**Cognitive Biases In Market Forecasts by Kenneth L. Fisher and Meir Statman – Fisher Investments**

*The frailty of forecasting.*

Some days it seems as if the world is divided into two groups, those who forecast that the DJIA will soar to 36,000 very soon and those who forecast, with equal confidence, that it will plummet to 3,600. We argue that forecasters often exaggerate the reliability of their forecasts, and trace this exaggeration to the illusion of validity.

“People are prone to experience much confidence in highly fallible judgment, a phenomenon that may be termed the illusion of validity,” write Kahneman and Tversky [1973]. “Like other perceptual and judgmental errors, the illusion of validity persists even when its illusionary character is recognized” (p. 249).

We discuss five cognitive biases that underlie the illusion of validity: overconfidence, confirmation, representativeness, anchoring, and hindsight. We use forecasts based on P/E ratios and dividend yields to illustrate the biases and offer remedies.

### Cognitive Biases – P/E Ratios, Dividend Yields, And Future Returns

The returns of 1980 will warm the hearts of those who believe that low P/E ratios forecast imminent high returns, but the returns of 1918 will break their hearts. The P/E ratio stood at a low 7.5 at the beginning of January 1980, and the S&P 500 index was up a healthy 32.42% for the year. But the P/E ratio stood at an even lower 6.3 at the beginning of January 1917, and stocks were down 15.09% for the year. Similarly, while the high 24.0 P/E ratio of 1934 was followed by a 1.44% loss, the even higher 25.8 P/E ratio of 1922 was followed by a 27.65% gain.

We study the P/E ratios and dividend yields at the beginning of the 128 years from 1872 through 1999, and find that they provide unreliable forecasts of future returns. (The sources of the data are described in the appendix.) As can be seen in Exhibits 1A and 1B, there is no statistically significant relationship between P/E ratios at the beginning of a year and returns during the following year or during the following two (non-overlapping) years. As can be seen in Exhibits 2A and 2B, there is no statistically significant relationship between dividend yields at the beginning of a year and returns during the following year or during the following two (non-overlapping) years. The results are similar when real returns replace nominal returns.

P/E ratios and dividend yields provide more reliable forecasts over longer periods. We discuss ten-year periods later.

Many investors are especially concerned about the short-horizon implications of very high P/E ratios, fearing that they forecast imminent disastrous returns. Yet history offers little support for such fear. For example, P/E ratios over 19 have never been followed by losses greater than 10% during the following year. While high P/E ratios can surely be followed soon by disastrous returns, it is ironic that investors believe that such returns are the common feature of stock market history.

As can be seen in Exhibit 3A, the six highest P/E ratios, ranging from 32.2 at the beginning of 1999 to 24.0 at the beginning of 1934, are were much higher than the 13.6 median P/E ratio. Yet the lowest return in a year following these six highest P/E ratios was a 1.44% loss in 1934. Indeed, the lowest returns have followed middling P/E ratios, not very high ones (Exhibit 3B). The lowest annual return, a 43.34% loss of 1931, followed a 16.5 P/E ratio. Similarly, the 26.47% loss of 1974 followed an 11.8 P/E ratio.

### Overconfidence

Overconfidence is one of the cognitive biases that underlie the illusion of validity. To understand the overconfidence bias, imagine that you are asked to estimate the typical gestation period of the Asian elephant. In particular, you are asked to provide two guesses of the gestation period—a low guess and a high one—such that you are 90% confident that the right answer lies between the two. Most people know, with justified confidence, that the average gestation period of humans is approximately nine months. So a 90% confidence interval ranging from a low of 8.5 months to a high of 9.5 months is well calibrated, not overconfident; there is at least a 90% chance that the true average gestation period of humans falls between the low and high guesses.

The average gestation period for an Asian elephant is approximately 21 months, and zoologists would not be overconfident if they were to provide an equally narrow 90% confidence interval around that number. But the rest of us should be mindful of overconfidence. We can avoid overconfidence by providing confidence intervals consistent with our knowledge, perhaps a low of 3 months and a high of 40.

Now imagine a set of ten questions similar to the one about the Asian elephant (e.g., what is the weight of a Boeing 747 airplane?). On average, one true answer of the ten will be higher than the high guess or lower than the low guess if people calibrate their 90% confidence level properly. But people are overconfident; on average, more than one in ten fall outside the 90% confidence interval.

Regression analysis is a good remedy for overconfidence. The scatter diagrams of the regressions in Exhibits 1A and 1B provide visual images of the right level of confidence in P/E-based forecasts of returns.We can see that the dots are scattered all over the place, so one should not place much confidence in P/E ratios as precise predictors of returns. Summary statistics, such as the R2 and standard errors, convert visual images into numbers. The standard error of the regression of one-year returns on P/E is 18.16%. This standard error implies, for example, that while the expected return for a P/E ratio of 20 is 9.54%, the 90% confidence interval for a return forecast extends from a 20.33% loss to a 39.41% gain. (The 90% confidence interval extends from 1.645 standard deviations (i.e., 29.87%) below the expected return of 9.54% to 1.645 standard deviations above it.)

Well-calibrated P/E-based forecasts have wide bounds. Such well-calibrated forecasts are likely to portray forecasters as timid. But bolder forecasters might be overconfident.

### Confirmation

Einhorn and Hogarth [1978] argue that the illusion of validity persists because people fall prey to the confirmation bias; they focus on information that is consistent with their beliefs while neglecting inconsistent information. As Robert Park, a physicist, said in an interview with William Broad about faulty research on electromagnetic fields: It’s often not deliberate fraud…. People are awfully good at fooling themselves. They’re so sure they know the answer that they don’t want to confuse people with ugly-looking data [1999, p. A1].

We can overcome the confirmation bias by examining all data, confirming as well as disconfirming. Consider, in particular, an examination of the hypothesis that low dividend yields forecast low returns while high dividend yields forecast high returns. Define dividend yields as high if they exceed their median over the 128 years from 1872 through 1999 and as low if they fall below it. The median dividend yield for the period was 4.43%. Define one-year returns as high and low in a similar fashion. The median return was 10.50%. Exhibit 4A presents a schematic view of the frequency of observations in the four cells of a matrix.

The first cell includes observations where dividend yields were low and subsequent returns were low. These are positive hits. The fourth cell has observations where dividend yields were high and subsequent returns were also high. These are negative hits. Positive hits and negative hits are confirming evidence, observations consistent with the hypothesis that low dividend yields forecast low returns and high dividend yields forecast high returns.

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