The Magic of Round Numbers Explained

During the last couple of days, my Twitter timeline is held hostage by the number 20,000. As the Dow Jones nears this ‘magic’ number anxiety among investors is rising. But why are people so intrigued by these big round numbers?

Changing behavior

Perhaps because big round numbers function as psychological barriers or natural resistance points. Donaldson & Kim (1993) were among the first to introduce the concept of psychological barriers in stock markets. They assume that investors change their behavior when round number index levels appear on the radar screen. To verify their hypothesis they look at return patterns of the Dow Jones Industrial Average (DJIA) surrounding ‘barriers’ at 100- and 1000-levels in the index.

Donaldson & Kim find that the DJIA closes significantly fewer times, on average, at index values in the neighborhood of 100-levels than at other levels. Their results imply that investors look at big round numbers as a point of resistance on the way up, but also as a support barrier once these numbers are broken.

Are people really influenced by random numbers? Some excellent research on this topic was done by Nobel Prize laureate Kahneman & Tversky (1974). In their groundbreaking publication ‘Judgment under Uncertainty; Heuristics and Biases’, the authors neatly demonstrate that people are easily fooled by random numbers.

Anchoring

Kahneman &Tversky demonstrate this by a number of simple experiments. In one example subjects were asked to estimate the percentage of African countries that is a member of the United Nations. Before the subjects gave their answers they were presented with a number between 0 and 100, determined by spinning a wheel of fortune. Interestingly, these arbitrarily generated numbers had a significant effect on the estimates made by the subjects. For example, people who ‘received’ the number 10 from the wheel of fortune estimated the percentage of African countries which are a member of the United Nations to be 25%. But people who were confronted with the number 65 after the wheel estimated the percentage to be 45%. Kahneman & Tversky dub this behavior ‘anchoring’, which refers to the phenomenon that ‘different starting points yield different estimates, which are biased toward the initial values.‘

Based on a series of experiments like the one discussed above, Kahneman & Tversky conclude that under uncertainty people (at least partly) base their estimates on randomly presented numbers. Psychological barriers in the stock markets also make good examples of anchoring. The observation that the index is approaching a big round number becomes part of investment decisions, even though this index level is as arbitrary as any other. It is this stock market anchoring that translates into the return patterns found by Donaldson & Kim.

Media hype

How would this work, exactly? There are a number of possible explanations. One of them is that the estimates of analysts, or so-called investment gurus, are predominantly expressed by using round numbers. Good chance you’re not taken seriously if you expect the Dow Jones to reach 21897,46 points by the end of the year.

The second possible explanation builds on the previous one. Not only do investment gurus work with round numbers, great chance that other investors do so as well. Many investors use round numbers as a reference for when to buy or sell shares. For example, you buy when a stock falls back to 90, only to sell when it reaches 100.

A third possible explanation for the anchoring effect related to round numbers is media attention. As mentioned in the intro, my Twitter timeline is clogged with the 20,000 number recently. The media love big numbers and they are mentioned and talked about extensively. This may trigger the perception that such a number is of great importance, or at least more important than other, random, index numbers, which leads to barrier effects.

In fact, Donaldson & Kim provide ‘evidence’ that media attention really is of importance. In their study mentioned above they did not only look at the return patterns of the DJIA but also of the more obscure Wilshire Associates 5000 index. Not familiar with it? No worries, this is exactly their intention. It is no coincidence that Donaldson & Kim do not find any signs of deviating return patterns when this less-known index is near 100- and 1000-levels. Hence, if the attention fades so does the magic of round numbers.

References

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty:Heuristics and biases. Science, 185, 1124–1131.

 Donaldson, R. G., & Kim, H. Y. (1993). Price barriers in the dow jones industrial average, Journal of Financial and Quantitative Analysis, 28(3), 313-330.

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