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TRANSCRIPT
CHAPTER 1
INTRODUCTION
1.1.Introduction
A portfolio is a collection of financial assets consisting of investments tools
such as stocks, bonds, gold, Forex exchange, assets-backed securities, real
estate certificates and bank deposits which are held by a person or group of
persons. The basic motive behind portfolio construction is risk dispersion.
Since the returns on the assets constituting a portfolio do not move in the same
direction, the risk of the portfolio will be lower than that of a single asset.
Therefore the portfolio management approach is based on the rule of increasing
the number of assets in a portfolio.
1.1.1. Approaches in Portfolio Construction
Commonly there are two approaches in the construction of portfolio
Traditional approach
Markowitz efficient frontier approach.
The common practice in the traditional approach is to evaluate the entire
financial plan of the individual. In the modern approach, portfolios are
constructed to maximize the expected return for a given level of risk. It
views portfolio construction in terms of the expected return and the risk
associated with obtaining the expected return. This can be applied more in
the selection of common stocks portfolio than the bond portfolio.
1.1.2. Modern Approach
The current study follows the modern approach for portfolio construction. The
stocks are selected on the basis of need for income or appreciation. But the
selection is based on the risk and return analysis. Return includes the market
return and dividend. They are assumed to be indifferent towards the form of
return. In constructing the stock portfolio, the following steps are adopted:
Selection of sectors
Selection of companies
Determining the size of participation
1.1.3 Sharpe Index Model
This ratio was developed by William Forsyth Sharpe in 1966. Sharpe
originally called it the "reward-to-variability" ratio before it began being
called the Sharpe Ratio by later academics and financial operators. The Sharpe
ratio is used to characterize how well the return of an asset compensates the
investor for the risk taken, the higher the Sharpe ratio numbers the better.
When comparing two assets each with the expected return E[R] against the
same benchmark with return Rf, the asset with the higher Sharpe ratio gives
more return for the same risk. Investors are often advised to pick investments
with high Sharpe ratios.
Strengths
It is directly computable from any observed series of returns without
need for additional information surrounding the source of profitability.
The returns measured can be of any frequency), as long as they are
normally distributed, as the returns can always be annualized.
Drawbacks
Herein lies the underlying weakness of the ratio - not all asset returns
are normally distributed.
Sometimes it can be downright dangerous to use this formula when
returns are not normally distributed.
1.2 Need for Study
Diversification of investments helps to spread risk over many assets. A
diversified portfolio has lower risk when compared to undiversified portfolio
and hence the return is also higher for a diversified portfolio. While
considering many stocks for a portfolio, some may yield a higher return while
some may yield lower returns. So the stocks must be carefully chosen so that
an optimum portfolio is built. Study of different stocks using Sharpe index
model helps to decide on the amount of investments to be made in each stock
based on their risk and return
1.3 Objectives of the study
Primary Objective
To construct a portfolio of stocks from the selected companies using
Sharpe Single Index Model, that maximizes the return and minimizes
the risk associated with the individual stocks.
Secondary Objectives
To analyze the risk and return of each stock under study
To know the proportions to invest in each security, through cut-off
point, through Sharpe index model.
1.4. Scope of the Study
To compare the performances of the 15 selected companies of the five
different sectors.
The application of the Sharpe Index model to do the risk and return
analysis.
It provides information to the investors about the risk and return
associated with each of the selected companies.
It provides the investor the optimum portfolio of the selected stocks.
1.5 Limitations of the study
The study is limited to 15 companies from 5 sectors, hence cannot be
generalized for the entire stocks available in the market.
The data remain restricted to the past five years (2005-2006 to 2009-
2010).
The data cannot be used to predict future trends in price movement or
other performance’s of the market or the individual stocks.
CHAPTER 2
REVIEW OF LITERATURE
Ayhan Kapusuzoglu and Semra Karacaer(2009), “the process of
stock portfolio construction with respect to the relationship between index,
return and risk evidence from turkey”, this study was conducted to
demostrate the effect of the relationship between the elements of index, return
and risk on the overall process of portfolio construction by the investors. The
researcher has selected stocks of an annual number of 30 firms publicly-traded
in the istanbul stock exchange national 100 index during the period august
2004-2007. It was found that the risk levels increased for the portfolio
constructed with 1% and 5% increases in the index returns, and that the
portfolio with high risk levels had also higher returns. It was further concluded
that he three most preferred stocks in the portfolios are the stocks IZCOM,
PRTAS and DEVA.
Giordano Pola and Gianni Pola (2009), “A Stochastic reachability
approach to portfolio construction in finance industry” In this paper the
authors propose one approach to optimal portfolio construction based on recent
results on stochastic reachability, which overcome some of the limits of current
approaches. Given a sequence of target sets that the investors would like their
portfolio to stay within, the optimal portfolio allocation is synthesized in order
to maximize the joint probability for the portfolio value to fulfil the target sets
requirements. A case study in the US market is given which shows benefits
from the proposed methodology in portfolio construction. A comparison with
traditional approaches is also included in the paper.
Gerald Kohers and Ninon Kohers and Theodor Kohers(2006),
“The risk and return characteristics of developed and emerging stock
markets: the recent evidence”, Finance theory suggests that the higher
volatility typically associated with emerging stock market returns translates
into higher expected returns in those markets. This study compares the risk
and return profile of emerging and developed stock markets over the period
from 1988 through April 2003. Specifically, this study investigates whether a
difference in risk characteristics exists between the two markets and whether
the realized rates of return in these two types of markets reflect these risk
characteristics. The results show that the risk associated with emerging
markets, as measured by the standard deviation of returns, is higher than the
risk in developed markets in most periods. Also, the returns in emerging
markets have been higher than those in developed markets for most of the time
frames examined. The findings suggest that risk-averse investors seeking
higher returns in emerging markets have been compensated for assuming the
higher risk associated with these markets.
Maria Bohdalova (2007), “A comparison of value-at-risk methods
for measurement of the financial risk”, in this study some methods that use
classical approach, and that uses copula approach computing VaR is studied.
The results produced by a VaR model are simple for all levels of staff from
areas of an organization to understand and appreciate. Form the study it was
found that VaR provides a consistent measure of risk across all types of
positions and across all kinds of markets and risk factors. Another finding is
VaR can take into account interrelationship between different risk factors
Ana Gonzalez and Gonzalo Rubio (2007), “portfolio choice and the
effects of liquidity”, this paper shows how to introduce liquidity into the well
known mean-variance framework of portfolio selection. Either by estimating
mean- variance liquidity constrained frontiers or directly estimating optimal
portfolio for alternative levels of risk aversion and preference for liquidity, we
obtain storng effects of liquidity on optimal portfolio selection. In particular,
portfolio performance, measured by the sharpe ratio relative to the tangency
portfolios, varies significantly with liquidity. Moreover, although mean-
variance performance becomes clearly worse, the levels of liquidity are much
lower than on those optimal portfolios obtained when there is a positive
preference for liquidity are much lower than on those optimal portfolios where
investors show no sign of preference for liquidity
Syed A. Basher and Perry Sadorsky(2007), “Oil price risk and
emerging stock markets”, The purpose of this paper is to contribute to the
literature on stock markets and energy prices by studying the impact of oil
price changes on a large set of emerging stock market returns. The approach
taken in this paper uses an international multi-factor model that allows for
both unconditional and conditional risk factors to investigate the relationship
between oil price risk and emerging stock market returns. This paper, thus,
represents one of the first comprehensive studies of the impact of oil price
risk on emerging stock markets. In general we find strong evidence that oil
price risk impacts stock price returns in emerging markets. Results for other
risk factors like market risk, total risk, skewness, and kurtosis are also
presented. These results are useful for individual and institutional investors,
managers and policy makers.
Debasish Dutt(2005), “ constructing an optimal portfolio using
sharpe’s single index model”, this paper attempts to construct an optimal
portfolio by applying sharpe’s single index model of capital asset pricing.
Taking BSE 100 as market index and considering daily indices for the Oct ’02-
April ’03 period, the proposed method formulates a unique cut off point and
selects stocks having excess of their ecpected return over risk free rate of return
surpassing this cut off point. In found out that ll the stock selected where bank
stocks. Another result is that the portfolio variance is substancially lowr than
the variances of any of the individual stocks in the portfolio and the portfolio
return is higher than the expected returns of the individual stocks in the
portfolio.
Jeroen Derwall(2009), “Portfolio concentration and the
fundamental law of active management” Concentrated funds with higher
levels of tracking error display better performance than their more broadly
diversified counterparts. We show that the observed relation between portfolio
concentration and performance is mostly driven by the breadth of the
underlying fund strategies; not just by fund managers’ willingness to take big
bets. Our results indicate that when investors strive to select the best
performing funds, they should not only consider fund managers’ tracking error
levels. It is of greater importance that they take into account the extent to
which fund managers carefully allocate their risk budget across multiple
investment strategies and have concentrated holdings in multiple market
segments simultaneously.
Sitikantha Pattanaik and Bhaskar Chatterjee (2000), “Stock
Returns and Volatility in India: An Empirical Puzzle?” In this paper the
researchers have concluded that the behaviour of equity premiums in India
shows that long term investors do get compensated for the systematic risk they
bear by holding equities. In the short to medium run, however, both the direct
and the indirect test suggested by French, Schewart and Stambaugh (1987) fail
to establish the expected risk-return relationship for Indian equities. Dominance
of short horizon players in the market and the associated avoidable volatility in
the equity market obscures the implications of monetary policy for the equity
cost of capital in India.
Anna Morrell(2010), “The Art and Science of Portfolio
Construction” Rather too many of us, I suspect, have portfolios that are just
collections of haphazardly acquired shares. As with asset allocation, so with
portfolio construction, you need to sit down first and do some thinking. What
is your preferred level of risk? It has to be moderately high for you to consider
getting involved in equity investment, but are you willing to take larger risks -
for instance, investing in AIM companies - for greater gains, or do you take a
more conservative approach?
That's a balance between how many stocks you can research and keep on top
of, and how many stocks you need to achieve the benefit of diversification
reducing your overall risk. That will differ from person to person, and it will
also be different depending on whether you use funds and ETFs to gain
broader exposure, or whether your portfolio is entirely equity focused.
Gupta, K. Locke, S. and Scrimgeour, F. (2009), “Can Momentum
Returns be Optimised?” This paper reports on an investigation of various
techniques to optimise momentum returns from share trading. Eight different
processes are applied to share returns from five countries, using United States
dollars as the common currency. The aim is to determine whether one method
is clearly superior to other algorithms in maximising the momentum returns
for the synthesised portfolios over a period of time. This is the first study of its
type where optimising programmes are applied to momentum returns and
portfolio selection. The analysis includes varying lengths of time periods with
the longest data set pertaining to the United States, covering the period 1973-
2007 and the shortest is India ranging from 1993 to 2007. The five countries
under investigation are Canada, India, Japan, United Kingdom, and the United
States. The practical importance of the research relates to the potential to
increase profits from trading using a momentum strategy through superior
information processing which in turn will generate greater returns for specified
risk levels.
CHAPTER 3
RESEARCH METHODOLOGY
3.1. Research Design
A descriptive study on the construction of portfolio of stocks with
reference to Sharpe’s single index model is carried out in this project.
Descriptive study is undertaken in order to ascertain and describe the
characteristics and association of the variables of interest in a situation. The
study is aimed at understanding the risk and return associated with different
stocks and the construction of an optimal portfolio that maximizes the overall
profit of the investment.
3.2. Time Horizon
The study is conducted with the past five years data from 2005-2006 to
2009-2010.
3.3. Method of Data Collection
Secondary Data
The study uses the secondary data collected from various sources such
as NSE website and the RBI website.
3.4. Sample
3.4.1. Sampling Technique
The sampling technique adopted is ‘purposive sampling’. Sampling is
done with the purpose of evaluating the risk and return variations.
3.4.2. Sample Size
The sample size is 15. They are a combination of stocks from five
different sectors namely, Automobile, Communications, FMCG, Oil and
Natural Gas, and Steel sector, with three companies in each sector.
3.4.3 List of Companies under Study
Automobile Communicatio
n
FMC
G
Oil &
Natura
l Gas
Steel
Ashok Leyland Airtel Dabur GAIL JSW
Tata Motors GTL HUL IOC SAI
L
Mahindra &
Mahindra
Tata Comm ITC ONGC Tata
Steel
Table 3.1 List of companies under study
All of the companies under study are listed in the National Stock Exchange.
3.5. Tools for Analysis
Beta Coefficient
Beta coefficient is the relative measure of non-diversifiable risk. It is an
index of the degree of movement of an asset’s return in response to a change in
the market’s return.
Beta , β=Correlation∗σ (Y )
σ (X)
Where, σ (Y ) = Standard Deviation of Individual Stock
σ (X ) = Standard Deviation of Market
Return
The total gain or loss experienced on an investment over a given period
of time, calculated by dividing the asset’s cash distributions during the period,
plus change in value, by its beginning-of-period investment value is termed as
return.
Return=Toda y' smarket price−Yesterda y ' s market price
Yesterda y ' s market price
Efficient Portfolio
A portfolio that maximizes return for a given level of risk or minimizes
risk for a given level of return is termed as an efficient portfolio.
Correlation
A statistical measure of the relationship between any two series of
numbers representing data of any kind is known as correlation.
Risk-free Rate of Return (RF)
Risk-free rate of return is the required return on a risk free asset,
typically a three month treasury bill.
Excess Return−Beta Ratio=Ri−R fβ i
Where, Ri = the expected return on stock i
R f = the return on a riskless asset
β i = the expected change in the rate of return on stock associated with
one unit change in the market return.
C i=σ m2
∑i=1
N (R¿¿ i−R f )β iσei
2
1+σ m2∑i=1
N β i2
σei2
¿
Where, σ m2 = variance of the market index
σ ei2 = variance of a stock’s movement that is not associated with the
movement of market index i.e. stock’s unsystematic risk.
X i=Z i
∑i=1
N
Z i
Where,
X i, is the proportion of investment of each stock
and
Zi=β iσei
2 (R i−Rfβi−C¿)
Where, C ¿ = the cut-off point.
CHAPTER 4
ANALYSIS AND INTERPRETATION
4.1 Comparison Of Market Return To Scrip Return
SCRIP RETURN(%) Standard
deviation
Beta
Ashok Leyland 151.196 3.031268 0.931111
Mahindra &
Mahindra
97.387 3.559291 0.981576
Tata Motors 117.642 3.159233501 1.082697884
Airtel 98.414 3.003404 0.904593
GTL 174.977 2.436876 0.455453
Tata
Communications
105.236 3.348978 1.06014
Dabur 104.093 3.065719 0.521145
HUL 88.812 2.182428 0.578617
ITC 35.158 3.42632 0.675516
GAIL 113.313 2.798112 0.844169
IOC 20.1966 2.97808498 0.62018769
ONGC 65.804 2.617362 0.911309
JSW 211.899 3.895991 1.242796
SAIL 216.518 3.607318 1.365418
Tata Steel 119.932 3.508721375 1.332412772
MARKET (index) 116.6209 1.948668
Table 4.1 Comparison of market return to scrip return
INTERPRETATION
SAIL yielded the highest return and IOC yielded the lowest return. When
compared to market nine scrips yielded a lower return and the rest were
comparatively better than the market. Apparently the risk is also high. The
unsystematic risk of all the scrips is high when compared to market risk of
1.948. Beta is less than one for five scrips which means that the systematic
risk is comparatively less.
4.2 Excess Return To Beta Ratio
SCRIP EXCESS RETURN TO
BETA
R i−R fβ i
NEW RANK
Ashok Leyland 0.931111 GTLMahindra & Mahindra 0.981576 JSWTata Motors 1.082697884 SAILAirtel 0.904593 Ashok LeylandGTL 0.455453 DaburTata Communications 1.06014 GAILDabur 0.521145 Tata motorsHUL 0.578617 Tata SteelITC 0.675516 Tata CommGAIL 0.844169 AirtelIOC 0.62018769 HUL
ONGC 0.911309 M&MJSW 1.242796 ONGCSAIL 1.365418 ITCTata Steel 1.332412772 IOCMARKET (index return)
Table 4.2 excess return to beta ratio
INTERPRETATION
Based on the excess return to beta ratio the the srips are ranked from 1 to 15,
with GTL in the first rank and IOC in the last. The excess return to beta ratio
was calculated using 6.2% as risk free rate of return.
4.3 Calculation Of Cut Off Point
STOC
KS
R i−R fβ i
(Ri−R f )∗β iσ ei
2 ∑i=1
N (Ri−R f )∗β iσei
2
βi2
σei2 ∑
i=1
N β i2
σ ei2
C i
GTL
1.021
8710.0061545
78 0.00615460.03492
57930.03492
57930.020
639
JSW
0.388
1820.0090140
08 0.0151685860.10174
12170.13666
70110.037
926
SAIL
0.117
7890.0119440
64 0.027112650.14327
00040.27993
70150.049
911
Ashok Leyland
0.103
9510.0061835
71 0.0332962210.09435
46850.37429
170.052
223
Dabur
0.097
2910.0012724
61 0.0345686820.02889
23480.40318
40480.051
869
GAIL 0.081 0.0032774 0.037846146 0.09100 0.49418 0.049
625 64 3529 7577 964
Tata motors
0.078
9820.0036771
68 0.0415233140.11743
07420.61161
83190.047
461
Tata Steel
0.071
9670.0038691
73 0.0453924870.14420
38230.75582
21420.044
542
Tata Comm
0.066
8490.0022567
53 0.047649240.10021
25430.85603
46850.042
57
Airtel
0.063
430.0018409
04 0.0494901450.09069
65550.94673
12390.040
9
HUL
0.062
7290.0012865
1 0.0507766550.07029
15571.01702
27960.039
66
M&M
0.049
0790.0013575
34 0.0521341890.07605
67511.09307
95470.038
437
ONGC
0.032
192
-0.0010642
52 0.0510699370.12123
1571.21431
11170.034
563
ITC
0.028
825
-0.0018861
82 0.0491837550.03886
86931.25317
9810.032
433
IOC
-
0.008
34
-0.0031328
99 0.0460508560.04336
96711.29654
94810.029
523
Table 4.3 Cut off point
asho
k le
ylan
d
M&
M
Tata
Mot
ors
Airt
el
GTL
Tata
Com
m
Dabu
r
HUL
ITC
GAIL
IOC
ONG
C
JSW
SAIL
TATA
Ste
el
0
0.01
0.02
0.03
0.04
0.05
0.06
CUTOFF
CUTOFF
Figure 4.1 Cutoff point
INTERPRETATION
The highest value of C i is taken as the cut-off point i.e. C*. Ashok
Leyland has the highest the cut-off rate of C*= 0.052223. All the stocks
having C i greater than C* have been included in the portfolio.
4.4 Construction Of An Optimal Portfolio
To construct the optimal portfolio the top four companies in the list above the
cut-off point are considered. The excess return to beta ratio is taken for
calculating the proportion of investment.
STOCKS CUT-OFF
POINT
GTL 0.020639
JSW 0.037926
SAIL 0.049911
Ashok Leyland 0.052223
Table 4.4 Cut off point of top four companies
4.5 Proportion of Investment
STOCKS Zi X i
GTL -0.00186 0.137836756
JSW -0.00215 0.159172556
SAIL -5.3E-05 0.003923812
Ashok Leyland -0.00943 0.699066877
SUM -0.01349 1
Table 4.5 Calculation of Proportion of Funds to be invested in Each Stock
In the table, Zi shows the relative investment in each stock. X i
indicates the weights on each security and they sum up to one.
4.6 Portfolio of Stocks
STOCKS PROPORTION OF
INVESTMENT
(%)
GTL13.783
JSW15.917
SAIL0.392
Ashok
Leyland
69.906
Table 4.6 Portfolio of Stocks
INTERPRETATION
Thus Sharpe model has helped us to find out the proportion of investments to
be made to obtaining an optimum portfolio. Ashok Leyland should be alloted
the maximum investment with a proportion of 69.906% . GTL and JSW have
almost equal proportions and SAIL should be made the last investment with
as low a percentage of 0.30%.
CHAPTER 5
FINDINGS AND SUGGESTIONS
5.1 Findings
When compared to market performance FMCG and Oil & Natural Gas
companies performed below average.
Steel is the only industry in the portfolio in which all the companies
have performed better than the market performance.
The systematic risk of all the companies in the portfolio is much higher
than the market overall market risk.
Mostly companies with higher Beta have performed better than other
companies in the portfolio.
In the overall portfolio GTL is the only company which had the lowest
Beta and also a very high return.
The excess return to beta ratio is positive for all the company except
IOC.
All the companies in the Steel sector included in the portfolio and Tata
motors and Tata communications have beta greater than one which is
riskier because, for 1 % change in market return, the change in stock
return is greater than 1%.
The final optimum portfolio is made of two companies from the Steel
sector and one from the Communication industry and the other from
Automobile sector. Thus a completely diversified portfolio is achieved.
Ashok Leyland has been allocated the highest proportion of investment
with 69.90% and the lowest investment has been made to SAIL
constituting about 0.30% of the portfolio.
GTL is the only company from the communications industry with a
significant proportion in the portfolio. The other two companies
provide telecom services, while GTL provides communication
infrastructures.
5.2 Suggestions
The maximum proportion of about 69.90% should be made in Ashok
Leyland.
GTL should be allocated 13.78% of the portfolio, and 15.91% of the
portfolio should be allocated to JSW.
The lowest portion of the portfolio of 0.30% should be allocated to
SAIL.
The stocks have been chosen from five different sectors in the market,
several other sectors could also be included to make a comprehensive
portfolio with much lower risk, achieved through diversification.
Figure 5.1 Proportion Of Investment
0.137836755520666
0.159172555817034
0.00392381162816384
0.699066877034137
PROPORTION
GTLJSWSAILAshok Leyland
CHAPTER 6
CONCLUSION
Three companies from five sectors namely automobile,
Communication, FMCG, Oil & Natural Gas and Steel where chosen. From the
study it was found that that the performance of all the sectors except FMCG is
good. Though the recession has brought out significant decline in the trends,
the rate of growth is remarkable. From the 15 companies four companies
where chosen based on their risk and return using sharpe index. The existence
of a cut-off rate is also extremely useful because most new securities that have
an excess return-to beta ratio above the cut-off rate can be included in the
optimal portfolio. From the cutoff rate proportion of investment is found out
which helps in deciding even the number of shares to be bought in each stock
other than selecting the best stock. Thus the study helps the investors to
minimize their overall risk and maximize the return of their investment over
any period of time.
REFERENCE
Giordano Pola and Gianni Pola 2009, “A Stochastic reachability
approach to portfolio construction in finance industry”. Management
Science, Vol 13, pg 123.
Ayhan Kapusuzoglu and Semra Karacaer 2009, “the process of stock
portfolio construction with respect to the relationship between index,
return and risk evidence from turkey”, issue 23, Page 193-206
Gerald Kohers and Ninon Kohers and Theodor Kohers 2006, “The risk
and return characteristics of developed and emerging stock markets:
the recent evidence”, Journal of Finance, Volume 42.
Maria Bohdalova (2007), “A comparison of value-at-risk methods for
measurement of the financial risk”, Journal of Finance Vol 39.
Ana Gonzalez and Gonzalo Rubio ,2007, “portfolio choice and the
effects of liquidity”, No.2, pages 1-23
Syed A. Basher and Perry Sadorsky 2007, “Oil price risk and emerging
stock markets”. Journal of Business, Pg 154.
Debasish Dutt 2005, “Constructing an optimal portfolio using Sharpe’s
single index model”.
Jeroen Derwall 2009, “Portfolio concentration and the fundamental
law of active management”. Journal of Finance, Vol 38.
Sitikantha Pattanaik and Bhaskar Chatterjee 2000, “Stock Returns and
Volatility in India: An Empirical Puzzle?”
Anna Morrell 2010, “The Art and Science of Portfolio Construction”.
Gupta, K. Locke, S. and Scrimgeour, F. 2009, “Can Momentum
Returns be Optimised?”