CONSTRUCTION OF OPTIMAL PORTFOLIO USING SHARPE S SINGLE INDEX MODEL - A STUDY WITH REFERENCE TO BANKING AND AUTOMOBILE SECTORS

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1 CONSTRUCTION OF OPTIMAL PORTFOLIO USING SHARPE S SINGLE INDEX MODEL - A STUDY WITH REFERENCE TO BANKING AND AUTOMOBILE SECTORS * Ms.S.SUBASHREE, Assistant Professor, Department of Commerce and Business Administration, SRM University, Chennai , Tamil Nadu, India. ** Dr.M.BHOOPAL, Assistant Professor, Department of Management Studies, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli , Tamil Nadu, India. ABSTRACT The main aim of this study is to construct an optimal portfolio using Sharpe s Single Index model. For this purpose monthly closing prices of 5 companies from banking sector and 5 companies from auto mobile sector listed in the Bombay stock exchange (BSE) were selected. Share prices for the period of October 2016 to September 2017 had been considered. Using all the collected data a cut-off rate had been calculated and that rate had been considered for the construction of optimal portfolio. The finding of the study will be very useful for investors, policy makers, corporations and their financial market participants. Key Words: Cut-off rate, Beta, Market Return, Sharpe s single index model, Systematic Risk. 1. INTRODUCTION The security analysis and portfolio management is the most concerned aspect for rational investment and decision making. A portfolio is a set of securities such as stocks, bonds and money market instruments. The process of blending together these assets classes, so as to obtain maximum return with minimum risk is called portfolio construction. It is a very difficult task to find out good investments among various types of investments. In an optimal portfolio every investor need maximum return with a minimum return. This process is done through the construction of an optimal portfolio. 2. STATEMENT OF THE PROBLEM The present study is prepared on the basis of studying the sectors in which an investor can invest their savings in a group of securities or portfolio. By creating a portfolio an investor get maximum return with a minimum rate of risk. Portfolio management deals with the analysis of individual securities as well as with the theory and practice of optimally combining securities into good portfolios. So the banking sector and automobile sector had been considered. Therefore, the present study is entitled as Construction of Optimal Portfolio using Sharpe s Single Index Model-A Study with Reference to Banking & Automobile Sectors 3. OBJECTIVES OF THE STUDY 1. To construct an optimal portfolio using Sharpe s single index model by using the selected sectors. 2. To calculate the return and risk of the constructed optimal portfolio by using Sharpe s Single Index Model. 3. To get a knowledge about Sharpe s single Index model. 232

2 4. RESEARCH METHODOLOGY This study is based on secondary data obtained from the website finance.com. Ten companies from the BSE Sensex index were selected for the study. The tools used are as follows. (a) Estimate the return on stock. The equation to be used P t = current year price P o = previous year price (b) Excess return to beta ratio R i = the expected return of stock i R f = risk free rate of return β i = systematic risk of stock i (c) Cut off C i is calculated by using the following equation σ 2 m =Variance of the market index σ 2 ei = stocks unsystematic risk 5. LIMITATIONS OF THE STUDY 1. Only 10 stocks from two sectors, i.e., Banking and Automobile sectors are taken for consideration into the study. 2. This studies result may not be universally applicable. 6. REVIEW OF LITERATURE Dr. S. Poornima, Aruna P Remesh 1 (2015) in their research construction of optimal portfolio using sharpe s single index model - a study with reference to banking & it sector in this research 10 companies from banking sector and 10 companies from it sector listed in the Bombay stock exchange (NSE) were selected. Share prices for the period of January 2011 to December Dr. K. V. Ramanathan, K. N. Jahnavi 2 (2014) in the study have referred that media and entertainment sector has been taken into consideration for constructing the optimum portfolio. Twenty companies like PVR, Sun Network, Inox, Raj television have been selected and the portfolio is constructed using sharpe optimal index to obtain the optimal and effective portfolio returns. Thangjam Ravichandra 3 (2014) endeavors to build an ideal portfolio by utilizing sharpe s single index model. For this reason, NSE Nifty and all the 50 stocks where are a part of it have been utilized as business record for planning portfolio for the period of April 2008 to December S. Devarajan and I. Francis Gnanasekar studied about the construction of optimal portfolio using sharpe's index model: a comparative analysis of Indian private and public-sector banks in post global financial crisis period the study helps to analyze the risk and return of 34 selected private and public sector banking stocks which are part of CNX 500 as market index. The portfolio is constructed using sharpe optimal index to obtain the optimal and effective portfolio returns. Desai, Radhika and Surti, Manisha 4 (2013) constructed an optimal portfolio using fifty companies which were listed on the NSE and the time duration of the study is three years. Among the fifty companies only ten companies were selected for the optimum portfolio. The proportion of investment made in each security has been calculated using the Sharpe s Single Index Model. The volatility of security has been analysed. The research provides direction to investors regarding performance of securities. Once the performance is analysed and optimum portfolio of securities is constructed, it enables the investor to take appropriate decisions. Dileep and Rao, Kesava 5 (2013) studied the applicability and utility of the Single Index Model in the Indian context and also evaluated the performance of the portfolio thus constructed in terms of its rate of return. A sample of thirty companies belonging to various sectors was chosen for study and the data required for this study was collected from secondary sources. It was found that only four companies were included in portfolio construction. The study concluded that William Sharpe s Single Index Model will be sustainable and applicable to the Indian market where investors can construct a portfolio for improving the expected returns on their investment. 233

3 Mandal, Niranjan 6 (2013) applied Sharpe s Single Index Model considering the daily prices of twenty one securities for the period of ten years i.e. April 2001 to March In order to determine the daily market return, the BSE Sensex was taken as the market performance index. After formulating the cut-off rate, those securities whose C i values greater than the cut-off point were selected. Then to arrive at the optimal portfolio the proportion of investment in each of the selected securities in the optimal portfolio was computed on the basis of beta value, unsystematic risk, excess return to beta ratio and the cut off rate of the security concerned. Different statistical tools and techniques charts and diagrams have been used for the purpose of analysis and interpretation of data. From the samples of twenty one securities an optimum portfolio was constructed using ten securities. From the study it is observed that the Sharpe s Single Index Model gives an easy mechanism for constructing an optimal portfolio of stocks for a rational investor by analyzing the reason behind the inclusion of securities in the portfolio with their respective weights. P. Varadharajan 7 (2012) says the construction of equity portfolio of large caps companies of selected sectors in India with reference to the sharpe index model in this research 18 stocks from three different large caps sectors are the risk and return of all the stocks are studied individually. Based on the study top five stocks are selected for forming optimum portfolio. The final step in the process is to determine the number of shares of each stock to be purchased. The portfolio is constructed using sharpe optimal index to obtain the optimal and effective portfolio returns. P. Varadharajan 8 (2011) constructed an equity portfolio (Oil, IT, Steel and Banking Stocks) with reference to the sharpe index model. The study includes 25 stocks from five different sectors. Only the secondary data for the past five years ( to ) are used in the study. The final portfolio thus constructed includes stocks from more than one sector. Ch. Naveen(2014) from have done research on the title application of sharpe single index model to BSE he has selected 30 blue chip companies of BSE with 6 years data i.e. from January 2007 to December 2012 have been considered. Besides this, an attempt has been made to test the validity of the sharpe model to construct the portfolio. 7. DATA ANALYSIS AND INTERPRETATION Secondary data were used for this study. Ten companies listed in the BSE sensex were chosen. The companies were selected listed below: Table - 1 Sample Companies Names S.No. Name of the Companies 1. Axis Bank 2. HDFC Bank 3. ICICI Bank 4. State Bank of India 5. IDBI Bank 6. Tata Motors 7. Mahindra & Mahindra 8. Hero Moto Corp 9. Ashok Leyland 10. TVS Motors Company [Source: Secondary Data] Table 1 shows the list of sample companies selected for the study. First five companies are from the banking sector and the remaining five from automobile sector. Table 2 Mean Returns of Sample Companies' Stocks S.No. Name of the Companies Mean Returns in (%) 1. Axis Bank 1.13% 2. HDFC Bank 3.92% 3. ICICI Bank 2.35% 4. State Bank of India 2.02% 5. IDBI Bank -0.25% 6. Tata Motors 0.28% 7. Mahindra & Mahindra 1.34% 8. Hero Moto Corp 2.15% 9. Ashok Leyland 5.03% 10. TVS Motors Company 6.42% Table 2 shows the mean returns of the ten companies selected for the construction of an optimal portfolio using Sharpe's Single Index Model. This table reveals that TVS Motor Company has the highest return of 6.42% and IDBI bank has the lowest mean return of -0.25%. In order to know the market risk face by each security, the beta values of sample companies stock returns were computed and tabulated below. 234

4 Table - 3 Beta values of the Sample companies' Stocks S.No. Name of the Companies Beta Values 1. Axis Bank HDFC Bank ICICI Bank State Bank of India IDBI Bank Tata Motors Mahindra & Mahindra Hero Moto Corp Ashok Leyland TVS Motors Company Table 3 shows the beta values of the ten companies stock returns. A beta below 1 indicates either an investment in stocks with lower volatility than the market, or a volatile investment whose price movements are not highly correlated with the market. The Tata Motors has the highest beta value of 2.15 which means it is highly volatile. Ashok Leyland (1.50), ICICI Bank (1.42), and IDBI Bank (1.16) have the beta values greater than 1 which means they are volatile. Mahindra & Mahindra has the lowest beta value is 0.26 which represents lower volatility. The beta values were calculated using the following formula: β = beta R m = return of market index R m = mean of market index R i = return of individual stock R i = mean of individual stock Table - 4 Ranking of the stocks based on excess return to Beta ratio S.No. Name of the Companies R i R i -R f Β R i -R f /β Rank 1. Axis Bank 1.13% HDFC Bank 3.92% ICICI Bank 2.35% State Bank of India 2.02% IDBI Bank -0.25% Tata Motors 0.28% Mahindra & Mahindra 1.34% Hero Moto Corp 2.15% Ashok Leyland 5.03% TVS Motors Company 6.42% Table 4 indicates that the excess return and excess return to beta ratio. Excess return is the difference between expected return on the stock and the risk free rate of interest. The risk free rate of interest is assumed to be 8% in this study. The excess return to beta ratio measures the additional return on a security per unit of systematic risk. Table 4 shows that the TVS Motors Company stock has the highest excess return to beta ratio of while that of Mahindra & Mahindra stock has the lowest of This ratio provides the relationship between potential risk and reward from a company's stock. The ranking of stocks done on the basis of excess return to beta ratio reveals that while the TVS Motors Company stock ranks first, the Mahindra & Mahindra stock ranks the last. In addition to the systematic risk of individual securities, their unsystematic risk as measured by σei 2 is also computed and tabulated in the table 5. It is the unique risk affecting the firm due to certain factors affecting only the company issuing such security. It is an avoidable or controllable risk. The companies are listed in this table based on their ranks. 235

5 S.No. Name of the Companies 1. TVS Motors Company 2. Ashok Leyland R i - R f /β ICICI Bank Tata - Motors HDFC - Bank State Bank - of India Hero Moto - Corp IDBI Bank Axis Bank Mahindra - & Mahindra Table - 5 Cut-off Values (C i ) of sample Companies Stock β^2/(δei)^2 {R i - R f /(δei)^2}/βi Once the composition of the optimal portfolio is ascertained, the next step is to calculate the percentage to be invested in each security which is shown in Table 6. Table 6 Proportion of Investment Proposed Sl.No. Scrip Name C i Proportion of Investment 1. TVS Motors Company Ashok Leyland ICICI Bank Table 6 represents the proportion of investment to be made in each security. The three securities ranking from 1 to 3 are selected for the optimal portfolio. The percentage of funds to be invested in each security is presented in figure 1: Figure 1 Proportion of Investment Proposed C i 236

6 The above figure shows the proportion of investment made by the investor. From the figure we can understand 58% of the investment made in TVS Motors Company, 32% of the investment made in Ashok Leyland and the remaining 10% of the investment in ICICI Bank. 8. FINDINGS The findings of the present study are presented below: 1. The TVS Motors Company has the highest return of 6.42% and the IDBI has the lowest return of -0.25%. If the investor wants to earn a maximum return without considering the risk aspect then investment can be made on those securities which yield high returns. Even though the return is high, the risk involved in the stock return should be considered while taking investment decisions. 2. The return from Tata Motors has the highest beta value of 2.15 which means it is highly volatile. 3. Ashok Leyland, ICICI bank and IDBI Bank have beta values greater than 1.ie.they are also volatile. 4. TVS Motors Company having the highest cut off value i.e., 2.22 and Mahindra & Mahindra having the lowest cut off value is The three securities ranking from 1 to 3 based on the C i values were identified along with the proportion of investment to be made. The proportion of the investment to be made is 58% in TVS Motors Company, 32% of the investment made in Ashok Leyland and the remaining 10% of the investment in ICICI Bank. This implies that the majority of funds may be invested on the TVS Motors Company stock. 9. CONCLUSION Constructing an optimal portfolio is a challenging task for the individual as well as the institutional investors. This paper made an attempt to construct an optimum portfolio using the Sharpe s Single Index Model. Thus the optimal portfolio is constructed by using the Sharpe s single index model. This method is more adequate. Portfolio is constructed by taking the past one year data. After constructing the portfolio only three companies were selected for the portfolio construction. From banking sector one company was selected and from automobile sector two companies were selected for optimal portfolio construction. REFERENCES 1. Poornima, S., & Remesh, A. P. (2015). Construction of optimal portfolio using Sharpe s single index model-a study with reference to banking & IT sector. IJAR, 1(13), Ramanathan, K. V., & Jahnavi, K. N. (2014) Construction of optimal equity portfolio using the sharpe index model with reference to banking and information technology sectors in india from International Journal of Business and Administration Research Review, 2(3). 3. Ravichandra, T. (2014). Optimal Portfolio Construction with Nifty Stocks. 4. Desai, Radhika and Surti, Manisha (2013), Optimal Porfolio Construction: Sharpe s Single Index Model, International Journal of Scientific Research, 2 (9), pp: Dileep, S. & Kesava Rao, G.V. (2013), A Study on Sustainability of William Sharpe s Single Index Model, IJAMBU,1 (1), pp: Mandal, Niranjan (2013), Sharpe s Single Index Model & its Application to Construct Optimal Portfolio: An Empirical Study, Great Lake Herald, 7 (1), pp: Varadarajan, P. & Ganesh (2012), Construction of Equity Portfolio of Large Cap Companies of Selected Sector in India with reference to the Sharpe Index Model, International Journal of Physical and Social Sciences, 2 (1), pp: Varadharajan, P., & VIKKRAMAN, D. (2011). A study on construction of equity portfolio (oil, it, steel and banking stocks) with reference to the sharpe index model. Chief patron chief patron. 9. Kevin.S, Securities Analysis and Portfolio Management, PHI Learning, New Delhi, WEBSITES