# MEASURING AND EVALUATING PERFORMANCE

This step would involve the measuring and evaluating of portfolio performance relative to a realistic benchmark.

We would measure portfolio performance in both absolute and relative terms, against a predetermined, realistic and achievable benchmark. Further, we would evaluate the portfolio performance relative to the objective and other predetermined performance parameters.

The investor or manager would consider two main aspects; namely risk and return. He would measure and evaluate, whether the returns were worth the risk, or whether the risk was worth the return. The issue here is, whether the portfolio has achieved commensurate returns, given the risk exposure of the portfolio.

Measuring and evaluating portfolio performance, would be used to give the investor or manager feedback. And would help the investor or manager in improving the quality and performance of both the portfolio and its management process in the future.

There are three popular portfolio performance measures formulated by Treynor, Sarpe and Jensen, respectively. We would study each of them separately.

Treynor measure: Jack Treynor after a study of the Capital Asset Pricing Model agreed that the beta (or systemic risk) would be an appropriate measure of risk. This would be to measure portfolio performance related to the excess return on a portfolio as compared with its beta. Thus,

Treynor's measure = Excess return of portfolio ÷ Beta of portfolio

= (Average rate of return of the portfolio − Average rate of return of a risk free investment) ÷ Beta of the portfolio

The numerator is the risk premium earned by the portfolio and the denominator is the systemic risk. As the systemic risk is also the measure of risk the Treynor's measure assumes that the portfolio is well diversified.

Sharpe Measure: William Sharpe's measure is similar to the one calculated by Treynor; but Sharpe gives a representation to the standard deviation in preference to the beta as the measure of risk. Thus,

Sharpe's measure = (Average rate of return on portfolio − Average rate of return on a risk free investment) ÷ Standard deviation of return of portfolio

The Sharpe measure would provide the excess return earned on a portfolio per unit of its total risk.

Both the measured proposed by Treynor and Sharpe propose that a linear relationship exists between risk and return, while employing their different measures of risk. You may take note that, in the case of a perfectly diversified portfolio both the measure would provide identical results as the total risk would be the same as the systemic risk.

Jensen Measure: Jensen like Treynor has based his measure on the Capital Asset Pricing Model, also called Jensen's alpha. It basically reflects the difference between the return a portfolio has actually earned and the return it was expected to have earned, given its beta as per the Capital Asset Pricing Model. Thus,

Jensen's measure = Average return on portfolio − {Risk free return + Portfolio beta (Average return on market portfolio − Risk free return)}