Sixty years of Nobel Prize-winning theory say no, it is not possible. But just maybe it is. Ironically, the widespread belief that it’s impossible helps to make it possible.

To see how, recall a high-buzz stock market event last December 21, when Tesla became a component of the S&P 500. Research Affiliates chairman Rob Arnott and colleagues made a bold prediction: Tesla stock “is likely to underperform the market (S&P 500) in the year after entry” and “Apartment Investment and Management, the stock removed from the S&P 500 to make room for Tesla, is likely to outperform the index over the next year by as much as 20%.”

Today, just over six months later, the only flaw in that prediction is that it may have been too modest. The S&P 500 is up 17%. Tesla is indeed underperforming badly; it’s flat. Apartment Investment and Management (known as Aimco) is outperforming the S&P, and by way more than 20%; it’s up 44%.

Arnott, whose firm develops investment strategies used in managing $166 billion of assets worldwide, argues that what happened is no fluke. It’s a particularly dramatic example of a predictable phenomenon that can be exploited by traders.

The opportunity, he says, is in the fundamental nature of index mutual funds and ETFs. Their objective, obviously, is to track the performance of an index, which means tracking it exactly. The index fund industry has become intensely competitive, and any divergence of a fund’s price from the index’s movement, known as tracking error, will be seized upon by competitors as evidence that the fund is poorly run. The danger of tracking error multiplies when one stock replaces another in the index. The reason: To avoid tracking error, every index fund wants to buy the new stock and sell the departing one at the closing prices on the day before that day because the index will be calculated on that basis. The result is trading mayhem on the trading day before the switch.

For Tesla traders, the big day was Friday, December 18, and trading mayhem duly ensued. On each of the previous few days about 5% of the company’s outstanding shares had been traded, but on December 18, 23% was traded as indexers stampeded to buy the stock as near to the closing price as possible. The price jumped 6%, then fell all the way back down the following Monday.

But that’s only half the story for Tesla or any other stock being added to the index. The S&P U.S. Index Committee announced Tesla’s addition a month in advance, on November 17, 2020, and for the next month hedge funds and other traders bought it up, knowing they could sell it to index funds that had to buy it on December 18. Partly as a result, Tesla rocketed 57% in that month from the announcement until December 17.

For Aimco it was the opposite: Over the same period, its stock fell 17% as investors dumped it.

The trading opportunity is obvious: Buy the outgoing stock, which has been pounded down, and sell the incoming stock, which has been pushed to the sky, on the big day before the switch becomes effective. Those opportunities occur fairly often, about ten times a year on average, Arnott’s research shows. Over the past 20 years, an average of 23 stocks have been exiled from the index annually, to be replaced by 23 newcomers. Most of those deletions are practically automatic when a company merges, is bought, or goes bankrupt. The rest are discretionary switches, like Tesla-Aimco, and those are the ones to focus on.

It isn’t necessary to follow the formula exactly. Individual investors may not own any of the incoming stock to sell and may not have the stomach for short-selling. That’s fine. Just buying the outgoing stock works great, on average.

“Stocks being dropped from the index inevitably are deep value stocks that have performed badly, are struggling as a business, and are dropped at distressed prices,” Arnott says.

His firm’s research finds that buying the outgoing stock in discretionary deletions from the S&P 500 at the closing price on the day it’s removed from the index has beaten the market by an average of nearly 20% over the following 12 months.

That is supposed to be impossible. The efficient market hypothesis holds that any reliable system for beating the market will quickly become known and almost immediately be arbitraged away as traders jump aboard. Why hasn’t it happened in this case? “The big force that prevents it from happening is the sheer scale of the indexers,” says Arnott.

Nearly $5 trillion of assets are indexed to the S&P 500, says the index’s parent, S&P Global. When the managers of all that money must buy a particular stock and sell a particular stock on a given day, almost at a given hour, that’s an opportunity for other traders. Everyone knows it’s coming, yet it doesn’t get arbitraged away because not enough money is trying to do so. In part—here’s the irony—that’s because so many trillions are invested in a wide array of index funds on the belief that picking individual stocks doesn’t work.

Investors in S&P 500 index funds are the losers. Consider that the fund giants wage war to attract customers by offering the lowest expense ratio; for Vanguard’s S&P fund it’s four basis points, for Charles Schwab’s it’s two, for Fidelity’s it’s 1.5. Yet the annual cost to clients of rebalancing for additions and deletions is 20 to 40 basis points on average, Arnott calculates.

That cost, which is significant over time, can be at least partially avoided. A strategy of rebalancing three months after the effective date rather than the day before the effective date has beaten the index by 13 basis points on average over 18 years, Arnott and his colleagues found. It seems an easy way for a fund to improve its performance. But index funds don’t do it because it would introduce tracking error—and never mind that it would be positive tracking error.

“The indexing community has trained customers to think zero tracking error is the goal,” Arnott says. “Even positive tracking error is bad.”

Index funds on the whole are a boon for investors. Turns out they can be a boon in an unexpected way. An S&P 500 rebalance, says Arnott, “is a great opportunity to do the opposite of what the index does: buy the deletion and sell the addition.” It may not pay off in every rebalance, but over time it “has historically proven to be an excellent investment idea.” Even if it is supposed to be impossible.