“Stationarity” and Investing: What Can We Learn from History

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The best way to explain stationarity is with an example. Suppose I want to estimate what the rainfall will be in Pasadena, California during the year 2020. The annual rainfall can be thought of as a random process with a given, but unobservable, mean and random variance around that mean. The process is stationary if that unobservable mean is constant. In that case, the mean can be estimated by an historical average. The longer the historical data period, the more accurately the mean is estimated. But all that assumes stationarity. What if the true mean is changing? To answer that question, consider a related problem. Suppose I want to estimate LeBron James’ scoring average during the 2020 NBA season. Averaging his scoring average over this career thus far is likely to be an upward biased measure. The true, unobservable mean for a player’s scoring average is not constant, particularly later in his career. It declines with age and at some point, it goes to zero when the player retires. The random process that generates annual scoring average is not stationary.

What does all this have to do with investing? Much quantitative investing is based on compiling massive data records and then searching them for relationships that can be used to predict future returns. Given the size of the data sets and the speed of modern computers many significant historical correlations are invariably discovered. But are they stationary? The world is a highly nonstationary place. Governments come and go. Wars are won and lost. Technology changes the way we live and work. Economic policies are in constant political flux. It is quite a stretch to think that in such a world historical correlations will be stationary. In other words, the LeBron James example is probably more accurate than the rainfall example. (Note even the rainfall process may not be stationary if there is climate change.) If that is the case, it is hard to know which relationships that computers kick out can be trusted and which cannot. In a non-stationary world, it is easy to exaggerate the benefits investors can derive from “big data analysis.” It may simply uncover past relations that are no longer applicable.

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Warren Buffett once quipped, “All we have learned from history is that people don’t learn from history.” But in a world characterized by significant non-stationarity, it is not clear what history has to teach.

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