Sharpe’s single index model
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The document discusses Sharpe's single index model for portfolio optimization. It relates individual security returns to a single market index and uses a characteristic line equation to define the relationship between security returns and market returns. The model simplifies earlier approaches by using a single market index rather than complex matrices but has practical limitations in compiling expected returns and covariances of securities.
Sharpe’s single index model
- 2. INTRODUCTION OF SINGLE’S SINGLE INDEX MODEL RELATED TO SINGLE MARKET INDEX CHARACTERISTIC LINE PROPORTION OF INVESTMENT MARKET AND NON-MARKET TISK AND RETURN CONTENT
- 3. The return on securities should be related to a single market index. A popular average can however, be a surrogate for the market index. This method was conceptually very sound and theoretically very elegant, but it had serious practical limitation involved due to complexities involved in compiling the expected returns, standard deviation, variance, covariance of each security to every other security in the portfolio. SHARPE’S SINGLE INDEX MODEL
- 4. It will have the following implication 1. The market Index would consist of all the securities traded on the market. 2. Single market index will reduce and simplify the work involved in compiling elaborate matrices of variances as between individual securities. RELATED TO SINGLE MARKET INDEX
- 5. A characteristic line express the relationship between on individual securities and returns on the market portfolio. The equation of the characteristic line is Ri – Rf = a + Bim (Rm – Rf) +Yi where Ri = Holding period return on Security Rf = Riskless rate of interest Excess Return on the Market Portfolio is = Ri – Rf a = Vertical intercept Bim = Beta which indicates the slop CHARACTERISTIC LINE
- 6. EXAMPLE
- 7. Once the choice of securities is made by using the cut off point, the next stage PROPORTION OF INVESTMENT