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]