Construction of Optimum Portfolio Using LMS Companies

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PSG INSTITUTE OF MANAGEMENT Peelamedu, Coimbatore

SECURITY ANALYSIS AND PORTFOLIO MANAGEMENT

MINI PROJECT REPORT ON

CONSTRUCTION OF OPTIMUM PORTFOLIO USING

SHARPE INDEX MODEL FOR LARGE, MID AND SMALL

CAPITAL COMPANIES

SUBMITTED TO:

DR. P. VARADHARAJAN MBA, PH.D.,

(Assistant Professor -Finance)

PSG INSTITUTE OF MANAGEMENT

SUBMITTED BY:

ASHOK KUMAR B T

MBAFINANCE


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CONSTRUCTION OF OPTIMUM PORTFOLIO USING

SHARPE INDEX MODEL FOR LARGE, MID AND SMALL

CAPITAL COMPANIES

Abstract

Indian securities market is a highly volatile and sensitive market where portfolio

construction is highly important to get good returns. The main focus of this research is to

construct an optimal portfolio in Indian Secondary market with the help of the Sharpe single

index model. Portfolio construction is an essential process of the investors for investment in

the equity market. A best combination of portfolio will effect in maximum return for a

particular level of risk. In this article, 20 selected stocks from large cap companies, mid-cap

companies and Small cap companies have been taken into consideration and these stocks are

member of the NSE Nifty index. The daily data for all the stocks for the period of September

2011 to August 2014 have been considered. The proposed method formulates a unique cut

off point (Cut off rate of return) and selects stocks having excess of their expected returnover risk free rate of return surpassing this cut-off point. Percentage of investment in each of

selected stocks is then decided on the basis of respective weights assigned to each stock

depending on respective beta value, stock movement variance unsystematic risk, and return

on stock and risk free return according to the cut off rate of return.

Keywords: Risk, Return, Beta, Portfolio, Residual Variance, Sharpe index and Index.

INTRODUCTION

Investing in more than one security has always been a subject of discussion in portfolio

management which includes the evaluation of a security to be finally included in an

optimum portfolio and to know as to how many securities ideally be included to form an

optimum portfolio. The developments to this regard started by Markowitz in 1952 by

propounding mean variance theory where an investor makes his decision based on the

expected return and the standard deviation of their overall portfolio.

Sharpe (1966) contributed Reward to Variability ratio (RVAR) which considers portfolio

performance as the ratio of excess portfolio return to the standard deviation, considering

total risk as the major concern while evaluating portfolio performance. Treynor (1965)

distinguished between total risk and systematic risk, implicitly assuming that portfolios arewell diversified, hence ignored unsystematic risk in his measure. He presented Reward to

Volatility ratio (RVOL) which is the ratio of excess portfolio return to beta.

William Sharpe (1964) has given model known as Sharpe Single Index Model which laid

down some steps that are required for construction of optimal portfolios. Stucchi (2006),

Smith (1969), Bansal and Gupta (2000), Singh (2007), Elton et al (1976) and Cristian (2006)

in their studies tested the efficiency of Sharpe Single Index Model to make optimum

portfolio selection. Their results are similar as all concluded that Single index model is

efficient in constructing optimal portfolio and portfolio return is much higher than the

portfolio variance. Paudel and Koirala (2006) checked the efficiency of Sharpe portfolio


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optimization model in Nepalese Stock market and identified that portfolio beta is

significantly lower than the market beta.

William F. Sharpe got the Nobel Prize in 1990, shared with Markowitz and Miller, for such

a seminal contribution in the field of investment finance in Economics (Brigham and

Ehrhardt, 2002). Sharpes Single Index Model is very useful to construct an optimalportfolio by analyzing how and why securities are included in an optimal portfolio, with

their respective weights calculated on the basis of some important variables under

consideration.

PROBLEM STATEMENT

Investing in individual securities is associated with high risk. Many investors are not able to

choose the best portfolio for investment. As Stock market has both high return and high risk,

investors should be aware about their investment decision. Not many people invest in stock

market and the level of awareness among Indians about stock market is less. Also, holding

two or three stocks is always better than holding one.

OBJECTIVE OF THE STUDY

PRIMARY OBJECTIVES

To construct an optimum portfolio of securities from the selected 20 companies in

Large, Medium and Small market capitalization categories using Sharpes Single

Index Model, which minimize the risk and maximize the return.

SECONDARY OBJECTIVES

The stock price movements, closing index points of the companies and beta values forthe past four years are collected for analysis

To find the movement of share prices, expected returns.

To calculate market variance, individual stock variance, standard deviation and beta

values.

To find the proportion of money to be invested in each of these companies.

SCOPE OF THE STUDY

Scope of the study is to construct the optimum portfolio in Large, Mid and small market

capitalization companies to reduce its risk and maximize the profits. Based on the historical

performance, risk and return of those companies should be analyzed and top companiesshould be selected for construction of portfolio.

LIMITATIONS OF THE STUDY

Portfolio is constructed based only on risk and return.

Stock prices considered only for 3 years so that the real impact cannot be found.

All the calculations could not be brought into the report.

This research should not be suitable for short-term investment.


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that there has been reduced diversification in the past several years. YASH PAL TANEJA

and SHIPRA BANSAL (2011) explained diversification across asset classes provides a

soften solution against market because each asset class has different risk and rewards to

economic events. Therefore, it becomes obligatory to drill down the evaluation to the level

of individual securities to ascertain whether the security is an admissible security in terms of

investment policy and to see whether it has added value to the portfolio. Niranjan Mandal(2013), stated that the Sharpe ratio can be calculated directly from the elasticity of the

stochastic discount factor with respect to consumption innovations as well as the volatility of

consumption innovations.

METHODOLOGY:

For constructing the portfolio in this project we have selected companies from three

sectors namely Large-cap, Mid-cap and Small-cap companies in NSE Listing. From each

sector companies are selected based on highly liquidation and most active securities.

This is a descriptive study in which statistical data is analyzed for construction. Data

collected from NSE India web portal for closing price of selected company shares and Nifty

value. Risk free rate (T-Bills) collected from Reserve Bank of India (RBI). The study is

conducted with the financial data for the past four years from September 2011 to August

2014. The sample size of the study is 22 and they are taken from two sectors namely Power

and Steel Industries. The sampling technique used here is random sampling.

STATISTICAL TOOLS USED

RETURN

The total gain or loss experienced on an investment over a given period of time,

calculated by dividing the assets cash distributions during the period, plus change in value,

by its beginning-of-period investment value is termed as return.

Return = ((Todays market price Yesterdays market price)/Yesterdays market price)*100

BETA COEFFICIENT

Beta coefficient is the relative measure of non-diversifiable risk. It is an index of the

degree of movement of an assets return in response to a change in the markets return.

Where, b = Beta x = stock return

= mean of stock return

Y = Nifty return

= mean of Nifty return


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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. (Current T-bill rate 8.65%)

EXCESS RETURN-BETA RATIO

It is the ratio of returns in excess of the risk-free rate.

Where, Ri= the expected return on stock i, Rf = the return on a riskless asset, = the

expected change in the rate of return on stock associated with one unit change

in the market return.

CUT-OFF POINT

This is the point at which an investor decides whether or not a particular security is worth

purchasing. The formula is given by Sharpe model as follows:

Where, = variance of the market index

= Residual variance i.e. variance of a stocks movement that is not associated

with the movement of market index.

INVESTMENT TO BE MADE IN EACH SECURITY

Where, = is the proportion of investment of each stock

And,


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Where, = the cut-off point.(highest value of the Ci)

ANALYSIS AND DISCUSSIONS

The best model to measure the risk is Residual Variance and beta and using this stock

return is calculated.

Table 1.1: Return, Variation and Beta of Individual Stock

Scrips Mean Daily Return RiBeta value

Residual Variance

ei

TCS 0.134839 0.557522 2.715985TATA MOTORS 0.092563 1.55077 14.39277

SUN TV 0.055097 0.887416 7.033215

SUN PHARMA 0.108105 0.538662 5.833132

SPARC 0.163777 0.670587 7.821989

RPOWER 0.015897 1.52237 6.544001

ORISSAMINE -0.08401 1.108587 22.7898

NAUKRI 0.056121 0.262317 7.355406

MRF 0.186556 0.819664 3.59483

MARUTI 0.145892 0.830917 3.734419LT 0.023426 1.342393 5.739821

LAKSHVILAS -0.00637 0.766644 5.77881

INFY 0.077678 0.644418 3.651979

IDFC 0.070273 1.676285 6.744081

GODREJIND 0.086915 1.074436 4.761549

GMRINFRA 0.040907 1.62431 10.11617

FORTIS -0.01649 0.591761 3.011634

ESSAROIL 0.094687 1.22524 9.603662

ASIANPAINT -0.02072 0.756739 13.42896

APOLLOTYRE 0.171577 0.946846 6.858298

*Risk free rate 8.65% pa

*

Risk free rate 0.0237% perday


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Table 1. 2: Excess return to beta ratio

Scrips (Ri-Rf)/ Rank New Ranking

TCS 0.199348 2 SPARC

TATA MOTORS 0.044406 11 TCS

SUN TV 0.035381 12 MRF

SUN PHARMA 0.156697 4 SUN PHARMA

SPARC 0.20889 1 APOLLOTYRE

RPOWER -0.00512 16 MARUTI

ORISSAMINE -0.09716 20 NAUKRI

NAUKRI 0.123599 7 INFY

MRF 0.198688 3 GODREJIND

MARUTI 0.147058 6 ESSAROIL

LT -0.0002 15 TATA MOTORS

LAKSHVILAS -0.03922 17 SUN TV

INFY 0.083765 8 IDFC

IDFC 0.027784 13 GMRINFRA

GODREJIND 0.058837 9 LT

GMRINFRA 0.010594 14 RPOWER

FORTIS -0.06791 19 LAKSHVILAS

ESSAROIL 0.057938 10 ASIANPAINT

ASIANPAINT -0.05869 18 FORTIS

APOLLOTYRE 0.15618 5 ORISSAMINE

Rf (8.65/365) 0.0237

SPARC (Sun Pharma Advance Research Center) yielded the maximum return among

the companies selected and Orissa Minerals Development Company yielded lower return

following that Asian Paint and Essar Oil Corporation yielded lower return. Small and Mid-

cap have shown a higher return in all the companies chosen for the analysis. It shows that

Mid- cap securities are the growing sector and it is most preferred investable securities in

India. Beta is greater than 1 in Tata power, Reliance power, Larsen turbo , IDFC, Orissa

mine, GMR Infra, Godrej Industries and Essar Oil , which shows that these securities havemore risk and at the same time the reward per unit of risks is also more . But in case of other

companies with regards to beta it is less than 1 which shows it is less risky when compared

to market risk.

Sharpe has provided a model for the selection of appropriate securities in a portfolio.

The excess return of any stock is directly related to its excess return to beta ratio. It measures

the additional return on a security (excess of the risk less asset return) per unit of systematic

risk. The ratio provides a relationship between potential risk and reward. Ranking of the

stocks are done on the basis of their excess return to beta. Based on the excess return to beta

ratio the scrips are ranked from 1 to 20, with SPARC being in the first rank and Orissa


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Minerals being in the last. The excess return to beta ratio was calculated using 8.65% as risk

free rate of return.

Table 1:3: Cut-off point calculation for 20 companies

Companies (Ri-Rf)/m((RiRf))/ei

1+m/ei Ci

SPARC 0.2088899 0.0135957 1.0650855 0.0127649

TCS 0.1993477 0.0394242 1.1946507 0.0330006

MRF 0.1986883 0.0814637 1.4062358 0.0579303

SUN PHARMA 0.1566965 0.0902880 1.4625507 0.0617333

APOLLOTYRE 0.1561803 0.1134013 1.6105412 0.0704119

MARUTI 0.1470584 0.1441816 1.8198481 0.0792273

NAUKRI 0.1235992 0.1454906 1.8304391 0.0794840

INFY 0.0837652 0.1562742 1.9591749 0.0797653

GODREJIND 0.0588371 0.1724236 2.2336512 0.0771936

ESSAROIL 0.0579381 0.1826768 2.4106201 0.0757800

TATA MOTORS 0.0444065 0.1910770 2.5997856 0.0734972

SUN TV 0.0353815 0.1955620 2.7265485 0.0717251

IDFC 0.0277841 0.2086678 3.1982473 0.0652444

GMRINFRA 0.0105942 0.2117959 3.4935137 0.0606255

LT -0.0002030 0.2117237 3.8489424 0.0550083

RPOWER -0.0051247 0.2096690 4.2498909 0.0493351

LAKSHVILAS -0.0392243 0.2051526 4.3650349 0.0469991

ASIANPAINT -0.0586911 0.2023191 4.4133121 0.0458429

FORTIS -0.0679120 0.1933793 4.5449502 0.0425482

ORISSAMINE -0.0971628 0.1874475 4.6060009 0.0406964

m 1.1321181

From the table 1.3. It seen that Excess return to Beta ratio values of the first 8

securities exceed the Ci values of the respective securities. The Ci value of the 8 the

securitys (INFOSYS) cut off value is highest value (C*=0.0797653) taken as the Cut-off

point that is C*below which excess to beta ratio is less than the respective Ci value of the

security and the collection of these top ten securities, having (Ri-Rf)/ >=C*,make it to the

optimal portfolio.


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PORTFOLIO INVESTMENT:

For determining the proportion of portfolio Zi value is calculated by,

Zi = /2ei ((Ri-Rf/ -C*))

Then Xi value is calculated as,

Xi = Zi / Zi

Table: 1:4: Proportion of Investment in each Stock

Companies Xi

SPARC 11%

TCS 25%

MRF 28%

SUN PHARMA 7%

APOLLOTYRE 11%

MARUTI 15%

NAUKRI 2%

INFY 1%

Table 1.4 shows the proportion of investment in each stock. And it indicates the

weights on each security and they sum up to 100 percentage. By using Sharpe index model

thus we are able to find out the proportion of investments to be made for an optimal portfolio.

The maximum investment should be made in MRFwith a proportion of 28%. Following that

TCS, Maruti, Sun Pharma Advance Research Centerand Apollo Tyreare the next four

companies where major percentage of investment can be made. Evidently, the companies

chosen for the investments are growing at a steady rate in the recent years.

FINDINGS

The Large-cap and Mid-cap companies are the major contributors for the portfolio.

Among selected 20 companies (large, mid and small-cap) large cap and mid cap companies

performing than small cap companies.

Beta value for those stocks lesser than 1 which indicates minimal risk involved in

those stocks. Here the 8 stocks have lesser beta value than 1.


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RECOMMENDATIONS

The recommended proportion investments to the companies according to constructed

portfolio are MRF 28%, TCS 25%, Maruti 15%, Sun Pharma Advance Research

Center 11%, Apollo Tyre 11%, Sun Pharma 7% Naukri 2% and Infosysis 15.

Investors expecting high return for the minimal risk can go for TCS & Naukri (


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is 39% (MRF & Apollo Tyre) and remain 13% Stocks from Small-cap companies (Sun

pharma advance Research Center, Naukri) of total investment.

REFERENCES

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companies of selected sectors in India with reference to the Sharpe Index Model.

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Dr. Sathya Swaroop Debasish and Jakki Samir Khan (2012). Optimal Portfolio

Construction in Stock Market- An Empirical Study on Selected Stocks in

Manufacturing Sectors of India. International Journal of Business Management

Volume 2, pp.37-44.

Ebner,M. and Neumann,T. (2008). Time-varying factor models for equity portfolio

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Varadharajan, P. (2011). Portfolio Construction using the Sharpe Index Model with

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Nithya J (2014). Optimal Portfolio Construction with Markowitz Model among

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Caps In India. Research journalis Journal of Finance, vol. 2 No.2, pp. 1-14.

Sandeep Bansal, Sanjeev Kumar and Surender Kumar Gupta (2012). Test of Sharpe

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optimal portfolio. Vol. 7, No. 1, pp.1-19.

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Construction of Optimum Portfolio Using LMS Companies

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