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[email protected] VCK Research reports are available on Bloomberg VCKR <Go>
Alternative Research 27th August 2012
Ayan Doss
+91 33 40099979
ForewordForewordForewordForeword
Stock picking is similar to life, both need decision making. Decision making is connected with psychology, skill, research method,
etc. Even the most skilled stock pickers know that there is a lot more to performance than simply picking stocks. Numerous
researches have shown that while humans are good at stock picking, they fail to achieve consistent return over and above the
benchmark index. Study by Andrew Clark, Chief Index Strategist, Thompson Reuters Indices, suggest that while most portfolio
managers do know how to pick stocks, their underperformance versus their benchmark can be attributed to portfolio
construction skills. The reason for poor portfolio construction skill is because of what Freud agreed: ‘we are ignorant of
ourselves’. In this report, we have tried to explain some of these human shortcomings regarding decision making and how to
overcome them.
Princeton professor and Nobel Laureate, Daniel Kahneman, in his book ‘Thinking, Fast and Slow’ has given an excellent overview
of the way we make decisions. Daniel put forth a very interesting and disturbing fact that most of the time our brain makes
decision that is easy and not necessarily what is right. To prove his point, he highlights experiments which shows that human
being suffers from many anomalies and the most prominent of those being ‘Cognitive biases’ and ‘the planning fallacy’.
Cognitive biases suggest that we're astonishingly susceptible to being influenced by features of our surroundings in ways we
don't suspect. Similarly planning fallacy highlights than when forecasting the outcome of risky projects, we overestimate positive
outcomes while overlooking potential for miscalculations. He further adds that another reason for our underperformance is
because human beings are ‘Risk Averse’ i.e., they do not maximize utility when confronted with choosing between uncertain but
profitable and certain but less profitable option.
Another reason for our inability to outperform on a consistent basis is because we are ‘incorrigibly inconsistent’ in making
summary judgment of complex information. When predictability is poor, which is the case always, inconsistency is destructive of
any predictive validity.
So, how do we outperform the market on a consistent basis? The answer is, through ‘Optimization’. Many psychological studies
show that under ‘low-validity’ environment (like evaluation of credit risk by banks, predicting the movement of stocks, longevity
of cancer patients, outcome of football game, etc), predictions based on some form of formula/algorithm proved to be more
accurate than intuitive predictions by experts.
Optimization helps us outperform as it does not suffers from any biases. However, there are researches that show that equal
weightage portfolio tend to outperform optimized portfolio which suggests that optimization adds no value in the absence of
informed inputs. However, Mark Kritzman, CFA, Sébastien Page, CFA, and David Turkington, CFA, in their paper ‘In Defense of
Optimization: The Fallacy of 1/N’ argues that with naive inputs (like expected return), optimized portfolios usually outperform
equally weighted portfolios. The ostensible superiority of the 1/N approach arises not from limitations in optimization but,
rather, from reliance on rolling short-term samples for estimating expected returns. This approach often yields implausible
expectations. By relying on longer-term samples for estimating expected returns or even naively contrived yet plausible
assumptions, optimized portfolios outperform equally weighted portfolios.
Hence, to overcome this shortcomings, while estimating stock return we have relied on Bloomberg estimates to avoid any kind of
biases and also to get an ‘Outside View’ and then used simple optimization technique to maximize utility and avoid inconsistency.
The final result was not disappointing. Our portfolio has outperformed the broader indices (Sensex and BSE 200) and generated
an average annual Alpha over BSE 200 of ~6% in last six years. Optimized portfolio tend to outperform the non-optimized
portfolio as it is i) more concentrated; ii) gives more weightage to non-correlated stocks and iii) at a given level of risk, it
maximizes the return of portfolio and not individual stock.
So if you’ve had extensive training in a predictable, rapid-feedback environment like chess, firefighting, anesthesiology — then
blink. In all other cases, think.
Deepak Tewary
+91 33 40099977
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Managing Biases: Key To Unlocking Alpha
IndexIndexIndexIndex
ContentsContentsContentsContents PagePagePagePage
I. Introduction 1
Cognitive Biases 1Decision making in a risky outcome 1Optimistic Bias and the illusion of knowing 2The Planning Fallacy 2How to overcome our Biases 3Improving return through Optimization 3
II. Optimization Methodology 4
III. Back-testing 5
IV. Alpha 6
V. Omega 7
VI. Optimization – A Critique 9
VII.Current Portfolio 10Portfolio Fundamentals 11
VIII. Portfolio Stress Testing 12
IX. Portfolio VaR Analysis 13
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““““As much money and life as you could As much money and life as you could As much money and life as you could As much money and life as you could want!want!want!want!
The two things most human beings would The two things most human beings would The two things most human beings would The two things most human beings would choose above all choose above all choose above all choose above all ––––
The trouble is, humans do have a knack of The trouble is, humans do have a knack of The trouble is, humans do have a knack of The trouble is, humans do have a knack of choosing precisely those things that are choosing precisely those things that are choosing precisely those things that are choosing precisely those things that are
worst for them.worst for them.worst for them.worst for them.””””
– J.K. Rowling, Harry Potter and the Sorcerer’s Stone
There are only two ways to beat the stock market in the long-
term, net of expenses: one, trade on superior information;
two, be lucky. In an efficient market, getting lucky has a much
higher probability of working than finding superior
information.
It’s widely known that most money managers underperform
the market; even with the deep and talented pool of analysts
they have access too. Research from Thompson Reuters Lipper
examining how successful actively managed mutual funds in
Europe have been in outperforming the indices over 20 years
period throws up some interesting facts which only reaffirm
market belief. This research concludes that typically 40% of
actively managed equity funds outperform their benchmark
indices in last 20 years. The proportion of funds that
outperformed varied from 26.7% in 2011, 40% over 3 years
and 34.9% over the past 10 years.
AVERAGE PROPORTION OF FUNDS' ROLLING
RETURNS OUTPERFORMING BENCHMARKS,
31/12/1991 TO 31/12/2011
1 yr
period
3 yr
period
10 yr
period
All Equity Funds 42.8% 41.4% 39.7%
Equity Asia Pacific Ex
Japan48.4% 48.9% 54.4%
Equity EmgMkt Global 38.5% 31.1% 24.6%
Equity Europe 37.7% 35.9% 27.0%
Equity Global 42.2% 38.4% 32.5%
Equity North America 36.2% 30.3% 20.8%
Equity UK 46.4% 47.6% 47.4%
Source: Lipper;Beating The Benchmark, March 2012
SoSoSoSo whywhywhywhy itititit isisisis sosososo hardhardhardhard totototo consistentlyconsistentlyconsistentlyconsistently beatbeatbeatbeatthethethethe market?market?market?market?
A logical answer to this question would be that top performing
fund attracts more capital and thus becomes less agile. In
addition, successful managers are disinclined to take new risky
bets that might tarnish their track records. Instead they often
start following their benchmark.
The above answer, though convincing, would be too simple to
explain the magnitude of underperformance. Princeton
professor and Nobel Laureate Daniel Kahneman helps explain
these underperformance in his new book, ‘Thinking, Fast and
Slow’.
CognitiveCognitiveCognitiveCognitive BiasesBiasesBiasesBiases
According to Kahneman, human mind is designed to find an
easy answer rather than right answer because of its ‘cognitive
biases’ - unconscious errors of reasoning that distort our
judgment of the world. Typical of these is the ‘anchoring
effect’: our tendency to be influenced by irrelevant numbers
that we happen to be exposed to. The human brain is
incapable of creating new information and it simply doesn’t
know what it doesn’t know. To compensate for the unknown,
our brains attempt to piece together the best possible story
based on what we do know. Sometimes this story is accurate
and sometimes not. When we’re right, we think it’s because
we’re smart, and when we’re wrong, we think it’s because we
didn’t have enough information and there was nothing we
could do about it.
ToToToTo furtherfurtherfurtherfurther understandunderstandunderstandunderstand thethethethe humanhumanhumanhumanunderperformance,underperformance,underperformance,underperformance, wewewewe needneedneedneed totototounderstandunderstandunderstandunderstand howhowhowhow decisiondecisiondecisiondecision isisisis mademademademade inininin aaaariskyriskyriskyrisky outcome?outcome?outcome?outcome?
Kahneman and his partner, Tversky, had showed that people
making decisions under uncertain conditions do not behave in
the way that economic models have traditionally assumed;
they do not ‘maximize utility’.
Decision under uncertain (read risky) circumstances, is
governed by the expected utility hypothesis, which states that
the decision maker (DM) chooses between risky or uncertain
prospects by comparing their expected utility values, i.e., the
weighted sums obtained by adding the utility (desirability of
money) values of outcomes multiplied by their respective
probabilities.
1
Managing Biases: Key To Unlocking Alpha
INTRODUCTION
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ForForForFor exampleexampleexampleexample::::
A. 80% chance to win INR 3 mn
B. 50% chance to win INR 5mn.
Given the above choice, most people will choose option B as it
gives maximum utility. Now consider this:
A. 50% chance to win INR 5 mn
B. 100% chance to win INR 2 mn.
In this case also, most people will choose option B though it
has lower utility. Swiss scientist Daniel Bernoulli observed that
most people dislike risk (the chance of receiving the lowest
possible outcome), and if they are offered a choice between a
gamble and an outcome equal to its expected value, they will
pick the sure thing. In fact a ‘risk-averse’ person will choose a
sure thing that is less than expected value, in effect paying a
premium to avoid the uncertainty. The psychological value of
a gamble is therefore not the weighted average of its
possible financial outcome but the average of the utilities of
these outcomes, each weighted by its probability.
OptimisticOptimisticOptimisticOptimistic BiasBiasBiasBias andandandand TheTheTheThe illusionillusionillusionillusion ofofofofknowingknowingknowingknowing
According to Kahneman, the planning fallacy is one of the
manifestations of a pervasive ‘optimistic bias’ which may well
be the most significant of the cognitive biases. However, a bias
toward optimism is obviously bad, since it generates false
beliefs — like the belief that we are in control, and not the
playthings of luck. Kahneman explains that the very belief
that we know something that the market does not, is not a
belief but illusion.
ReasonReasonReasonReason forforforfor thisthisthisthis illusionillusionillusionillusion
Kahneman explains that the reason for this illusion is that the
person who acquires more knowledge becomes unrealistically
overconfident. Philip Tetlock, a psychologist at the University
of Pennsylvania in his book ‘Expert Political Judgment: How
Good It Is? How Can We Know?’ writes, experts are just
human in the end. They are dazzled by their own brilliance and
hate to be wrong. Experts are led astray not by what they
believe, but by how they think.
However, after all we are Darwinian survivors and Kahneman
adds that but without this ‘illusion of control’, would we even
be able to get out of bed in the morning?
Optimists are more psychologically resilient, have stronger
immune systems, and live longer on average than their more
reality-based counterparts. Moreover, as Kahneman notes,
exaggerated optimism serves to protect both individuals and
organizations from the paralyzing effects of another bias, ‘loss
aversion’: our tendency to fear losses more than we value
gains. It was exaggerated optimism that John Maynard Keynes
had in mind when he talked of the ‘animal spirits’ that drive
capitalism.
Decisions and Errors:The Planning Fallacy
When forecasting the outcome of risky
projects, we too easily fall victim of planning
fallacy. In its grip, we overestimate positive
outcomes while overlooking potential for
miscalculations.
So,So,So,So, howhowhowhow dodododo wewewewe overcomeovercomeovercomeovercome ourourourour Biases?Biases?Biases?Biases?
Many psychological studies show that under ‘low-validity’
environment (like evaluation of credit risk by banks, predicting
the movement of stocks, longevity of cancer patients,
outcome of football game, etc), predictions based on some
form of formula/algorithm proved to be more accurate than
intuitive predictions by experts.
WhyWhyWhyWhy isisisis forecastingforecastingforecastingforecasting inferiorinferiorinferiorinferior totototoalgorithm?algorithm?algorithm?algorithm?
According to Paul E. Meehl, one of the most versatile
psychologists of the twentieth century, forecasters think out
of box and consider complex combinations of features in
making their predictions. Complexity may work in the odd
cases, but more often than not it reduces validity.
Another reason for the inferiority of forecasters is that
humans are ‘incorrigibly inconsistent’ in making summary
judgment of complex information. A review of 41 separate
studies of reliability of judgment made by auditors,
pathologists, psychologists, organizational managers, and
other professional suggests that level of inconsistency is
typical, even when a case is revaluated within few minutes.
Unreliable judgments cannot be valid predictors of anything.
2
Managing Biases: Key To Unlocking Alpha
INTRODUCTION
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Because we have little direct knowledge of what goes in our
mind, we will never know that we might have made a different
judgment or reached a different decision under very slightly
different circumstances. Formulas do not suffer from such
problems. Given the same input, they always return the same
answer. When predictability is poor, which is the case always,
inconsistency is destructive of any predictive validity.
We are not making a case for formulas/algorithms; even they
do not add value beyond a point. We know this from various
research that the best statistical algorithms, although more
accurate that human judgments, were never very accurate.
Robyn M. Dawes, an American psychologist who specialized in
the field of human judgment, in his famous article ‘The Robust
Beauty of Improper Linear Models in Decision Making’ opined
that the complex statistical algorithm (multiple regression) add
little or no value in decision making. More recent research
suggests that formulas that assign equal weightage to all the
predictors are often superior, because they are not affected by
accidents of sampling.
ImprovingImprovingImprovingImproving returnreturnreturnreturn throughthroughthroughthroughoptimizationoptimizationoptimizationoptimization
When investor preferences are complex, optimization has
repeatedly been shown to be performing better than
traditional portfolio choice models (‘IMPROVING
QUANTITATIVE MODELS THROUGH OPTIMIZATION’ BERNARD
TEW & RICHARD BERNSTEIN). Bernard & Bernstein observe
that individual security weights can often mean the
difference between outperforming or underperforming a
benchmark.
Andrew Clark, Chief Index Strategist, Thompson Reuters
Indices, published a white paper ‘SECURITIES SELECTION &
PORTFOLIO OPTIMIZATION: IS MONEY BEING LEFT ON THE
TABLE?’ where he concludes that portfolio managers do know
how to pick stocks. However, optimization techniques
increases return once the security selection is done.
On a final note, we agree with the finding of the paper that the
observed underperformance of fund managers versus their
benchmark can be attributed to portfolio construction skills
and not to stock-picking skills as so many have claimed.
Strangely, human beings are not as Strangely, human beings are not as Strangely, human beings are not as Strangely, human beings are not as emotionally disturbed by longemotionally disturbed by longemotionally disturbed by longemotionally disturbed by long----term risk term risk term risk term risk
as they are by short term risk.” as they are by short term risk.” as they are by short term risk.” as they are by short term risk.”
-William Bernstein
3
Managing Biases: Key To unlocking Alpha
Managing Biases: Key To Unlocking Alpha
INTRODUCTION
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OPTIMIZATIONMETHODOLOGY
BSE-200 Stocks
BEst. Consensus Target
and Covariance Matrix
Mean Variance Optimization
with Constraints
Stocks and Weights
We begin our stock selection process by defining a universe consisting of stocks
included under the BSE-200 stocks. We believe that this set of stocks provide the
perfect balance of liquidity and outperformance potential (as it covers ~85% of
listed market cap). There on we calculated the expected return for each stocks on
the basis of Bloomberg Consensus Target Price. The covariance matrix among the
stocks was derived on the basis of the weekly returns of the last five years. We
then filtered our data by removing the stocks that did not have either the
Bloomberg Consensus Target Price or 5 years of price data. There after we fed the
data to a Mean Variance Optimization model in order to get the list of stocks to
invest and their corresponding weights in the portfolio. To summarize, the key
tenants of our model is given in the table below –
** Markowitz, H., 1952. Portfolio Selection. Journal of Finance, 7(1), p.77-91.
Sl.
No.Particulars Details
1 Expected ReturnOn the basis of Bloomberg Consensus Target
Price.
2. Covariance Matrix Five years of weekly return data.
3. Optimization Engine Markowitz Mean Variance Optimization.
4. Risk Free Rate 10 Yr Govt. Bond Yields.
5Optimization
Constraints
A. No Short Selling.
B. No Leverage.
C. Maximum allocation to a particular
scrip limited to 5%.
Mean Variance Optimization is a quantitative technique for allocating
investments within a portfolio. MVO does this by evaluating the trade-off
between risk and return and then choosing those combination of assets that
helps maximize the return while minimizing the risk. This concept was
developed by economist Harry M. Markowitz and is part of Modern Portfolio
Theory (MPT).
The MVO requires three data sets: expected return, standard deviation of
each stocks, and the correlation among them. These three data sets generate
a feasible set of asset combinations that Markowitz called the ‘efficient
frontier’. The efficient frontier consists of those combination of assets that as a
whole is expected to produce better returns given a level of risk, or, produce
lower risk given a level of return.
Combining the efficient frontier with the risk free rate of return generates the
Capital Market Line (CML) on the basis of which investors can choose the
assets to invest in and their corresponding weights.
A primer on Mean Variance Optimization (MVO)
4
Managing Biases: Key To Unlocking Alpha
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BACKTESTING
In order to verify how our quantitative portfolio strategy performed we created a portfolio on the basis of the
aforementioned methodology and rebalanced it yearly. The chart below shows how our portfolio performed vis-à-
vis BSE 200 –
Particulars Portfolio Sensex BSE 200
Time Horizon July 3, 2006 to July 3, 2012
Return (Annualized) 18.1% 12.06 13.3%
Risk (Annualized) 29.6% 26.9% 32.4%
Beta 1.17 (vs. BSE-200) 0.97 (vs. BSE-200) 1
Source: VCK Research; Bloomberg
The summary statistic of the portfolio , BSE 200 and Sensex is given in the table below –
Source: VCK Research
5
Managing Biases: Key To Unlocking Alpha
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BACKTESTING
ALPHA
Risk Adjusted Return Analysis
Particulars Portfolio Benchmark BSE-200
Sharpe Ratio 0.57 0.36
Jensen Alpha 6.69 0.00
Information Ration 0.36 0.00
Treynor Ratio 12.9 6.3
Source: VCK Research
Source: VCK Research; Bloomberg
6
Managing Biases: Key To Unlocking Alpha
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BACKTESTING
Introduction to Omega
The above mentioned performance matrices do not capture all the
characteristics of the portfolio performance. Most of the matrices
discussed above are not robust enough for measuring
performance, since they take into account only the two moments
of returns distribution namely, the mean and variance while
ignoring the other moments like skewness and kurtosis.
A measure, known as Omega, which employs all the information
contained within the returns series was introduced by Keating &
Shadwick[1] in 2002. It can be used to rank and evaluate portfolios
unequivocally and takes into consideration all the characteristics of
the return distribution. Mathematically it can be defined as –
Omega Ratio Ω( ) =
where (a,b) is the interval of returns, r is the required rate of return
and F is the cumulative distribution of returns.
[1] Keating, C., & Shadwick, W. F. (2002). A Universal Performance Measure. Journal of Performance Measurement, 6(3), 59-84. Retrieved from http://edge-
fund.com/KeSh02a.pdf
According to Keating & Shadwick, in the simplest of terms, Omega
ratio involves partitioning returns into gain and loss above and
below a return threshold and then considering the probability
weighted ratio of returns above and below the partitioning.
Diagram 1, shows the cumulative distribution F for Asset A, which
has a mean return of 5%. The return threshold is at r=7%. I2 is the
area above the graph of F and to the right of 7%. I1 is the area
under the graph of F and to the left of 7%. Omega for Asset A at
r=7% is the ratio of probability weighted gains, I2 , to probability
weighted losses, I1[1]
By considering this Omega ratio at all values of the returns
threshold, we obtain a function which is characteristic of the
particular asset or portfolio. We illustrate this in Diagram 2. Omega
for Asset A as a function of returns from r=-2 to r=15. Omega is
strictly decreasing as a function of r and takes the value 1 at Asset
A’s mean return of 5. [1]
Thus an omega score of more than 1.0 indicates the probability of
achieving the threshold return is more than the probability of not
achieving it. The more the omega score, the better the investment
at the given level of threshold return. The omega function as
discussed above can be used to evaluate different investment
opportunities.
7
Managing Biases: Key To Unlocking Alpha
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BACKTESTING
OMEGA RATIO
The Omega Ratio chart shows clearly that our
portfolio outperformed the benchmark at the
15% threshold level. An omega score of 1.33
indicates that there is a 57% chance that the
portfolio will generate a return of 15% or
more. Compared to this the benchmark BSE-
200 had an omega score of 0.93 meaning that
there is just 48% change of the benchmark
returning 15% or more.
Another important observation is that given the
threshold return of 15%, the portfolio
outperformed the BSE-200 over most of the
distribution range, with the outperformance
increasing above the 90% annual return range.
The omega ratio chart shown above confirmed
that our portfolio outperformed the BSE-200 at
the given threshold level of 15%. However, in
order to truly evaluate the portfolio
performance vis-à-vis BSE-200, we should
compare the omega score across whole
spectrum of required return range. The Omega
Function chart shows just that. It plots the
omega score of the portfolio at various
threshold levels. From the chart, it is clear that
our portfolio outperforms the BSE-200 at all
points of required return spectrum.
Source: VCK Research
Source: VCK Research
8
Managing Biases: Key To Unlocking Alpha
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The above back testing result clearly shows that our quantitative portfolio
optimization outperformed its benchmark on all the risk adjusted
parameters. However the efficacy of Mean Variance Optimization have been
under constant debate in the last few decades. There are many proponents
both in favour and against it.
Duchin and Levy (2009) argued that M-V optimization does not beat equally
weighted (1/N) portfolios. According to them Employing the 1/N rule for
investment purposes has the disadvantage of not utilizing information on the
various parameters, but by the same token, it has the advantage of not being
biased in relying on historical parameters that may be much different from
future relevant parameters. They found that 1/N optimization does beat M-
V albeit only for small portfolios.
Do Optimization Really Work?
Optimization – A Critique
Optimization 1500 Years Ago
““““A man should always place his A man should always place his A man should always place his A man should always place his money, one third in land, a third money, one third in land, a third money, one third in land, a third money, one third in land, a third into merchandise, and keep a into merchandise, and keep a into merchandise, and keep a into merchandise, and keep a
third in hand.third in hand.third in hand.third in hand.” ” ” ” - Babylonian Talmud
The most plausible argument against optimization came from the study by DeMiguel, Garlappi, and Uppal (DGU 2009). They
demonstrated then none of the different optimization techniques are consistently better than the 1/N rule in terms of Sharpe
ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more
than offset by estimation error. They attributed the poor performance of the quantitative optimization to the length of the
estimation period and parameter instability.
Arguing in favour of optimization are Kritzman, Page, and Turkington (2010). In their paper titled “In Defense of Optimization :
The Fallacy of 1 / N” they argued that the ostensible superiority of the 1/N approach arises not from limitations in optimization
but, rather, from reliance on rolling short-term samples (60-120 months) for estimating expected returns. Even Markowitz
(1952) did not propose the use of past return for predicting future return. According to Markowitz, optimization is about the
choice of a portfolio given a set of beliefs and is not about how to form those beliefs.
The table summarize the major drawback of M-V optimization vis-à-vis 1/N optimization and the step we have taken to correct
them.
1. Duchin, Ran, and Haim Levy. 2009. “Markowitz versus the Talmudic Portfolio Diversification Strategies.” Journal of Portfolio Management, vol. 35, no. 2 (Winter):71–74.
2. DeMiguel, Victor, Lorenzo Garlappi, and Raman Uppal. 2009. “Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?” Review of Financial Studies, vol.
22, no. 5 (May):1915–1953.
3. Kritzman, M., Page, S. & Turkington, D., 2010. In Defense of Optimization : The Fallacy of 1 / N. Financial Analysts Journal, 66(2), p.31-39.
Drawbacks of MVO Our Modification
Use of short term returns data to forecast future return.We have used the BEst. Consensus target Price to compute the
expected return.
Parameter instability because of the use of small data
sets (~60-120 data points).
We have used weekly returns data for the last 5 years (259 data
points) to compute the variance of each stock and the covariance
matrix among stocks.
M-V underperforms when the portfolio is small (~10-15
stocks portfolio) because small portfolios maximises
estimation error.
We have chosen moderate sized portfolios (~24-27 stocks) and
have constrained the weight to a particular stock to a maximum of
5%.
By constraining the maximum weight of a particular stock to 5% we have ensured that our portfolio will always be moderately
sized (20 stocks at minimum) which will help us in minimizing the impact of estimation error. Also the way MVO works results
in equal weights for most of the stocks. This helps us in getting the benefits of both worlds - MVO as well as 1/N. The result of
our back testing confirms our beliefs that the above modification does help in generating alpha.
9
Managing Biases: Key To Unlocking Alpha
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Current Portfolio
The current portfolio as per our
optimization is given below. We
believe that our portfolio is
optimally diversified with adequate
upside potential and descent risk
reduction. Our portfolio covers
most of the prominent sectors in
India and no single sector have
more than ~20% weightage in the
portfolio which protects our
portfolio from sector specific
shocks.
Particulars Value
Expected Return - 24.96%
Expected Risk (σ) - 32.15%
Beta (β) - 0.89 X
Stocks Weights Stocks Weights
Andhra Bank 4.38% India Cements Ltd 4.38%
Apollo Hospitals Enterprise Ltd 4.38% Indian Bank 4.38%
Aurobindo Pharma Ltd 4.38% Indian Oil Corp Ltd 4.38%
Bank of Baroda 4.38% Jaiprakash Power Ventures Ltd 4.38%
Bharat Electronics Ltd 4.38% MAX India Ltd 4.38%
Bharti Airtel Ltd 4.38% PTC India Ltd 4.38%
Britannia Industries Ltd 4.38% Reliance Infrastructure Ltd 4.38%
Cadila Healthcare Ltd 4.38% Sintex Industries Ltd 2.15%
Dr Reddy’s Laboratories Ltd 4.38% Syndicate Bank 1.44%
GSK Pharmaceuticals Ltd 0.78% Torrent Power Ltd 4.38%
GMR Infrastructure Ltd 4.05% Union Bank of India 3.94%
Gujarat State Petronet Ltd 4.38% United Phosphorus Ltd 4.38%
Hero Motocorp Ltd 4.38%
Source: VCK Research; Bloomberg
Source: VCK Research; Bloomberg
10
Managing Biases: Key To Unlocking Alpha
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Portfolio Fundamentals
Port Bench +/- Port Bench +/- Port Bench +/-
Utilities 1.91 1.93 -0.02 100.81 117.93 -17.12 7.64 10.35 -2.70
Banks 4.35 1.62 2.73 218.51 244.06 -25.55 10.82 11.82 -1.00
Capital Goods 0.75 1.28 -0.53 194.09 181.55 12.54 13.29 11.20 2.10
Pharma 0.96 0.84 0.12 70.89 37.44 33.44 12.08 13.66 -1.58
Materials 2.27 1.54 0.73 76.06 70.96 5.09 5.14 7.04 -1.91
Autos 4.14 1.85 2.28 23.58 94.13 -70.56 8.44 6.54 1.90
Energy 3.77 1.96 1.82 123.59 53.19 70.40 5.60 6.04 -0.43
FMCG 1.81 1.57 0.24 147.61 56.43 91.18 16.48 17.33 -0.85
Health Care 0.64 1.30 -0.66 29.89 45.56 -15.67 20.09 11.55 8.54
Telecom. 0.38 0.39 -0.01 136.38 125.84 10.54 6.25 6.41 -0.16
Port Bench +/- Port Bench +/- Port Bench +/-
Utilities 0.86 1.35 -0.49 7.32 13.95 -6.63 10.12 10.80 -0.68
Banks 0.64 1.72 -1.09 3.70 10.28 -6.57 17.89 16.42 1.48
Capital Goods 1.12 2.02 -0.90 21.10 14.80 6.30 4.00 13.77 -9.76
Pharma 2.59 4.09 -1.50 59.82 34.76 25.06 20.29 10.16 10.13
Materials 0.80 1.29 -0.49 8.21 9.76 -1.55 10.42 15.08 -4.67
Autos 8.23 2.68 5.55 13.92 9.17 4.75 66.18 31.85 34.33
Energy 0.93 1.41 -0.48 12.40 9.80 2.60 7.15 16.52 -9.38
FMCG 12.54 7.28 5.26 24.10 30.16 -6.06 54.47 24.18 30.29
Health Care 3.07 2.49 0.58 31.84 10.93 20.91 10.01 21.26 -11.25
Telecom. 1.80 1.24 0.55 20.02 22.30 -2.28 8.55 4.90 3.65
ROE
Sectors
Sectors
Div Yld Debt/Equity EV/EBITDA
P/B P/E
Source: VCK Research; Bloomberg
11
Managing Biases: Key To Unlocking Alpha
[email protected] VCK Research reports are available on Bloomberg VCKR <Go>
Portfolio Stress Testing
-39% 88%
In the model portfolio that we have created, the expected Risk and Return are dependent on various factors. For example, if the
expected return changes, the Risk and Return characteristics of the portfolio will also change. In order to stress test the portfolio
and see what is the likely Risk-Return characteristics that we can expect, we have run a Monte Carlo Simulation on the portfolio.
We have done a 3,000 run Monte Carlo simulation by using the theoretical distribution of the various variables and their mean
and dispersion. Our simulation shows that we can expect a return of 24.83% with a risk of 32.57%.
Parameter Modifier Distribution
Expected Return Natural Log of Expected Return ln(x) Normal
Source: VCK Research
12
Managing Biases: Key To Unlocking Alpha
[email protected] VCK Research reports are available on Bloomberg VCKR <Go>
Portfolio Stress Testing
However, in the real world, people are more concerned about downside volatility rather than upside potential. So, we have
calculated the probability of incurring a loss and also the probability of not getting the expected return using the parameters
from our Monte Carlo simulation. The result is summarised below –
Particulars Value
Probability of Loss 22.36%
Probability of return less than 8% 30.5%
Probability of return less than 15% 38.21%
Thus, even from a safety first approach, the portfolio is quite desirable. The probability of loss in all the three scenarios is well
within respectable limits. Thus, to sum up, we can say that even after stress testing, the risk-return characteristics of the portfolio
is quite appropriate.
Value-at-Risk (VaR) Analysis
Methodology – Daily VaR 95% VaR 97.5% VaR 99% VaR
Monte Carlo Simulation VaR 6.63% 8.28% 10.69%
Historical 1 Year Simulation VaR 7.68% 9.84% 13.38%
Historical 2 Year Simulation VaR 7.23% 9.57% 11.95%
Historical 3 Year Simulation VaR 6.94% 8.88% 11.03%
Parametric VaR 6.94% 8.27% 9.81%
Source: VCK Research; Bloomberg
Source: VCK Research
13
Managing Biases: Key To Unlocking Alpha
[email protected] VCK Research reports are available on Bloomberg VCKR <Go>
Key to our Recommendation Structure
BUY Absolute) Stock expected to give a positive return of above 15% over a 1 year horizon
SELL (Absolute) Stock expected to give a negative return of less than (-5%) over a I year horizon
ACCUMULATE Stock expected to give a positive return between 5%-15% over a 1 year horizon
REDUCE Stock expected to give a return in the range of (-5%) to 5% over a 1 year horizon
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