__________________________________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

This 3x3 performance matrix shows the result of optimizing strategy parameters w.r.t to each criteria... Any comments about Sharpe Ratio vs. Calmar Ratio vs. Sortino Ratio?

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.

Could be dependent on the periods you choose... Yes, this is on 30+ securities ... Your definition of "sample size" is across the basket constituents?

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.

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.

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.

It's not because the numbers don't look pretty to me. It's because they are highly unlikely. My point is, either use real data or use generated numbers (either Pareto distribution or Gaussian distribution), if you make them up by hand they are highly unlikely to be useful in real situations. If a formula always works, does the P/E ratio always work? What about when the earnings are zero? (This is not realistic since earnings are never exactly zero, however it becomes realistic because of rounding errors, earnings of between -0.005 and +0.005 can be rounded to 0.) I kindof see what you're saying, but the question is "Does Sortino ratio make any sense?" My answer is, it makes sense if it's predictive of future risk. And, with the data given, the data is invalid and/or the Sortino ratio isn't useful with this data.