Sharpe, Treynor and Jensen Measures

Portfolio evaluating refers to the evaluation of the performance of the investment portfolio. It is essentially the process of comparing the return earned on a portfolio with the return earned on one or more other portfolio or on a benchmark portfolio.

Portfolio performance evaluation essentially comprises of 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, on the other hand, address such issues as whether the performance was superior or inferior, whether the performance was due to skill or luck etc.

The ability of the investor depends upon the absorption of latest developments which occurred in the market. The ability of expectations if any, we must able to cope up with the wind immediately. Investment analysts continuously monitor and evaluate the result of the portfolio performance. The expert portfolio constructor shall show superior performance over the market and other factors. The performance also depends upon the timing of investments and superior investment analysts capabilities for selection. The evolution of portfolio always followed by revision and reconstruction. The investor will have to assess the extent to which the objectives are achieved. For evaluation of portfolio, the investor shall keep in mind the secured average returns, average or below average as compared to the market situation. Selection of proper securities is the first requirement.

Portfolio Performance Evaluation Methods

The objective of modern portfolio theory is maximization of return or minimization of risk. In this context the research studies have tried to evolve a composite index to measure risk based return. The credit for evaluating the systematic, unsystematic and residual risk goes to Sharpe, Treynor and Jensen.

The portfolio performance evaluation can be made based on the following methods:

1. Sharpe’s Measure
2. Treynor’s Measure
3. Jensen’s Measure

1. Sharpe’s Measure

Sharpe’s Index measure total risk by calculating standard deviation. The method adopted by Sharpe is to rank all portfolios on the basis of evaluation measure. Reward is in the numerator as risk premium. Total risk is in the denominator as standard deviation of its return. We will get a measure of portfolio’s total risk and variability of return in relation to the risk premium. The measure of a portfolio can be done by the following formula:

SI =(Rt – Rf)/σf

Where,

• SI = Sharpe’s Index
• Rt = Average return on portfolio
• Rf = Risk free return
• σf = Standard deviation of the portfolio return.

2. Treynor’s Measure

The Treynor’s measure related a portfolio’s excess return to non-diversifiable or systematic risk. The Treynor’s measure employs beta. The Treynor based his formula on the concept of characteristic line. It is the risk measure of standard deviation, namely the total risk of the portfolio is replaced by beta. The equation can be presented as follow:

T_n =(R_{n –} Rf)/β_m

Where,

• T_n = Treynor’s measure of performance
• R_n = Return on the portfolio
• Rf = Risk free rate of return
• β_m= Beta of the portfolio ( A measure of systematic risk)

3. Jensen’s Measure

Jensen attempts to construct a measure of absolute performance on a risk adjusted basis. This measure is based on Capital Asset Pricing Model (CAPM) model. It measures the portfolio manager’s predictive ability to achieve higher return than expected for the accepted riskiness. The ability to earn returns through successful prediction of security prices on a standard measurement. The Jensen measure of the performance of portfolio can be calculated by applying the following formula:

R_p = R_f + (R_MI – R_f) x β

Where,

• R_p = Return on portfolio
• R_MI= Return on market index
• R_f= Risk free rate of return