# Performance Appraisal

Five methods of performance appraisal in their ex post (historical) forms include: Jensen Alpha, Treynor Measure, Sharpe ratio, M^2 and Information ratio. I’ve memorized all the formulas and can do all the calculations accurately but don’t know how to interpret the results. I know Jensen and Treynor use beta (systematic risk) in the formula whereas Sharpe and IR use standard deviation (total risk) in the formula but again how do you compare and translate the results. Can someone explain it in a plain language?

You just said it - Jensen and Treynor use beta and are measures of systematic risk while Sharpe and M2 are measures of total risk. What you want to look is for divergence between the first two and the second two, which tells you whom is taking what kind of risk.

Also, from what I remember from a few practice exams, Jenson and Treynor are good measures if they asset is being added to an already diversified portfolio. If not being added to a diversified portfolio, standard deviation will be a better risk measure than beta and Sharpe would be a better risk measure.

probably also important to note that if the m2 measure is greater than the market return, the portfolio will plot above the cml. i’ve seen the diversification issue with treynor come up a few times now. if you’re assessing the performance of a diversified portfolio, sharpe is more appropriate because diversified portfolio assumes all non-systemic risk has been diversified away. on the other hand, if you’re evaluating a small or non-diversifed, portfolio, treynor is the better metric because it takes into account specific risk (non-systemic).

ridgefield Wrote: ------------------------------------------------------- > > i’ve seen the diversification issue with treynor > come up a few times now. if you’re assessing the > performance of a diversified portfolio, sharpe is > more appropriate because diversified portfolio > assumes all non-systemic risk has been diversified > away. on the other hand, if you’re evaluating a > small or non-diversifed, portfolio, treynor is the > better metric because it takes into account > specific risk (non-systemic). If you are assessing the performance of a diversified portfolio, why would you use Sharpe Ratio? SR measures active return per unit of TOTAL risk, which includes unsystematic risk… I would say, we should use Treynor measure when analyzing a well diversified portfolio, because this measure only accounts for the systematic risk…

ridgefield Wrote: ------------------------------------------------------- > probably also important to note that if the m2 > measure is greater than the market return, the > portfolio will plot above the cml. > > i’ve seen the diversification issue with treynor > come up a few times now. if you’re assessing the > performance of a diversified portfolio, sharpe is > more appropriate because diversified portfolio > assumes all non-systemic risk has been diversified > away. on the other hand, if you’re evaluating a > small or non-diversifed, portfolio, treynor is the > better metric because it takes into account > specific risk (non-systemic). I think you meant other way around, right?