Once Burned, Twice Shy: Naïve Learning, Counterfactuals, and the Repurchase of Stocks Previously Sold

We establish two previously undocumented patterns in the purchase selections of individual investors and confirm a related pattern. These patterns hinge on investors’ previous experience with a stock. We demonstrate that investors prefer to (1) repurchase stocks that they previously sold for a gain, (2) repurchase stocks that have lost value subsequent to a prior sale, and (3) purchase additional shares of stocks that have lost value subsequent to being purchased. We document these trading patterns by analyzing trading records for 66,465 households at a large discount broker between January 1991 and November 1996 and 665,533 investors at a large retail broker between January 1997 and June 1999. We argue that the first trading pattern results from a simple form of learning whereby investors repeat actions that previously resulted in pleasure while avoiding actions that previously led to pain (i.e., they repurchase their previous winners but not their previous losers). We argue that the second trading pattern is tied to counterfactuals. Investors who buy a stock at a higher price than they previously sold it for are painfully aware that they are worse off than if they had simply never sold that stock. Investors who buy a stock at a lower price than they previously sold it for experience the pleasure of knowing they are better off than if they had never sold that stock. We argue that the third pattern can also be understood in terms of counterfactuals. Investors who purchase additional shares of a stock at a higher price than they originally paid are aware that they would have been better off making a larger initial purchase, while those who purchase additional shares at a lower price are better off than if they had made a larger initial purchase. Furthermore, by purchasing additional shares at a lower price, investors increase the likelihood that they will be able to sell their shares for more than the average purchase price. From a Prospect Theory perspective, investors are lowering their reference point for this position. Buying stocks that have gone down in price since they were sold, or first purchased, is inconsistent with the general preference of investors for buying stocks with strong recent performance. Investor returns do not reliably benefit from any of the three patterns we document.