Investment AUM Fee Costs: Evaluating a Simple Formula

How much do financial management fees cost investors? This article studies an approximate formula for the cumulative costs of annual Assets Under Management (AUM) fees. The formula states that an investment paying an annual fee of $\epsilon$% of AUM over $N$ years loses almost $N\epsilon$% of its value, compared to an investment with the same returns paying no fee. The article explains this formula intuitively, derives it analytically, and studies its approximation error. The article concludes with a discussion of the formula's uses and limitations.