Learning outcomes, after watching this video you will be able to discuss the need for risk-adjusted performance measures, list and calculate various risk-adjusted performance measures. List the circumstances under which you will use the various risk adjusted performance measures. Benchmarks for portfolio performance evaluation, investors should compare the return of their investments to what they would have obtained from investing in an alternate portfolio with identical risks. Performance must always be evaluated on a relative basis, and not on an absolute basis. However, it may be difficult to identify portfolios with identical risk. And so, it is better to use a risk-adjusted measures of performance. In this video, we will look at some commonly used risk-adjusted performance measures. The Sharpe ratio is one of the more widely used measures. It is similar to the Sharpe ratio we saw earlier. The Sharpe measure of a portfolio is the difference between its average return over the sample period- the risk free rate divided by the standard deviation of its returns over the sample period. It measures the return to total variability trade-off. If we believe that CAPM holds then we know that returns compensates only systematic risk. While the Sharpe measure is based on total risk. The Treynor measure uses the CAPM beta as a measure of risk. It is the difference between the portfolio's average return over the sample period- the risk free rate divided by its beta. A drawback of both Sharp and Treynor measures is that they don't quantify how much additional value the portfolio manager is adding. All they say is how much excess returns the portfolio has earned for each unit of risk. Hence, they can largely be used as a ranking criteria only. A measure that addresses this drawback is the Jensen measure, or portfolio alpha. It quantifies the portfolio's average return in excess of that predicted by the CAPM. It tells us how far away from the security market line the asset is. Jensen's measure denoted by alpha's of p is the difference between the average portfolio returns,- within square brackets this theory + the portfolios beta times the difference between the average market returns and the risk period. The term within the square brackets is CAPM's prediction of the portfolios returns. A fourth risk adjusted performance measure is the appraisal of information ratio. It is defined as the portfolio alpha, or Jensen's measure, divided by the diversifiable risk of the portfolio. This ratio gives us the abnormal return per unit of diversifiable risk. Let's look at an example that illustrates the use of these four risk adjusted performance measures. We have two portfolios, P and Q. P has an average return of 35%, a beta of 1.20, standard deviation of returns of 42%, and diversifiable risk of 18%. Q has an average return of 28%, a beta of 1.00, standard deviation of returns of 30%, and diversifiable risk of 0%. The risk-free rate is 6%. We can say that Q is the market portfolio. Why is that? It has a beta of 1.00 and 0 diversifiable risk. Let's start off by calculating the Sharpe measure of P. It is 35%- 6% divided by 42% which is 0.69. Q has a Sharpe measure of 28% -6% divided by 30% which comes out to 0.73. P's Treynor measure is 35% -6% divided by 1.2 which is 24.17%. To use Treynor measure is 28% -6%, divided by 1 which is 22%. P as alpha is 35%- within square brackets, 6% +1.2 times 28% -6% which comes out to 2.6%. Since Q is a market portfolio, it's alpha will be 0. Finally P's appraisal ratio is its alpha 2.6% divided by it's diversifiable risk of 18% which gives us 0.14. Since Q's alpha is 0, its appraisal ratio is also 0. Looking at these values, the Sharpe measures say that P performed worse than Q. But the other measures say that it has performed better than Q. So which measure should we use to decide whether portfolio P has performed better or worse? The rule of thumb is as follows, if you have to decide on the portfolio manager's compensation, then use the Jensen measure. It tells us how much value the manager is actually added. If you have to decide an optimal portfolio choices, use the Sharpe measure if the portfolio represents your entire investment. Use the Treynor measure if the portfolio is one of many portfolios combined into a large fund. Use the appraisal ratio for actively-managed funds that are held in combination with passively-managed portfolios. There are still some drawbacks of using this risk-adjusted performance measures. One, they rely on the validity of the CAPM. Two, they use a proxy for the true market portfolio, rather than the true market portfolio itself. Three, they still cannot statistically distinguish skill from luck. We found that portfolio P's Sharpe measure was 0.04, lower than that of portfolio Qs. But we can't say if that is statistically a large difference or not as this number is not the rate of return. Next time we will look at a measure that helps address this last drawback.