Nobel laureate William F. Sharpe published "The Arithmetic of Active Management" in the January/February 1991 issue of The Financial Analysts Journal.

The article makes a very powerful but simple argument using a concept called "equilibrium accounting."  It explains that investors, in the aggregate, hold the "market portfolio" - there are no "orphan" stocks and they must all be held by someone.  As such, in the aggregate, passive investors will receive the market rate of return less expenses, but active investors will also receive the market rate of return less their expenses.  In any given period there will be active managers who outperform the market portfolio - but by definition they can do so only at the expense of other active managers.  Based on this simple logic it is clear that active management is a zero sum game.  After fees and expenses active management is a "negative sum game" relative to passive management because passive investing always captures the market rate of return at a lower cost.

The active investor must not only identify the manager with a strategy that will outperform the market in a given period (and we would argue that this is simply the result of random chance), he must do so in advance of the period  - because evidence shows that "winners" rarely repeat their winning performance in subsequent periods.

Kenneth French of Dartmouth  has quantified the "excess cost" of active management (over passive) to be 0.67% per year on average.  This cost has a tremendous negative impact on an investor's portfolio when compounded over time.

Additional Resources
Ken French explains equilibrium accounting

Standard and Poors Indices Versus Active  (SPIVA) Scorecard

The Morningstar Box Score Report

Vanguard Investment Counseling & Research: The Active-Passive Debate: Market Cyclicality and Leadership

 Vanguard Investment Counseling & Research: The Case for Indexing