Understanding Sharpe's portfolio selection model over the standardized portfolio called market portfolio in respect of
the stock market operations in India


By

KP Ramakrishnan
Professor-Finance
Rohit Malhotra
Professor-Finance
Dhruv Jain
Student
Graduate Business Program
Modi Apollo International Institute
New Delhi
 


"Understanding Sharpe's portfolio selection model over the standardized portfolio called the market portfolio in respect of the stock market operations in India" focused upon technique of selecting optimal portfolio using the model given by William Sharpe called Single Index Model.

Investment are made to secure future and for fulfillment of objectives. First step in investment process is to set the investment policy which involves determining the investor objective and the amount of wealth available for investing. Second step is security analysis involving examining several individual securities or group of securities within the broad categories of financial assets. Portfolio construction is the third step where investor has to consider several issues of selectivity, timing and diversification. In the final phase of investment process the portfolio constructed is revised and evaluated.

Portfolio management is the process of selecting securities in a manner that helps to reduce risk for the same level of return or increase return for same level of risk. Return is gain or loss of an investment over a specific period, expressed as a percentage increase over the initial investment. Risk can be of various types. Business risk is that risk when a company does not have adequate cash flow to meet its operating expenses, further it will not be able to meets its obligation towards shareholders and creditors then it is knows as financial risk. Other categories of risk are interest rate risk, liquidity risk, political risk, credit risk, inflation risk and exchange rate risk.

Traditional Portfolio Theory depends upon subjective approaches to the portfolio analysis. This theory recognizes the key importance of risk and return to the investors but do not necessarily hold in every portfolio management exercise. To overcome the problems of traditional portfolio theory, modern portfolio theory has evolved. Harry Markowitz is considered as the father of modern portfolio theory.

According to this theory, it is not enough to look at the expected risk and return of a particular stock but diversifying into more than one security can actually lead to reduction in risk. Modern Portfolio theory helps in quantifying the benefits of diversification. Modern Portfolio theory states the risk for individual stock return has two component, systematic risk and unsystematic risk. The risk which cannot be diversified away like interest rate risk and recession is known as systematic risk. Unsystematic risk is stock specific and can be diversified away as the investor increase the number of stocks in his or her portfolio.

The construction of an optimal portfolio is simplified if a single number measures the desirability of including a stock in the optimal portfolio. Single index model can provide such number. In this case, the desirability of any stock is determined by excess return to beta ratio (Ri-Rf)/i. Stocks are ranked by order of excess return to beta (from the highest to the lowest in that order), which would represent the desirability of a stock's inclusion in a portfolio. The number of stocks selected would then depend on a unique cutoff rate such that all stocks with higher ratios of (Ri-Rf)/i would get included and all stocks with lower ratio would similarly get excluded

Research Objective

The study proposes to understand the Sharpe's Portfolio Selection Model over the Standardized Index Portfolio called Market portfolio in respect of stock market operations in India

The researcher had selected 17 securities of the companies comprised in Bombay Stock Exchange (BSE) 100 Index with this report to construct an efficient portfolio. The return provided of which had been tracked continually for the period from January 2001 to December 2006 using the ratio equation postulated for the computation of the Sharpe ratio and the mean return, excess return, beta, unsystematic risk and the excess return to beta had all been calculated using the sub-formula postulated by William Sharpe, for assessing mainly using that formula the ratio called the Sharpe ratio for ranking performance of companies included in the efficient portfolio devised by the researcher to out beat the market.

The proportion sheet had then been constructed to determine what proportion of securities to be selected for inclusion in an efficient portfolio based on the ratings of the companies in terms of return provided by securities issued by then in the capital market is based on the Sharpe ratio determination.

After the above decision had been made, then the efficient portfolio assembled by the researcher based on the company security rating as determined by applying the model for the Sharpe ratio computation over the period from January 2006 to December 2006 and the portfolio return on the index are displayed reflecting that the portfolio selected by the researcher based on application of Sharpe ratio computation model had outperformed the index by leaps and bounds thereby evidencing that this model is most appropriately useful for the construction of an efficient portfolio that beats the index return.

References

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Barua, S.K., Raghunathan, V. & Varma, J.R. (1992). Portfolio management. New Delhi: Tata McGraw Hill.

Bhalla, V.K. (2008). Investment Management. New Delhi: S Chand & Co.

Bodie, Z., Marcus, A.J. & Kane, A. (2002). Investment (5th ed.). New Delhi: Tata McGraw Hill.

Bikhchandani, S., Hirshleifer, D. & Welsh, I. (1992). A theory of fads, fashion, custom and cultural change as information cascade. Journal of political economy, 992-1026.

Cohen, J.B., Zinbarg, E.D., & Zeikal, A. (1982). Investment analysis and portfolio Management (4th ed.). Homewood, Illinois: Richard D. Irwin.

Considine, G. (2007). Projecting portfolio risk and return. Retrieved January 23, 2008, from http://www.seekingalpha.com/article/38568-projecting-portfolio-risk-and-return
 


KP Ramakrishnan
Professor-Finance
Rohit Malhotra
Professor-Finance
Dhruv Jain
Student
Graduate Business Program
Modi Apollo International Institute
New Delhi
 

Source: E-mail August 9, 2008

           

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