[MUSIC] Hi there, in this set of videos, we are going to have a look at how to measure performance and adjust measure for risks. So we are 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 a 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% inn 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're making a deposit. If that yield is say, 1% then if that same risk free return is 10%, in this case you're going to tell me, well, Mr. Gianna, 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, 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 of 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 discussed long, short, equity strategies. And we did that with this illustration here, which I will summarize here. It's the example of ice cream versus umbrellas. Remember, you're a hedge fund manager for a traditional manager. And if 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 will be hot, the company A which produces ice cream will have good returns and the company and if the summer is, the weather is rather miserable you should be invested in 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, your 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, you know, in May you're not really quite sure what to do in terms of 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 enhance what you do is 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, I computed the returns. And you see the performance, umbrella -26% ice cream +23%. The 50:50, well you get 50% of 23 + 50% of -26, that's a -1.5 loss. And the long short strategy of long ice cream and 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 umbrella, so on result not surprisingly the Sharpe ratio. Which will be measuring the performance less the risk free assets return which we put here in brackets and it's at 1%, so you do 23- 1 all 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? 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 an excess to a risk free return, and you divide it by risk. End of story, pretty simple. The problem with the Sharpe ratio is that it relies on a strong assumption that the distribution of the returns is normal, that bell shape. Actually in reality, we may have deviations from this normal distribution. And we're, more often than not, encounter 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 and a normal distribution or also at the other end a very, very very, very negative returns that also should normally entail if the distribution is normal and variable probability of occurring. But if we have factors that probability is higher. And here we talk about cartosis. 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 sharp ratio. [MUSIC]