Active and Passive Investing, and the Arithmetic Underneath the Argument

The two approaches

Passive investing means holding the market as it is, in the proportions it comes in, and accepting whatever it does. In practice that means an index fund — how an index fund works.

Active investing means someone deciding to hold more of some things and less of others, in the belief that this will produce a better result than holding everything.

The public argument about which is better is normally conducted with performance figures, and those figures are genuinely hard to establish — the reasons are in why past performance is not enough to choose a fund. The more durable argument requires none of them.

The arithmetic

Every share is owned by somebody. Add up all the portfolios and you get the entire market, because there is nowhere else for the shares to be.

Passive investors hold the market in its own proportions. Whatever remains — everything held by investors who deliberately deviate — must therefore also add up to the market in its own proportions, because the two parts have to sum to the whole.

So before costs, the average active investor gets exactly the market return. Not approximately. Necessarily. It is an accounting identity, not an empirical finding, and it does not depend on anybody being skilful or foolish.

Now add costs. Active management involves research, higher charges and considerably more trading; passive involves less of each. Since both groups earn the same return before costs, and one group pays more of them, the average active rupee must return less than the average passive rupee after costs. Again necessarily.

That is the whole argument. It needs no data, no market and no assumption about how efficiently prices are set.

What this does not prove

It is worth being exact, because the identity is often stretched past what it supports.

It does not say no active manager can outperform. It says the average cannot, after costs. The distribution around that average can be wide, and somebody occupies the top of it. What the arithmetic denies is that most can, or that the average can.

It does not tell you who they are in advance. That is a separate question and a much harder one: distinguishing skill from luck among many funds needs far more evidence than a track record supplies, and the funds that failed are missing from the comparison. The identity is silent on it.

It does not say active management is useless to the market. Somebody has to do the work of deciding what things are worth, or prices would carry no information and the index would be weighting companies by nothing in particular. Passive investors are taking those prices as given. There is a genuine question about how much active management a market needs to price things sensibly, and nobody knows the answer.

And it does not settle any individual choice. Your alternatives are two specific funds with specific costs, not the averages of two categories.

Where the honest case for active management sits

Three places, none of which is contradicted by the arithmetic.

Where an index does the job badly. Indices are usually weighted by size, which is a sensible default for shares and a peculiar one elsewhere — in bonds, weighting by size means lending most to whoever has borrowed most. A market where the index rule is a poor description of what you want to own is a market where deviating from it is not obviously a mistake.

Where you want something an index does not offer. A specific constraint, an exclusion, a shape of income. That is not a bet on outperformance; it is a different objective.

Where the cost gap is small. The identity's force comes from costs. Where an active option costs very little more, the argument against it weakens proportionally — and the arithmetic of that gap over a long holding period is in how investment fees reduce wealth.

The version of the question worth asking

Not "is active or passive better" — which cannot be answered in general — but: what would have to be true for this particular active fund, at this particular cost, to be worth it?

That question has a concrete answer. The fund must outperform its benchmark by more than the extra cost, reliably, for as long as you hold it. You can compute the hurdle from the two charges. Then you can ask whether anything about the fund gives you reason to expect it: a specific structural advantage, a mandate you cannot otherwise get, a manager whose approach you can actually describe.

If the only reason is the past record, the arithmetic above is the reason to be cautious, and why past performance is not enough is the reason the record cannot settle it.

The honest gap

This page quotes no figures on how Indian active funds have actually done against their benchmarks, and no proportion that outperformed over any period.

That would need fund-level history including the funds that closed or merged, matched to appropriate benchmarks. This site holds index and inflation history only. The identity above holds regardless — that is its virtue — but it is a statement about averages and costs, and it should not be presented as though it were a measurement of the Indian market.

What to take away

Before costs, active investors collectively are the market. After costs, they are the market minus what they spent. That is arithmetic and it is not in dispute.

What follows for you is narrower than the debate suggests: not that active management is wrong, but that any active choice starts behind by the size of its cost advantage, and needs a reason to expect it will make that back. "It did well recently" is not that reason.