[MUSIC] Hi there. In this set of videos, we're going to have a look at how to measure performance and adjust the measure for risks. So we're going to have a look at risk adjusted returns. And we'll see how these measures can be refined by making more precise definitions of risk. So we're going to start with the Sharpe ratio. Sharpe with an e, remember? We saw that, please put an e at Sharpe, for he's a man. And he came with this measure back in 1966 and you see it's made out of two things, two simple things, it's excess return divided by risk as measured by volatility. So excess, excess to what? Excess relative to the risk-free return. Why do we do this? Well, for one simple reason. If I tell you, you buy this fund and you will make 12% in 12 months time, you're going to tell me, okay 12%, that's interesting. But you will probably be much more interested if that return compares say to a risk-free return, i.e., the kind of return you make on a deposit. If that yield is say 1%, then if that same risk-free return is 10%, in this case, you going to tell me, well Mr. Giardin, you come with 12% promise expected return. Number one, well I'm not sure to make that kind of return in 12 months time and I have an alternative, which is the risk-free return. And this, I'm pretty sure I can make this kind of return at 10%. So this is why we compare the return to a risk-free return. And we divide that by the risk. So clearly, the higher the Sharpe ratio, the better the investment, the stronger the case for buying a fund which has a high Sharpe ratio. So this is why in the fund industry, the Sharpe ratio is widely used, it's actually the most widely used measure. Okay, now I want to give you an illustration of this and we saw that already. Remember? Course one, we talked about hedge funds. What? I'm sure you remember. If not, please go back to course one and take a look at the video where we discuss long short equity strategies. And we did that with this illustration here which I will summarize here. It's the example of ice creams versus the umbrellas. You remember you're a hedge firm manager or a traditional manager. And we're at the beginning of the summer right, like now, May, and you have to make a prediction as to whether the summer will be hot or not. And hence, if the summer it will be hot, the company A which produces ice cream will have good returns. And if the summer is, the weather is rather miserable, you should be invested in the companies that produces umbrellas, okay. So this is the end result, in September this has been a hot summer, so ice creams have been doing good, umbrellas badly. And here we compare these four strategies. The first three strategies are traditional ones. You're long, so +IC+UM. You have a long position. You buy the ice cream company, +UM, you buy the umbrella company. 50:50 is you don't know, really. In May, you don't really quite sure what to do in terms of the weather forecasting, so you put half of your money in the ice cream company and half of the money in the umbrella company. And the fourth one is the only strategy which is alternative, which is the typical strategy used by hedge funds, would be to be you have the strong conviction that the summer will be hot and sunny. And hence what you do is you go long the ice cream and you sell short the umbrella company. Okay, so now what is the end result of all this? We computed here, or I computed the returns and you see the performance umbrella minus 26%, ice cream plus 23%. The 50:50, well you get 50% of 23.0 plus 50% of -26.0, that's a -1.5 loss. And the long short strategy of long ice cream short umbrella yields the highest return at 24.5%. And look at the volatility of the long ice cream, short umbrella it's actually lower than the volatility of the long ice cream or the volatility of the long umbrellas. So and results not surprisingly, their Sharpe ratio, which will be measuring the performance less the risk-free asset return, which we put here in brackets and it's at 1%. So you do 23 minus 1 for the ice cream divided by 10.8 gives you a Sharpe ratio of 2.04. So the winner is clearly the long short strategy because you see the Sharpe ratio here is the maximum of 2.22. Now what are the pros and cons of the Sharpe ratio? Well the merits of the Sharpe ratio is that it's simple and intuitively appealing. You can explain it very easy, you take the performance, you measure it in excess to a risk-free return and you divide it by risk and end of story, so pretty simple. The problem with the Sharpe ratio is that it relies on a strong assumption that distribution of the returns is normal, that bell shape. Actually in reality we may have deviations from this normal distribution. And we have more often than not encountered two. One is the fact that the distribution may not be symmetric. And here we talk about skewness. And the problem also is that in the ends, in the tails of the distribution, we have what we call fat tails. So normally if you have very, very, very, very high returns this would be a low probability in the normal distribution or also at the other end very, very, very, very negative returns. That also should normally entail, if the normal distribution is normal at very low probability of occurring, but if we have fat tales, that probability is higher. And here we talk about kurtosis. There are ways of measuring, one such measure is called the omega measure of taking into account, incorporating these deviations from the normal distribution. So in another video, the next video, we're going to have a look at ways to improve the Sharpe ratio. [MUSIC]