Active fund managers are, as a group, a passive manager

Over at Aleph Blog, we have a riff on a popular misconception:

And, maybe, just maybe this means that indexing will have to get to be a much larger proportion of the markets before active managers would have alpha after fees as a whole.

Active managers cannot have, as a whole, alpha, regardless of how much of the market is passive managed.

Let’s simplify, and imagine the market is, for a while, a closed circuit second-hand market (no issuance or redemptions) and entirely managed by 2 managers: one active, who is required to be fully invested (no cash), and one passive with a capitalisation weighted index mandate. For every stock, the passive manager owns, as per their mandate, a fixed proportion P of the total shares in issue. The active manager by definition owns (1-P) of every stock, that is the market portfolio or index.

As external investor preferences between active and passive shift, one manager sells to (buys from) the other, all stocks in the same quantity proportional to their cap. The quantity is set by the passive manager’s mandate, and at all times both managers hold the market portfolio.

But, you will tell me, the passive manager is a price taker, as they have to rebalance as per their mandate. This is correct, at every rebalance the active manager can set the price, and choose to pay more for stocks it finds undervalued and conversely, but regardless of the price they pay, they will keep the market portfolio. The active manager pricing activity, if successful, makes the market externally better priced, and benefits equally both managers and their investors. This is the magic of indexing: it allows passive investors to free ride on the alpha of active investors as it gets incorporated into beta (in our 2 managers world, the active alpha is always zero).

The only ones to benefit differentially from the active managers activity are (external) investors who time switches between passive and active when the active guys have an edge or lost it. Investors passively holding either of the active or passive manager’s funds get the same performance.

Of course, if we bring back the real world the situation is a bit more messy with many investors and many indices, inflows and outflows into the market, and fees, but none of these distractions change the basic mechanics that alpha = 0 at the collective level for active managers, regardless of the proportion of passive managed funds (this is as true for 1% passive as it is for 99.999% passive).

Some argue that there is truly dumb money that is a category apart from passive and active managers, but even money outside funds is managed by people who are not categorically different from passive and active managers who run funds. Even the dumbest retail noise trader is, statistically, a passive manager — intense random trading converges with no trading at the limit — and cannot lose by more than their transaction costs (which can be a lot but are not negative alpha as such) as a category.

This has been observed empirically, with many studies finding that active managers return something really close to the index less fees, pretty much what the simplified model predicts.

Basically alpha is a zero sum game and as a class active mangers cannot outperform the index. With small enough fees it might be worth taking a chance — the positive side of the equation is that active managers cannot collectively underperform by more than the fee drag either.

An interesting and seldom discussed point is that morally, indexing could be seen as a form of theft: at the collective level passive investors benefit from the work of active investors, which is paid for entirely by active investors. It is though saved from the tragedy of the commons by hope internally (which keep some active) and externally by plurality: if the entire stock market was passive, the prices would be set by issuers and investors entering/leaving the stock market as a whole (investing or raising funds elsewhere) which should still result in equilibrium prices (modulo frictions) as long as there’s at least one asset class that is not fully passive (a condition fulfilled structurally by any illiquid enough market).

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