# How to combine trading signals to achieve higher capital efficiency?

I trade use a completely automated approach where all signals are generated by proprietary trading strategies. However, recently I encountered an challenging problem:

Imagine we have 3 Strategies that all make 5% return annually with the same volatility and they rarely trade together. The question is how to make the best use of capital to maximize the portfolio returns.

A. The naive approach is to allocate 1/3 of cash to each strategy, and we will end up with $1/3 * 5 + 1/3 * 5 + 1/3 * 5 = 5\%$. This is effectively the weighted average approach. It does have the merit of diversification, but the cash is undoubtedly utilized inefficiently. This is in fact the lower bond of portfolio returns.

B. Another approach is to try to share the risk capital among the 3 strategies in some efficient way. Ideally, if they never trade together and we are allocating the full capital to each strategy should any signal sets up, then we will end up the upper bond of return, which is $5\% * 3 = 15\%$ for the entire portfolio.

In reality, 3 strategies tend to have trades that set up together. So, what do you think is the optimal solution for achieving maximum capital utilization?

Svisstack has provided a good starting point for discussion. Now, I will refine my questions based on his reply:

1. How to combine signals efficiently when there are N strategies, shall we keep capital fully invested while weighting each strategy by their performance?

2. What type of strategies, if combined together, can yield maximum benefits? For example, shall we combine two strategies that are both based on similar hypothesis, similar holding period, or two strategies that rarely traded together regardless of other characteristics?

3. Is it wise to combine 2 strategies that traded on different assets?

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Optimal scenario should use all available capital for 3 strategies, in way that when only 1 strategy trading then using all available capital, when second trying to create trade while first taken all capital, then half of capital can be moved from 1 strategy to cover 2 strategy trades or 2strategy wait for release capital from 1 strategy.

When third strategy try to get in then same, should wait for capital release or capital allocation from 1 and 2 strategy should be moved to cover third strategy trades in proper ratio.

In your scenario when 3 strategies have same performance estimation, capital should be spitted equally between active (trading) strategies at every moment.

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Thank you. Your approach is in fact very similar to my own approach. The general framework you described, if implemented well enough, can be truly capital efficient. Based on your answer, I've added some more thoughts into my question. – Simon Jun 26 '14 at 2:09
@Simon: one question at time – BlackMamba Jul 20 '14 at 13:20

Can't you combine them with a Black-Litterman model of their covariant risk/return?

This should work well enough, though I would recommend also implementing Idzorek's extension for numerically calculating the appropriate omega matrix based on view confidence as a percentile:

http://datalab.morningstar.com/knowledgebase/aspx/files/Step_by_Step_Guide_to_the_Black_Litterman_Model.pdf

I have also been meaning to get around to reading Meucci's book, which apparently covers this sort of thing:

http://www.amazon.com/Asset-Allocation-Springer-Finance-Textbooks/dp/3642009646

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Thank you experquisite, but your answer may not be really suitable for the problem in discussion. – Simon Jun 26 '14 at 2:17
I've pointed out an approach that takes into account the covariance of the strategies' returns, the strength of the trading signals as well as your own risk tolerance. This is all well-trodden ground. The next level is stochastic control. But if you want to mess around talking about manually mixing and matching strategies, I guess that's your prerogative. – experquisite Jun 26 '14 at 2:41
Hi experquisite, don't get me wrong. Your answer is quite useful but just not suitable for my own application. I'm trading these in quite short time horizon, thus I prefer methods that are simple and robust. Framework like Black-Litterman model is of course useful, but so far I haven't found ways to integrate them in a time-efficient way into live trading. Let me read the links you provide as well. – Simon Jun 26 '14 at 3:19
It is possible to online calculation of most of what you would need, see: thalesians.com/archive/public/academic/finance/papers/… But, as you say, perhaps that wouldn't be fast enough if you are doing HFT. – experquisite Jun 26 '14 at 17:05