A Paper on
"Risk - Return Relationship & the effect of Diversification
on Unsystematic Risk using Market Index Model"


Prof. Rajalakshmi
Prof. Priyanka R. Gohil
Institute of Business Management and Research


"Sometimes your best investments are the ones you don't make." This is a maxim which best explains the complexity of making investments. There are many investment avenues available for investors today. Different people have different motives for investing. For most investors their interest in investment is an expectation of some positive rate of return. But investors cannot overlook the fact that risk is inherent in any investment. Risk varies with the nature of return commitment. Generally, investment in equity is considered to be more risky than investment in debentures & bonds. A closer look at risk reveals that some are uncontrollable (systematic risk) and some are controllable (unsystematic risk). Risk can be categorized into two types:

The risk that 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. Scarcities in raw material supply, labour strike, and management inefficiency are all problems specific to a company and are internal in nature. These negative factors can make the share price fall sharply but can be avoided if well thought. An investment in the shares of certain other companies with sound management can help minimize this risk. Therefore diversification is the mantra for any prudent investor. Diversification is done in many ways. Investors can diversify across one type of asset classification - such as equities or among different asset classes such as stocks, bonds, fixed income and bullion etc. But the question to be answered is: How many stocks help diversify unsystematic risk? Theory suggests that 18-20 stocks in a portfolio helps to reduce unsystematic risk. But again, tracking 18-20 stocks becomes cumbersome for investor. Whatever be the number of stocks, it is an undeniable fact that Diversification helps reduce unsystematic risk. This paper stands to investigate the effect of diversification on unsystematic risk by applying Sharpe's Single Index Model and also analyzes the relationship between return & risk.

Research Objective:

The broad objective of the paper is to examine whether unsystematic risk declines with diversification. Also effort has been made to find out the extent of correlation between portfolio return and risk i.e. the relationship between portfolio's beta & expected return. The analysis also makes an attempt to find out whether stocks with high beta values give high return to investors. For research purpose, 30 securities of the companies comprised in BSE Sensex between the period April 2006 to March 2007 has been selected

Sharpe's Single Index Model

The major assumption of Sharpe's single-index model is that all the covariation of security returns can be explained by a single factor. This factor is called the index, hence the name "single-index model." One version of the model, called the market model, uses a market index such as the BSE Sensex as the factor (any factor that influences security returns can serve as the index).

Methodology used.

The data consists of daily closing prices of BSE- Sensex for the period from April 2006 to March 2007. For study purpose, inorder to calculate Return on stock, Return on market index (BSE Sensex), and Expected Return on securities and portfolios it is assumed that market will give 15 percent annual return.

Portfolio Return and Risk







Syst. rick B1 2ox2

Unsy-stam atic ei2

Cor.Co. eff. R2


Exp. Ret. E(R)





















The above table shows the statistical summary of two portfolios constructed on the basis of beta value of thirty stocks.  P1 is low market risk portfolio and high market risk portfolio is P2. Total risk of P1 is low as compared to P2. The expected return is consistent with its market risk. If invested in P1 can realize 13% annual return whereas investment in P2 offers 14% annual return. Therefore it is evident that with diversification as a tool unsystematic risk can be minimized. As per the investor's risk appetite portfolio can be constructed.  To conclude, several vaccinations are needed to protect one's portfolio from vagaries of market. "DIVERSIFICATION" which is much talked about but seldom practiced can be the right tool for any investor. So all investors in order to counter unsystematic risk vaccinate your portfolios with diversification.





"Testing of capital Asset pricing. Model in Indian Environment," Decision.


Dhankar, R.S.


(i)'An Empirical Testing of Capital Asset pricing Model in the Indian context'. Journal of financial management and Analysis. July-Dec., 1996.
(ii)Dhankar, R.S. A New look at the criteria of performance Measurement for Business Enterprises in India : A study of public sector undertakings, Finance India, March 1988.


Dhankar, R.S. and   Singh, R.


Arbitrage pricing Theory and the Capital Asset Pricing Model Evidence from the Indian stock Market, Journal of Financial Management and Analysis, Jan-June.2005.


Sehgal, S.


'An Empirical Testing of Three Parameter Capital Asset Pricing Model in India', Finance India.


Klemlosky, R.C. and Martin J.D.


'The Effect of Market Risk on Portfolio Diversification', The Journal of Finance.


R.S. Dhankar and   Rakesh Kumar


'Risk return relationship and Effect of Diversification Non Market Risk  Application of Market Index Model in Indian Stock Market', The Journal of Finance, 2007


Kent Womack and       Ying Zhong


'Understanding Risk and Return, the CAPM, and the Fama-French Three Factor Model, Tuck School of Business at Dartmouth.


It's a matter of pleasure to have our article published in the management website indianmba.com. We would like to express our gratitude to all those who gave us the possibility to complete this article. We want to thank the Dean & Director of IBMR Dr.R.K.Balyan for being a constant source of inspiration and Prof.Kavita Sharma for stimulating us.

Prof. Rajalakshmi
Prof. Priyanka R. Gohil
Institute of Business Management and Research

Source: E-mail October 25, 2008


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