Forums  > Risk Management  > what’s the case for sharpe anyways?  
     
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Eulers


Total Posts: 1
Joined: Apr 2020
 
Posted: 2020-04-26 09:06
Using metrics to track performance it has always boggled my mind why sharpe is being used. I mean whats the usecase when return / max DD is the end goal anyways? Using martingale/ higher dimensional momentum scale in/out position sizing, it can go as far to really hurt the “sharpe”. What and why do people use sharpe, whats justified?

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svisstack


Total Posts: 341
Joined: Feb 2014
 
Posted: 2020-05-08 10:55
I would say that maximizing terminal utility or CAGR is the end goal and the return / max DD is just another approximation like Sharpe?

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kloc


Total Posts: 32
Joined: May 2017
 
Posted: 2020-05-08 15:33
Well, there are Stirling and Calmar ratios if you prefer CAGR/DD type of risk metrics?

Not as popular as Sharpe, but they're pretty standard...

gamerx


Total Posts: 11
Joined: Sep 2012
 
Posted: 2020-05-10 08:25
There are many problems with the sharpe ratio, but same goes for other metrics.

Guess it is the preferred one simply because everyone else is using it. Makes performance comparable across the board this way.

EspressoLover


Total Posts: 419
Joined: Jan 2015
 
Posted: 2020-05-10 22:06
Optimal Kelly sizing is linearly proportional to Sharpe ratio. Therefore for a risk-neutral investor in an infinite period game without leverage constraints, logarithmic utility scales quadratically with Sharpe regardless of higher moments.

Optimal log-returns are equal to Sharpe^2. For example a strategy of Sharpe 0.5 can achieve 25% annualized log-returns at optimal leverage. Sharpe 1.0 can achieve 100%. Sharpe 2.5 can achieve 625% returns. Sharpe 0.1 can achieve 1%. Etc.

Another way to think about this is to consider the law of large numbers. Consider period to period returns of an asset as an i.i.d. process. (For any reasonably liquid and efficient asset, some sufficiently large period will have sufficiently small auto-correlation between periods.) In the long run, the investors log-wealth converges to a normal random variable. The variance of this "cumulative wealth" variable is linearly dependent on the variance of the assets' return variance. Any higher moments converge to zero.

In other words, for a sufficiently long-term investor without leverage constraints, all risk metrics besides Sharpe become irrelevant.

Good questions outrank easy answers. -Paul Samuelson
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