Learning outcomes, after watching this video, you will be able to calculate the M-squared measure, calculate the T-squared measure. Alternate performance measures, one of the drawbacks of risk adjusted performance measures, as we saw last time, was their inability to say whether a difference in the measures is statistically significant or not. The M-squared measure, which is a variation of the Sharpe measure, will help address this draw back. To illustrate how to calculate the M-squared measure, let's use the same two portfolios P and Q from last time. You can see all the relevant values on the slide. The first step in calculating the M-squared measure is to determine what combination of P and the risk-free asset matches the total risk of the market index. In our example, P has a standard deviation of 42%, whereas the market index, which is portfolio Q, has a standard deviation of 30%. We are interested in combining P and the risk free asset in such a way that it gives us a standard deviation of 30%. We know that the risk-free rate has no standard deviation and its covariance with P is zero. So we have the rate of P w times its standard deviation of 42% equals portfolio Q standard deviation of 32%. This gives w to be 30% over 42%, which is 0.71. The remaining 1- 0.71, which is 0.29, is invested in the risk-free rate. A combination of 0.71 in P and 0.29 in the risk-free asset has the same standard deviation as portfolio Qs. Let's call this portfolio P*. What is the return of portfolio P*? It is 0.71 x 35% + 0.29 x 6%, which is 26.59%. Portfolio Q has a return of 28%. The difference of 26.95%-28% is the M-squared measure, this comes to -1.41%. Clearly the difference in performance is substantial and cannot be ignored. There is also a similar measure analogous to the Treynor measure. This is called the T-squared measure. To calculate the T-squared measure, we first need to combine portfolio P and the risk-free asset in such a way as to give a beta of 1. Calculate the return on this portfolio, the difference between this return and the market index return is the T-squared measure. What combination of portfolio P and the risk-free rate will give a beta of 1? Remember, the risk-free rate has a beta of 0. So we have the weight in portfolio P, w times its beta of 1.2 equals 1, which gives us a w of 1 over 1.2, which is 0.83. The return of a portfolio of 0.83 in P and 0.17 in the risk-free asset, which we call portfolio P*, is 0.83 x 35% + 0.17 x 6%, which equals 30.07%. Portfolio Q, with a beta of 1, has a return of 30%. The T-squared measure is 30.07%- 30%, which equals 0.07%. This tells us that portfolio's P performance is slightly better than the market portfolio Q. This wraps up the course on portfolio management. You have learned about developing your own investment philosophy. You have also learned about some of the important steps in the investment process, namely, understanding your or your client's investment needs, the asset allocation and selection decisions, and finally performance evaluation. I hope you enjoyed the course as much as I did bringing it to you, good bye.
