In a classic 1991 Financial Analysts’ Journal article, Nobel Laureate William F. Sharpe discusses active and passive investment management.

Nobel Laureate Bill Sharpe lays out a basic mathematical proof showing that the average passively managed investment will outperform the average actively managed investment over time. ‘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. Moreover, they depend only on the laws of addition, subtraction, multiplication and division. Nothing else is required.’

Link to The Arithmetic of Active Management