Match Correlation Weighting to Exponentially Weighted Volatility

Summary

The document asks how to estimate portfolio volatility when each of two assets has an exponentially weighted variance estimate. The central guidance is to calculate correlation using the same weighting convention as the variances. Applying common weights to the products of daily excess returns gives a consistent weighted covariance matrix and is described as the theoretically preferred approach.

The answer acknowledges that practitioners also combine weighted variances with an unweighted correlation estimate. It provides no empirical comparison or details on selecting the decay rate, so the practical performance of the alternatives is not established. Its main lesson is about internal consistency when assembling covariance inputs for a two-asset portfolio, rather than about which weighting scheme will forecast risk best in a particular market.

Key ideas

• Portfolio variance depends on both asset variances and their covariance.
• Use the same observation weights for correlations as for the variance estimates when building a weighted covariance matrix.
• An unweighted correlation combined with weighted variances is also used in practice.
• The discussion recommends consistent weighting on theoretical grounds but supplies no comparative empirical evidence.

Tags

# Answer by Kermittfrog (score 1, accepted)


# Decay factor and volatility (2 assets): do you keep simple correlation to calculate vol? or exponentially weighted correlation?












I have calculated exponentially weighted variances (and covariance) for a future and the underlying index.

Now that I have exponentially weighted variances for my 2 assets using a lookback period of 1 year, and knowing that the portfolio of 2 assets volatility depends on the correlation between these 2 assets, do I need to use the simple correlation (simple returns with no decay) or do I need to use the correlation between the new exponentially weighted variances?

## Answer by Kermittfrog (score 1, accepted)

https://quant.stackexchange.com/a/52914

From a theoretical point of view, you are supposed to use the correlation calculated under the same measure (i.e. multiplying daily excess returns and weighting that product by your weights).

In practice, I have seen both approaches: Weighted correlations and weighted variances, i.e. a weighted covariance matrix, and a mixture: unweighted correlations with weighted variances. Again, the first approach is theoretically sound and should be preferred.

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