The Misuse of Expected Returns

Abstract

Much textbook emphasis is placed on the mathematical notion of expected return and its historical estimate via an arithmetic average of past returns. But those wanting to forecast a typical future cumulative return should be more interested in estimating the median future cumulative return than in estimating the mathematical expected cumulative return. For that purpose, continuous compounding of the mathematical expected log gross return is more relevant than ordinary compounding of the mathematical expected gross return. Self-test

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