costs
The arithmetic of active management
The rule
Before costs, active investors as a group own the same market as everyone else. After costs, the active group must trail the index. It is simple maths, not opinion.
Where it flips
The maths is about the group, not the individual. It does not prove every active fund is bad. A truly low-cost, low-trading active plan can still clear its own hurdle. The rule forbids the average from winning, not every single player.
Sharpe's point is not a study you can argue with; it is simple arithmetic. All the money in a market is owned by someone. So before costs, the average active rupee and the average passive rupee earn exactly the market return. Now subtract the higher fees, trading friction, and taxes that active management carries. The active group as a whole must earn less than the index it together owns. This says nothing about any one manager; some will beat the market. It says the average active investor starts one fee behind, and that gap is guaranteed. So ask: how does the active path earn back that sure head start?
A worked example
Two investors each put ₹10,00,000 into the same market for a decade. Before costs both earn the market's return. The one paying 1.4% in total simply keeps 1.2% a year less than the one paying 0.2%, and no skill was needed to predict it. [illustrative]
How to spot it
- ·you consider the whole active group before any single manager
- ·you state the cost hurdle as a number
- ·you do not believe skill alone escapes the group maths
William F. Sharpe · The Arithmetic of Active Management