Hi there, welcome back. In the previous lectures, you learned about the number of different risk adjuster and return measures. Now the big question, of course, is which one is appropriate to use when? They all measure different things and therefore are useful in different ways. In this lecture, we're going to compare and contrast different risk adjuster return measures in order to understand why you would choose to use one versus another. As I mentioned earlier, the Sharpe Ratio is an appropriate risk measure to use when you're evaluating the entire portfolio of an investor. The portfolio that represents the entire wealth of the investor. For example, suppose you're going to invest in one fund and one fund only, where you're going to put in all your wealth. This portfolio will represent your entire risky investment, and you're choosing among several different funds, then in this simplest case, all you would have to do is choose the one with the maximum Sharpe Ratio. Now, you might need to decide what the appropriate benchmark is. That is, if you were to follow a passive strategy, what would that be, for example, maybe a broad market index? And compare the Sharpe Ratio based on this market index? Of course, remember, the biggest caveat, there is no guarantee that the same risk adjusted return of the past will continue into the future. So that's about the Sharpe Ratio. Now suppose you already hold a diversified portfolio. Now let's say maybe you already hold a passive market index, let's call that fund m. Now you're trying to evaluate whether or not you should add another actively managed portfolio P to your mix. You have the index portfolio and you're trying to add another actively managed portfolio to your mix. In this case, you want to evaluate how much reward this portfolio P provides. What is the alpha versus the non-systematic or the tracking error of risk that it entails. Ring a bell? Exactly. In this case, the appraisal ratio or the information ratio are more appropriate measures on the type of benefit and cost analysis that is needed to evaluate the desirability of the portfolio P. You want to know how much additional reward you're getting per additional residual risk you're incurring. That's the idea. Let's look at yet another scenario. Suppose now, you're going to select a number of actively managed funds to allocate your wealth to. So, your total portfolio will consist of all of them but you're allocating them to a bunch of different actively managing funds. Now, how would you compare them? For starters, of course, you might want to look at the alpha. For example, you might see I have portfolio P, it has an alpha of 2%, I say not bad, and then you see another portfolio, portfolio Q, and you see it has an alpha of 3%. You say, hm, should I transfer some of my wealth from P to Q? Think about it. Now, since P and Q are just two of the many other sub-portfolios you hold in your total portfolio, you're less concerned about the non-systemic risk. Because altogether, the non-systematic risk will be diversified away. But which leaves you to be more concerned with the systematic risk. In this case, Treynor measure gives you the kind of benefit cost analysis that you need. How much excess return does P provide or Q provide per unit of systematic risk? So finally, of course, if the return distribution is asymmetric or skewed or if the investor has a return target, in that case, as we saw before, the Sortino measure is a better alternative to the Sharpe Ratio. Now having said all that, a very important caveat. Be very aware of the estimation error, I can't emphasize this enough. Remember that averages, standard deviations, regressions, all these are estimates and they are notoriously susceptible to outliers. One outlier or one unusual observation can change your estimate values significantly. You should also be concerned about sample size or what the r squared looks like in order to assess how well your models fit. Finally, remember again that there is no guarantee that the future return distributions will be like the past returns. In this lecture, you learned when each risk adjustment return measure is more appropriate to use and in which situation. They are all useful, but they measure different things. It's important to understand their differences and you should probably use more than one single measure. Ultimately, if our goal is to evaluate the performance of an active fund manager, remember we want to separate the excess return that is generated by skill, than from the excess return that is simply compensation for risk.