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When following Lewellen (2015) (open access here), I am confused as to whether I need to estimate any lambdas. As I already have values for lagged firm characteristics such as ROA and accruals etc. that I can multiply with their respective betas based on rolling return windows. Do I then need to still regress returns on these betas to get lambdas for each month? In other words, what are the in- and out-of-sample FM slopes? And how should I calculate the predicted returns?

References

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Unlike for the CAPM, where we obtain the beta's by regressing a firm's returns against the market return over the same period, here we already have firm specific characteristics.

So we can simply regress the returns on the lagged firm characteristics in a past rolling window. This will give us the out of sample slopes that we can multiply with the firm characteristics to calculate predicted returns.

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    $\begingroup$ Exactly, you estimate a cross-sectional regression each month. Future excess return on current firm characteristics. Those characteristics might be simple accounting variables (ROA), price information (log(size)) or estimated betas (from rolling windows). It doesn't matter. You first get all the firm characteristics, then run all the cross-sectional regressions, and then take the averages of the estimated regression slopes. That's it. $\endgroup$
    – Kevin
    Dec 10, 2023 at 17:53

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