Sorry, typing equations is a bad habit. With Pearson correlation, we can directly relate the portfolio volatility to the allocations, market volatilities, and correlations. However much non-linear behavior is skewing the model, you can easily write the equations that hold retractively. Saying that you have factored the variance in the data into normal and cointegrated components can be extremely useful. I would love to know if anyone has found a way to start with Spearman's Rank Correlation and relate it to portfolio management.
Don't you need to factor in liquidity somehow? Correlation doesn't mean anything when liquidity dries up...
I can't speak to illiquid trading. I select Futures markets which have a consistent core volume and open interest. CFTC tracked markets with a persistent commercial interest are ideal. Then I limit positions to 10% of the average volume and 5% of the open interest.
If your goal is improved prediction of the correlation matrix between assets (here: systems), then why not keep it even more robust than non-parametrics... I doubt if we should try to beat the naive weighting scheme... in-sample gains can be propagated by momentum but eventually the overallocation errors will catch up with us, once the profits of our historically best systems revert to the mean...
I don't know that I understand "the naive weighting scheme." I have seen a variety: margin weighting, volatility weighting, stop-loss % of trading account, ... Yes, one wishes to understand the system-market combination. (If a system is a pair-trading system, it is the combination of the system and the pair of markets.) I agree with you that the the performance of the system-market combination should not be chased blindly as it is a trailing indicator. For me, the main thing is the correlation of the underlying markets. If I have a system which wants to buy Euro futures and a system which wants to sell Swiss Franc futures, then I can get more contracts with the same risk than if it had been buy-buy or sell-sell. The principle purpose for keeping a performance metric in a Portfolio Allocation scheme, IMHO, it to objectively weed-out non-performers. It is too easy to backtest 100 markets, and then publish an allocation on the top 4. I would want to know that my market selection did not unduly bias my results. (Unfortunately, showing all 100 tends to confuse prospective investors, but knowing that you have done things honestly means that you can safely bring-up the topic when productive.) The place that Modern Portfolio Theory gets complicated is that one needs money management constraints to make it real. Here are things that I find relevant: Current Positions Likelihood that a combination will enter today Transaction Cost Estimates Maximal Position Size per combination (Vol %, OI %) Expected return per combination (this is where both historical performance and current market conditions enter) Forecast market volatility Forecast market correlation Is Rebalancing allowed today? Target Portfolio Volatility Maximum Allowed Margin Are non Synergistic Trade Allowed? Modern methods can do a good job of forecasting the size of the market return (if not direction), market volatility and market correlation. If you stick to systems that hold positions at least a few days, then this tells you system-market correlation and volatility. The biggest negatives to sophisticated Portfolio Allocation are that the costs of rebalancing can be high, that the market model can be unrealistic, and that trading more markets is more error prone. If you can nail these issues down, your drawdown and especially the volatility of your portfolio balance should go way down even with fairly modest systems. Having a real Portfolio Allocation system in place allows us to replay historical stress periods. Of course ones worst day is always in the futures. The electric company can't be sure we won't all turn on our vacuum cleaners together, but the measured affect is that our house voltage stays within a small range. Probability/statistics does work.
Have you ever looked at the correlation of the underwater equity curve between markets and systems?. We added this to TradersStudio Professional because many of our customers requested it. The correlations of the equity curve of the systems or even correlation between markets is not as important as the correlation of drawdowns.
Yes, inside of tradersstudio we use a drawdown (equity curve) and take the correlation of each market trading a given system. This allow us to get a correlation of drawdown between markets. You can use this correlation of drawdown as a filter so you can trade a larger basket and limit positions based on the correlation of drawdown. Since this is calculated as the system trades, these correlations might change over time. This means different markets would be traded over the testing period as markets evolve over time. Also these adjustment would continue as we go forward.