Investment Principles and Procedures - An update on our thinking

OUR INVESTMENT PRINCIPLES
& PROCEDURES
AN UPDATE ON OUR THINKING
July 2023

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TABLE OF CONTENTS
REASON FOR THIS DOCUMENT ..................................................................................................... 3
A BRIEF HISTORY .......................................................................................................................... 3
MODERN PORTFOLIO THEORY (MPT)............................................................................................ 4
THE RECENT STATE OF MARKETS .................................................................................................. 5
THE IMPROVEMENTS WE IDENTIFIED ........................................................................................... 8
BUILDING ON VARIANCE .............................................................................................................. 8
VALUE AT RISK (VaR).................................................................................................................... 9
TESTING FOR NORMALITY .......................................................................................................... 10
CRAMÉR-VON MISES .................................................................................................................. 11
MODIFIED VALUE AT RISK (MVaR).............................................................................................. 13
MVaR BACKTESTING .................................................................................................................. 15
EXCEL SOLVER ............................................................................................................................ 15
EXPONENTIAL SMOOTHING ........................................................................................................ 17
PUTTING THIS ALL TOGETHER ..................................................................................................... 19

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REASON FOR THIS DOCUMENT
We don’t usually send out complex technical documents, but many clients have expressed an
interest in what happens ‘under the bonnet’. This is as unashamedly technical document, which we
hope satisfies that interest <strong>and</strong> gives a better insight into the level of detail that we employ.
We have undertaken a series of changes <strong>and</strong> incorporated additional features into our investment
principles <strong>and</strong> procedures. This document has been produced as a means of explaining these
developments <strong>and</strong> why we have made the decisions we have. For a quicker explanation, please see
the summary within section “Putting This All Together” on page 19.
Our st<strong>and</strong>ard investment principles <strong>and</strong> procedures document, which is usually produced quarterly,
will also be modified to reflect these changes. However, going forward, it will not see quarterly
revisions. For those that utilised that document for the purposes of reviewing our <strong>update</strong>d fund list,
this will now be provided via a separate “Fundfolio Shortlist” document, which, as a shorter
document, we hope improves readability.
A BRIEF HISTORY
Traditionally, <strong>and</strong> for a very long time, we used our professional experience of markets <strong>and</strong> individual
asset types to develop a range of lower risk to higher risk portfolios.
However, this strategy places a significant reliance upon experience <strong>and</strong> knowledge, which exposed
the investment decisions to a plethora subjective factors like intuition, personal insights, <strong>and</strong> past
successes. For example, one person’s view of what constitutes “low risk” may be different to
another. What’s more, human decision-making is essentially flawed by the influence of emotions,
biases, <strong>and</strong> cognitive limitations. For a while we explored ways in which we could remove that
subjectivity, which we felt was becoming an increasing <strong>and</strong> material risk <strong>and</strong> move to an objective
model.
The delayed transition from a subjective to an objective investment model was primarily due to the
challenge of accessing reliable historic data. Limited availability <strong>and</strong> reliability of data posed
obstacles in constructing a robust objective model. However, in the middle of 2017, technological
advancements enabled us to overcome these challenges <strong>and</strong> make the brave decision to
fundamentally change our approach to investment.

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MODERN PORTFOLIO THEORY (MPT)
When exploring different investment concepts to use with our newfound source of data, Modern
Portfolio Theory (MPT) very quickly became the obvious choice. It is widely regarded as a
fundamental concept in finance <strong>and</strong> forms a basis for how different investments can be used to
together. It has stood the test of time too: it was developed by an economist in the 1950s, who was
later awarded a Nobel peace prize for the framework.
At its core, MPT assumes that investors are rational <strong>and</strong> risk-averse, seeking to achieve the highest
possible return for a given level of risk or the lowest possible risk for a given level of return. The
theory revolves around the idea of diversification, which involves spreading investments across
different asset classes to reduce overall risk.
By using MPT principles, portfolios with multiple investment exposures can be constructed in a way
that, based on historic data, would offer a balance between risk <strong>and</strong> reward, in essence “optimising”
the investment strategy at different levels of targeted return.
We enacted the MPT methodology by building propriety software ourselves (we called it
‘pfOptimise’ (with the ‘pf’ st<strong>and</strong>ing for ‘Portfolio’)), <strong>and</strong>, since late 2017, the methodology has
underpinned all of our investment decisions. We are very proud of it, <strong>and</strong> it has been a testament to
what makes us difference to other financial advisers.

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THE RECENT STATE OF MARKETS
The following charts show the performance for the ‘AFI Balanced’ <strong>and</strong> the IA Mixed <strong>Investment</strong> 20-
60% Shares over various periods. These benchmarks are fairly comparable to our portfolios in that
they consist of diversified portfolios that contain many asset types <strong>and</strong> geographic locations.

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These charts show us that diversified portfolios, similar to the ones we recommend, have seen
virtually no growth <strong>and</strong> have been less than tranquil for the last three years. This combination of
poor returns <strong>and</strong> increased risk leads to a fair <strong>and</strong> reasonable anxiety for anyone holding invested
capital. However, while it may be difficult to remain calm during a considerable market instability, it
is important to remember that volatility is a normal part of investing <strong>and</strong>, reacting emotionally to
volatile markets may be more detrimental to long-term performance than the drawdown itself.
We pay careful <strong>and</strong> frequent attention to investment markets. However, we felt that the volatility we
were experiencing was not worthy of a knee-jerk reactions or fundamental changes in our model.
We continued to support the underlying principles behind MPT.
The mathematical calculations for generating outputs via MPT use past performance as the input,
<strong>and</strong> we feed the model fifteen years’ worth of weekly data across various asset classes. For the
majority of this period, if we look at the broad asset classes of just equities <strong>and</strong> fixed interest, they
have not just been popular for their positive returns, but also because of their correlation.

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The correlation between equities <strong>and</strong> fixed interest has been negative since the start of the century,
resulting in a material <strong>and</strong> obvious diversification benefit. In the years when equities suffered their
unusual losses, that loss was offset by the consequent increase in the value of fixed interest assets. A
portfolio comprised of 60% in global equity <strong>and</strong> 40% in global fixed interest would have seen ten
consecutive positive years between 2009 <strong>and</strong> 2019. Ten positive years on the trot.
So, why are things different now? Well, the major difference is because, unfortunately, equity-bond
correlations turned positive in 2020, when Covid hit. This means that, when one fell, so did the
other. It was driven by all manner of disasters: combine the inflationary pressures caused by covid
with the growth <strong>and</strong> volatility shocks. Both equity <strong>and</strong> bond valuations were depressed <strong>and</strong> there
was no investment shelter. Even the value of cash was positively correlated, with the value falling
due to inflation, which is traditionally a non-correlated asset. Everything flipped.
Because of this, the “protection” that our model suggested was not working in reality. We did see a
semblance of normality towards the end of 2021, but this was then squashed by Russia <strong>and</strong> the same
culprits: inflationary pressures among growth <strong>and</strong> volatility shocks. We have seen two market events
that normally occur once every 15-20 years, happen twice in three years.
So, the question we believed needed answering was whether this was the new normal? We
mentioned inflationary <strong>and</strong> growth pressure above, <strong>and</strong> these two are key. Unexpected inflation
movements tend to be rather bad news for both equities <strong>and</strong> bonds, which reinforces a positive
equity-bond correlation relationship going forward. On the flip side, unexpected growth movements
tend to be positive for equities but negative for bonds, which brings us back to a more familiar <strong>and</strong>
traditional negative equity-bond correlation.
Early into the instability, it was easier to take the view that the situation was atypical <strong>and</strong> that things
would return to normal in due course. However, we have now seen three consecutive years of
turmoil with no obvious end in sight <strong>and</strong> thus, we have reached the conclusion that something needs
to be done.

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THE IMPROVEMENTS WE IDENTIFIED
It is worth noting that MPT has itself been subject to criticisms <strong>and</strong> limitations, such as assumptions
of perfect markets <strong>and</strong> reliance on historical data. However, we remain positive that MPT is the
cornerstone of portfolio management <strong>and</strong> thus we are taking the view to build on what we have
already, rather than fundamentally change to a different way of thinking.
After much deliberation, we established three overarching upgrades that we felt our model needed:
a. A way to explain volatility <strong>and</strong> its implications.
b. A way to test the historic data set that we were passing to the model.
c. A way to place a greater importance of recent data, than on older data.
BUILDING ON VARIANCE
Our optimisation framework uses the historic average returns for each asset class (we refer to this as
the ‘mean’) as well as the fluctuations of returns around the mean (we refer to this as the ‘variance’).
Thus, the output in terms of the efficient portfolios can be illustrated on a chart that shows returns
on one axis, <strong>and</strong> variance on the other.
However, when explaining variance in the context of mean-variance optimisation, it can be
challenging to underst<strong>and</strong> due to a few reasons:
The percentage that variance is expressed as seems unintuitive <strong>and</strong> arbitrary. For example, a
mean return of 7% per annum that carries a variance of 7% per annum could mean many
different things to someone unfamiliar with statistical concepts, <strong>and</strong> it can be difficult to grasp
the mathematical principles involved in calculating <strong>and</strong> interpreting variance. Variance is not an
easily relatable concept in everyday life. Unlike the concept of average or mean, which people
commonly encounter <strong>and</strong> underst<strong>and</strong>, variance is an abstract measure that doesn't have a direct,
intuitive interpretation.
Mean-variance optimisation places a significant emphasis on risk, specifically the volatility or
variability of returns. Variance is used as a proxy for risk, assuming that higher variance indicates
higher risk. However, risk can be a subjective concept, <strong>and</strong> clients may have different
perspectives or risk tolerances that don't align with the sole consideration of variance.

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VALUE AT RISK (VaR)
While Value at Risk (VaR) is not an expansion of MPT, it complements MPT by offering an expansion
on variance. VaR estimates the potential loss, in percentage terms, that an investment portfolio may
experience over a specific time horizon at a given confidence level.
MPT focuses on the relationship between risk <strong>and</strong> return, aiming to optimise the trade-off through
diversification <strong>and</strong> asset allocation. However, MPT does not provide a precise measure of the
maximum potential loss a portfolio may face.
We believe this is where VaR comes into play. VaR quantifies the downside risk of a portfolio by
estimating the maximum loss that could occur over a specified time period at a given probability
level (e.g. a 95% confidence level). It provides an estimate for the worst-case loss an investor can
expect to experience for any given composition of asset types. We believe this allows for a much
easier reflection of risk <strong>and</strong> what someone may feel comfortable with, as it is easier to relate to.
As an expansion of variance, VaR similarly takes into account the distribution of portfolio returns, the
historic volatility, <strong>and</strong> the historic correlation between asset types. It just presents that data in a
language that we feel will provide a more comprehensive underst<strong>and</strong>ing of the portfolio’s risk <strong>and</strong>
allow for more informed decisions to be made.

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TESTING FOR NORMALITY
A drawback of the VaR expansion is the significant reliance it places on the distribution for returns. It
assumes that returns will be normally distributed. The chart below illustrates how a normal
distribution appears:
When it comes to financial returns, a normal distribution implies that the majority of returns are
clustered around the mean or average return (0% in the above example), with fewer returns
deviating significantly from the mean. This means that most returns are close to the average, <strong>and</strong> the
further away we move from the mean, the fewer returns we encounter.
But how sure can we be that returns follow this distribution <strong>and</strong>, if they don’t, are we comfortable
relying on the VaR output when we know that its major assumptions are not the case?

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CRAMÉR-VON MISES
The Cramér-von Mises test is a statistical test commonly used to assess the goodness-of-fit for a data
set to a particular theoretical distribution. We can therefore use it to test the historic data for the
normality assumption that VaR relies upon.
The test evaluates the discrepancy between the empirical cumulative distribution function (ECDF) of
the sample <strong>and</strong> the cumulative distribution function (CDF) of the theoretical distribution being
tested. It then computes a test statistic (we refer to this as the ‘t-stat’) based on the squared
differences between the observed <strong>and</strong> expected cumulative probabilities.
Using the t-stat, we can then obtain a probability value (we refer to this as the ‘p-value’), which
provides a measure of this likelihood i.e. how likely does the distribution follow the normal
distribution we are testing for, assuming that the null hypothesis is true. The null hypothesis in this
case is that the empirical data <strong>and</strong> the theoretical ‘normal’ distribution being tested are the same.
The result of our Cramér-von Mises test was a p-value of 0.00000589%. This indicates a strong level
of confidence that the null hypothesis is false, <strong>and</strong> thus the distribution of returns is not normally
distributed.

We have also illustrated the difference between the empirical distribution of our historic data set
<strong>and</strong> the theoretical ‘normal’ distribution on the following chart:
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MODIFIED VALUE AT RISK (MVaR)
Modified Value at Risk (MVaR) addresses the limitation of traditional Value at Risk (VaR), by
capturing the asymmetry of returns, which we have statistical evidence of via the Cramér-von Mises
test.
In contrast to VaR, which relies upon a normal distribution, MVaR allows for more flexibility in
capturing the shape of the return distribution, particularly when exhibit characteristics such as
asymmetry (we refer to this as ‘skewness’) <strong>and</strong> fat tails (we refer to this as ‘kurtosis’), which deviate
from the normal distribution assumption.
To help illustrate the effect of ‘skewness’, please see the following chart:

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To help illustrate the effect of ‘kurtosis’, please see the following chart:
By incorporating skewness <strong>and</strong> kurtosis into the calculation, MVaR can construct a more robust
output, <strong>and</strong> in our opinion, suitably achieves our objective to better explain <strong>and</strong> present volatility.

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MVaR BACKTESTING
Our second objective was to incorporate a way of testing the historic data set that we were passing
to the model. While we have already introduced an element of this under the Cramér-von Mises
test, we felt it was appropriate to also test the adequacy of our MVaR model.
The Kupiec model is a widely used statistical test for backtesting the adequacy of VaR models. It
assesses whether the number of VaR exceedances matches the expected number of exceedances
based on a chosen confidence level. For example, for a 95% confidence level, the threshold would be
the value at the 5th percentile of the distribution.
If the observed number of exceedances significantly deviates from the expected number, it suggests
that the MVaR model may not be adequately capturing the risk. In such cases, the MVaR model may
require adjustment or improvement.
Similarly, to the Cramér-von Mises test, the p-value plays a crucial role in the Kupiec Model. It
represents the probability of observing a certain number of MVaR breaches or more, assuming that
the MVaR model is accurate. In other words, it measures the consistency between the actual <strong>and</strong>
expected number of breaches under the assumption that the MVaR model is correctly calibrated.
EXCEL SOLVER
Excel Solver is an add-in tool in Microsoft Excel that find optimal solutions to complex problems. It is
a powerful optimisation tool that can be used to solve mathematical models <strong>and</strong> perform various
types of analysis.
The basic idea behind Solver is to maximise or minimise an objective function while satisfying certain
constraints. We can define the objective function to optimise, which in this case, is the associated p-
value. Solver then uses various mathematical techniques, including linear programming <strong>and</strong>
nonlinear optimisation algorithms, to search for the optimal values of the variables that satisfy the
constraints <strong>and</strong> optimise the objective function.

The result of our analysis was a p-value of 99.9% at a confidence level of 95.8%. This indicates a
strong level of confidence between the observed number of exceedances with the expected number
of exceedances that the MVaR model suggested at this specific confidence level. Please see the chart
below for how the p-value changed with varying confidence levels, based on our historic data set:
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EXPONENTIAL SMOOTHING
Our final objective was to introduce a way of placing a greater significance on recent data, than on
older data.
Firstly, we investigated a technique called ‘Bootstrapping’. This is a resampling technique that is
commonly used to estimate statistical properties or quantify uncertainty in data (we refer to the
uncertainty as the ‘noise’). Bootstrapping can be applied to various types of data, including timeseries
data like financial returns, with its purpose to identify the "signal" in the data, then remove the
‘noise’.
However, the dilemma we faced was whether or not to accept that our empirical historic data set
had any noise. The historic record for each asset class is indeed the historic record for each asset
class <strong>and</strong> what happened in terms of performance <strong>and</strong> volatility, actually happened. Removing part
of the data points within the set exposed us to the risk of incorrectly removing the wrong data. We
didn’t feel comfortable with this risk.
Exponential smoothing is an alternative technique for regulating time-series data, including historic
returns. It offers several advantages that made it an appealing approach. For example:
It’s simple <strong>and</strong> intuitive: Exponential smoothing is a straightforward <strong>and</strong> easy-to-underst<strong>and</strong>
method. It involves assigning weights to past observations based on their recency, with more
weight given to recent data points. This simplicity makes it accessible to both beginners <strong>and</strong>
experienced analysts, requiring minimal technical knowledge or complex mathematical
calculations.
Adaptability to Trends <strong>and</strong> Patterns: Exponential smoothing allows for the detection <strong>and</strong>
adjustment to underlying trends <strong>and</strong> patterns in the data. By assigning higher weights to recent
observations, the method is inherently responsive to changes in the data, making it effective at
capturing short-term variations <strong>and</strong> adjustments in historic returns. We believe this adaptability
helps to provide more accurate <strong>and</strong> up-to-date forecasts.
Computational Efficiency: Unlike Bootstrapping, exponential smoothing calculations are
computationally efficient <strong>and</strong> can h<strong>and</strong>le large datasets without significant burdens. This makes it
a more practical choice for extensive historical data sets <strong>and</strong> incorporating real-time data
<strong>update</strong>s efficiently, as we do on a regular basis.

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Flexibility: Exponential smoothing offers flexibility in the choice of smoothing parameters, such as
the smoothing factor or the level of weighting assigned to past observations. We can adjust
these parameters to strike a balance between responsiveness to recent data <strong>and</strong> the stability of
the forecast.
As mentioned above, Exponential smoothing requires a smoothing parameter. For this, we decided
on the half-life theory. Using half-life in exponential smoothing refers to the time it takes for the
weight assigned to an observation to decrease by half. A shorter half-life implies faster adaptation to
changes in the data, while a longer half-life results in a smoother <strong>and</strong> more persistent forecast. The
half-life theory also carries the advantage of being created via a commonly used formula that you
may remember from your physics or chemistry classes:
α = 1 - exp(-ln(0.5) / h)
To obtain the appropriate decay rate (α) value, we specified a half-life (h) of five years. This means
that the weight of each data point will decrease progressively <strong>and</strong> by half every five years. Please see
the chart below for a visual illustration of how this weighting applies to our historic data:

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PUTTING THIS ALL TOGETHER
We are very pleased with the upgrades we have now implemented to our investment model. These
upgrades address crucial aspects of our existing model, which we hope will lead to a more
comprehensive underst<strong>and</strong>ing of risk, your own tolerances, <strong>and</strong> overall market dynamics. To
summarise, the enhancements <strong>and</strong> their implications for our investment advice are as follows:
a. Explanation of Volatility:
One of the primary upgrades is the integration of a robust framework to explain volatility <strong>and</strong> its
implications. We underst<strong>and</strong> that market fluctuations can be unsettling, <strong>and</strong> we believe that
transparency is paramount in fostering trust <strong>and</strong> confidence. The <strong>update</strong>d model incorporates
sophisticated algorithms that we believe will provide clearer insights into the nature <strong>and</strong> impact of
volatility. By better underst<strong>and</strong>ing volatility, this directly leads to informed decisions <strong>and</strong> a clearer
picture of the potential risks <strong>and</strong> rewards associated with your investments.
b. Rigorous Historic Data Testing:
To further enhance the reliability <strong>and</strong> accuracy of our investment model, we have implemented two
advanced testing mechanisms for the historic data set used by our model. This testing ensures that
the data employed in our investment strategies is robust, relevant, <strong>and</strong> reflective of market
conditions. By subjecting the data to comprehensive analysis, we can identify any potential biases or
anomalies, allowing us to fine-tune our strategies <strong>and</strong> provide you with what we hope to be more
reliable investment recommendations.
c. Emphasising Recent Data:
Recognising the evolving nature of financial markets, we have placed a greater emphasis on recent
data in our upgraded model. While historical data remains an essential component of our analysis,
the new approach recognises that recent market trends <strong>and</strong> developments can have a more
immediate impact on investment outcomes. By prioritising recent data, we aim to capture timely
insights <strong>and</strong> adapt to changing market dynamics more effectively.
Our aim is to provide you with a more transparent investment experience, helping you achieve your
financial goals with greater precision <strong>and</strong> confidence.
Should you have any questions or require further clarification regarding these upgrades, we are
ready to assist. We appreciate your trust <strong>and</strong> continued partnership <strong>and</strong> look forward to the
prosperous journey ahead.