Hi all, Suppose you have a long $100 short $100 strategy, how do I leverage it up? Is long $200 short $200 (double the size of the above market-neutral strategy) a leverage by 2? How does that affect the Sharpe ratio of the strategy? If I have several of these market-neutral strategies, and non-market-neutral strategies, what's the best way to form a portfolio and size each strategy? Let's do a simple one, let's not do the optimal portfolio, we just the most naive one, the 1/N rule, how do I size these strategies? Please shed some lights on me. Thank you!

Do some computer modeling. If the strategies are mechanical trading systems, backtest them together, trading out of a shared pool of capital. If the strategies are discretionary, model them using random number generators with appropriate frequency distributions, and test out the idea of "trading" them simultaneously out of a shared pool of capital (using computer modeling). This humble activity goes by the fancy name "Monte Carlo testing". You can teach yourself "the Kelly criterion" (for each strategy there exists a unique betsize fraction f which maximizes the rate of growth of capital) simply by varying the betsize in your computer modeling, and plotting (growth rate "CAGR") versus (betsize). You can discover whether or not there exists a unique set of betsizes { f1, f2, f3, ..., fn } which maximize the rate of growth of capital when you trade n strategies simultaneously. You can also discover the horrendous, crippling, sanity-destroying drawdowns that Kelly betting unavoidably produces. Then you can explore the trade-off curve, GrowthRate versus Drawdown, by running your computer model at many different betsizes. Then you can choose the sub-Kelly betsize that's right for you: the one that gives drawdowns you can live with, accompanied by a GrowthRate that you are willing to accept.

Also I'd suggest running some regressions on the returns of each strategy vs. the Fama French factors. This will give you an idea of what influences the returns for each strategy. If you build a covariance matrix for the strategies, you can make a mean-variance-optimized portfolio out of them similar to what you would do with a portfolio of stocks.

Risk management is still important whether at stocks and portfolio level. Whether you need a portfolio of trading strategies, you are still evaluating the risk isn't it? Money management is very important to trading success and even more important than picking the right stocks or securities. So if you need some related information, here it is: <a href="http://www.stock-trading.me/2010/05/risk-management-in-stock-trading/">Risk management in Stock trading</a> <a href="http://www.stock-trading.me/2010/05/stock-portfolio-risk-management-%E2%80%93-understanding-the-strategy/">Stock Portfolio Risk Management â Understanding the Strategy</a> Wish you good luck in managing your trades.

Is the Kelly ratio yet another parameter that's subject to being overfitted, possibly? It should be a time-varying number - how sensitive and how easily it gets overfitted?

I never got the mean-variance stuff worked. How do you get future/expected mean and future/expected covariance?

You use past returns. If you have daily returns for each strategy, you can use that data series to build the cov matrix. These relationships don't always hold, but there are reasons for different strategies to be profitable at different times. Some do well with volatility while others might not, etc.

I tried past returns, and using historical means and covs to approximate expected means and covs... Never worked... too sensitive to noise, even in backtest, you've got good results from using the mean-variance stuff? And you did mean-variance portfolio optimization?

Maybe you can create an allocation algorithm for the strategies.... Like an overlay... If Strategy X and Strategy Y are at Max or Worst profit levels, switch to strategy Z.... So its a kind of regime shift, or a position size allocation shift... This kind of trading could propagate up or down through the individual strategies... The overlay could be biased towards being uncorrelated, or towards risk aversion.... You could allocate on the basis of some statistical properties like correlation, drawdown, returns, etc...