In a 2003 contribution to CFA Magazine,  Vanguard founder and former CEO Jack Bogle introduced the cost matters hypothesis, or CMH. Bogle presented his theory as a substitute for the efficient-market hypothesis, or EMH, as a means of framing the task facing investors aspiring to beat the market:
We don't need the EMH to explain the dire odds that investors
face in their quest to beat the stock market. We need only the CMH.
Whether markets are efficient or inefficient, investors as a group must
fall short of the market return by the amount of the costs they incur.
This same harsh math was elegantly laid out by William Sharpe in his
seminal 1991 piece "The Arithmetic of Active Management" :
If 'active' and 'passive' management styles are defined in sensible ways, it must be the case that
> before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar;
> 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. Moreover, they
depend only on the laws of addition, subtraction, multiplication and
division. Nothing else is required.