Add everybody up and you get the market
Split every rupee invested in Indian shares into two piles. One pile is passively managed — it holds the index, in the index's proportions, as 01.06.01 described. The other is actively managed: somebody is choosing. Not only fund managers: every individual picking shares is in the active pile too.
The two piles together are the whole market, because there is nothing else. The argument is exact when the passive pile holds the whole of the market being divided; a real index is the practical stand-in for that market, and the closer the index comes to it, the tighter the arithmetic. Every share is held by someone in one pile or the other. And the passive pile, by construction, holds the market in the market's proportions.
Which forces the rest. If the whole market returns some amount, and the passive pile returns that same amount, then the active pile as a whole must return it too. Not approximately. Exactly, before costs — there is no third pile for the difference to hide in.
The step that does the damage
Nothing here is a finding. Every arrow is arithmetic.
This argument is William Sharpe's, and its force is that it needs no evidence at all. It does not measure managers or study any period. It says that if two groups start equal and one is charged more, that one ends behind — which is true of anything, not just funds.
The hurdle nobody mentions
Turn the same point around and it becomes a practical number. An active fund charging 1.80% a year does not need to match the index to leave you level with an index fund charging 0.20%. It needs to beat it by the difference in fees, every year, before you are even square.
That is the hurdle. It is not a one-off. It resets each year, and it is charged whether the manager clears it or not — 01.06.01 showed the fee coming out of the NAV daily, quietly, in good years and bad alike.
So the question is not "can a manager beat the index?" Some do. The question is whether this manager will beat it by more than the fee, for as long as you hold, and whether you could have known that in advance rather than afterwards.
- Index fund's expense ratio
- 0.20% a year
- Active fund's expense ratio
- 1.80% a year
- Difference
- 1.60 percentage points
- Needed to leave you level
- index return + 1.60 points
Why must the average actively managed rupee trail the index after costs?
What this does not say
It does not say that active management is worthless, and Granthara will not tell you which to own. Some managers do beat their benchmark, sometimes for a long time. The arithmetic is about the average, and an average is not a verdict on every member of it.
What it does say is harder to escape. Whoever beats the index is funded by someone else in the active pile who lagged it, because the pile as a whole cannot beat itself. Active management is a competition between actives, and the index is only the scoreboard.
And there is an asymmetry in what you can know. The fee is certain and charged whether or not the manager delivers; the outperformance is uncertain and arrives, if at all, afterwards. Those two things are not comparable, and a decision that treats them as comparable has already gone wrong.
A fee is charged on the whole holding, every year, including on the gains the earlier years produced. So it does not subtract — it compounds, in the same direction and at the same time as everything else. This is why 1.60 percentage points reads as trivial and does not behave that way, and why the next figure is larger than most people expect when they first see it.
An active fund beat its index by 3% last year. What does that tell you about next year?
Cheap, rule-driven, and mathematically hard to argue with on average. It would be easy to finish here and conclude that a fund is simply the right answer. It is not always — and knowing when it is not is the last thing this chapter owes you.