[MUSIC] Learning outcomes, after watching this video, you will be able to, one, define some more performance measures such as Sortino ratio and Tail ratio. [MUSIC] So this is a graphical representation of the Sharpe ratio and the squared ratio. Now, we will move on to figure out solutions to the problems I identified with the Sharpe ratio. The first problem is that arithmetic mean is used, which is not truly accurate. The second, of course, is with the volatility in the denominator. It's really upside, as well as downside qualitivity. So now, we are going to look at a couple of ratios. One called the Sortino ratio and the other other called the symmetric downside Sharpe ratio. Now, both of them have the advantage that they fix both of these are highlighted. In the numerator, we have the geometric mean. In the case of the Sortino ratio, what you subtract from the geometric mean is something called the minimum acceptable ratio. That could be zero, that could be the risk-free rate, whatever the analyst might wish to choose. And the SDR Sharpe ratio, almost as a rule, uses the risk-free rate. The other difference from the Sharpe ratio is that in the denominator, these two ratios use something called the downside deviation. If you look at the formula carefully, you will observe that the downside deviation only measures the deviation below the average return and ignores all the deviation or volatility above the arithmetic mean. Notice that this is the way most of us think about risk. For most of us, risk is loss of money that's below average return. Now, the SDR Sharpe ratio has another small issue with it. It has a root 2 factor. A square root of 2 factor in the denominator. That is for technical reasons. So what we need to notice at this point is these two ratios are better at capturing what we think of as the notion of risk, a little bit than their Sharpe Ratio. Now, the final ratio I'm going to be talking about in this section is something called the Tail Ratio. Now, this is a very simple ratio. It takes a percentile number, p, let's say, 90th percentile, and says, what is the average of all returns which are above the 90th percentile during the period under consideration? So if you stack up all the returns, find out the 90th percentile point, obviously, the 10% of returns above that will have a certain average. Now, take that in the numerator and divide that by the average return in the bottom 10%. Since you have chosen 90% on the upside, choose 10% on the downside. So essentially, what this is telling you is I am going to give you a ratio of the best month, the best 10% month, to the worst 10% months. And you want to see where the variation of this fund's returns are coming from. Obviously, the higher this ratio, the better the fund's performance. Now, stand alone, this is not great. But it's very useful as an agent to other measures. And I'm going to run you through a quick example. I'm going to just show you a graph across 73 months of two funds, hypothetical funds A and B. Notice the important thing, that both of them start off at the hypothetical value of 1000 and both of them end up, 73 months later, at this hypothetical value of 2000. Which is to say, for somebody who has and investment horizon of 73 months or more, both of these funds might look identical, in the sense that they start from the same point and take you to the same point. But it is not where you have traveled from and where you have traveling to. It is also how bumpy the ride has been throughout, right? In other words, we care about risk. Now, just have a look at this graph and tell me what you think, in your own mind or at least make up your mind, as to what you think is the riskier fund, A or B? And most of us would agree that A has a lot of big hills, ups and downs, right? And B seems to sort of coursed along, and then go up, and then some, and go up again, right? Now, in fact, if you work out the standard deviation of these two funds, it turns out that B has the highest standard deviation. Now, notice that the arithmetic, as well as geometric means of these two funds are going to be almost the same. The geometric mean, for sure, is going to identical because you started at the same point and ended at the same same point. It turns out that arithmetic mean is roughly the same also. But given that B has the highest standard deviation, if you use Sharpe ratio, you would conclude that A is the better performing fund than B. But then, if you look at downside deviation and proceed to calculate the Sortino ratio or the SDR Sharpe ratio, or the symmetric downside Sharpe ratio, what you will find is that the conclusion is reversed. Because now, you confirm in numbers what you saw for yourself in the picture, which is that most of the volatility of fund B is really on the upside rather than downside. And for fund A, volatility is upside, as well as downside. So that's a real big take away here. And by the way, if you calculate the tail ratio here, you will also find that fund B does better than fund A on that round also. So what we conclude from this small example is that traditional measures such as to alpha are hopeless as detecting timing ability. So here, we have a manager who's showing timing ability. Clearly, he's reaching the beta of his fund in response to anticipated market conditions. However, traditional alpha or beta measures are not capturing his ability.