Sharpe's Single Index Model
SHARPE’S PORTFOLIO THEORY
This model was developed by William Sharpe. According to Sharp’s model, the theory estimates the expected return and variance of indices which may be one or more and are related to economic activity. This theory has come to be known as Market Model. Sharpe’s single index model will reduce the market related risk and maximize the returns for a given level of risk. Sharpe’s model will take into consideration the total risk of portfolio. The total risk consists of both systematic and unsystematic risk. The risk may be eliminated by diversification. If the diversification is perfect and unsystematic risk is negligible, then it is very easy to overcome the systematic risk.
Assumptions:
1. The securities returns are related to each other. 2. The expected return and variances of indices are the same. 3. The return on individual securities is determined by unpredictable factors.
The return on security’s increases or decreases is depending upon a great extent in the market index. The movement of security return shows the correlation with the market index. The individual security’s return is determined by the following equation:
Ri = αi + βiI + ei
Where,
Ri = Expected return on security αi = Alpha coefficient βi = Beta coefficient
I = the level of market return index ei = Error (residual risk of a company) Beta is a measure of volatility faced by a financial asset or portfolio or a project return. Alpha is the measurement of difference between actual earned return at a level of systematic risk.
Calculation of expected return on portfolio can be calculated as follow;
Rp = ∑Xi (αi + βiI)
Where,
Xi = proportion of security
Equation for portfolio risk:
σ2p = [(∑Xiβi)2×σ2I] + [∑Xi2 ei2]
Where,
σ2p = Portfolio risk or variation of portfolio return
σ2I = Expected variance of market index
ei2 = Unsystematic risk (residual risk of company)
The following table reveals the meaning of various
This model was developed by William Sharpe. According to Sharp’s model, the theory estimates the expected return and variance of indices which may be one or more and are related to economic activity. This theory has come to be known as Market Model. Sharpe’s single index model will reduce the market related risk and maximize the returns for a given level of risk. Sharpe’s model will take into consideration the total risk of portfolio. The total risk consists of both systematic and unsystematic risk. The risk may be eliminated by diversification. If the diversification is perfect and unsystematic risk is negligible, then it is very easy to overcome the systematic risk.
Assumptions:
1. The securities returns are related to each other. 2. The expected return and variances of indices are the same. 3. The return on individual securities is determined by unpredictable factors.
The return on security’s increases or decreases is depending upon a great extent in the market index. The movement of security return shows the correlation with the market index. The individual security’s return is determined by the following equation:
Ri = αi + βiI + ei
Where,
Ri = Expected return on security αi = Alpha coefficient βi = Beta coefficient
I = the level of market return index ei = Error (residual risk of a company) Beta is a measure of volatility faced by a financial asset or portfolio or a project return. Alpha is the measurement of difference between actual earned return at a level of systematic risk.
Calculation of expected return on portfolio can be calculated as follow;
Rp = ∑Xi (αi + βiI)
Where,
Xi = proportion of security
Equation for portfolio risk:
σ2p = [(∑Xiβi)2×σ2I] + [∑Xi2 ei2]
Where,
σ2p = Portfolio risk or variation of portfolio return
σ2I = Expected variance of market index
ei2 = Unsystematic risk (residual risk of company)
The following table reveals the meaning of various