Using Overlapping Returns to Estimate Stock–Market Correlations
Summary
The document asks how to apply a three-day overlapping log-return correction when estimating stock betas, following the approach described in the Betting Against Beta paper. The key practical point is that the same overlapping-return construction should be applied to both the individual stock and the market proxy before calculating their correlation.
The questioner reports that smoothing only stock returns produced unexpectedly low correlations, while using overlapping returns for both series gave higher, more plausible values. An answer says the original paper’s author confirmed that both return series should be treated this way. The evidence is a reported author clarification rather than a derivation or independent empirical comparison. The note does not explain the statistical mechanics of nonsynchronous trading, discuss overlapping observations’ dependence, or provide a reference on pitfalls, so it offers a narrow implementation clarification rather than a full methodological treatment.
Key ideas
- Apply overlapping three-day log returns to both the stock and the market proxy when estimating their correlation.
- The correction is presented as a way to address correlation effects from nonsynchronous trading.
- The reported clarification came from an author of the original research paper.
- The note does not provide a derivation or discuss statistical caveats of overlapping observations.
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Full text
# Control for non-synchronous trading in correlations
# Control for non-synchronous trading in correlations
I am trying to replicate some results from the Betting Against Beta paper by Frazzini & Pedersen.
In section 3.1, Estimating Ex Ante Betas, they illustrate their approach to correlations:
> [we use] overlapping three-day log returns, $r_{i,t}^{3d}=\sum_{k=0}^2ln(1+r_{t+k}^i)$, for correlation to control for nonsynchronous trading (which affects only correlations).
So basically they just make the return of period i equal the average of the returns of period i and the next two periods.
My question is the following:
Do I use overlapping three day log returns for both stock and market returns, or just for the stock returns?
I've tried both. Just using overlapping stock returns give me very low correlations, none above 0.55 (for stock that should be highly correlated with the market proxy, as they are part of it's constituents)
Using overlapping returns on both stock and market returns gives me a maximum correlation of 0.95, and higher correlations in general, which I find more plausible.
Bonus question:
Can you refer me to a journal article or textbook that explains the reasoning of this correction and potential pitfalls (if any)?
Background info: I'm replicating the results for the Danish equity market. MSCI Denmark is used as a market proxy (author's choice)
Cheers! Thanks.
## Answer by Mike Haye (score 4, accepted)
https://quant.stackexchange.com/a/33953
I contacted one the authors of the original paper. He confirmed that the overlapping three day log returns are to be used on both stock and market returns.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.