When Pairwise Deletion Is Appropriate for Stock Returns

Summary

The document explains how to think about missing observations when estimating covariance between two stocks using only dates when both returns are available. It frames the decision around whether the missingness mechanism could affect the inference, rather than whether missing dates appear irregular or systematic.

A recurring missing day, such as every Monday, may still be treated as missing at random if there is a sound reason to believe that the schedule does not affect the results. The answer cautions that this assumption can be difficult to defend: missingness related to liquidity, for example, could matter. Mondays are a particular concern if a Monday return pattern is plausible, since omitting those observations could distort estimates. The discussion is a conceptual warning, not a test for diagnosing missingness or a complete treatment of covariance estimation; its conclusion depends on the market and the reason observations are absent.

Key ideas

• Pairwise deletion estimates covariance using dates when both stock returns are observed.
• Systematic missingness can be compatible with missing at random if it does not affect the inference.
• A relationship between missingness and liquidity can undermine the missing-at-random assumption.
• Omitting Mondays may matter if a Monday return effect is plausible.

Tags

# How to deal with missing stock returns?


# How to deal with missing stock returns?












If I want to calculate the Covariance between two stocks but there are missing days in both, how can I deal with missing data? I want to use Pairwise deletion and only use the days of which both observations are seen. I have been reading up on pairwise deletion and I have seen that the data must be missing at random. If the missing days where every Monday for example, would this be missing a random?

## Answer by kurtosis (score 1, accepted)

https://quant.stackexchange.com/a/57452

If the days are missing is a systematic way but you have reason to believe that the mechanism for missingness would not affect your inferences... then yes, your data are MAR and you can proceed. However, that belief tha the missingness mechanism is immaterial is often tough to defend: even a relation to liquidity would undermine a claim of MAR.

Regarding your example about Mondays... The Monday Effect is the purported effect that stocks which declined Friday are more likely to rise on Monday. The effect is often attributed to short sellers not risking being short over a weekend since more news comes out on weekends and good news would cause losses. If you (or your critics) believe there is a Monday Effect, then data missing on Mondays would not be MAR.

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