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Handling Zero Returns in CAPM Excess-Return Analysis

Article Quant Q&A · Author: Razbolt
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Summary

The note addresses whether days with zero observed stock returns should be removed before calculating excess returns in a CAPM analysis. Its main guidance is to first determine whether the zeros represent genuine market observations or data errors. Erroneous values may warrant exclusion or imputation, while authentic zero returns should generally remain in the dataset.

Removing genuine observations changes the sample to days with nonzero returns, which can make conclusions less representative because future zero-return days cannot be identified in advance. The answer also recommends checking whether including or excluding the zeros materially changes the findings. This is a preprocessing principle rather than a full CAPM procedure; it does not diagnose why zeros occur in the example data or prescribe a specific method for validating or imputing them.

Key ideas

  • Verify whether zero returns are genuine observations or data errors before preprocessing.
  • Removing real zero-return days can bias results toward nonzero-return days.
  • Keeping valid observations supports findings that apply across all trading days.
  • Compare results with and without the zeros to assess their practical impact.

Tags

EquitiesStatisticsBacktesting
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# How to Handle Zero Stock Returns When Calculating Excess Return in CAPM Analysis?


# How to Handle Zero Stock Returns When Calculating Excess Return in CAPM Analysis?












everyone. I am new to this beautiful quantitative field, and I have a question regarding CAPM. I'm using daily frequency data of S&P500 from Jan 1990 to September 2024. When analysing my dataset, I noticed some days where the stock returns (e.g., for ADI) are exactly 0 after conversion. I'm unsure how to handle these 0 values when calculating the excess return.

Specifically, should I:

- Remove the 0-value return days from the dataset?

- Keep them and calculate the excess return as usual?

Here is the following dataset:

I would be glad if someone could give me any idea about data on financial datasets like the pre-processing of the S&P 500.

## Answer by Richard Hardy (score 0, accepted)

https://quant.stackexchange.com/a/81226

If this is erroneous data, you may want to exclude it or replace with more typical values (data imputation). But if it is actual data, excluding it would distort the picture. Your findings would only apply to days when the returns are nonzero. Since it is hard to predict which day will have zero return in the future, these findings would be less useful than ones that use all data and thus apply to all days.

But perhaps these zero returns do not make a significant difference in your results? If you get about the same results when including vs. excluding them, you need not worry much about which option you choose.

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.