Matt Levine is a Bloomberg Opinion columnist covering finance. He was an editor of Dealbreaker, an investment banker at Goldman Sachs, a mergers and acquisitions lawyer at Wachtell, Lipton, Rosen & Katz, and a clerk for the U.S. Court of Appeals for the 3rd Circuit.

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A basic stylized fact of financial markets is that active investment managers, as a group, do not outperform a monkey throwing darts at the stock tables. This is an embarrassing stylized fact, but you cannot, if you are an active manager, feel too bad about it. The monkey is cheating. He is free-riding on your work. The reason his investments are good is that he is buying stocks of companies that have already been vetted by active investors, and at prices that represent the active investors’ consensus about their value. The monkey is not doing any deep fundamental analysis of the cash flows and business prospects of the companies whose stocks he buys, because you have already done it for him, and you have told him what those stocks are worth. He just has to throw darts. If his dart lands on a good company, he will invest in a good company at a fair price. If his dart lands on a bad company, the price of the stock will reflect the risks and badness of the company, and will still, in expectation, give him a fair return. If you and your active-management competitors have done a good job, the monkey can’t lose.

Of course, if you’ve done a really good job, you can’t lose either. But you also can’t win: All the stocks will be fairly priced, and your business—of buying stocks at prices below their intrinsic value—will be impossible. You and the monkey and everyone else will just get the overall market return; your fundamental research can’t add any more value than the monkey’s darts. This is called the Grossman-Stiglitz paradox. (The paradox is that, if this is really true, then you won’t do the good work of making the prices right, which means they will be wrong, which means that the markets won’t be efficient, which means that you can in fact outperform the monkey, which means that you will do the good work of making the prices right, which means that you won’t outperform the monkey, etc.)

The monkey will work cheaper than you will: You probably want some analysts and a Bloomberg Terminal and a research budget and a big salary, while the monkey needs only some bananas and a box of darts. In fact in our modern age it is easy to dispense with the darts, and the monkey: An index fund can just buy all the stocks, or some large representative sample of them, without doing any fundamental analysis or anything else, just relying on the good hard work of the fundamental active managers to make sure that the prices are right. The index fund will be cheap. The active managers will be expensive. Their gross-of-fee returns, in expectation, will be the same. The people who pay the active managers’ fees will effectively subsidize the people who only pay for index funds: Everyone will benefit from the work of making prices right, but only the active investors will pay for it.

Here’s a paper from Robert Stambaugh of Wharton, titled “Skill and Fees in Active Management”:

Greater skill of active investment managers can mean less fee revenue in a general equilibrium. Although more-skilled managers earn more revenue than less-skilled managers, greater skill for active managers overall can imply less revenue for their industry. Greater skill allows managers to identify mispriced securities more accurately and thereby make better portfolio choices. Greater skill also means, however, that active management corrects prices better and thus reduces managers’ return opportunities. The latter effect can outweigh managers’ better portfolio choices in equilibrium. Investors then rationally allocate less to active funds and more to index funds if active management is more skilled.

Then there is some math, but the basic idea is extremely intuitive. The better the active managers are as a group, the fewer mispricing opportunities there will be, and so the harder it will be for them to outperform indexes. The harder it is, the better the active managers will have to be: The bad ones will quit, and the good ones will invest in alternative data and machine-learning strategies and whatever else they can find to get better at their jobs. This will make it even harder to outperform indexes, etc. Investors will observe all this, and as the active managers make the indexes more efficient—as they make the monkeys’ jobs easier—the investors will allocate more to the indexes.

This all feels extremely straightforward and almost obvious, but it is worth thinking about how this fundamental math translates into the subjective experience of active managers. That experience might look like:

1. You’re good at finding mispriced stocks and are richly rewarded for it.
2. Through your good work and the work of your peers, prices get more efficient and it gets harder to find mispriced stocks.
3. At the same time you are gaining in experience and cleverness and technology and scale and so forth, so you get better at it, and continue to be richly rewarded.
4. But you grumble a bit because you have to work harder for the same results.
5. Eventually the curves cross: The benefits to you of increasing experience and scale and so forth taper off, while the market keeps getting more efficient, and you get left behind.
6. You get mad at the market for not yielding its secrets to you anymore.

And in fact you can find many examples of exactly this, long-time successful active managers getting cranky because their techniques don’t work anymore. We talked in Januaryabout one such article:

“Financial markets have significantly evolved over the past decade, driven by new technologies, and the market itself is becoming more difficult to anticipate as traditional participants are imperceptibly replaced by computerised models.” …

There has been recently a flurry of finger-pointing by humbled one-time masters of the universe, who argue that the swelling influence of computer-powered “quantitative”, or quant, investors and high-frequency traders is wreaking havoc on markets and rendering obsolete old-fashioned analysis and common sense. …

“These ‘algos’ have taken all the rhythm out of the market, and have become extremely confusing to me,” Stanley Druckenmiller, a famed investor and hedge fund manager, recently told an industry TV station.

I think that pretty much all of those words mean “the markets have gotten more efficient so it’s harder for me to make money by finding obvious mispricings,” but none of them say that; they all sound like complaints about bad crazy algos rather than good efficiency. The sad fact of life for active managers is that they devote their careers to making markets more efficient, but if they succeed too well then they put themselves out of work.