The extrapolation error

May 16, 2018

A cool head is better than a hot hand

“He has a hot hand.” That is what basketball fans whisper in awe if a player sinks the shot repeatedly. In other words, the player is on a roll: He has scored a number of times already, so he will continue to score.

Sounds irrational? Well, it is. The player may, for instance, become overconfident or tired and start making mistakes as a result. Statistically speaking, the assumption that he will continue to put the ball into the basket is approximately as flawed as betting on red at the roulette table because it has won four times in a row. The tendency of anticipating future events based on past ones is what is called the hot-hand fallacy (a term derived from basketball) or the extrapolation error. It is a psychological distortion causing people to ignore statistical probabilities and make predictions by relying on imaginary trends.

Picture of a Laptop showing graphs
Making predictions based on imaginary trends can be a risky business. Photo © CC0 Licence

In an investment context, this psychological distortion is fatal. Many investors are overly optimistic in their assessments of investment forms with proven track records, giving only insufficient consideration to other factors that influence stock prices. As a result, they tend to buy (more) shares following an increase in prices. Conversely, they often rush to sell their shares when prices are going down, expecting the decline to continue. This extrapolation error keeps stock prices artificially high or makes them fall excessively.


This leads to an overreaction on the financial markets, as was illustrated by the financial crisis between 2007 and 2009: In October 2008, when prices had dropped by 40% already, many investors sold their shares. In spring 2009, the pendulum started to swing in the opposite direction, and prices were moving up sharply. It is very likely that the extrapolation error played a significant role in this context. The investors—in particular those who had little financial knowledge, as Bucher-Koenen and Ziegelmeyer found in their 2014 study—assumed that prices would continue to fall. Laboring under this illusion, they decided to sell their shares, thinking that the winds were still favorable. Another example is the CA-Immo share:  From early 1992 to spring 2007, its price increased slightly and with remarkable stability. Many investors, and investment advisors for that matter, expected that the share would continue to show low volatility and a more or less monotonous upward trend. But, all of a sudden, it took a nosedive; more and more investors divested themselves of their holdings—and by spring 2009, the share had lost over 85% of its value.

Picture of a stock change graph
The financial crisis showed that the extrapolation error can lead to an overreaction on the financial markets. Photo © CC0 Licence

In the long run, the trend is not your friend

The belief in a “momentum”, i.e. the tendency to toe past trends, is also reflected by the stock-market adage “The trend is your friend”, which is popular with many investment advisors. Hungarian stock-market guru André Kostolany holds a different view, saying: “The relation between the stock market and the economy is like a man walking his dog. The man moves forward at a steady pace; the dog runs back and forth.” The man symbolizes the economy or the fundamental value of a share, that is the present value of future dividend payments. The dog represents the stock market or the share price. Sometimes, the man is ahead of the dog; sometimes, it is the other way round, and sometimes, the two are side by side. What Kostolany intends to say with his analogy is this: In the long run, the stock market will not do better or worse than the economy. Eventually, a share’s price will converge towards its fundamental value: When share prices go up excessively, they will sooner or later decline again—and vice versa.

So: Don’t let past trends influence you in your decisions to buy or sell shares. It is best to calculate the fundamental value of “your” share, for instance by using a company valuation method. Irrespective of the share’s track record, buy it only if its price is lower than its fundamental value, and sell it only if its price is higher than its fundamental value. Good luck in making your investments—with a cool head rather than a hot hand!

This article was published in the Austrian business magazine GEWINN. Read the original article here (in German).

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