The Arithmetic of Active Management: An Example

Many people find it hard to believe that smart, well-paid, motivated, hard-working active fund managers fail to achieve, far more often than not, their goal of outperforming their benchmarks, particularly over long periods. However, the evidence on this is both substantial and unquestionable. This note provides an example of what is often called the arithmetic of active management; that is, the theoretical result that states that active management is a zero-sum game, with each winning dollar being exactly compensated by another losing dollar. The note also shows why, once the costs of investing are taken into account, active managers as a group should be expected to underperform.