Hi there, welcome back. All right, so in the last lecture you learned what the Jensen's alpha is, as a risk adjusted return measure. How it is estimated, right? It's a very popular measure because it's easy to calculate and interpret. Now one problem with Jensen's alpha, however, is that it does not adjust for the amount of idiosyncratic risk in the portfolio, right? In other words, how much residual risk was taken in order to obtain the alpha, right? So in this lecture, you're going to learn about two additional performance measures, the appraisal ratio and the information ratio. Which essentially correct for this missing piece. While they are sometimes used interchangeably and are, essentially, designed to capture the same idea, the appraisal ratio and the information ratio are slightly different from each other. And you'll learn about that, too. All right, so let's start with the appraisal ratio, right? So like I said, looking at the alpha by itself, right, does not give us an idea of how much residual risk or unsystematic risk was taken by the manager in order to obtain the alpha, all right? So what we want to know is really some kind of a benefit/cost ratio, right? How much excess return per unit of residual risk, and this is, essentially, what the appraisal ratio represents, all right? So specifically, the appraisal ratio, Is given by, or defined as, the portfolio alpha, right, divided by the, Portfolio residual risk, right? So let me define here that this is the Jensen's alpha for the portfolio. And this is the residual risk, Or the idiosyncratic risk for the portfolio. Right, basically it's the volatility of the residuals. All right? The more alpha a manager produces, right, for a given amount of residual risk, the higher is this ratio, right? Now furthermore, also note that the less the residual risk, right, the more the fund can be combined a diversified portfolio without driving up the total variance too much, all right? Now, how do we estimate this residual risk? Well we know how to estimate the alpha, right? How do we estimate the portfolio residual risk? Well, it's simply the standard deviation of the residuals that we obtained from that regression, right? So basically what you do is you compute the residual for each observation, right? What is it? Well, it's basically the actual return minus the predicted return given your alpha and beta estimates. The difference is the residual, right, the error term. And now you take the standard deviation of all those residuals and that is your portfolio residual risk, right? Or the idiosyncratic volatility of the portfolio. Okay, so the information ratio is similar in nature, right? But it captures the idea that an active manager has to depart from the benchmarks so that it's defined relative to the benchmark, right? It is given by the excess return on the portfolio, right. How much to find bits to benchmark per unit of tracking error risk. All right, let me define terms here, right. This is your average return on the portfolio, is the average return on the benchmark. And this is oops, p volatility of the, volatility, Of the difference. Of course which is the tracking error, all right. So you can see that information ratio is also a benefit cost ratio. But this time it's comparing the portfolio simply to the benchmark. Note that the information ratio is closely tied to what you choose as a benchmark, right? So it's best used when comparing return series based on the same benchmark. All right, so in this lecture you learn two additional risk adjusted performance measures. The appraisal ratio and the information ratio, right? Both of these measures are giving you some kind of benefit to cost ratios that capture the abnormal return per unit of risk, that could be diversified away with a larger index portfolio.