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Accounting for Strategy Correlation in a Combined Portfolio

Article Quant Q&A · Author: web_ninja
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Summary

The document asks how to adjust existing weights when combining multiple strategies whose returns are correlated. Its answer begins by tying the adjustment to the portfolio objective: if the goal is return diversification, strategies with highly correlated returns could receive relatively lower weights than less correlated strategies. It does not prescribe a single adjustment formula or specify a target risk level.

For more structured approaches, the answer suggests Bayesian methods such as Black–Litterman or covariance blending, which can combine chosen weights with information derived from a factor-model covariance matrix. It also proposes treating strategy returns like asset returns and using mean-variance portfolio optimization. These are options to investigate rather than worked procedures: the document provides no estimates, optimization inputs, constraints, or empirical comparison. The appropriate method therefore depends on the intended portfolio objective and the assumptions used to estimate expected returns and covariance.

Key ideas

  • The right correlation adjustment depends on the portfolio objective.
  • For diversification, highly correlated strategies may be assigned relatively less weight.
  • Covariance blending can combine chosen weights with covariance information from a factor model.
  • Mean-variance optimization can treat strategy returns as asset returns, but requires suitable inputs and assumptions.

Tags

Portfolio constructionRisk managementStatistics
Full text
# How to account for correlation between strategies when they are added linearly?


# 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?

## Answer by Matt Wolf (score 3)

https://quant.stackexchange.com/a/17101

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.