Combining Covariance Matrices with Weighted Averages

Summary

The document asks whether a weighted average of three variance-covariance matrices is a sound way to combine risk estimates derived from the same return series. The candidates are a basic sample estimate, a version with a correlation shock, and an exponentially weighted estimate that emphasizes more recent observations. The proposed combination assigns each matrix a weight and sums the weighted entries.

No answer, derivation, or empirical evidence is included, so the document does not establish whether a particular weighting scheme improves forecasts or portfolios. A practical assessment would need to specify how weights are chosen and check whether the combined matrix retains valid covariance properties, including positive semidefiniteness. It also leaves open whether the shock-adjusted and time-weighted estimates use compatible assumptions. The text is best read as a question about model averaging for portfolio risk inputs, rather than as a validated method.

Key ideas

• The proposed method combines sample, shock-adjusted, and exponentially weighted covariance estimates.
• A weighted sum combines corresponding matrix entries using chosen weights.
• The document provides no evidence that this combination improves risk forecasts.
• A candidate combined matrix should be checked for valid covariance properties.

Tags

# Weighted Average of Var/Covar Matrix


# Weighted Average of Var/Covar Matrix












I have three different types of variance-covariance matrices derived from the same series of returns:

- A simple variance-covariance matrix using ret.corr().

- A variance-covariance matrix adjusted with a shock on the correlation.

- A variance-covariance matrix calculated using the EWMA method, which places more weight on the most recent data.

I am considering combining these matrices to create a new variance-covariance matrix. My proposed method is to take a weighted average of the three matrices:

My idea was to do weighted average sum of all this matrix :

new_var_covar = w1 * var/covar1 + w2 * var/covar2 + w3 * var/covar3

I would like to know if this approach is mathematically sound or if there are any issues with it. I'm not an engineer or obtained a degree in applied math. Be simple and detailed in your explanation please !

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