1. A Research Paper in Partial Fulfilment of Dissertation Project
On
“Study of Creating Portfolios Based on the Risk Profile of
Investors”
Submitted By:
Ashish Agarwal
Roll No: 121115
MBA FT (II)
Faculty Guide: Prof. Neeraj Amarnani.

2. Abstract
This is a study of the portfolios of different investors based on their risk aversion and
behavioural portfolio that the investor has in his mind. The main objectives of this research
are to estimate the risk aversion and classify the investors into different categories and
profile them. To achieve this we have done a primary survey using a standard risk ruler and
undertook a discriminant analysis to verify the results. It gives 98% accuracy in categorizing
the investors into different groups. The profiling of the investors have also been done and
risk return characteristics based on S&P 500 and risk free investment vehicles have been
done. Much further detailed profiling can be done by probing the customer further.
Introduction
With the dramatic growth in the number of investment avenues where a saver can park his
money to transfer money from the present to the future, investment decision has no longer
become simple one. The financial system has become a complex one which aims at allocation
of capital to the best uses. Little effort has been to detail the investment advice given by
banks and other financial institutions to the investors who wish to gain maximum out of their
capital. Also measurement of the risk aversion is not an easy task as it may be subjective and
may vary from investor to investor or different classes of investors. While theories of
portfolio selection have been developed, very little is known about how individuals actually
go about constructing their asset portfolios. Also the investment advisors recommend
changing the portfolios to suit the needs but individual investors sometimes do not
understand where to invest in order to satisfy the need. Also some investors have their
reservations regarding a particular investment vehicle. Here we come into the realm of
behavioural portfolio theory. Mean–variance investors consider their portfolios as a whole. In
contrast, behavioural investors begin by dividing the whole of their portfolios into mental
accounts, each dedicated to a particular goal and each with its own time horizon for example:
retirement, children’s education and maybe bequeathing. Firstly we need to understand the
concept of risk and how the risk arises. Risk can be defined as uncertainty in the outcome of
the desired output. It may be due to the volatility in the market or may be due to some factors
which are beyond the control of the investor. It may be due to the irrationality present in the
market and the behavioural biases which may cause a deviation from the actual. This
irrationality may cause loss to the rational investors. Theoretically we always assume that all
the investors are risk averse and demand a higher return per extra risk assumed which we

3. generally denote as a risk premium. Basically every investor is different and has different
degrees of aversion towards risk. Risk aversion is also determined by the purpose for which
the investment is done and life stage in which the investor is currently. We need to take into
account these all factors before we can go forward and estimate the risk profile of an investor
or a class of investor and our choice of portfolio should resonate the risk the investor or rather
the class of investor is willing to undertake.
Objectives
Some major objectives of this paper are as follows:
1. To classify the different classes of investors based on their risk taking abilities and
determine the preferences for allocation of portfolios.
2. To gain an insight into the way the different investors evaluate and select the different
investment vehicle for the purpose of investment.
3. To study and estimate the risk aversion of different class of investors.
4. To create the risk return profile of the different classes of investors.
Literature Survey
Markowitz’s mean–variance portfolio theory has been preferred by the investors due to its
logic and practicality but internally an investor or rather a saver has made mental accounts to
cater to the investments needs and each accounts may have a different level of risk aversion
and may lie in different portion of the Markowitz’s efficient portfolio frontier (Das et. al.
2010). Cass and Stiglitz have analyzed theoretically the effects of changes in wealth on risk-
bearing behaviour in the presence of multiple risky assets. They have also shown necessary
and sufficient conditions for individual portfolios to consist of combinations of a riskless
asset and a portfolio of risky assets, in the same context.
Asset allocation strategies yield a superior dispersion in returns than security selection
strategies, especially during economic crises. The most important periods for asset allocation
from 1991 to 2011 were February 1991, during the Gulf War; August 1998, when Russia
defaulted; March 2000, the beginning of the bursting of the dotcom bubble; and September
2008, when Lehman Brothers collapsed near the start of the subprime mortgage crisis. Asset
allocation is more important than security selection, especially in times of greater volatility in
the markets. (Rau R. March 2013). As stated by Graham and Dodd “The stock market is not a

4. weighing machine, on which the value of each issue is recorded by an exact and impersonal
mechanism. Rather it is like a voting machine, whereon countless individuals register choices
which are the product partly of reason and partly of emotion.” (1934, p. 23).
A Wharton survey contributed empirical data for the study of these research streams by
examining how demographic variables influence the investment selection and portfolio
composition process, and Blume and Friend (1978) provided a comprehensive study and
overview of the Wharton survey results and its implications for behavioural finance.
Furthermore, Cohn et al. (1975) provided tentative evidence that risk aversion decreases as
the investor’s wealth increases, while Riley and Chow showed that risk aversion decreases
not only as wealth increases, but also as age, income and education increase. LeBaron,
Farrelly and Gula (1992) added to the debate, by advocating that individuals’ risk aversion is
largely a function of visceral rather than rational considerations. Some of the factors which
affect the investor’s decision(in order of significance) are accounting information, personal
opinion, neutral information like coverage in the press and recent price movements, advocate
recommendations and lastly personal financing needs.(The Case Of The Greek Stock
Exchange, Journal of Applied Business Research, Volume 20, Number 4). All individuals
exhibit decreasing relative risk aversion, the relative risk aversion of single women is
significantly greater than that of married couples. Compared to the oldest group in the sample
(over 65), the younger households have higher allocations to risky assets. Individuals with
higher measures of risk aversion (based on income risk) are found to have higher risky
allocations of wealth after controlling for other factors, although the statistical significance of
this result is fairly low. This result is consistent with the work of Jianakoplos and Bernasek
(1998) who find that stated risk tolerance in the Survey of Consumer Finances is not
correlated with the same individuals’ portfolio choices. As compared to the highest wealth
quartile, lower wealth quartiles allocate a lower proportion to risky assets when housing
wealth is not included, but a higher proportion when housing wealth is included. (Evidence of
Risk Aversion in the Health and Retirement Study, Bajtelsmit V.L. 1999). Morin and Suarez
[1983], in a cross-sectional study of 14,034 Canadian households surveyed in 1969 find
evidence of increasing risk aversion with age although the households appear to become less
risk averse as their wealth increases. Shorrocks [1982] used a survey of UK households’ finds
cash and savings increase with age. Bossons[1973] also finds similar results using the 1962
survey.

5. Research Methodology
The research is a primary survey in which there will be a questionnaire which measures the
risk quota of the individual investors based on some questions asked. This questionnaire will
help us in understanding the risk aversion of different classes of investors and the factors
which have a significant influence on the asset selection criterion of the individual investor.
The sample data consists of people from diverse backgrounds, profession and income levels
and their risk profile will be determined based on their responses and their preferences. The
questionnaire is a standard questionnaire developed by Fidelity Investments. It consists of 12
questions which measures the attitudes of investors towards risk and towards the type of
investments preferred by him. This is the starting point of discussion between the investor
and the financial planner to help evaluate the investor’s tolerance of risk. The scoring is done
using a coding in which for every ‘a’ answer we give 1 point, 2 points for every ‘b’, 3 points
for every ‘c’, 4 points for every ‘d’ and 5 points for every ‘e’. The sample size that I have
taken is of 50 respondents which consist of people with different net worth and different age
groups with different perceptions about the markets and their risk taking abilities.
Now we export the data into SPSS and undertake a discriminant analysis using categorical
variable as DV and all other factors as IV to check whether the classification is accurate.
After classifying the categories we will do a descriptive study of each of the category and
would profile each category. Also we will get a discriminant equation which can also be used
to club the investors into different categories. Next we profile them based on their risk return
profile.
Analysis and Results
Based on the questionnaire we identified 12 variables which should have an effect on the
allocation of funds to create a portfolio. These variables are scale variables. The descriptions
of the variables are as follows:
Salary Expectation (sal_exp): Future expectation of the salary by the individual.
Retirement Plan (retire): Measure whether for retirement a person chooses stability or
higher returns.
Stock Market Perception (st_mrkt): The investors’ perception about the stock markets.

6. Stock Choice Criteria (st_crit): The investor’ stock selection criteria
Child education funding (child_edu): How risk averse an investor is about his children’s
education.
No of Dependents (dep): The number of dependents to support.
Retirement Years Left (ret_yr): The no of years remaining for retirement (An indirect
reference to age).
Net Worth (net_worth): The net worth of the investor.
Emergency Savings (savings): The emergency savings of the investor for emergency
purposes.
Mutual Funds or Individual Stocks (mut_funds): Does the investor prefer mutual funds or
individual stocks.
Debt Reduction (debt_reduce): Does the investor want and require debt reduction.
Low Return Vs High Risk (risk_ret): Will the investor settle for low returns for low risk
assumption.
These are the IV’s now we get a DV after calculating the total and putting the criteria. The
DV is:
Risk Category (Category): This is the dependent variable and the ordered with 5 levels with
1 being the most risk averse and 5 being the most risk loving.
We will divide this analysis into two types of results.
Classification results:
Classification Results(a)
Category
Predicted Group Membership Total
Cat1 Cat2 Cat3 Cat4 Cat5 Cat1
Original Count Cat1 6 0 0 0 0 6
Cat2 0 12 0 0 0 12
Cat3 0 0 11 1 0 12
Cat4 0 0 0 15 0 15
Cat5 0 0 0 0 5 5
% Cat1 100.0 .0 .0 .0 .0 100.0
Cat2 .0 100.0 .0 .0 .0 100.0

7. Cat3 .0 .0 91.7 8.3 .0 100.0
Cat4 .0 .0 .0 100.0 .0 100.0
Cat5 .0 .0 .0 .0 100.0 100.0
a 98.0% of original grouped cases correctly classified.
We see that 98% of our results are being classified successfully so we can say that the model
is viable as it correctly separates the different categories based on the variables and our
model.
Cannonical Discriminant Functions:
The categorical variable has 5 levels hence we have 4 different discriminant functions.
Eigenvalues
a First 4 canonical discriminant functions were used in the analysis.
We see that function 1 has a very high eigenvalue of 15.225 which is a good sign as it
denotes that the function 1 has discriminated the different categories substantially so it is a
very good measure. The other functions are not that good so we will take the function 1
which discriminates the categories.
The discriminant function is as follows:
This is the equation which can also be used to predict the categories of different investors
based on the functions of group centroids:
Function Eigenvalue % of Variance Cumulative %
Canonical
Correlation
1 15.225(a) 95.7 95.7 .969
2 .362(a) 2.3 98.0 .515
3 .192(a) 1.2 99.2 .401
4 .125(a) .8 100.0 .333
D= -24.830 + .626*risk_net + .7*debt_reduce + .807*mut_funds + .653*savings + .
733*net_worth + .668*ret_yr + .519*dep + .789*child_edu + .881*st_crit + .
295*st_mrkt + .434*retire + .718*sal_exp

8. Functions at Group Centroids
Category
Function
1 2 3 4
Cat1 -6.681 -.111 .427 .579
Cat2 -2.963 -.472 -.418 -.305
Cat3 .242 .566 .440 -.345
Cat4 2.755 .379 -.354 .262
Cat5 6.284 -1.227 .498 .080
Unstandardized canonical discriminant functions evaluated at group means
These values show the optimum level at which the ‘D’ value should be to get classified into
different risk categories.
Profiles of Different Categories and Risk Return Estimates
Category 1 (Highly Risk Averse): They are not very optimistic that their salary would rise
greatly. Stability and fixed yield is their main motto of investment. They are of the perception
that investing in stock market is only a game of chance or a gamble. They are very averse
about fund allocation and safety of principal. They also have a lot of dependents to support.
They are in their end of the careers and may be of the age groups >48 and above. They have a
net worth of around 50 lakhs. Emergency funds are limited to 3-4 months of salary, not very
safe and would happily accept lower returns if risk is lower. The optimal allocation in stocks
for this group would be 0-15% rest for simplicity has been taken to be invested in risk free
assets with a return of 8% (Government Bonds) in Indian context. Min Return: 8% Min
Risk: 0% (All investment in risk free.) Max Return: 9.5% Max Risk: 4.87%.
Category 2 (Risk Averse): They hold a neutral view that their salary would rise greatly.
Stability and fixed yield still remains main motto of investment. They hold a neutral view
about that investing in stock market is only a game of chance or a gamble. They are a little
averse about fund allocation and safety of principal is demanded though to a letter extent.
They also have dependents to support. They are in their mid of the careers and may be of the
age groups 40 and above. Here increasing net worth becomes prime importance. They have a
net worth of less than 50 lakhs.and lesser than 70 lakhs, emergency funds are limited to 6-8
months of salary, somewhat safeand would reluctantly accept lower returns if risk is lower.
The optimal allocation in stocks for this group would be 16%-30% rest for simplicity has
been taken to be invested in risk free assets with a return of 8% (Government Bonds) in
Indian context. Min Return: 9.6% Min Risk: 5.2% Max Return: 11% Max Risk: 9.75%

9. Category 3 (Risk Indifferent): They hold a slight optimistic view that their salary would
rise greatly. They hold a neutral view about stability and fixed yield as the main motto of
investment. They hold a neutral view about that investing in stock market is only a game of
chance or a gamble. They are neutral about fund allocation and safety of principal is
demanded though corporate bonds which may have a slight degree of risk. They have less
number of dependents to support. They are in their later growth phase of the careers and may
be of the age groups 33 and above. Here growth is more important for them. They have a net
worth of lesser than 50 lakhs but upside potential is higher. Emergency funds are limited to 5-
7 months of salary, somewhat safe and would reluctantly accept lower returns if risk is lower
but greater probability towards higher returns and high risk. The optimal allocation in stocks
for this group would be 31%-45% rest for simplicity has been taken to be invested in risk free
assets with a return of 8% (Government Bonds) in Indian context. Min Return: 11.1%
Min Risk: 10.1% Max Return: 12.5% Max Risk: 14.6%.
Category 4 (Risk Loving): They hold an optimistic view that their salary would rise greatly.
Stability and fixed yield is not the main motto of investment. They want returns. They hold a
negative about that investing in stock market is only a game of chance or a gamble. They
look upon stock market as a money making machine. They are aggressive about fund
allocation and high returns on principal is demanded though stocks investments which may
have a higher degree of risk. They have less number of dependents to support. May be in a
nuclear family or more than one breadwinners so they are risk tolerant. They are in their
middle growth phase of the careers and may be of the age groups 28-32 and above. Here
growth is more important for them. They have a net worth of lesser than 50 lakhs but upside
potential is higher. Emergency funds are limited to 7months-1 year of salary, safe and would
not accept lower returns if risk is lower have an appetite for higher returns and high risk. The
optimal allocation in stocks for this group would be 46%-70% rest for simplicity has been
taken to be invested in risk free assets with a return of 8% (Government Bonds) in Indian
context. Min Return: 12.6% Min Risk: 14.95% Max Return: 15% Max Risk: 22.75%.
Category 5 (Highly Risk Loving): They hold a highly optimistic view that their salary
would rise greatly. Stability and fixed yield is not at all a motto of investment. They want
higher returns on investments. They hold a highly negative about that investing in stock
market is only a game of chance or a gamble. They look upon stock market as a money
making machine. They are highly aggressive about fund allocation and high returns on
principal is demanded though stocks investments which may have a higher degree of risk.

10. They have less number of dependents to support or may be in a nuclear family or more than
one breadwinner so they are risk tolerant. They may also have lot of idle funds to invest so
they can assume higher losses and not back out. They are in their initial or middle growth
phase of the careers and may be of the age groups 28-32 and above. Here growth is more
important for them. One more criteria may be that net worth being higher they can afford to
take greater risks or this factor may get diluted in that case. They have a net worth of between
1 crore to 5 crore so lot of idle funds or excess funds to invest. Emergency funds are limited
to 2-6 months of salary may be because they invest everything as they have lot of capital at
their disposal and would never lower returns if risk is lower have an appetite for higher
returns and high risk. They would have benchmarked their investment to match the returns
required. The optimal allocation in stocks for this group would be 70%-100% rest for
simplicity has been taken to be invested in risk free assets with a return of 8% (Government
Bonds) in Indian context. Min Return: 15.1% Min Risk: 23.1% Max Return: 18%
Max Risk: 32.5%
Conclusion
We conclude by saying that different investors have different preferences and needs. We also
saw that different investors have different goals and different perceptions based on their age,
salary expectation, perception about different vehicle based on past experiences. We need to
take into account before suggesting a portfolio to him. We also need to look at his investment
horizon and investment goals before investing so broad categorization of investors on the
basis of risk aversion is the first process in the financial planning exercise. After the broad
planning we have the asset allocation after that we can go for the individual stock allocation
which has not been covered in this study but we can undertake the same process by further
probing and re visiting the investor and discussing different vehicles in detail. There is a
scope of future study with respect to that. Thus, we finally conclude saying that risk and
return depends upon the investor at hand and every investor must be catered to specifically
after categorizing them into a broad class and then detail his portfolio accordingly. The model
which is made here will help to broadly classify the investor based on some variables and we
have much scope of improvement by refining the variables taken by adding and removing
some variables.

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