Upload
ashokkumarbunja
View
222
Download
0
Embed Size (px)
Citation preview
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
1/13
1 | P a g e
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
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
2/13
2 | P a g e
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
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
3/13
3 | P a g e
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.
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
4/13
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
5/13
5 | P a g e
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
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
6/13
6 | P a g e
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,
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
7/13
7 | P a g e
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
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
8/13
8 | P a g e
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
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
9/13
9 | P a g e
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.
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
10/13
10 | P a g e
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.
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
11/13
11 | P a g e
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 (
8/10/2019 Construction of Optimum Portfolio Using LMS Companies
12/13
12 | P a g e
is 39% (MRF & Apollo Tyre) and remain 13% Stocks from Small-cap companies (Sun
pharma advance Research Center, Naukri) of total investment.
REFERENCES
Varadharajan. P and Ganesh (2012). Construction of equity portfolio of large caps
companies of selected sectors in India with reference to the Sharpe Index Model.
International Journal of Physical and Social Sciences vol. 2, Issue 8, pp.37-50.
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
construction, The European Journal of Finance 14, pp.381- 395.
Varadharajan, P. (2011). Portfolio Construction using the Sharpe Index Model with
Reference to Banking and Information Technology Sectors. Prime Journals ofBusiness Administration and Management, Vol 1, pp.392-398.
Naveen Ch. (2014). Application of Sharpe Single Index Model to BSE.
Management Today Journal. Vol.4,
Rachel C, Ronald H, Kees K (2001). Journal of Banking & Finance. Amsterdam 25,
pp.1789.
Mokta Rani Sarker (2013). Optimal Portfolio Construction: Evidence from Dhaka
Stock Exchange in Bangladesh. World Journal of Social Sciences, vol. 3, pp. 75-87.
Hiroshi Konno and Hiroaki Yamazaki (1991), mean-absolute deviation portfolio
optimization model and its applications to Tokyo stock market. Management
Science, vol. 37, No. 5, pp. 519-531. Kapil Sen and Disha CA Fattawat (2014). Sharpes Single Index Model and its
Application Portfolio Construction: An Empirical Study. Vol. 6, No.6, pp. 511-516.
Nithya J (2014). Optimal Portfolio Construction with Markowitz Model among
Large
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
ratio on selected mutual fund schemes. International Journal of Marketing, Financial
Services & Management Research. Vol. 1, no. 9, pp.60-19
Ward, David J Griepentrog, Gary L (1993), Risk and Return in Defaulted Bonds,
Financial Analysts Journal. vol.3, pp.61-75. Rudin, Alexander M, Morgan and Jonathan S. Journal of Portfolio Management vol.
32. No. 2, pp.81-89, 6.
Yash Pal Taneja, Shipra Bansal (2011). Efficient security selection: a study of
portfolio evaluation techniques. ZENITH International Journal of Business
Economics & Management Research. Vol.1, No.3, pp.48-60.
Niranjan Mandal (2013). Sharpes single index model and its application to construct
optimal portfolio. Vol. 7, No. 1, pp.1-19.
http://www.nseindia.com
http://www.moneycontrol.com
http://www.indiainfoline.com
http://www.nseindia.com/http://www.moneycontrol.com/http://www.indiainfoline.com/http://www.indiainfoline.com/http://www.indiainfoline.com/http://www.moneycontrol.com/http://www.moneycontrol.com/http://www.nseindia.com/8/10/2019 Construction of Optimum Portfolio Using LMS Companies
13/13
13 | P a g e
http://www.rbi.org.in
http://www.screener.in/
http://www.rbi.org.in/http://www.rbi.org.in/http://www.rbi.org.in/