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Â Hi there.

Â In this set of videos, we're going to have a look at how to measure performance and

Â adjust the measure for risks.

Â So we're going to have a look at risk adjusted returns.

Â And we'll see how these measures can be refined

Â by making more precise definitions of risk.

Â So we're going to start with the Sharpe ratio.

Â Sharpe with an e, remember?

Â We saw that, please put an e at Sharpe, for he's a man.

Â 1:01

Why do we do this?

Â Well, for one simple reason.

Â If I tell you, you buy this fund and you will make 12% in 12 months time,

Â you're going to tell me, okay 12%, that's interesting.

Â But you will probably be much more interested if that return compares say

Â to a risk-free return, i.e., the kind of return you make on a deposit.

Â If that yield is say 1%, then if that same risk-free return is 10%,

Â in this case, you going to tell me, well Mr. Giardin,

Â you come with 12% promise expected return.

Â Number one, well I'm not sure to make that kind of return in 12 months time and

Â I have an alternative, which is the risk-free return.

Â And this, I'm pretty sure I can make this kind of return at 10%.

Â So this is why we compare the return to a risk-free return.

Â 2:05

And we divide that by the risk.

Â So clearly, the higher the Sharpe ratio, the better the investment,

Â the stronger the case for buying a fund which has a high Sharpe ratio.

Â So this is why in the fund industry, the Sharpe ratio is widely used,

Â it's actually the most widely used measure.

Â 2:42

What?

Â I'm sure you remember.

Â If not, please go back to course one and take a look at the video

Â where we discuss long short equity strategies.

Â And we did that with this illustration here which I will summarize here.

Â It's the example of ice creams versus the umbrellas.

Â You remember you're a hedge firm manager or a traditional manager.

Â And we're at the beginning of the summer right, like now, May,

Â and you have to make a prediction as to whether the summer will be hot or not.

Â And hence, if the summer it will be hot,

Â the company A which produces ice cream will have good returns.

Â 3:42

So this is the end result, in September this has been a hot summer,

Â so ice creams have been doing good, umbrellas badly.

Â And here we compare these four strategies.

Â The first three strategies are traditional ones.

Â You're long, so +IC+UM.

Â You have a long position.

Â You buy the ice cream company, +UM, you buy the umbrella company.

Â 50:50 is you don't know, really.

Â In May, you don't really quite sure what to do in terms of the weather forecasting,

Â so you put half of your money in the ice cream company and

Â half of the money in the umbrella company.

Â 4:29

And the fourth one is the only strategy which is alternative,

Â which is the typical strategy used by hedge funds, would be to be you

Â have the strong conviction that the summer will be hot and sunny.

Â And hence what you do is you go long the ice cream and

Â you sell short the umbrella company.

Â Okay, so now what is the end result of all this?

Â 4:54

We computed here, or I computed the returns and you see the performance

Â umbrella minus 26%, ice cream plus 23%.

Â The 50:50, well you get 50% of 23.0 plus 50% of -26.0, that's a -1.5 loss.

Â And the long short strategy of long ice cream

Â short umbrella yields the highest return at 24.5%.

Â And look at the volatility of the long ice cream,

Â short umbrella it's actually lower than the volatility of

Â the long ice cream or the volatility of the long umbrellas.

Â So and results not surprisingly, their Sharpe ratio,

Â which will be measuring the performance less the risk-free asset return,

Â which we put here in brackets and it's at 1%.

Â So you do 23 minus 1 for

Â the ice cream divided by 10.8 gives you a Sharpe ratio of 2.04.

Â So the winner is clearly the long short strategy because you

Â see the Sharpe ratio here is the maximum of 2.22.

Â Now what are the pros and cons of the Sharpe ratio?

Â Well the merits of the Sharpe ratio is that it's simple and

Â intuitively appealing.

Â You can explain it very easy, you take the performance, you measure it in excess to

Â a risk-free return and you divide it by risk and end of story, so pretty simple.

Â The problem with the Sharpe ratio is that it relies on a strong

Â assumption that distribution of the returns is normal, that bell shape.

Â Actually in reality we may have deviations from this normal distribution.

Â And we have more often than not encountered two.

Â One is the fact that the distribution may not be symmetric.

Â And here we talk about skewness.

Â And the problem also is that in the ends, in the tails of the distribution,

Â we have what we call fat tails.

Â So normally if you have very, very, very,

Â very high returns this would be a low probability in the normal distribution or

Â also at the other end very, very, very, very negative returns.

Â That also should normally entail, if the normal distribution is normal at very low

Â probability of occurring, but if we have fat tales, that probability is higher.

Â And here we talk about kurtosis.

Â There are ways of measuring,

Â one such measure is called the omega measure of taking into account,

Â incorporating these deviations from the normal distribution.

Â So in another video,

Â the next video, we're going to have a look at ways to improve the Sharpe ratio.

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Â