Computing absolute excess returns over market from portfolio CAPM alpha

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strakert
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Joined: Sat Oct 02, 2021 12:06 pm

Computing absolute excess returns over market from portfolio CAPM alpha

Post by strakert »

Factor investing papers typically report CAPM alphas for factor-mimicking portfolios (e.g. SMB, HML) or for quintile/decile portfolios formed by single or double sorts to show the outperformance of these strategies.

I'm interested in knowing what my absolute (not risk adjusted) excess (over market) returns for a dollar invested in such portfolios would be. I.e., returns on a dollar invested in these portfolios vs a dollar invested in total market.

How should I convert reported CAPM alphas to this absolute excess return over a market?

CAPM says that:
Ri - Rf = ai + bi(Rm - Rf)
where ai is the alpha of the portfolio and bi is the beta (or regression slope against market returns).

By subtracting Rm - Rf from both sides, it should be:
(Ri - Rf) - (Rm - Rf) = ai + (bi - 1) (Rm - Rf)

However bi is calculated ex post, and is typically not reported in papers. Is there another obvious or approximate relation between these two quantities that I'm missing?

Thanks!
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