Shrunken Earnings Predictions are Better Predictions

Analysts’ earnings forecasts are not perfectly correlated with actual earnings. One statistical consequence is that the most optimistic and most pessimistic forecasts are usually too optimistic and too pessimistic. The forecasts’ accuracy can be improved by shrinking them toward the mean. Insufficient appreciation of this statistical principle may partly explain the success of contrarian investment strategies, in particular why stocks with the most optimistic earnings forecasts underperform those with the most pessimistic forecasts. This research was supported by the TIAA-CREF Institute Shrunken Earnings Predictions are Better Predictions Predicted earnings are not perfectly correlated with actual earnings. One consequence is that the largest predicted earnings growth rates are more likely to be excessively optimistic predictions than to be overly pessimistic. Similarly, the lowest predicted growth rates are more likely to be too pessimistic than too optimistic. If so, the adjustment of stock prices when earnings turn out to be closer to the mean than was predicted may partly explain the success of contrarian strategies. This paper’s objective is to see whether the statistical principle of regression toward the mean can be used to improve analysts’ forecasts of earnings growth rates. Section 1 gives a brief overview of the literature on contrarian strategies. Sections 2 and 3 focus on regression toward the mean and its implications. Section 4 presents our forecasting model, Sections 5 and 6 apply it to analysts’ forecasts, and Section 7 looks at the performance of portfolios based on earnings predictions. 1. Contrarian Strategies There is considerable evidence of abnormal returns from “value” strategies that select stocks with low ratios of price to: dividends (O’Higgins and J. Downes, 1992; McQueen, Shields, and Thorley, 1997), earnings (Nicholson, 1960, 1968; Basu, 1977; Jaffe, Keim, and Westerfield 1989), book value (Rosenberg, Reid, and Lanstein, 1985; Fama and French, 1992), and cash flow (Chan, Hamao, and Lakonishok, 1991). Believers in market efficiency (such as Chan, 1988; Fama and French, 1992) argue that these abnormal returns must be a compensation for the riskiness of value strategies; skeptics (for example, Lakonishok, Shliefer, and Vishny, 1994) argue that systematic pricing mistakes (such as the incautious extrapolation of earnings growth rates or a failure to distinguish between a good company and a good stock) create opportunities for 1 contrarian investors. Other evidence of successful contrarian strategies is provided by Debondt and Thaler (1985 and 1987), who found that portfolios of poorly performing “loser” stocks outperformed portfolios of previous winners by substantial margins, even though the winner portfolios were riskier. Similarly, Fama and French (1988) and Poterba and Summers (1988) conclude that stock returns are mean-reverting over long horizons. Bauman and Dowen (1988), La Porta,(1996), and DeChow and Sloan (1997) found negative relationships between predicted earnings growth rates and subsequent stock returns. 2. Regression Toward the Mean Regression to the mean is often observed in sequential data, but it actually occurs in a much wider range of contexts (Schmittlein, 1989). For instance, any bivariate normal variables with equal variances and a correlation between 0 and 1 exhibit regression to the mean (Maddala, 1992). Suppose, for example, that height and weight are bivariate normal and that each has been standardized to have mean zero and standard deviation one. Because height and weight are imperfectly correlated, the tallest person is usually not the heaviest and the heaviest person is usually not the tallest. Height and weight regress to the mean relative to each other. The same principle applies to corporate earnings. Suppose that the distributions across firms of 1997 and 1998 earnings growth rates are bivariate normal and have each been standardized to have zero mean and zero standard deviation. The company with the highest growth rate in 1997 usually does not have the highest growth rate in 1998, and vice versa. Or suppose that predicted and actual 1998 earnings growth rates are bivariate normal and have each been standardized. The company with the highest predicted growth rate usually does not have the highest actual growth rate, and vice versa. The educational testing literature provides a framework for explaining this statistical 2 phenomenon. A person’s observed test scores fluctuate about the unobserved latent trait measured by the test. This latent trait (the “true score”) can be interpreted as the expected value of a person’s test score, with the difference between a person’s test score and true score called the “error score” (Lord and Novick, 1968). Among a group of test takers, those who score the highest are likely to have had positive error scores: it is possible, but unusual, for someone to score below his or her true score and still have the highest score on a test. Since a score that is high relative to the group is also likely to be high relative to that person’s true score, this person’s score on another test is likely to regress toward the mean. This framework is directly applicable to a company’s earnings. Actual earnings and predicted earnings both deviate from the probabilistic expected value of a company’s earnings (“true earnings”). Actual or predicted earnings that are high relative to a group of companies are also likely to be high relative to that company’s true earnings. It is possible, but unlikely, that the most profitable company in 1998 had a negative error score that year, with earnings below its expected value. It is possible, but unlikely, that the company predicted to be the most profitable in 1998 had a negative error score that year, with the prediction below the expected value of earnings. We can consequently anticipate regression toward the mean when comparing consecutive earnings data or when comparing predicted and actual earnings. Freeman and Tse (1992) and Fama and French (2000) investigate the first question and find that successive earnings regress to the mean, although Fama and French attribute this regression to competitive forces rather than the purely statistical explanation that the error scores of companies with relatively high earnings are more likely to be positive than negative. Here, we investigate the second question: regression to the mean in comparing predicted and actual earnings. 3. Are We Aware of Regression to the Mean? 3 There is well-established evidence that regression to the mean is a pervasive but subtle statistical principle that is often misunderstood or insufficiently appreciated. Kahneman and Tversky (1973) note that people are often surprised when regression occurs and invent fanciful theories to explain it. If pilots who excel in a training session do not do as well in the next session, it is because the flight instructors praised them for doing well. If bright wives have duller husbands, it is because smart women prefer to marry men who are not as smart. In the stock market, Keynes (1936) observed that “day-to-day fluctuations in the profits of existing investments, which are obviously of an ephemeral and nonsignificant character, tend to have an altogether excessive, and even absurd, influence on the market.” Lakonishok, Shliefer, and Vishny (1994) and La Porta (1996) provide formal evidence. The regression to the mean explanation is that investors do not fully appreciate the extent to which profit fluctuations are random variation about true earnings. Regression toward the mean should not be confused with the fallacious law of averages, which states that an unusual run of successes must be balanced by a run of failures; for example, the incorrect belief that a short-run surplus of heads in coin flips must be balanced by an offsetting future deficit. With corporate earnings, the fallacious law of averages implies that companies with above-average earnings growth rates are due to have below-average growth rates. The correct principle of regression toward the mean implies that those companies with the highest growth rates will, on average, continue having above-average growth rates, but not as high as previously since their high growth rates were more likely affected by good luck than bad. One regression-toward-the mean fallacy is to misinterpret the temporary nature of extreme observations as evidence that the standard deviation is shrinking. In the 1930s, Horace Secrist, a statistics professor at the Northwestern University, wrote a book with the provocative title The Triumph of Mediocrity in Business. Secrist had found that businesses with exceptional profits in 4 any given year tend to have smaller profits the following year, while firms with very low profits generally do somewhat better the next year. From this evidence he concluded that strong companies were getting weaker, and the weak stronger, so that soon all would be mediocre. The president of the American Statistical Association wrote an enthusiastic review of this book (King 1934); another statistician pointed out that Secrist had been fooled by regression toward the mean (Hotelling 1933; see also Friedman, 1992). In any given year, companies with exceptional profits relative to other companies are likely to have experienced good fortune. 4. A Model of Regression Towards the Mean Let the analysts’ forecast growth rate f and the actual growth rate g both depend on a company’s true earnings growth rate m and the usual independent error terms: f = m + e (1) and g = m + u (2) Because we are concerned here with idiosyncratic risks that affect individual companies, rather than macro risks that affect all companies, all variables are measured as deviations from their respective means across companies. A firm’s true earnings m is the expected value of its earning growth rate. If e is independent of m then the variance of the forecast f across companies is equal to the variance of m plus the variance of e, and is therefore larger than the variance of true earnings across companies. If we estimate the relationship between actual and predicted earnings g = bf + w the least-squares slope is: † b = fg  f 2 = m + e ( ) m + n ( )  m + e ( ) (3) 5