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Sharpe Ratio vs. Calmar Ratio vs. Sortino Ratio

Discussion in 'Strategy Development' started by mizhael, Jun 22, 2010.

1. mizhael

__________________________________SharpeR CalmarR SortinoR
Optimized Strategy Maximizing Sharpe Ratio 1.82 0.48 2.3
Optimized Strategy Maximizing Calmar Ratio 1.48 0.69 2
Optimized Strategy Maximizing Sortino Ratio 1.78 0.54 2.35

2. mizhael

This 3x3 performance matrix shows the result of optimizing strategy parameters w.r.t to each criteria...

3. mizhael

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Whichever one is best is whichever one is most predictive. That is, whichever one correlates most with future risk (volatility/drawdown). In other words, take 12 months of a strategy, calculate these ratios, then for the following 12 months see if the risk is approximately as predicted. If not, back to the drawing board.

Note I personally would only look at these ratios if trading 30+ investments in a basket of vehicles. If you're talking strategies, a mix of 30+ strategies then. Otherwise any measure of risk is unlikely to be predictive because your sample size is too small.

5. mizhael

Could be dependent on the periods you choose...

Yes, this is on 30+ securities ...

If it's dependent on the periods you choose then Sharpe, Calmar, Sortino ratios are meaningless.

What is the question? I'm trying to say there has to be enough data to base a hypothesis on. You might be able to get away with, say, 30 months of data to predict 1 month of future volatility. You'd be better off, I think, with 30 months of data on 30 equities, to try and predict the next 1 month of risk/drawdown/volatility. Some would argue, use as much data as possible, going back decades.

7. mizhael

It is based on the standard deviation of the down returns.

What if my down returns are stable, always:

-9%, -9%, -9%, -9%, etc...

i.e. lets say I have the following return stream:

+10%, -9%, 10%, -9%, +10%, -9%, 10%, ...

then the standard deviation of all those down streams is 0.

What's the Sortino ratio?

If either all 30 stocks have -9% down always, or for 30 months a single stock is -9% down always, something's wrong with your data because this has never happened in the history of the world.

Also Sortino ratio does *not* use standard deviation. It uses semi-standard deviation. The semi-standard deviation of those downstreams is *not* 0.

9. blackjack007

what's wrong with a data set consisting of -9%, -9% -9% etc?

what if a stock had monthly returns as follows:
-5.43%, -2.38%, +7.34%, -2.01%, +0.72%, +2.18%, +15.4%, -9.04%, -11.22%, +6.47% on so on.

i'd bet a trillion dollars no stock in the history of the world has had those monthly returns. are you saying that data set is also invalid even though it looks "realistic"?

what makes -9%, -9%, -9%, an invalid data set? just because the numbers look too pretty to you?

a formula either always works or never works.