June 17, 2022

It’s human nature to want to think that seemingly unrelated things are related. We look for patterns and cycles. The same thing is true for investments. Sometimes the data can (seemingly) verify this. As laid out in the article below, there are some measures of the overall economy such as GDP growth, inflation and employment that are highly correlated. But change in stock market prices? They are way too fast moving & any autocorrelation is negligible. One period’s return tells you almost nothing about the next. Yet we may keep looking for it & hence actually see it.

Hope you enjoy the article!

-Neel

Investors can be both motivated and well-equipped to see patterns in stock returns. Motivated, because successfully predicting market movements can be lucrative, and well-equipped, because evolution has programmed humans to err on the side of seeing patterns even when they’re not present. Many investors believe markets to be cyclical and search for signs of cycle status in an attempt to predict which investment styles are coming into and out of favor. Rolling stock returns are like a Venus fytrap for these investors. Multiyear returns expressed over overlapping periods often appear cyclical, implying prior returns are useful indicators of future returns. However, this is one cycle investors may want to avoid riding; rolling performance simply obscures the volatility in stock returns that is impeding predictability.

Investors can be both motivated and well-equipped to see patterns in stock returns. Motivated, because successfully predicting market movements can be lucrative, and well-equipped, because evolution has programmed humans to err on the side of seeing patterns even when they’re not present. Many investors believe markets to be cyclical and search for signs of cycle status in an attempt to predict which investment styles are coming into and out of favor. Rolling stock returns are like a Venus fytrap for these investors. Multiyear returns expressed over overlapping periods often appear cyclical, implying prior returns are useful indicators of future returns. However, this is one cycle investors may want to avoid riding; rolling performance simply obscures the volatility in stock returns that is impeding predictability.

One period’s stock return tells you almost nothing about the next.

OPTICAL ILLUSIONS

Many economic indicators can be described as cyclical. Measures such as GDP growth, infation, and employment are relatively slow-moving and therefore highly autocorrelated —their values in any one period are strongly related to their values in the preceding period. Changes in stock market prices, on the other hand, are fast-moving. As such, autocorrelation of stock returns is negligible. One period’s return tells you almost nothing about the next. Rolling returns look cyclical because of the overlap among rolling periods. For example, fve-year rolling returns computed at the end of consecutive months have 59 out of 60 months in common. Rolling windows effectively create a smooth and slow-moving series with massive autocorrelation among observations, masking the underlying sequence of returns. We can see this autocorrelation through the proportion of Russell 3000 Index returns explained by past return observations. A regression of the index’s monthly returns on the return in the preceding month2 produces an R-squared3 of just 0.2%. In other words, consecutive monthly returns have almost no correlation. However, rolling returns measured each month are highly correlated with the rolling return observed the following month—the percent of variation explained ranged from 82.7% using 12-month returns to 96% for fve-year returns (see Exhibit 1). These values stand in stark contrast to the regressions of non-overlapping, rolling returns, for which consecutive observations are totally independent.

The strong autocorrelation of rolling, overlapping returns produces a cyclical appearance in returns. We can even demonstrate this using a series of returns drawn at random from a normal distribution, essentially precluding autocorrelation. The annual returns of this series, illustrated in the top panel of Exhibit 2, convey the randomness through an absence of any perceptible pattern. However, rolling returns in the bottom panel of Exhibit 2 exhibit periodic waxing and waning that would seem to imply predictability. Of course, the “predictability” is just an artifact of the overlap among consecutive observations. One year’s rolling return clearly has information about the next year’s rolling return, but this is about as insightful as me successfully guessing your name after you tell me what your name is.

COMING FULL CIRCLE

A cyclic stock market would present frequent opportunities for market timing. However, the paucity of outperforming active equity managers suggests predicting stock market movements is not that easy. Cyclicality may also imply expected stock returns periodically go negative, a diffcult concept to square with a market that refects risk and return. Stock markets have positive expected returns every day, and research tells us the most reliable way to capture those returns is to stay invested for the long haul.

By: Wes Crill, PhD
Head of Investment Strategists and Vice President

Sources: Dimensional Fund Advisors LP is an investment advisor registered with the Securities and Exchange Commission.

Investment products: • Not FDIC Insured • Not Bank Guaranteed • May Lose Value Dimensional Fund Advisors does not have any bank affliates.