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?”