Make Hay While the Sun Shines: an Empirical Study of Maximum Price, Regret, and Trading Decisions

Time-constant trading thresholds are optimal for a large class of preferences and asset price dynamics, including, Expected Utility and the S-shaped reference-dependent utility of Prospect Theory. Such thresholds imply selling stocks at the maximum price since purchase. We use a large discount brokerage dataset containing US households’ trading records between 1991 and 1996 to document that in 31.6% of cases the stocks sold for a gain are sold on the day when the maximum since purchase occurs. However, not all stocks are sold at a maximum since purchase and the propensity to sell changes depending on how far in time and price the stock is with respect to this past maximum. We find that the propensity to sell initially increases as the price is closer to the past maximum but it then decreases when the price gets in the closest region to the past maximum, leading to an inverse U-shape; and that investors are less likely to sell a gain, the further away in time the maximum price occurred. Studying the joint effect of price and time distance, we find that the propensity to sell is highest at low time distance and high price distance from the maximum since purchase. We relate these findings to regret, belief updating, and attention.