Testing for the Disposition Effect on Optimal Stopping Decisions

摘要

The disposition effect-the tendency of individual investors to sell assets whose price has increased and hold on to assets that have dropped in value-is a cornerstone of behavioral finance. More generally, the disposition effect is an important notion for behavioral economics as it exemplifies the idea that decision-makers suboptimally delay realizing disappointing outcomes but suboptimally rush to realize outcomes that are better-than-expected. However, previous evidence has been mostly indirect. For instance, the typical procedure used in studies on the disposition effect in stock markets involves testing whether the frequency of sales is larger for winning stocks than for losing stocks. I propose and conduct a sharper test of the disposition effect using a laboratory experiment that produces an unambiguous benchmark of rational stopping decisions. I design a security that bundles a risky asset, whose price follows a stochastic process in continuous time, with the option to liquidate the asset at a constant salvage value. I analyze an impatient decision-maker who makes a decision about when, if ever, to liquidate the investment. Optimal behavior entails maintaining the current position in the security until either: (ⅰ) the asset price reaches an upper threshold B~* above which the expected benefit from waiting is outweighed by the immediate reward from selling the asset and the decision-maker reaps this opportunity, or (ⅱ) the asset price reaches a lower threshold b~* and the decision-maker capitulates, liquidating at an exogenously fixed salvage value and forgoing potential future price increases. Thus my model provides a clear rational benchmark against which to evaluate the disposition effect. Indeed, the original formulation of the disposition effect by Shefrin and Statman (1985) as the tendency to sell winners too early and ride losers too long can be formally characterized in terms of the stopping times induced by the optimal thresholds. There is a disposition effect if the actual thresholds (B and b) are both lower than optimal: b ＜ b~* and B ＜ B~*. Laboratory research provides an important complement to studies on the disposition effect that use financial market data. Obtaining and skillfully analyzing field evidence is a necessary step for understanding the behavior of individual decision-makers, however important aspects of the decision-making process are unobservable in naturally occurring settings. It is often difficult to identify a normative benchmark against which the disposition effect can be measured. In practice, field data studies rely on the implicit assumption that a rational decision about how long to hold on to an investment should be independent of whether the investment is a winner or a loser. Thus, the typical test of the disposition effect involves checking whether sales of winners are more likely than sales of losers. However, these tests are not grounded in any specific theory and the results may be subject to different interpretations. In my experiment I consider a deliberately stylized optimal stopping problem (not meant to replicate the environment real investors face) and this allows me to define an unambiguous benchmark. While important laboratory work has been conducted on the disposition effect, such as Weber and Camerer (1998), most face potential confounds that make the effect difficult to interpret and difficult to distinguish from rational behavior. At a basic level my design differs from Weber and Camerer (1998) in the mechanism used to induce stopping decisions: while in Weber and Camerer (1998) liquidation decisions arise from portfolio choice motives, here stopping is induced by inter-temporal trade-offs. In (lab and field) environments where decision-makers are actively engaged in portfolio choice, risk aversion, and other diversification motives may lead to differences in the propensity to sell winners and losers. In the multiple heterogeneous asset framework of Weber and Camerer (1998) the optimal, expected-value maximizing behavior is to hold on to the single asset that the decision-maker identifies as the winner based on her beliefs at a point in time. However, this is also a very risky strategy, because of uncertainty about which asset is the actual winner. Thus holding on to losers might just be a way to hedge some risk when the quality of the assets is uncertain. This potential confound does not apply to my design, where a known stochastic process drives the value of the decision-maker's investment.