Fama and french calculated value weighted portfolio return while framing SMB, HML and WML factor. But why not equal weighted portfolio returns because I think equal weighted portfolio have more diversification as compared to value weighted portfolio. Because value weighted portfolio is biased by giving more weight to large cap companies so the mean return are mostly driven by large cap. I also found one study which found equal weighted portfolio outperform price - weighted or value weighted portfolio. So can someone enlighten me which one to use while framing these factors.

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