Choosing a Covariance Window for Weekly and Fortnightly Portfolio Returns

Summary

The document asks how to estimate covariance when optimizing a minimum-variance portfolio over weekly or fortnightly cumulative returns. It contrasts calculating covariance directly from returns sampled at the target frequency with scaling a daily covariance matrix to represent a longer holding period. The example uses a rolling historical window and frames the issue in the context of replicating research on portfolio selection with option-implied volatility and skewness.

No answer or empirical comparison is included, so the document does not establish which calibration approach is appropriate. The question highlights that the return horizon used for optimization and the assumptions behind covariance scaling need careful alignment. In particular, simply multiplying daily covariance by the number of days is a proposed alternative in the question, not a validated method here. Readers will need additional analysis to account for how returns are compounded, sampled, and estimated over the chosen horizon.

Key ideas

• The document asks whether portfolio covariance should be estimated at the same frequency as the cumulative return horizon.
• It contrasts direct covariance estimation from periodic returns with scaling daily covariance by the number of days.
• The example concerns minimum-variance weights and a replication involving option-implied volatility and skewness.
• No answer, derivation, or evidence is provided to resolve the estimation choice.

Tags

# Calibration of Covariance Matrix for a Cumulative Period Return


# Calibration of Covariance Matrix for a Cumulative Period Return












I am trying to compute optimized weights (minimum-variance portfolio) for a cumulative return over a period (weekly or fortnightly). In a daily return setting, it is quite simple, I just compute a daily covariance matrix over the past 21 days (yes I used a monthly historical rolling window for the calibration in this case) and optimize the weights based on a minimized volatility/variance goal.

My question is, if I were to change from a daily return to periodic cumulative return setting (be it weekly or fortnightly), do I need to change the frequency of the covariance matrix for optimizing the weights? i.e. calibrating the covariance matrix using historical periodic returns (weekly or fortnightly) OR calibrating the covariance matrix using historical daily returns and 'lengthening' the covariance matrix by multiplying the whole thing element-wise by 5 (weekly) or 10 (fortnightly).

I am attempting a replication of DeMiguel, Plyakha, Uppal, Vilkov (2013): Improving Portfolio Selection Using Option-Implied Volatility and Skewness.

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