Modulus matters

I’ve wondered about the following question a number of times: How might the fact that we operate in base-10 (0,10,20…100…200) influence our decisions? We all know that we occasionally make decisions based on simply rounding up or down. But do round numbers influence trading in the stock market – for example, when setting stop or limit orders? Consult a new paper in Management Science:

This paper provides evidence that stock traders focus on round numbers as cognitive reference points for value. Using a random sample of more than 100 million stock transactions, we find excess buying (selling) by liquidity demanders at all price points one penny below (above) round numbers. Further, the size of the buy–sell imbalance is monotonic in the roundness of the adjacent round number (i.e., largest adjacent to integers, second-largest adjacent to half-dollars, etc.). Conditioning on the price path, we find much stronger excess buying (selling) by liquidity demanders when the ask falls (bid rises) to reach the integer than when it crosses the integer. We discuss and test three explanations for these results. Finally, 24-hour returns also vary by price point, and buy–sell imbalances are a major determinant of that variation across price points. Buying (selling) by liquidity demanders below (above) round numbers yield losses approaching $1 billion per year.

Utpal Bhattacharya, Craig W. Holden, and Stacey Jacobsen – Penny Wise, Dollar Foolish: Buy–Sell Imbalances On and Around Round Numbers

So would we be better off with a base with a higher or lower modulus? Now that’s an interesting cross-discipline  (economics and pure math) theory PhD waiting to happen. If Krugman hasn’t off-handedly done it yet. 

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