A Note on the Sources of Portfolio Returns: Underlying Stock Returns and the Excess Growth Rate

A portfolio's compound return over time is not simply the weighted sum of the compound returns of its underlying stocks. Instead, it is due to (a) the underlying constituent stocks' compound returns, and (b) a component induced by constituent covariances. This can be important. The average smallest-cap decile portfolio outperformed its largest-cap counterpart by 44 basis points per month (bps/mo), but the smallest-cap decile stock constituents on average underperformed their largest-cap counterparts by 74 bps/mo. Thus, the "size effect" is not a small-firm effect, but a small-firm portfolio effect. In contrast, our high-minus-low (HML) and up-minus-down (UMD) portfolios outperformed because their individual stock constituents outperformed on average. Value and momentum are simultaneously portfolio and individual stock effects.