Shefrin - Behavioral & Neoclassical asset pricing theories - 2008

Behavioural and Neoclassical 

Asset Pricing Theories: Combining 

the Best of Both 

Oxford-Man Behavioural Finance Conference 

Hersh Shefrin 

Mario L. Belotti Professor of Finance 

Santa Clara University

Outline 

 

 

 

Looking back. 

Neoclassical and behavioural asset pricing 

theories 

 

strengths and weaknesses. 

Behaviourally-based SDF approach. 

 

 

 

Formal definition of sentiment. 

How sentiment is manifest within asset prices. 

Unified treatment of behavioural beliefs and 

behavioural preferences. 

Copyright Hersh Shefrin 2008 

1

Neoclassical 

Asset Pricing Theory 

 

Modern asset pricing theory is based on the 

SDF. 

Neoclassical treatment in Cochrane (2005). 

 

 

Strength of approach is power of analytical 

techniques in unified, coherent framework. 

Weakness is unrealistic rationality 

assumptions and the absence of 

psychologically realistic assumptions. 


2

Behavioural 

Asset Pricing Theories 

 

 

Behavioural asset pricing models involve 

assumptions that reflect human psychology. 

Strength of behavioural models is focus on 

rich features such as: 

 

 

 

Heuristics and biases such as overconfidence, 

gambler’s fallacy and hot hand fallacy 

Fundamental attribution error 

Gains/losses, conditional risk tolerance, probability 

weighting 


3

Weaknesses in Behavioural 

Asset Pricing Literature 

The behavioural asset pricing journal 

literature lacks a well-defined formal 

definition of sentiment. 

Models largely restricted to one risk-free 

asset and one risky asset. 

Psychological assumptions vary 

considerably from model to model. 


4

Best of Both Worlds 

 

I argue that going forward asset pricing theory 

will bring together psychologically-based 

assumptions from behavioural finance and the 

rigorous, integrated SDF-based methodology 

from neoclassical finance. 

 

 

Behavioural features will improve upon the 

neoclassical assumption of perfect rationality. 

Neoclassical methodology will improve upon the ad 

hoc, fragmented approach that is characteristic of 

the current behavioural asset pricing journal 

literature. 


5

BAAP 2e 

The rest of my talk will describe 

the elements of a behavioural 

SDF-based approach. 

This is the approach described in 

BAAP. 

2 nd edition just out. 


6

Quick Survey 

What is your expectation for the return 

to the S&P 500 over the next 12 

months? 

Quick tally. 


7

Heterogeneity is Behavioural 

Challenge is Market Aggregation 

Distribution of Average of Survey Expected Returns 1998 - 2001 

35% 

30% 

1998 2001 

Relative Frequency 

25% 

20% 

15% 

10% 

5% 

0% 

30% 

Expected Return 


8

Behavioural Aggregation 

Begin with neoclassical EU model with 

CRRA preferences and complete 

markets. 

In respect to judgments, markets 

aggregate pdfs, not moments. 

Generalized Hölder average theorem. 

In respect to preferences, markets 

aggregate coefficients of risk tolerance 

(inverse of CRRA). 


9

Representative Investor Models 

Many asset pricing theorists, from both 

neoclassical and behavioural camps, 

assume a representative investor in 

their models. 

Aggregation theorem suggests that the 

representative investor assumption is 

typically invalid. 


10

Representativeness Bias 

In Academic Research 

It is typically invalid to assume the 

existence of a representative investor 

with expected utility preferences and 

correct beliefs. 

It is typically invalid to assume the 

existence of a representative investor 

with prospect theory preferences whose 

beliefs exhibit common behavioural 

biases. 


11

Simple Example of T14.1 

Errors in First Moments Only 

Complete markets, 2 investors 

equal wealth. 

CRRA = 1, log-utility. 

One investor is excessively bullish 

about mean returns, the other is 

excessively bearish. 

Correct beliefs about volatility. 

How does the market aggregate the 

different investor judgments? 


12

Market (Red) Aggregates pdfs 

Blue Aggregates Moments 

Underlying Probability Density Functions 

0.045 

0.040 

0.035 

0.030 

0.025 

0.020 

0.015 

Bearish Density 

Objective Density 

Bullish Density 

Equilibrium Density 

0.010 

0.005 

0.000 

96% 

97% 

98% 

100% 

101% 

102% 

103% 

105% 

106% 

Consumption Growth g (Gross Rate) 


13

Defining Sentiment Intuitively 

In these examples, sentiment is a 

function that indicates by what % the 

market’s (equilibrium) probability density 

exceeds the objective probability density. 

Market efficiency Sentiment = 0 


14

Sentiment 

Probability 

0.045 

6 

0.040 

0.035 

0.030 

5 

0.025 

Bearish Density 

Bullish Density 

0.020 

Objective Density ¬ 

0.015 

Equilibrium Density PM 

4 

0.010 

0.005 

3 

0.000 

96% 

97% 

98% 

100% 

101% 

102% 

103% 

105% 

106% 

Consumption Growth g (Gross Rate) 

2 

1 

0 

96% 

97% 

98% 

100% 

101% 

102% 

103% 

105% 

106% 

-1 

Consumption Growth Rate g (Gross) 


15

Formally Defining Sentiment Λ 

General Model 

Measured by the random variable 

Λ = ln(P R (x t ) / Π(x t )) + ln(δ R / δ R , Π ) 

 

 

δ R , Π is the δ R that results when all traders hold 

objective beliefs 

Sentiment is not a scalar, but a stochastic 

process < Λ, Π>, involving a log-change of 

measure. 


16

Market Efficiency 

Sentiment Λ = 0 

The market is efficient when the 

representative trader, aggregating the 

beliefs of all traders, holds objective 

beliefs. 

 

and 

i.e., efficiency iff P R = Π 

When all investors hold objective beliefs 

Φ = (P R /Π) (δ R / δ R , Π ) = 1 

Λ = ln(Φ) = 0 


17

When is Sentiment = 0? 

Consider the illustrative example. 

There are effectively two conditions 

required for market efficiency. 

Errors are unsystematic, meaning average 

error across the investor population is zero. 

Error-wealth covariance = 0, meaning 

errors are not concentrated in the investor 

population. 


18

What is the Shape of 

the Sentiment Function? 

Begin with case when investors have 

log-normal beliefs and log-utility. 

Mistakes about 1 st moments but not 

about 2 nd moments. 

Here are some examples of shapes and 

what they reflect. 


19

106.19% 

105.82% 

105.46% 

Shape of Sentiment Function 

Optimism - Bullishness 

105.10% 

Sentiment Function 

0.8 

0.6 

0.4 

0.2 

0 

20 

104.74% 

95.82% 

96.15% 

96.48% 

96.81% 

97.14% 

97.48% 

97.81% 

98.15% 

98.48% 

98.82% 

99.16% 

99.50% 

99.84% 

100.18% 

100.53% 

100.87% 

101.22% 

101.56% 

101.91% 

102.26% 

102.61% 

102.96% 

103.32% 

103.67% 

104.03% 

104.38% 

-0.2 

-0.4 

-0.6 

-0.8 


Consumption Growth Rate g (Gross)

Change of Measure is Log-linear 

Typical for a variance preserving, right 

shift in mean for normally distributed 

variable. 

This function applies to sentiment of 

individual investor as well as to 

sentiment of the market. 


21

106.19% 

105.82% 

105.46% 

105.10% 

104.74% 

Bearishness - Pessimism 

104.38% 


0.8 

0.6 

22 

0.4 

0.2 

0 

95.82% 

96.15% 

96.48% 

96.81% 

97.14% 

97.48% 

97.81% 

98.15% 

98.48% 

98.82% 

99.16% 

99.50% 

99.84% 

100.18% 

100.53% 

100.87% 

101.22% 

101.56% 

101.91% 

102.26% 

102.61% 

102.96% 

103.32% 

104.03% 

103.67% 

-0.2 

-0.4 

-0.6 

-0.8 



106.19% 

105.82% 

105.46% 

105.10% 

104.74% 

Mix of Bulls and Bears 

104.38% 


23 

0.25 

0.2 

0.15 

0.1 

0.05 

0 

95.82% 

96.15% 

96.48% 

96.81% 

97.14% 

97.48% 

97.81% 

98.15% 

98.48% 

98.82% 

99.16% 

99.50% 

99.84% 

100.18% 

100.53% 

100.87% 

101.22% 

101.56% 

101.91% 

102.26% 

102.61% 

104.03% 

102.96% 

103.32% 

103.67% 

-0.05 



Mistakes About 2 nd Moments 

Suppose that investor make mistakes 

about 2 nd moments. 

The most likely mistake stems from 

investor overconfidence. 

This means that investors 

underestimate the 2 nd moment. 

What shape will the sentiment function 

assume? 


24

106.19% 

Overconfidence With Homogeneous 

Errors About 1 st Moments 


0.5 

0 

95.82% 

96.15% 

96.48% 

96.81% 

97.14% 

97.48% 

97.81% 

98.15% 

98.48% 

98.82% 

99.16% 

99.50% 

99.84% 

100.18% 

100.53% 

100.87% 

101.22% 

101.56% 

101.91% 

102.26% 

102.61% 

102.96% 

103.32% 

103.67% 

104.03% 

104.38% 

104.74% 

105.10% 

105.46% 

105.82% 

-0.5 

-1 

-1.5 

-2 

25 

-2.5 



106.19% 

Mix of Underconfident Pessimist 

and Overconfident Optimist 


0.6 

0.5 

0.4 

0.3 

26 

0.2 

0.1 

0 

105.82% 

95.82% 

96.15% 

96.48% 

96.81% 

97.14% 

97.48% 

97.81% 

98.15% 

98.48% 

98.82% 

99.16% 

99.50% 

99.84% 

100.18% 

100.53% 

100.87% 

101.22% 

101.56% 

101.91% 

102.26% 

102.61% 

102.96% 

103.32% 

103.67% 

104.03% 

104.38% 

104.74% 

105.10% 

105.46% 

-0.1 

-0.2 



Empirical Evidence 

on Investor Mix 

Several sources for return expectations 

UBS/Gallup for individual investors 

Livingston data for professional forecasters 

Wall $treet Week for analysts, strategists, 

and money managers 

BusinessWeek for market strategists. 

What do the distributions look like? 


27

Histogram Return Expectations December 1998 for 1999 

40% 

35% 

UBS 

30% 

Livingston 


25% 

20% 

15% 

W$W 

BusinessWeek 

10% 

5% 

0% 

30% 

Percent Change 


28

Distribution of Average of Survey Expected Returns 1998 - 2001 

35% 

30% 

1998 2001 

25% 


20% 

15% 

10% 

5% 

0% 

30% 

Expected Return 


29

Pricing Kernel (SDF) 

Stochastic discount factor is a state 

price per unit probability. 

SDF version 1 M = ν/Π 

SDF version 2 

M = ν/P R 

Both different routes to studying the effect 

of sentiment Λ on prices. 

Price of any one-period security Z is 

q Z = νZ = E π {MZ} 

E t [R i,t+1 M t+1 ] = 1 

30 

Copyright Hersh Shefrin 2008

T16.1. Decomposition of SDF 

m ≡ ln(M) 

m = Λ - γ R ln(g) + ln(δ R,Π ) 

Process 

Note: In CAPM with market 

efficiency, M is linear in g with a 

negative coefficient. 


31

106.19% 

105.82% 

105.46% 

105.10% 

104.74% 

104.38% 

60.00% 

50.00% 

40.00% 

30.00% 

ln(SDF) 

20.00% 

10.00% 

ln SDF & Sentiment 

104.03% 

Sentiment 

Function 

32 

0.00% 

95.82% 

96.15% 

96.48% 

96.81% 

97.14% 

97.48% 

97.81% 

98.15% 

98.48% 

98.82% 

99.16% 

99.50% 

99.84% 

100.18% 

100.53% 

100.87% 

101.22% 

101.56% 

101.91% 

102.26% 

102.61% 

103.67% 

102.96% 

103.32% 

-10.00% 

ln(g) 

-20.00% 

-30.00% 


Gross Consumption Growth Rate g

How Different is a Behavioural SDF 

From a Traditional Neoclassical SDF? 

Behavioral SDF vs Traditional SDF 

1.2 

1.15 

Behavioral SDF 

1.1 

1.05 

1 

0.95 

0.9 

Traditional Neoclassical SDF 

0.85 

0.8 

96% 

97% 

97% 

98% 

99% 

100% 

101% 

102% 

103% 

103% 

104% 

105% 

106% 

Aggregate Consumption Growth Rate g (Gross) 


33

Fundamental Theorem for 

U-shaped Case 

ln SDF & Sentiment 

25% 

20% 

15% 

ln(SDF) 

Sentiment 

10% 

5% 

0% 

95.8% 

96.6% 

97.5% 

98.3% 

99.2% 

100.0% 

100.9% 

101.7% 

102.6% 

103.5% 

104.4% 

105.3% 

106.2% 

-5% 

ln(g) 

-10% 

Gross Consumption Growth Rate g 


34

The AFLAC Duck 

Behavioural Arrow-Debreu ’87 

WFA ’89 

Shefrin-Statman ’94 

Chicago Board of Trade ’97 

Univ Michigan ’99 

Neoclassical & behavioural status 

quo bias? 

It’s sentiment 

~ change of measure! 


35

Market Prices Reflect 

Both Fundamentals and Sentiment 

Fundamental behavioural theorem 

about the SDF, the market’s DNA. 

The log-SDF can be decomposed into 

the sum of a neoclassical fundamental 

component and sentiment. 

SDF provides an integrated approach to 

asset pricing. 


36

Empirical SDF 

Aït-Sahalia and Lo (2000) study 

economic VaR for risk management, 

and estimate the SDF. 

Rosenberg and Engle (2002) also 

estimate the SDF. 

Both use index option data in 

conjunction with empirical return 

distribution information. 

What does the empirical SDF look like? 


37

Aït-Sahalia – Lo’s SDF Estimate 

What underlies the lumps and bumps? 


38

Rosenberg-Engle’s SDF Estimate 

What accounts for the difference in the two curves? 

How to 

measure 

sentiment? 

Sample Computation at Left 

sentiment = ln(SDF)-ln(fundamental component) 

ln(SDF) = ln(5.0) = 1.61 

ln(fundamental component) = ln(2.25) = 0.81 

sentiment = 79.9% 


39

Dittmar (2002) 

Human Capital 


40

Pricing Kernel (SDF) 

Stochastic discount factor is a state 

price per unit probability. 

SDF version 1 M = ν/Π 

SDF version 2 M = ν/P R 

Both different routes to studying the 

effect of sentiment Λ on prices. 

But route 2, using P R , leads to a 

neoclassical, downward sloping SDF 

without the lumps and bumps. 

SDF version 2 M = ν/P R 

41 


Barone Adesi- 

Engle-Mancini (2008) 

 

 

 

 

 

Empirical SDF based on index options data for 

1/2002 – 12/2004. 

Asymmetric volatility and negative skewness 

of filtered historical innovations. 

Equality broken between physical and risk 

neutral volatilities. 

BEM obtain a neoclassical SDF! 

When BEM use the traditional Gaussian 

approach for the period they study, the 

estimated SDF features the behavioural 

oscillating shape. 


42

Mean-Variance Efficiency 

Is there a different path to establishing 

whether the SDF is neoclassical or 

behavioural? 

What does sentiment imply about the 

nature of the returns to a mean-variance 

efficient portfolio? 

What is the priced risk which investors 

face? 


43

Relationship Between SDF and 

Mean-Variance Returns 

Theorem 17.1 

r MV = a – bM 

where 

a = ξ, whose variation generates the MVfrontier 

 

The higher is ξ, the stronger the linear term 

relative to the quadratic term in the quadratic 

utility function 

b = (ξ/i 1 – 1) / E Π (M 2 ) 


44

How Different are Returns to a Behavioural 

MV-Portfolio From Neoclassical Counterpart? 

110% 

Gross Return to Mean-variance Portfolio: 

Behavioral Mean-Variance Return vs Efficient Mean-Variance Return 

105% 

100% 

Mean-variance Return 

95% 

90% 

85% 

Neoclassical Efficient MV Portfolio Return 

Behavioral MV Portfolio Return 

80% 

75% 

96% 

97% 

99% 

101% 

103% 

104% 

106% 



45

MV Function ∼ Quadratic 

2-factor Model, Mkt and Mkt 2 

Gross Return to Mean-variance Portfolio: 

Behavioral Mean-Variance Return vs Efficient Mean-Variance Return 

1.03 

1.02 

Efficient MV Portfolio Return 

1.01 

Mean-variance Return 

1 

0.99 

0.98 

0.97 

Behavioral MV Portfolio Return 

Return to a Combination of the Market Portfolio and 

Risk-free Security 

0.96 

0.95 

95.82% 

96.64% 

97.48% 

98.31% 

99.16% 

100.01% 

100.87% 

101.74% 

102.61% 

103.49% 

104.38% 

105.28% 

106.19% 



46

When a Coskewness Model 

Works Exactly 

The MV return function is quadratic in g, 

risk is priced according to a 2-factor 

model. 

The factors are g (the market portfolio 

return) and g 2 , whose coefficient 

corresponds to co-skewness. 


47

Oscillating SDF 

 

 

The general 

oscillating shape is 

similar to the U- 

shaped at the left, 

and deviates at the 

right. 

The market and 

coskewness are 

pricing factors, but 

there are other 

factors. 

1.2 

1.15 

1.1 

1.05 

1 

0.95 

0.9 

0.85 

0.8 

96% 

97% 

97% 

Behavioral SDF vs Traditional SDF 

Behavioral SDF 

Traditional Neoclassical SDF 

98% 

99% 

100% 

101% 

102% 

103% 

103% 

104% 

Aggregate Consumption Growth Rate g (Gross) 

105% 

106% 


48

What We Know About 

the Pricing and Coskewness 

Barone-Adesi and Talwar (1983). 

Harvey-Siddique (2000). 

The correlation between coskewness and 

mean returns of portfolios sorted by size, 

book-to-market equity, and momentum is - 

0.71. 

This means that much of the explanatory 

power of size, B/M, and momentum 

plausibly derives from coskewness. 


49

Additional Explanatory Power 

 

 

 

 

CAPM only explains 3.5% of cross-sectional 

returns. 

But CAPM + coskewness explains 68.1% of 

cross-sectional returns! 

Market, size, and B/M explain 71.8%. 

For momentum, recent winners feature lower 

coskewness than that of recent losers. 

Other factors? Empirical evidence in Barone 

Adesi, Gagliardini, Urga 


50

Prospect Theory 

Prospect theory has provided an 

important focal point for identifying 

where expected utility theory fails as a 

descriptive framework. 

Unfortunately, prospect theory itself has 

very severe weaknesses. 

Shefrin-Statman (1985) 

Hens-Vlcek (2006) 

Barberis-Xiong (forthcoming) 

De Georgi, Hens, Rieger (2008) 


51

My prediction is that asset pricing theory 

will develop around some alternative 

psychologically-based risk theory to 

capture behavioural preferences. 

Shefrin-Statman (2000) develop 

behavioural portfolio theory around 

SP/A theory (Lopes 1987). 


52

SP/A Theory & Prospect Theory 

 

 

 

 

SP/A theory is more tractable to use in 

respect to asset pricing theory. 

SP/A theory provides a more parsimonious 

framework for understanding the psychology 

of risk. 

SP/A theory consistent with neuro-anatomy. 

SP/A theory explains behaviour that prospect 

theory cannot explain. 


53

SP/A Focuses on Hope and Fear 

Affect-based Representation 


0.25 

0.2 

0.15 

Fear 

Hope 

(anterior insula) 

(nucleus accumbens) 

0.1 

0.05 

0 

106.19% 

95.82% 

96.15% 

96.48% 

96.81% 

97.14% 

97.48% 

97.81% 

98.15% 

98.48% 

98.82% 

99.16% 

99.50% 

99.84% 

100.18% 

100.53% 

100.87% 

101.22% 

101.56% 

101.91% 

102.26% 

102.61% 

102.96% 

103.32% 

103.67% 

104.03% 

104.38% 

104.74% 

105.10% 

105.46% 

105.82% 

-0.05 


54 


Inverse S in SP/A 

Rank Dependent Utility 

Functional Decomposition of Decumulative Weighting Function in SP/A Theory 

1.2 

1.0 

h2(D) 

0.8 

h(D) 

0.6 

0.4 

h1(D) 

0.2 

0.0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

D 


55

SP/A “Sentiment” with 

Aspiration Reference Point 

SP/A Sentiment Function 

1.5% 

Consumption = Aspiration 

Level 

1.0% 

0.5% 

0.0% 

1 2 3 4 5 6 7 8 

-0.5% 

-1.0% 

-1.5% 

 

 

-2.0% 

State 

Oscillating shape and skewness. 

Behavioural portfolio theory, Shefrin-Statman (2000). 

Contribution of skewness to coskewness. 


56

Progress Since BAAP 1e 

Neoclassical asset pricing theorists are 

beginning to build behavioural SDFbased 

models. 

Jouini-Napp (2007) 

Dumas-Kurshev-Uppal (forthcoming) 

Bakshi-Wu (2006) 

Behavioural asset pricing theorists 

moving to recognition of SDF-based 

behavioural approach. 

Baker-Wurgler (2007) 


57

Summary 

 

 

 

 

Comprehensive SDF-based behavioural asset 

pricing model brings together the best of what 

neoclassical and behavioural asset pricing 

has to offer. 

Behavioural beliefs, behavioural preferences, 

neoclassical beliefs, neoclassical preferences. 

Markets aggregate pdfs, not moments. 

Behavioural SDF-based theory predicts how 

shape of SDF reflects behavioural traits of 

investors. 


58

Shefrin - Behavioral & Neoclassical asset pricing theories - 2008

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