Active Return

The active return (RA)—of an actively managed portfolio is driven by the difference in weights between the active portfolio and the benchmark:


Ri = the return from security i

ΔWi = the active weight, the difference between portfolio and benchmark weight, for security i

Conceptually, a manager can generate active returns by

  • strategically adjusting the active weights of the securities to create long-term exposures to rewarded risks that are different from those of his benchmark
  • tactically adjusting the active weights of the securities using his skills/expertise in identifying mispricing in securities, sectors, rewarded risks, and so on, to generate alpha that cannot be explained by long-term exposure to rewarded risks
  • assuming excessive idiosyncratic risk that may result in lucky or unlucky returns. It is labeled luck in the sense that it is not due to market risk exposure or value-added alpha.

The decomposition of realized (ex post) active return can be seen in the next equation:



βpk = the sensitivity of the portfolio (p) to each rewarded factor (k)

βbk = the sensitivity of the benchmark to each rewarded factor

Fk = the return of each rewarded factor

(α + ε) =  the return not explained by exposure to rewarded factors—alpha (α) is the active return attributable to manager skill, and ε is the idiosyncratic return—noise or luck (good or bad)

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