indices in the other markets. On the 

other hand, indices in South Korea and 

Taiwan, though they exhibit more stable 

composition of growth/value during 

the test period, display an obvious bias 

towards value stocks. The FTSE STI Index 

shows a neutral style exposure until 2008 

and later exhibits a bias to growth stocks. 

Now we turn to show the style exposure 

for developing country indices. 

Figure 4.2.f.Evolution of style exposure for the FTSE TWSE Taiwan 50 Index from 2002 to 2010 

This figure presents the style exposure for the FTSE TWSE Taiwan 50 Index from January 2002 to December 2010. The time series of 

the style exposure is obtained by using a 250-day-rolling window return based style analysis. The exposure to value and growth 

at each point is obtained by regressing the daily index return on a constant and the MSCI Taiwan Value and Growth Index returns 

subject to two constraints: the sum of the factor exposures should be 1 and the factor exposure should be above zero. 


87



24 - See Lee (2009) for the 

literature review on this 

point. 

4.2.4 Developing countries 

China 

The CSI 300 Index displays a smooth 

transition between the value and growth 

exposure over time. In the beginning of 

2003, the index had a clear value bias, 

with the composition of growth/value 

at 60%/40%. Subsequently, the index 

gradually increased exposure to the 

growth factor. Up to 2008, the composition 

of growth/value was nearly equally 

distributed, however, after 2008 the index 

switched back to a value-oriented style 

exposure, with the growth/value ratio 

at about 30%/70%, at the end of period 

analysed. 

In contrast to the relatively stable exposure 

to value/growth factors, FTSE China 25 

Index exhibits a significant variation 

in the style exposure over the period 

of analysis, with a value bias persisting 

throughout most of the analysed period. 

The composition of the growth/value 

exposure began at 11%/89% and gradually 

changed to about equally exposure during 

2005-2007. Since 2008, the composition 

of growth/value switched back to about 

25%/75%. In addition, the style exposure 

seems to be more volatile after 2008. 

The huge difference in the style exposure 

characteristics between the two China 

indices may come from different properties 

in various share classes included in the 

indices. As we explained before, the CSI 

300 includes only A-shares from both the 

Shanghai and Shenzhen stock exchanges, 

but FTSE China 25 Index is created based on 

the H-share and the Red-chip shares traded 

on the Hong Kong Stock Exchange. There 

is a large body of literature showing that 

the A-share market and H-share market 

exhibit different characteristics because 

of distinct investor interests, company 

profiles, liquidity, etc 24 . Therefore, it is 

somewhat expected to observe different 

style exposures in these two indices. 

Figure 4.2.g.Evolution of style exposure for the CSI 300 Index from 2003 to 2010 

This figure presents the style exposure for the CSI 300 Index from January 2003 to December 2010. The time series of the style 


point is obtained by regressing the daily index return on a constant and the MSCI China A Value and Growth Index returns subject 





Figure 4.2.h.Evolution of style exposure for FTSE China 25 Index from 2002 to 2010 

This figure presents the style exposure for Topix 100 Index from March 2002 to December 2010. The time series of the style exposure 

is obtained by using a 250-day-rolling window return based style analysis. The exposure to value and growth at each point is 

obtained by regressing the daily index return on a constant and the MSCI China Value and Growth Index returns subject to two 



89



India 

Figure 4.2.i shows that the NIFTY Index 

exhibits relatively stable evolution of the 

composition of the growth/value over 

the time of analysis, while there are small 

fluctuations in the composition throughout 

the entire period, Through most of the 

period, however, the index had a bias 

towards the value style with a small growth 

tilt in the first quarter of 2003 which quickly 

disappeared. 

In summary, unlike the sector exposure, 

the style exposure of indices in developing 

markets does exhibit higher volatility 

compared to indices in more developed 

markets, except the FTSE China 25 Index. 

But still, the variation in the composition 

of growth/value is larger than 10%, which 

imposes a potential bias to asset allocation 

strategies over time. In addition, these 

indices are more likely to exhibit a value tilt, 

which implicitly assumes investors prefer 

value stocks rather than growth stocks. 

Figure 4.2.i.Evolution of style exposure for the Nifty Index from 2002 to 2010 

This figure presents the style exposure for the Nifty Index from January 2002 to December 2010. The time series of the style exposure 

is obtained by using a 250-day-rolling window return based style analysis. The exposure to value and growth at each point is 

obtained by regressing the daily index return on a constant and the MSCI India Value and Growth Index returns subject to two 





25 - The indices for the US 

markets are found to have 

very different style exposure 

stability – S&P500 has a score 

of 2.3%, DJIA 30 is 26%, and 

Russell 2000 is 11%. So we 

did not compare our results 

with them. 

4.2.5 Summary of results in style 

stability test 

Similar to the analysis on the sector 

exposure stability, our style analysis 

shows that the risk exposures, this time 

represented by different styles, vary over 

time, exposing investors to implicit style 

allocation decisions which they do not 

control. 

In order to summarise the variability of 

style exposure by a single indicator, we 

still apply the style drift score used above 

to the variation of the style exposures 

(see Table 4.4). It is worth noting that all 

indices show considerable variability of 

style exposure. The range of style drift 

scores varies from 5.8% to 20.59%, which 

is much wider than what we have seen for 

sector drift scores (4.39% to 11.51%). The 

Japanese market has the highest variation 

in the evolution of the style exposure, for 

both the NIKKEI 225 Index and TOPIX 100 

Index (20.59% and 12.79%, respectively). 

FTSE China 25 Index also demonstrates 

significant variation in the evolution of 

the composition of growth/value exposure 

(from 89%/11% to 25%/75%). Market 

indices from Singapore, Taiwan and India 

exhibit the lowest value in the drift score, 

which is about 5-7%. Unlike the findings 

from sector stability tests, where the 

indices in developing countries exhibit 

higher variation in the composition of 

sector weights over time, the NIFTY Index 

shows a much lower style drift score than 

most of the indices from the developed 

countries. 

In addition, we also compare our results 

with the findings from Amenc et al. 

(2006). It is clear that Asian market indices 

have more unstable style exposures than 

European market indices, whose style 

drift scores range from 2.6% to 5.5%. 25 

The indices in Japan are found to exhibit 

higher style drift than the previous study 

(the style drift scores are 20.59% and 

12.79% for Nikkei 225 and Topix 100, 

respectively, in our study; and 17.6% 

and 8.2% for Nikkei 225 and Topix 500 in 

Amenc et al., 2006.). This could be due to 

the different time period, as the current 

study also covers the global financial 

crisis 2007-2008, which may affect the 

stability of style exposure. 

We also present the annual index return 

volatility during the testing period to 

investigate whether the large variation 

in the style exposure comes from 

higher volatility in the same period. The 

result is clear that there is no causative 

relationship between the changes in style 

exposure and the annual volatility. For 

instance, the index return volatilities are 

the highest for indices in China and India 

(26.82% to 31.85%), but their style drift 

scores are not among the highest, except 

with the FTSE China 25 Index. In addition, 

the indices in Hong Kong, Japan and 

South Korea have even lower volatilities 

than the Nifty Index, but their style 

exposures are less stable than the Nifty 

Index. Therefore, the stability of style 

exposure cannot be easily derived from 

the volatility of the index returns. In other 

words, an index with lower volatility does 

not mean that its style exposure will be 

less volatile. An investor seeking a less 

risky index may end up not tolerating 

biased and unstable exposure in style 

factors. 


91



Table 4.4: Table below provides a summary of the style drift score based on style exposure. The style drift score is calculated 

according to the method of Idzorek and Bertsch (2004) described in the text. The calibration period is approximately one-year for 

each index (The rolling window is 250 trading days). We also include one column to indicate the annual volatility of the index 

returns (assume 250 trading days). 

Geographical 

zone 

Index Period Max. Weight 

(value) 

Min. Weight 

(value) 

Style drift 

score 

Index return 

volatility (p.a.) 

Hong Kong Hang Seng Index Jan 2002 to Dec 2010 53.04% 16.55% 11.77% 25.68% 

Japan NIKKEI 225 Index Jan 2002 to Dec 2010 57.75% 0% 20.59% 25.32% 

TOPIX 100 Index Jan 2002 to Dec 2010 70.98% 35.64% 12.79% 24.67% 

Singapore FTSE Strait Times Index Jan 2002 to Dec 2010 56.15% 33.39% 6.39% 20.38% 

South Korea KOSPI 200 Index Jan 2002 to Dec 2010 70.53% 46.87% 8.48% 25.91% 

Taiwan FTSE TWSE Taiwan 50 Index Jan 2002 to Dec 2010 73.83% 56.01% 5.80% 22.81% 

China CSI 300 Index Jan 2003 to Dec 2010 72.68% 44.28% 8.96% 29.99% 

FTSE China 25 Index Mar 2002 to Dec 2010 88.96% 45.37% 19.53% 31.85% 

India NIFTY Index Jan 2002 to Dec 2010 67.18% 46.31% 6.64% 26.82% 

In summary, we find that Asian indices are, 

in general, lacking stability in terms of the 

risk factor exposure. And such instability 

is somehow more serious than what 

Amenc et al. (2006) found for indices 

in Europe and US. This finding will have 

a severe impact on the investor’s asset 

allocation strategy. Especially for passive 

investors, holding the index portfolio 

will not be a risk factor neutral portfolio 

in the long-run. Furthermore, besides 

the implicit factor exposure, investors 

also have to bear the changes in such 

exposure or even the switch of the focus 

from one to another. Since all of these 

choices are embedded within the index 

portfolio, investors do not have the option 

to say “yes” or “no”. A bias would rise for 

investors without awareness of such risk 

towards the asset allocation strategies 

and risk management. By observing such 

instability of the market index in terms 

of the risk factor exposure, it suggests 

that investors should analyse the index 

factor exposure before they build up 

the portfolio and regularly examine the 

changes in the index. 


5. Conclusion 


93


5. Conclusion 

There has been increasing demand for 

equity indices in Asia. This is because 

global investors want to benefit from 

the region’s growth, and consequently 

from its financial markets. As a lot of US 

and Europe based investors do not have 

the expertise to conduct stock picking in 

Asia, equity investments are often passive 

for Asian oriented portfolios. Therefore, 

the question of index quality in Asia 

is an important issue. We address the 

question in this study by focusing on the 

three following aspects: (i) efficiency; (ii) 

concentration; and (iii) stability. 

From the study, it thus appears that 

all the popular indices used in Asia as 

reference benchmarks are inefficient, 

with some of them being more so than 

others. Meanwhile, for all of them, an 

equal-weighted index constructed from 

the same components outperforms the 

corresponding cap-weighted market 

index. The levels of inefficiency of Asian 

market indices were found to be quite 

comparable to those of European and US 

indices. 

One of the explanations of this inefficiency 

is that most of the indices in the Asia- 

Pacific region are highly concentrated, as 

also highlighted in this study. In addition, 

the level of concentration is not constant 

over time. The concentration in indices 

leads to less diversified portfolios and 

performance drag. Finally, the study 

evidenced a lack of stability in risk 

factor exposures for Asian indices, to a 

greater extent than what was previously 

evidenced in Europe and US by Amenc 

et al. (2006). This latter issue is a major 

concern, particularly for passive investors 

who are confronted with unexpected 

changes in style bets when they are 

holding the index portfolio. 

Investing in Asian Indices may come 

with important challenges for investors, 

including operational challenges for 

running portfolios which include stocks 

from different markets and in different 

time zones. This effort may be worthwhile 

due to the expected outperformance of 

these markets. However, an important 

question is whether the distance of 

equity investments in standard indices 

compared to improved indices in terms 

of performance is, in the end, not as 

meaningful as the distance between 

US standard indices and Asian standard 

indices, for example. Our study assesses 

the distance from optimal in sample 

portfolios in Asian markets and finds that 

this distance is significant, but all the 

same comparable to the distance found in 

US markets, for example. 

In order to conclude our study it may 

be interesting to present a comparison 

between the performance of a capweighted 

index and the performance of 

an index using an improved weighting 

scheme. We perform the comparison on 

both the US market and an Asian market. 

We choose to use a minimum volatility 

strategy as the improved weighting 

scheme. Table 5.1 displays the Sharpe 

ratios obtained for the US Minimum 

Volatility index and for the S&P 500 (capweighted) 

index on various time periods. 

In all cases, the US Minimum Volatility 

index exhibits higher Sharpe ratios than 

the S&P 500 index. If results obtained on a 

one-year period appear to be comparable, 

the gap between the two Sharpe ratios 

became wider for longer periods, with, 



5. Conclusion 

for example, a Sharpe ratio of 0.15 over a 

5-Year period for the minimum volatility 

index, compared to a Sharpe ratio of 0.05 

for the cap-weighted index. Similarly, 

over the period corresponding to all the 

data history available for the minimum 

volatility index, and including more than 

10 years of data, the minimum volatility 

index significantly outperforms the S&P 

500 index with a Sharpe ratio of 0.33 

versus 0.19 for the cap-weighted index. 

Now, alternatively, the investor may have 

invested in an Asian index instead of the 

US index. In order to show the possible 

improvement, we compared the Sharpe 

ratio of the MSCI Developed Asia-Pacific 

ex-Japan index and the Sharpe ratio of the 

S&P 500 index. The results are displayed in 

Table 5.2. We see that investing in an Asian 

index leads to a significant performance 

improvement both for the shortest period 

and the longest period. Over the one-year 

period, the US index produced a Sharpe 

ratio of 1.25, while the Asian index 

produced a Sharpe ratio of 1.54. Over the 

12-year period, the Sharpe ratio of the US 

index was not far from zero (0.03), while 

the Asian index produced a Sharpe ratio 

of 0.47. Over the 5-year period (2008- 

2012), both indices produced respective 

Sharpe ratios that were not far from zero. 

In view of the two Tables 5.1 and 5.2, it 

appears that if investing in an Asian market 

rather than in the US market can lead to 

significant improvements in performance, 

the performance improvement provided 

by the choice of a better weighting scheme 

is more constant through time, and less 

related to the choice of the investment 

period, as shown by results obtained for 

the US (displayed in Table 5.1). 

If investors want to efficiently capture 

the premium of Asian markets, they have 

the possibility, as on the US market, to 

use an improved weighting scheme for 

the Asian stocks. Table 5.3 displays the 

Sharpe ratios obtained for the Developed 

Asia-Pacific ex-Japan Minimum Volatility 

index and for the MSCI Developed Asia- 

Table 5.1. Comparison of the Sharpe ratio of a Minimum Volatility index and a Cap-weighted index (US indices) 

US Min Volatility 

S&P500 

1Y 1.32 1.25 

3Y 0.78 0.58 

5Y 0.15 0.05 

History* 0.33 0.19 

* The history period refers to the inception of the US Min Volatility index and begins on June, 21st, 2002. All the computations were 

done on December 31st, 2012. 

Table 5.2. Comparison of the Sharpe ratio of a US index and an Asian index 

MSCI Developed Asia-Pacific ex-Japan 

S&P500 

1Y 1.54 1.25 

3Y 0.36 0.58 

5Y 0.01 0.05 

12Y* 0.47 0.03 

* We choose the longest period for which daily data were available for MSCI index on DataStream. All the computations were 

done on December 31st, 2012. 


95


5. Conclusion 

Pacific ex-Japan (free-float weighted) 

index on various time periods. The Asian 

Minimum Volatility index exhibits higher 

Sharpe ratios than the MSCI Asia index for 

all the time period. The most significant 

improvements are obtained for the threeyear 

period, with a Sharpe ratio of 0.56 

for the minimum volatility index versus 

0.36 for the MSCI index, as well as for the 

history period, which includes more than 

10 years (0.78 versus 0.52). 

Overall, if investors want to capture the 

risk premium in Asia, it is regrettable 

that they then suffer the drawback from 

a sub-optimal weighting scheme choice. 

Indeed, investors should recognise that 

the choice of an efficient weighting 

scheme to capture the outperformance is 

probably as important as the choice of the 

right geographic exposure. 

Table 5.3. Comparison of the Sharpe ratio of a Minimum Volatility index and a Cap-weighted index (Asia-Pacific indices) 

Developed Asia-Pacific ex-Japan Min Volatility* MSCI Developed Asia-Pacific ex-Japan 

1Y 1.72 1.54 

3Y 0.56 0.36 

5Y 0.11 0.01 

History** 0.78 0.52 

* We calculate the out of sample returns of a quarterly rebalanced norm constrained minimum volatility strategy based on the 

largest 400 stocks in the Developed Asia-Pacific ex Japan universe.. 

* *The history period refers to the inception of the Asian Min Volatility index and begins on June 21st, 2002. All the computations 

were done on December 31st, 2012. 


References 


97


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About EDHEC-Risk Institute 


103



Founded in 1906, EDHEC is one 

of the foremost international 

business schools. Accredited by 

the three main international 

academic organisations, 

EQUIS, AACSB, and Association 

of MBAs, EDHEC has for a 

number of years been pursuing 

a strategy of international 

excellence that led it to set up 

EDHEC-Risk Institute in 2001. 

This institute now boasts a team 

of 90 permanent professors, 

engineers and support staff, as 

well as 48 research associates 

from the financial industry and 

affiliate professors.. 

The Choice of Asset Allocation 

and Risk Management 

EDHEC-Risk structures all of its research 

work around asset allocation and risk 

management. This strategic choice is 

applied to all of the Institute's research 

programmes, whether they involve 

proposing new methods of strategic 

allocation, which integrate the alternative 

class; taking extreme risks into account 

in portfolio construction; studying the 

usefulness of derivatives in implementing 

asset-liability management approaches; 

or orienting the concept of dynamic 

“core-satellite” investment management 

in the framework of absolute return or 

target-date funds. 

Academic Excellence 

and Industry Relevance 

In an attempt to ensure that the research 

it carries out is truly applicable, EDHEC has 

implemented a dual validation system for 

the work of EDHEC-Risk. All research work 

must be part of a research programme, 

the relevance and goals of which have 

been validated from both an academic 

and a business viewpoint by the Institute's 

advisory board. This board is made up of 

internationally recognised researchers, 

the Institute's business partners, and 

representatives of major international 

institutional investors. Management of the 

research programmes respects a rigorous 

validation process, which guarantees the 

scientific quality and the operational 

usefulness of the programmes. 

Six research programmes have been 

conducted by the centre to date: 

• Asset allocation and alternative 

diversification 

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• Operational risks and performance 

• Asset allocation and derivative 

instruments 

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These programmes receive the support of 

a large number of financial companies. 

The results of the research programmes 

are disseminated through the EDHEC-Risk 

locations in Singapore, which was 

established at the invitation of the 

Monetary Authority of Singapore (MAS); 

the City of London in the United Kingdom; 

Nice and Paris in France; and New York in 

the United States. 

EDHEC-Risk has developed a close 

partnership with a small number of 

sponsors within the framework of 

research chairs or major research projects: 

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partnership with Amundi ETF 

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Investment, in partnership with AXA 

Investment Managers 

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Institutional Investment Management, 

in partnership with BNP Paribas 

Investment Partners 

• Risk and Regulation in the European 

Fund Management Industry, in 

partnership with CACEIS 

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Risk Premium: Implications for 

Asset Allocation and Regulation, in 

partnership with CME Group 




• Asset-Liability Management in Private 

Wealth Management, in partnership 

with Coutts & Co. 

• Asset-Liability Management 

Techniques for Sovereign Wealth Fund 

Management, in partnership with 

Deutsche Bank 

• The Benefits of Volatility Derivatives 

in Equity Portfolio Management, in 

partnership with Eurex 

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Instruments, sponsored by the French 

Banking Federation (FBF) 

• Optimising Bond Portfolios, in 

partnership with the French Central 

Bank (BDF Gestion) 

• Asset Allocation Solutions, in 

partnership with Lyxor Asset 

Management 

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Management and Benchmarking, 

in partnership with Meridiam and 

Campbell Lutyens 

• Investment and Governance 

Characteristics of Infrastructure Debt 

Investments, in partnership with Natixis 

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Investments, in partnership with 

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Liability Hedging for Inflation Risk, 

in partnership with Ontario Teachers’ 

Pension Plan 

• The Case for Inflation-Linked 

Corporate Bonds: Issuers’ and Investors’ 

Perspectives, in partnership with 

Rothschild & Cie 

• Solvency II, in partnership with Russell 

Investments 

• Structured Equity Investment 

Strategies for Long-Term Asian Investors, 

in partnership with Société Générale 

Corporate & Investment Banking 

The philosophy of the Institute is to 

validate its work by publication in 

international academic journals, as well as 

to make it available to the sector through 

its position papers, published studies, and 

conferences. 

Each year, EDHEC-Risk organises three 

conferences for professionals in order to 

present the results of its research, one in 

London (EDHEC-Risk Days Europe), one 

in Singapore (EDHEC-Risk Days Asia), and 

one in New York (EDHEC-Risk Days North 

America) attracting more than 2,500 

professional delegates. 

EDHEC also provides professionals with 

access to its website, www.edhec-risk.com, 

which is entirely devoted to international 

asset management research. The website, 

which has more than 58,000 regular 

visitors, is aimed at professionals who 

wish to benefit from EDHEC’s analysis and 

expertise in the area of applied portfolio 

management research. Its monthly 

newsletter is distributed to more than 1.5 

million readers. 

EDHEC-Risk Institute: 

Key Figures, 2011-2012 

Nbr of permanent staff 90 

Nbr of research associates 20 

Nbr of affiliate professors 28 

Overall budget €13,000,000 

External financing €5,250,000 

Nbr of conference delegates 1,860 

Nbr of participants 

at research seminars 

640 

Nbr of participants at EDHEC-Risk 

Institute Executive Education seminars 

182 


105



The EDHEC-Risk Institute PhD in 

Finance 

The EDHEC-Risk Institute PhD in Finance 

is designed for professionals who aspire 

to higher intellectual levels and aim to 

redefine the investment banking and asset 

management industries. It is offered in two 

tracks: a residential track for high-potential 

graduate students, who hold part-time 

positions at EDHEC, and an executive track 

for practitioners who keep their full-time 

jobs. Drawing its faculty from the world’s 

best universities, such as Princeton, 

Wharton, Oxford, Chicago and CalTech, 

and enjoying the support of the research 

centre with the greatest impact on the 

financial industry, the EDHEC-Risk Institute 

PhD in Finance creates an extraordinary 

platform for professional development and 

industry innovation. 

School of Management to set up joint 

certified executive training courses in 

North America and Europe in the area of 

investment management. 

As part of its policy of transferring knowhow 

to the industry, EDHEC-Risk Institute 

has also set up ERI Scientific Beta. ERI 

Scientific Beta is an original initiative 

which aims to favour the adoption of the 

latest advances in smart beta design and 

implementation by the whole investment 

industry. Its academic origin provides the 

foundation for its strategy: offer, in the 

best economic conditions possible, the 

smart beta solutions that are most proven 

scientifically with full transparency in 

both the methods and the associated 

risks. 

Research for Business 

The Institute’s activities have also given 

rise to executive education and research 

service offshoots. EDHEC-Risk's executive 

education programmes help investment 

professionals to upgrade their skills with 

advanced risk and asset management 

training across traditional and alternative 

classes. In partnership with CFA Institute, 

it has developed advanced seminars based 

on its research which are available to CFA 

charterholders and have been taking 

place since 2008 in New York, Singapore 

and London. 

In 2012, EDHEC-Risk Institute signed two 

strategic partnership agreements with 

the Operations Research and Financial 

Engineering department of Princeton 

University to set up a joint research 

programme in the area of risk and 

investment management, and with Yale 


EDHEC-Risk Institute 

Publications and Position Papers 

(2010-2013) 


107


EDHEC-Risk Institute Publications 

(2010-2013) 

2013 

• Goltz, F., V. Le Sourd, M. Mukai, and F. Rachidy. Reactions to “A review of corporate 

bond indices: Construction principles, return heterogeneity, and fluctuations in risk 

exposures” (January). 

• Joenväärä, J., and R. Kosowski. An analysis of the convergence between mainstream 

and alternative asset management (January). 

• Cocquemas, F. Towards better consideration of pension liabilities in european union 

countries (January). 

• Blanc-Brude, F. Towards efficient benchmarks for infrastructure equity investments 

(January). 

2012 

• Amenc, N., and F. Ducoulombier. Proposals for better management of non-financial risks 

within the european fund management industry (December). 

• Cocquemas, F. Improving Risk Management in DC and Hybrid Pension Plans (November). 

• Amenc, N., F. Cocquemas, L. Martellini, and S. Sender. Response to the european 

commission white paper "An agenda for adequate, safe and sustainable pensions" 

(October). 

• La gestion indicielle dans l'immobilier et l'indice EDHEC IEIF Immobilier d'Entreprise 

France (September). 

• Real estate indexing and the EDHEC IEIF commercial property (France) index (September). 

• Goltz, F., S. Stoyanov. The risks of volatility ETNs: A recent incident and underlying 

issues (September). 

• Almeida, C., and R. Garcia. Robust assessment of hedge fund performance through 

nonparametric discounting (June). 

• Amenc, N., F. Goltz, V. Milhau, and M. Mukai. Reactions to the EDHEC study “Optimal 

design of corporate market debt programmes in the presence of interest-rate and 

inflation risks” (May). 

• Goltz, F., L. Martellini, and S. Stoyanov. EDHEC-Risk equity volatility index: Methodology 

(May). 

• Amenc, N., F. Goltz, M. Masayoshi, P. Narasimhan and L. Tang. EDHEC-Risk Asian index 

survey 2011 (May). 

• Guobuzaite, R., and L. Martellini. The benefits of volatility derivatives in equity portfolio 

management (April). 

• Amenc, N., F. Goltz, L. Tang, and V. Vaidyanathan. EDHEC-Risk North American index 

survey 2011 (March). 

• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, L. Martellini, and S. Sender. Introducing 

the EDHEC-Risk Solvency II Benchmarks – maximising the benefits of equity investments 

for insurance companies facing Solvency II constraints - Summary - (March). 




(2010-2013) 

• Schoeffler, P. Optimal market estimates of French office property performance (March). 

• Le Sourd, V. Performance of socially responsible investment funds against an efficient 

SRI Index: The impact of benchmark choice when evaluating active managers – an update 

(March). 

• Martellini, L., V. Milhau, and A.Tarelli. Dynamic investment strategies for corporate 

pension funds in the presence of sponsor risk (March). 

• Goltz, F., and L. Tang. The EDHEC European ETF survey 2011 (March). 

• Sender, S. Shifting towards hybrid pension systems: A European perspective (March). 

• Blanc-Brude, F. Pension fund investment in social infrastructure (February). 

• Ducoulombier, F., Lixia, L., and S. Stoyanov. What asset-liability management strategy 

for sovereign wealth funds? (February). 

• Amenc, N., Cocquemas, F., and S. Sender. Shedding light on non-financial risks – a 

European survey (January). 

• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, Martellini, L., and S. Sender. Ground 

Rules for the EDHEC-Risk Solvency II Benchmarks. (January). 

• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, Martellini, L., and S. Sender. Introducing 

the EDHEC-Risk Solvency Benchmarks – Maximising the Benefits of Equity Investments 

for Insurance Companies facing Solvency II Constraints - Synthesis -. (January). 

• Amenc, N., F. Cocquemas, R. Deguest, P. Foulquier, Martellini, L., and S. Sender. Introducing 

the EDHEC-Risk Solvency Benchmarks – Maximising the Benefits of Equity Investments 

for Insurance Companies facing Solvency II Constraints (January). 

• Schoeffler.P. Les estimateurs de marché optimaux de la performance de l’immobilier 

de bureaux en France (January). 

2011 

• Amenc, N., F. Goltz, Martellini, L., and D. Sahoo. A long horizon perspective on the 

cross-sectional risk-return relationship in equity markets (December 2011). 

• Amenc, N., F. Goltz, and L. Tang. EDHEC-Risk European index survey 2011 (October). 

• Deguest,R., Martellini, L., and V. Milhau. Life-cycle investing in private wealth 

management (October). 

• Amenc, N., F. Goltz, Martellini, L., and L. Tang. Improved beta? A comparison of indexweighting 

schemes (September). 

• Le Sourd, V. Performance of socially responsible investment funds against an 

Efficient SRI Index: The Impact of Benchmark Choice when Evaluating Active Managers 

(September). 

• Charbit, E., Giraud J. R., F. Goltz, and L. Tang Capturing the market, value, or momentum 

premium with downside Risk Control: Dynamic Allocation strategies with exchange-traded 

funds (July). 


109



(2010-2013) 

110 An EDHEC-Risk Institute Publication 

• Scherer, B. An integrated approach to sovereign wealth risk management (June). 

• Campani, C. H., and F. Goltz. A review of corporate bond indices: Construction principles, 

return heterogeneity, and fluctuations in risk exposures (June). 

• Martellini, L., and V. Milhau. Capital structure choices, pension fund allocation decisions, 

and the rational pricing of liability streams (June). 

• Amenc, N., F. Goltz, and S. Stoyanov. A post-crisis perspective on diversification for risk 

management (May). 

• Amenc, N., F. Goltz, Martellini, L., and L. Tang. Improved beta? A comparison of indexweighting 

schemes (April). 

• Amenc, N., F. Goltz, Martellini, L., and D. Sahoo. Is there a risk/return tradeoff across 

stocks? An answer from a long-horizon perspective (April). 

• Sender, S. The elephant in the room: Accounting and sponsor risks in corporate pension 

plans (March). 

• Martellini, L., and V. Milhau. Optimal design of corporate market debt programmes in 

the presence of interest-rate and inflation risks (February). 

2010 

• Amenc, N., and S. Sender. The European fund management industry needs a better 

grasp of non-financial risks (December). 

• Amenc, N., S, Focardi, F. Goltz, D. Schröder, and L. Tang. EDHEC-Risk European private 

wealth management survey (November). 

• Amenc, N., F. Goltz, and L. Tang. Adoption of green investing by institutional investors: 

A European survey (November). 

• Martellini, L., and V. Milhau. An integrated approach to asset-liability management: 

Capital structure choices, pension fund allocation decisions and the rational pricing of 

liability streams (November). 

• Hitaj, A., L. Martellini, and G. Zambruno. Optimal hedge fund allocation with improved 

estimates for coskewness and cokurtosis parameters (October). 

• Amenc, N., F. Goltz, L. Martellini, and V. Milhau. New frontiers in benchmarking and 

liability-driven investing (September). 

• Martellini, L., and V. Milhau. From deterministic to stochastic life-cycle investing: 

Implications for the design of improved forms of target date funds (September). 

• Martellini, L., and V. Milhau. Capital structure choices, pension fund allocation decisions 

and the rational pricing of liability streams (July). 

• Sender, S. EDHEC survey of the asset and liability management practices of European 

pension funds (June). 

• Goltz, F., A. Grigoriu, and L. Tang. The EDHEC European ETF survey 2010 (May). 

• Martellini, L., and V. Milhau. Asset-liability management decisions for sovereign wealth 

funds (May).



(2010-2013) 

• Amenc, N., and S. Sender. Are hedge-fund UCITS the cure-all? (March). 

• Amenc, N., F. Goltz, and A. Grigoriu. Risk control through dynamic core-satellite portfolios 

of ETFs: Applications to absolute return funds and tactical asset allocation (January). 

• Amenc, N., F. Goltz, and P. Retkowsky. Efficient indexation: An alternative to cap-weighted 

indices (January). 

• Goltz, F., and V. Le Sourd. Does finance theory make the case for capitalisation-weighted 

indexing? (January). 


111


EDHEC-Risk Institute Position Papers 

(2010-2013) 

2012 

• Till, H. Who sank the boat? (June). 

• Uppal, R. Financial Regulation (April). 

• Amenc, N., F. Ducoulombier, F. Goltz, and L. Tang. What are the risks of European ETFs? 

(January). 

2011 

• Amenc, N., and S. Sender. Response to ESMA consultation paper to implementing 

measures for the AIFMD (September). 

• Uppal, R. A Short note on the Tobin Tax: The costs and benefits of a tax on financial 

transactions (July). 

• Till, H. A review of the G20 meeting on agriculture: Addressing price volatility in the 

food markets (July). 

2010 

• Amenc, N., and V. Le Sourd. The performance of socially responsible investment and 

sustainable development in France: An update after the financial crisis (September). 

• Amenc, N., A. Chéron, S. Gregoir, and L. Martellini. Il faut préserver le Fonds de Réserve 

pour les Retraites (July). 

• Amenc, N., P. Schoefler, and P. Lasserre. Organisation optimale de la liquidité des fonds 

d’investissement (March). 

• Lioui, A. Spillover effects of counter-cyclical market regulation: Evidence from the 2008 

ban on short sales (March). 



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For more information, please contact: 

Carolyn Essid on +33 493 187 824 

or by e-mail to: carolyn.essid@edhec-risk.com 

EDHEC-Risk Institute 

393 promenade des Anglais 

BP 3116 - 06202 Nice Cedex 3 

France 

Tel: +33 (0)4 93 18 78 24 

EDHEC Risk Institute—Europe 

10 Fleet Place, Ludgate 

London EC4M 7RB 

United Kingdom 

Tel: +44 207 871 6740 

EDHEC Risk Institute—Asia 

1 George Street 

#07-02 

Singapore 049145 

Tel: +65 6438 0030 

EDHEC Risk Institute—North America 

1230 Avenue of the Americas 

Rockefeller Center - 7th Floor 

New York City - NY 10020 USA 

Tel: +1 212 500 6476 

EDHEC Risk Institute—France 

16-18 rue du 4 septembre 

75002 Paris 

France 

Tel: +33 (0)1 53 32 76 30 

www.edhec-risk.com

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