Rapid advances in machine learning and artificial intelligence should, in theory, make statistical arbitrage investing a lot easier and more lucrative.

But there is a ceiling on the opportunities to cash in on price discrepancies, according to an analysis by Chicago Booth’s Stefan Nagel and Dacheng Xiu and Booth PhD student Rui Da. And it is much lower than what investors might anticipate, they find.

Statistical arbitrage is a broad term for an investment strategy often described in finance as picking up nickels in front of a steamroller. Stat arb investors use quantitative methods, increasingly augmented by machine learning, to identify investment opportunities in volatile assets such as stocks, bonds, currencies, and commodities. Arbitrageurs compete with each other over a limited set of opportunities, making the practice challenging. Opportunities also disappear as they become widely known. No bargain persists long.

But how reliably, in an age of powerful computation, can investors find these opportunities —and is there an upper limit on how good a stat arb strategy can be? Exploring the upper limits of stat arb investing in a theoretical analysis, the researchers conclude that highly lucrative profit-making opportunities are rare. Even the most powerful and versatile machine-learning strategies are hampered by a remarkably low signal-to-noise ratio in historical data, a consequence of the steep competition in financial markets, the study finds. By analyzing stock returns between 1965 and 2020, the researchers were able to pinpoint the rarity and fleetingness of stat-arb opportunities, especially in recent years, which suggests that however much investors might fine-tune their strategies, there are finite opportunities to exploit.

In a lecture at the 2023 Hong Kong Conference for Fintech, A.I., and Big Data in Business, Xiu described the problem by bringing up an old joke about the economist who doesn’t pick a $100 bill up off the sidewalk because he can’t imagine a way that free money could be lying around without somebody having taken it already.

But, Xiu said, arbs aren’t looking for $100 bills but rather a bunch of singles scattered all over the place. A perfect strategy for quickly gathering up all those single dollars would be a sure moneymaker. It would obtain what the researchers call an “infeasible Sharpe ratio,” which they estimate to be 3 on the basis of empirical data. (A Sharpe ratio compares an investment’s return with its risk.) As Sharpe ratios are generally less than 1, that’s the kind of high return/low volatility that you don’t see in real life.

The world is not awash with mispriced assets—and in the stock market, what may seem to be dollar bills lying around are actually counterfeit, of no real value. Instead, arbs try to develop reliable strategies for finding real potential profit, known as alpha, in challenging situations. The better the chance of making money, the faster the market reacts and the fewer the opportunities that arise. The best Sharpe ratio an arbitrageur can achieve is 0.5, according to the researchers’ analysis—meaning that returns are fairly low given the risks involved. “Non-zero alphas are rather rare and weak,” the researchers write.

Thus, finding alpha-generating opportunities is challenging, they explain, and historical data are full of noise that can confound even the most sophisticated computational systems. Although capabilities in statistical analysis hold promise, Da, Nagel, and Xiu conclude that identifying the new opportunities won’t be easy, even with sophisticated machine learning.

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