# Difference Between The Following Performance Measures

829 WordsNov 29, 20154 Pages
Difference between the following performance measures: The Sharpe ratio It is a ratio that describes how much excess return on investment the business is receiving for the extra volatility experienced by holding a riskier asset. It is the reward for holding a risky asset in a portfolio. The ratio is calculated by dividing the portfolio risk premium by the portfolio standard deviation. The ratio is given as follows: Sharpe ratio = (r P – r f )/ σ P Where: r- is the average rate of return of asset P. rf- The best variable rate of return of risk-free security. σ P-Is the standard deviation. The ratio is used to measure the performance of the portfolio since it makes it easier to compare the performance of one portfolio to another while…show more content…
Jensen’s alpha It is a performance index that is used in the determination of the abnormal return of a portfolio of securities or just a security over the theoretical expected return. The Jansen 's index is another version of the standard alpha whose computation is based on an academic performance index rather than a market index. It can also be described as the difference in return earned by the portfolio compared to the return implied by the (CAPM) Capital Asset Pricing Model. The following formula gives the Jansen 's alpha: α P = r P –[r f + β P (r M - r f )] risk premium Describe how the above three performance measures are computed. Sharpe ratio The ratio is calculated by the use of the historical data that are justified based on the predicted and justified relationships (Murphy &University College, Dublin. 2010). In its application; it can be applied both theoretically and practically. The practical implementation uses the ex-post results while the theoretical uses the ex-ante results or values. For this to hold, an assumption is made that the predictive results have the predictive ability. The ex-ante Sharpe ratio The following are the assumptions: Let RF be the rate of return on fund Q in the future periods RB- the return on the benchmark portfolio or security Therefore, the differential return (d) is given as: d’≡RF-RB Let the above-computed d ' be the