The Sharpe, Treynor and Sortino ratios - Treynor and Sortino

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Del curso dictado por University of Geneva

Planning your Client's Wealth over a 5-year Horizon

203 calificaciones

University of Geneva

Planning your Client's Wealth over a 5-year Horizon

203 calificaciones

Curso 5 de 5 en SpecializationInvestment Management

In this Capstone project, you will have to choose between three different characters (each with a unique set of financial constraints and objectives) and design an appropriate wealth plan for them over the next 5 years. You will have to use the knowledge you gained in each of the four preceding courses to reach that objective. Indeed, you will need to know which assets to consider and how to manage them depending on changes in the economic outlook (Course 1), how to evaluate and deal with your character's emotional biases in order to suggest them a wealth strategy they will be able to follow (Course 2), how to build an optimal portfolio and manage its risk once the strategy has been designed (Course 3) and how to adequately measure the performance of your plan while taking advantage of investment vehicles and future trends in the investment management industry to further your character's goals (Course 4). This Capstone project was designed in collaboration with UBS, our corporate partner, who benefits from years of experience in guiding clients with their wealth planning.

De la lección

Final Reporting

The Sharpe, Treynor and Sortino ratios - Sharpe8:05

The Sharpe, Treynor and Sortino ratios - Treynor and Sortino8:12

Beating the benchmark or the peer group? - Peer group analysis12:00

Beating the benchmark or the peer group? - Screening criteria8:51

Conoce a los instructores

University of Geneva- Michel Girardin
Lecturer in Macro-Finance - Project Leader for the "Investment Management" specialization
Geneva Finance Research Institute

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

ratio.

How is it computed?

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

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

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

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

Okay, why do we take the beta here?

Well the reason is simple.

Actually Mr. Treynor believed that you should only be rewarded for

the non-diversifiable risk.

Do you remember this chart?

We saw it previously.

It shows the evolution of the total risk of a portfolio

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

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

Why?

Because basically, the more stocks you add,

the more diversification you bring in your portfolio.

And hence you are able to reduce, you are able to diversify away the part of

the risk which is diversifiable by adding more stocks.

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

here the estimation is that at roughly 25 stocks, you're only left

with market risk, i.e., non-diversifiable risk.

And that's the beta of your portfolio.

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

It's the risk which you cannot diversify away.

And this why Treynor doesn't look at the whole

risk of the portfolio but only the market risk.

So this is the measure used by Treynor.

A very recent study published in April 2016 in

the Journal of Economic Literature by this Mr.

Javier Vidal Garcia made an interesting analysis of comparing various measures.

The Sharpe, the Treynor, as well as others, the Modigliani square.

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

measures clearly but the ranking, what he did, he looked at the sample

of more than 16,000 actively managed funds worldwide.

And the conclusion is that basically the ranking does not change.

And so the Sharpe ratio provides a very good measure for

ranking the best funds in terms of risk adjusted returns.

Okay, but now we need to look at another improvement of the Sharpe ratio.

And this is provided by the Sortino.

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

hedge funds than for traditional money managers.

The Sortino ratio is computed likewise.

You see here the formula.

Basically, the main difference between the Sortino and

the Sharpe ratio is here again the denominator.

The numerator is the same, excess return over the risk free asset.

The denominator is different, and here we're talking about downside deviation.

No what is downside deviation?

Basically it's the deviation,

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

The subpar returns.

Why is this?

Assume you are, I'm managing a fund, right?

And you are my customer, okay?

And I promise you, I say I have a target return of 12%, okay?

In one year's time, my return,

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

I promised I would give you 12%, and I come up with 35%.

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

This is a higher volatility with this 35%,

it deviates so much from what you promise, from the average,

that [LAUGH] this is increasing my volatility measure.

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

If it's to the right of the average.

But if it's to the left, if I promise 12%,

and in 12 months' time I deliver -28, I bet I'm

going to get some nasty call from you and say, hey, what's going on here?

So, just to illustrate that we care much more about subpar volatility,

about below-average volatility, than above-average volatility.

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

Going back to the example we saw of ice creams and

umbrellas, we see here that the Sortino ratio also is big for

the long-short strategy, the last one, long ice cream, short umbrellas.

You see that it's 1.58.

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

we compute the performance over the risk-free return of 1%, and

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

14.9.

And we see that it's highest for this long-short strategy.

And indeed, the Sortino ratio is the ratio

which is most widely used when we look at hedge funds.

Because clearly there, this is,

we have here a kind of asymmetry that hedge funds should be

delivering good returns, and should be striving for absolute returns.

Basically they have this asymmetric attitude towards risk.

Take more risk when they think the market is going up, and hedge away

some of the risk either by raising the bucket of short position or

by taking some hedging against market folds when they expect market turmoil.

And so this why the Sortino ratio is actually more suitable

to measure the risk-adjusted returns when we are dealing with hedge funds.

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

we see with the study that we quoted here that it actually

gives the best possible result when we need to rank

funds by their risk and return characteristics.

We may improve the Sharpe ratio by taking into account that

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

may have the skewness and kurtosis.

So there are measures that adjusted for

these kind of deviations from the normal distribution.

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

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

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