The Arithmetic of Investment Expenses

William Sharpe

Financial Analysts Journal, 2013, vol. 69, issue 2, 34-41

Abstract: Recent regulatory changes have brought a renewed focus on the impact of investment expenses on investors’ financial well-being. The author offers methods for calculating relative terminal wealth levels for those investing in funds with different expense ratios. Under plausible conditions, a person saving for retirement who chooses low-cost investments could have a standard of living throughout retirement more than 20% higher than that of a comparable investor in high-cost investments. Recent regulatory changes have brought a renewed focus on the impact of investment expenses on investors’ financial well-being. Moreover, in a recent issue of this publication, Charles Ellis argued eloquently that the impact of such fees is much larger than many think.In this article, the author provides methods for calculating relative terminal wealth levels for those investing in funds with different expense ratios. For cases in which a lump-sum investment is made and held for many years and both low-cost and high-cost funds have the same gross returns, the terminal wealth ratio is a simple function of the expense ratios and the number of years the investments are held. For cases in which returns are subject to risks and/or recurring investments are made, the calculations are more complex and may require Monte Carlo simulation. The author shows how to analyze such cases and provides quantitative results.Whether one is investing a lump-sum amount or a series of periodic amounts, the arithmetic of investment expenses is compelling. Under plausible conditions, a person saving for retirement who chooses low-cost investments could have a standard of living throughout retirement more than 20% higher than that of a comparable investor in high-cost investments. Although a long-term investor may be able to find one or more high-cost managers who can beat an appropriate benchmark by an amount sufficient to more than offset the added costs, the negative impact on an investor’s wealth can be very large. Managers with extraordinary skills may exist, but another exercise in arithmetic indicates that such managers are in the minority. And as Ellis has reminded us, they are very hard indeed to identify in advance. Caveat emptor.

Date: 2013
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DOI: 10.2469/faj.v69.n2.2

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