The authors simulate investor trading behavior that follows prospect theory to see if such behavior leads to a disposition effect for individual investors. Simulations based on annual gains and losses show a disposition effect only when risky investments have low expected returns or when many trading opportunities exist. Simulations based on realized gains and losses demonstrate a disposition effect over a wider range of inputs. These results indicate that realized gains and losses may provide more insight into investor behavior than do returns based on a fixed time frame.
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
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
The realized gains and losses simulation uses a three-period structure
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.