I read William Sharpe’s essay “The Arithmetic of Investment Expenses” (2013) with interest and applause (of course!). It brought to my mind what was likely his first article on the subject of fund costs—“Mutual Fund Performance”—published way back in 1966. In that article, Dr. Sharpe was right in his conclusion that “all other things being equal, the smaller a fund’s expense ratio, the better the results obtained by its stockholders” (p. 137).

CFA Journal: The Arithmetic of “All-In” Investment Expenses, By John Bogle

Sharpe’s credibility, objectivity, and quantification expertise are peerless. He was the 1990 recipient of the Nobel Prize in Economic Sciences and is now professor emeritus of finance at Stanford University, where he has taught thousands of students over some 43 years. He was right again in his 2013 article: “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” (p. 34). However, as I will explain, he understated the gap in favor of low-cost investments.

The 1991 Article

Sharpe has taken up this subject often. In “The Arithmetic of Active Management” (Sharpe 1991), he analyzed mutual fund returns and found the same forces at work:

Statements such as [“the case for passive management rests only on complex and unrealistic theories of equilibrium in capital markets”] are made with alarming frequency by investment professionals.

In some cases, subtle and sophisticated reasoning may be involved. More often (alas), the conclusions can only be justified by assuming that the laws of arithmetic have been suspended for the convenience of those who choose to pursue careers as active managers.

If “active” and “passive” management styles are defined in sensible ways, it must be the case that (1) before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar and (2) after costs, the return on the average actively managed dollar will be less than the return on the average passively managed dollar. These assertions will hold for any time period.


Full PDF here: cfapub