A “disposition effect” occurs if investors are more likely to sell stock that has increased in price relative to its initial cost than stock that has decreased in price. This effect is well documented for individual investors, but modeling its cause has been troublesome. The authors propose an alternative model that uses prospect theory, which is based on differing utility for gains and losses rather than utility of final wealth level. According to prospect theory, investors are risk averse for moderate gains (a concave utility function) and risk seeking for moderate losses (a convex utility function). Also, they react more negatively toward losses than they do positively toward gains of an equal magnitude. Based on parameters developed in prior finance literature, the authors use simulation analysis to see if prospect theory leads to a disposition effect for investors. They use two approaches: First, investors receive utility only at the end of each year, and second, investors receive immediate utility when a trade is made and gains or losses are realized.

In the model, investors may invest in a risky asset or a risk-free asset. The potential gain on the risky investment is larger than the potential loss, thus making the expected return on the risky investment positive. Investors have T opportunities to trade within the year. Each trading period, the price of the risky asset either increases or decreases, implying t + 1 possible outcomes, where t = time, at any point in time. At the end of each trading period, investors make the trade decision based on a utility function that follows prospect theory. Each period, the authors calculate the proportion of gains realized (PGR) ratio, which is the number of stocks with a gain that are sold relative to the number of stocks with a gain that could be sold. They also develop a similar proportion of losses realized (PLR) ratio and then compare the two ratios. If the disposition effect holds, the average PGR should be larger than the average PLR.

The authors predict, and the simulation results confirm, that expected returns on the risky asset must exceed a “threshold” before investors are willing to invest in the risky asset. The level of the threshold decreases as the number of trading opportunities increases.

Results based on annual gains and losses do not show consistent evidence of a disposition effect. The objective of this model is to maximize the gain at the end of the year, but intermediate results have no utility and investors are averse to a loss at the end of the year. Because the magnitude of a gain is greater than the magnitude of a loss for any one period within the year, if investors have a gain in a given period, they can buy more shares and have a year-end gain even if they lose in the next period. If investors have a loss in a period, they can sell shares and reduce their year-end loss, but the gain on the remaining shares may be sufficient to cause a year-end gain if the return is positive in the following period. Therefore, investors buy shares following a gain and sell shares following a loss, which is the opposite of a disposition effect. In this model, the disposition effect holds only if many trading opportunities exist (T is large) and the expected return on the risky investment is low, thus making the magnitude of the gain and loss more similar.

The realized gains and losses simulation uses a three-period structure (T = 2). Results based on this approach find the disposition effect over a wider level of expected returns. Under this model, investors want to experience a loss only once, so they do not sell losers at the intermediate period (t = 1). Investors are more likely to spread the positive experience of a gain over multiple periods and to sell at least some of the winners immediately.

This research suggests that investors are more focused on realized gains and losses than on a fixed-period time horizon. This approach differs from common finance paradigms.