# 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.