# How to account for correlation between strategies when they are added linearly?

There are n strategies which are going to be combined linearly. Using a pre-exisiting model I get a set of n weights which will be used to combine the strategies. But the model does not take correlation between strategies into account. How do we account for correlation between strategies when they are added linearly?

Mathematically,

w_1, w_2 ... w_n are the weights assigned to n strategies. I have the correlation matrix C of the returns from these n strategies. How will these weights be adjusted then to account for correlation between the strategies?

You are not forced to apply a certain way to account for correlations.

I recommend you think about the big picture first: Why do you want to account for correlations? Do you want to have a diversified book, return wise? Then you should look at which strategy returns correlate highly and weigh those strategies relatively lesser than other strategies, possibly in a way to have the sum of weights of highly correlating strategies equal the weights of lowly correlating strategies.

You may specifically want to look at a Bayesian approach, such as the Black-Litterman or a Blend Covariance approach before delving into more complex models. The latter allows you to blend chosen weights with factors derived from a covariance matrix implied from a factor model.

Alternatively you could treat the strategies as traded assets (which they essentially are) and build a mean-variance optimized portfolio.

• Mean variance optimization would have been my first approach to solve the actual problem of combining strategies. However, what we need is a way to alter these weights that is an output of some series of optimizations to account for correlation. – web_ninja Mar 25 '15 at 8:05
• I do not fully understand your comment. M-V optimization does exactly that. It takes the return volatility of each asset into account and optimizes the weights as function of return volatility. – Matt Mar 25 '15 at 8:09
• I meant to say if I had to come up with the weights for strategies I'd have used mean variance optimization but I am already given these weights from some other kind of optimization. The task that I have at hand now is to modify the weights such that it takes correlation into account. I hope I am clearer now. – web_ninja Mar 25 '15 at 8:34
• well then make adjustments as I suggested in the first part of my answer; adjust weights up and downward based on pairwise correlations between strategy returns, though I would also take into account the correlation between return variations. I will edit my answer to provide more specific recommendations. – Matt Mar 25 '15 at 8:37