Unit V: Portfolio Performance Measurement MBA & MBA – Banking and Finance (Term-IV) Course : Security Analysis and Portfolio Management Unit V: Portfolio Performance Measurement

PORTFOLIO EVALUATION It refers to the evaluation of the performance of the portfolio. It is essentially the process of comparing the return earned on a portfolio with the return earned on one or more other portfolios or on a benchmark portfolio. Portfolio evaluation essentially comprises two functions, performance measurement and performance evaluation. Performance measurement is an accounting function which measures the return earned on a portfolio during the holding period or investment period. Performance evaluation addresses such issues as whether the performance was superior or inferior.

Performance Measures for Portfolios 1) Sharpe Method 2) Treynor’s method 3) Jensen Method

Sharpe’s Performance Measure for Portfolios The performance measure developed by William Sharpe is referred to as the Sharpe ratio or the reward to variability ratio. It is the ratio of reward or risk premium to the variability of return or risk as measured by the standard deviation of return.

Sharpe’s performance measure where: St = Sharpe index = average return on portfolio t r* = risk less rate of interest σt = standard deviation (risk) of the returns of portfolio t

Treynor’s Performance Measure for Portfolios The performance measure developed by Jack Treynor is referred to as Treynor ratio or reward to volatility ratio. It is the ratio of the reward or risk premium to the volatility of return as measured by the portfolio beta.

Treynor’s Performance Measure where: Tn = Treynor index = average return on portfolio n r* = risk less rate of interest βn = beta coefficient of portfolio n

Jensen’s Performance Measure for Portfolios The Treynor and Sharpe Indexes provide measures for ranking the relative performances of various portfolios, on a risk-adjusted basis. Jensen attempts to construct a measure of absolute performance on a risk-adjusted basis – that is, a definite standard against which performances of various funds can be measured. The Jensen measure attempts to measure the differential between the actual return earned on a portfolio and the return expected from the portfolio given its level of risk.

The CAPM model is used to calculate the expected return on a portfolio The CAPM model is used to calculate the expected return on a portfolio. It indicates the return that a portfolio should earn for its given level of risk. The difference between the return actually earned on a portfolio and the return expected from the portfolio is a measure of the excess return or differential return that has been over and above what is mandated for its level of systematic risk. The differential return gives an indication of the portfolio manager’s predictive ability or managerial skills.

Jensen’s Performance Measure where: = average return on portfolio j for period t RFt = risk less rate of interest for period t αj = intercept that measures the forecasting ability of the portfolio manager βj = a measure of systematic risk = average return of a market portfolio for period t

Portfolio Rp (%) β Rf (%) A 15 1.2 5 B 12 0.8 C 1.5 Market index 1.0 Example: The following table gives the portfolio return and the market return. Rank the performance according to Jensen’s performance measure. Portfolio Rp (%) β Rf (%) A 15 1.2 5 B 12 0.8 C 1.5 Market index 1.0