0:00

[MUSIC]

Â So one improvement we can make over the Sharpe ratio is the so-called

Â Treynor ratio.

Â How is it computed?

Â Well, you see that the numerator is actually the same at the Sharpe ratio.

Â It's the excess return over the risk-free rate, Rf.

Â It's the denominator that changes and we see here beta i,

Â which is the beta of portfolio i or asset or fund.

Â Why do we take the beta here?

Â Well, the reason is simple.

Â Actually, Mr. Treynor believed that you should

Â only be rewarded for the non-diversifiable risk.

Â Do you remember this chart?

Â We saw it previously.

Â It shows the evolution of the total risk of a portfolio,

Â as a function of the number of stocks you include in a portfolio.

Â You see that the more stocks you include in a portfolio, the lower the total risk.

Â Why?

Â Because basically, the more stocks you add,

Â the more diversification you bring in your portfolio.

Â And hence, you're able to reduce,

Â you're able to diversify away the part of the risk,

Â which is diversifiable by adding more stocks.

Â And basically, in the end after a certain number of stocks,

Â here the estimation is that at roughly 25 stocks you're

Â only left with market risk i non-diversifiable risk and

Â that's the beta of your portfolio.

Â And hence, this is the part of the total risk, which you be rewarded from.

Â It's the risk, which you cannot diversify away.

Â And this is why Treynor doesn't look at the whole risk of the portfolio,

Â but only the market risk.

Â So, this is the measure used by Treynor.

Â A very recent study published in April 2016 in the Journal

Â of Economic Literature by this Mr. Javier Vidal Garcia made

Â an interesting analysis of comparing various measures,

Â the Sharpe, the Treynor as well as others, the Modigliani squared.

Â And basically, what he came up with the result is that you have

Â different measures clearly, but the ranking, what he did.

Â He looked at the sample of more than 16,000 actively

Â managed funds worldwide and the conclusion is that,

Â basically, the ranking does not change.

Â And so, the Sharpe ratio provides a very good measure for

Â ranking the best funds in terms of risk-adjusted returns.

Â 3:11

But now, we need to look at another improvement of the Sharpe ratio and

Â this is provided by the Sortino and

Â we'll see why this measure is actually more suitable for

Â hedge funds than for traditional money managers.

Â The Sortino ratio is computed likewise, you see here the formula.

Â Basically, the main difference between the Sortino and

Â the Sharpe ratio is here again, the denominator.

Â The numerator is the same.

Â Excess return over the risk-free asset.

Â The denominator is different.

Â And here, we're talking about downside deviation.

Â Now, what is downside deviation?

Â Basically, it's the deviation,

Â it's the volatility measure to the left of your distribution.

Â 4:11

Assume you are managing a fund and

Â you are my customer and I promise you,

Â I say, I have a target return of 12%.

Â In one year's time, my return,

Â the return of your fund you bought from me is actually 35%.

Â I promise I would give you 12% and I come up with 35%.

Â I bet you're not going to call me and say, what did you do?

Â This is a higher volatility with this 35%.

Â It deviates so much from what you promised,

Â from the average that [LAUGH] this is increasing my volatility measure.

Â Not many people are going to complain about this kind of volatility,

Â if it's to the right of the average.

Â But if It's to the left, if I promise 12% and

Â in 12 months time, I deliver minus 28.

Â I bet I'm going to get some nasty call from you and

Â say, hey, what's going on here?

Â So just to say, just to illustrate that.

Â We care much more about subpar volatility,

Â about below average volatility than above average volatility and

Â this is precisely what this downside volatility measure aims at capturing.

Â Going back to the example we saw of ice creams and umbrellas.

Â We see here that the Sortino ratio also speak for

Â the long-short strategy, the last one.

Â The long ice cream, short umbrellas.

Â You see that's 1.58.

Â So, here is what we do is we take the performance.

Â We compute the performance over the risk-free return of 1% and

Â we divide not by the volatility, but the downside volatility, i.e,

Â 14.9 and we see that is highest with the for this long-short strategy.

Â And indeed, the Sortino ratio is the ratio,

Â which is most widely used when we look at head funds.

Â Because clearly there, we have here a kind of asymmetry

Â that hedge funds should be delivering good returns and

Â should be striving for absolute returns, i.e.

Â Basically, they have this asymmetric attitude towards risk.

Â Take more risk when they think the market is going up and

Â hedge away some of the risk, either by raising the bucket of short positions or

Â by taking some hedging against the market falls when they expect marker turmoil.

Â And so, this is why the Sortino ratio is actually more usable to measure

Â the risk-adjusted returns when we're dealing with hedge funds.

Â So in conclusion, the Sharpe ratio is the most wildly used measure and

Â we'd see with the study that we are a quoted here that it

Â actually gives the best possible result when we need to

Â rank funds by their risk and return characteristics.

Â We may improve the Sharpe ratio by taking into account

Â the fact that the distribution of returns may not be normal and

Â may have the skewness and kurtosis or there are measures that are adjust for

Â this kind of deviation from a normal distribution.

Â But all in all, I would say that the Sharpe ratio provides a very good first

Â measure and a good proxy to use when you want to assess the risk-adjusted returns.

Â [MUSIC]

Â