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A number of authors have suggested that investors derive utility from realizing gains and losses on assets that they own. We present a model of this “realization utility,” analyze its predictions, and show that it can shed light on a number of puzzling facts. These include the disposition effect, the poor trading performance of individual investors, the higher volume of trade in rising markets, the effect of historical highs on the propensity to sell, the individual investor preference for volatile stocks, the low average return of volatile stocks, and the heavy trading associated with highly valued assets.

When economists model the behavior of individual investors, they typically assume that these investors derive utility only from consumption or from total wealth. In this paper, we study the possibility that investors also derive utility from another source, namely from realized gains and losses on assets that they own. Suppose, for example, that an investor buys shares of a stock and then, a few months later, sells them. We consider a model in which he receives a burst of utility right then, at the moment of sale. The amount of utility depends on the size of the gain or loss realized—on the difference between the sale price and the purchase price—and is positive if the investor realizes a gain, and negative otherwise. This source of utility, which we label “realization utility,” is not new to our paper: other authors also discuss it. Our contribution is to offer a comprehensive analysis of its implications for trading behavior and for asset prices. Why might an investor derive utility from realizing a gain or loss? We think that realization utility is a consequence of two underlying cognitive processes. The first has to do with how people think about their investing history. Under this view, people do not think about their investing history purely in terms of the return they have earned on their portfolio. Rather, they often think about it as a series of investing episodes, each one defined by three things: the name of the investment, the purchase price, and the sale price. “I bought IBM at $80 and sold it at $100” might be one such episode. “We bought our house for $260,000 and sold it for $320,000” might be another. The second cognitive process that, in our view, underlies realization utility has to do with how people evaluate their investing episodes. We suspect that many investors use a simple heuristic to guide their trading, one that says: “Selling a stock at a gain relative to purchase price is a good thing—it is what successful investors do.” After all, an investor who buys a number of stocks in sequence and manages to realize a gain on all of them does end up with more money than he had at the start. The flip side of the same heuristic says: “Selling a stock at a loss is a bad thing—it is what unsuccessful investors do.” Indeed, an investor who buys a number of stocks in sequence and realizes a loss on all of them does end up with less money than he had at the start. In summary, an investor feels good when he sells a stock at a gain because, by selling, he is creating what he views as a positive investing episode. Conversely, he feels bad when he sells a stock at a loss because, by selling, he is creating what he views as a negative investing episode. We do not expect realization utility to be important for all investors or in all circumstances. For example, we expect it to matter more for individual investors than for institutional investors who, as trained professionals, are more likely to think about their investing history in terms of overall portfolio return than as a series of investing episodes. Also, since realization utility depends on the difference between sale price and purchase price, it is likely to play a larger role when the purchase price is more salient. It may therefore be more relevant to the trading of individual stocks or to the sale of real estate than to the trading of mutual funds: the purchase price of a stock or of a house is typically more salient than that of a fund. In our view, the idea that some investors derive utility directly from realizing gains and losses is a plausible one. But in order to claim that realization utility is a significant driver of investor behavior, we cannot appeal to mere plausibility. To make a more convincing case, we need to build a model of realization utility and then see if the model explains a range of facts and leads to new predictions that can be tested and confirmed. In this paper, we take up this challenge. We construct a model of realization utility, discuss its predictions, and show that it can shed light on a number of empirical facts. We start with a partial equilibrium framework but also show how realization utility can be embedded in a full equilibrium model. This allows us to make predictions not only about trading behavior but also about prices. Our partial equilibrium model is an infinite horizon model in which, at each moment, an investor allocates his wealth either to a risk-free asset or to one of a number of stocks. If the investor sells his holdings of a stock, he receives a burst of utility based on the size of the gain or loss realized and pays a proportional transaction cost. He also faces the possibility of a random liquidity shock: if such a shock occurs, he must immediately sell his asset holdings and exit the asset markets. At each moment, the investor makes his allocation decision by maximizing the discounted sum of expected future utility flows. In our baseline model, we assume a linear functional form for realization utility. Later, we also consider a piecewise-linear specification. We find that, under the optimal strategy, an investor who is holding a position in a stock will voluntarily sell this position only if the stock price rises sufficiently far above the purchase price. We look at how this “liquidation point” at which the investor sells depends on the expected stock return, the standard deviation of the stock return, the time discount rate, the transaction cost, and the likelihood of a liquidity shock. The model has a number of interesting implications. One of the more striking is that, even if realization utility has a linear or concave functional form, the investor can be risk seeking: all else equal, his initial value function can be an increasing function of the standard deviation of stock returns. The intuition is straightforward. A highly volatile stock offers the chance of a large gain which the investor can enjoy realizing. Of course, it may also drop a lot in value; but in that case, the investor will simply postpone selling the stock until he is forced to sell by a liquidity shock. Any realized loss therefore lies in the distant, discounted future and does not scare the investor very much at the time of purchase. Overall, then, the investor may prefer more volatility to less. We use our model to link realization utility to a number of financial phenomena. Among the applications we discuss are the disposition effect (Shefrin and Statman, 1985 and Odean, 1998), the subpar trading performance of individual investors (Barber and Odean, 2000; Barber, Lee, Liu, and Odean, 2009), the higher volume of trade in bull markets than in bear markets (Stein, 1995; Statman, Thorley, and Vorkink, 2006; Griffin, Nardari, and Stulz, 2007), the effect of historical highs on the propensity to sell (Grinblatt and Keloharju, 2001), the individual investor preference for volatile stocks (Kumar, 2009), the low average return of volatile stocks (Ang, Hodrick, Xing, and Zhang, 2006), and the heavy trading associated with highly valued assets—as, for example, in the case of U.S. technology stocks in the late 1990s (Hong and Stein, 2007). Of these applications of realization utility, the most obvious is the disposition effect, the greater propensity of individual investors to sell stocks that have risen in value, rather than fallen in value, since purchase. In combination with a sufficiently positive time discount rate, realization utility generates a strong disposition effect: the investor in our model voluntarily sells a stock only if it is trading at a gain relative to purchase price. While the link between realization utility and the disposition effect is clear, we emphasize that realization utility is not a “relabeling” of the disposition effect. On the contrary, it is just one of a number of possible theories of the disposition effect and can be distinguished from other theories through carefully constructed tests. For example, another theory of the disposition effect, one that has nothing to do with realization utility, is that investors have an irrational belief in mean-reversion. Later in the paper, we discuss an experiment that can distinguish this view from the realization utility view. Our other applications are more subtle. For example, our model predicts that individual investors—the investor group that is more likely to think in terms of realization utility—will have a much greater propensity to sell a stock once its price moves above its historical high. Imagine a stock that rises to a high of $45, falls, and then rises again, passing its previous high of $45 and continuing upwards. Our model predicts that there will be relatively little selling as the stock approaches $45 for the second time—any realization utility investors with liquidation points of $45 or lower will have sold already when the stock first approached $45—but once the stock moves above the historical high of $45, realization utility investors with liquidation points higher than $45 will start to sell. In line with the evidence of Grinblatt and Keloharju (2001), then, our model predicts that historical highs will have a sharp effect on individual investors' propensity to sell. The idea that people derive utility from gains and losses rather than from final wealth levels was first proposed by Markowitz (1952), but is particularly associated with Kahneman and Tversky (1979): it is a central element of their prospect theory model of decision-making. Finance researchers have typically taken Kahneman and Tversky's message to be that they should study models in which investors derive utility from paper gains and losses. Benartzi and Thaler (1995), for example, assume that investors derive utility from fluctuations in their financial wealth, while Barberis, Huang, and Santos (2001) and Barberis and Huang (2001) assume that they derive utility from fluctuations in the value of their stock market holdings or in the value of specific stocks that they own. The idea that people might derive utility from realized gains and losses has received much less attention. The concept first appears in Shefrin and Statman (1985). Among several other contributions, these authors point out, with the help of a numerical example, that if an investor derives utility from realized gains and losses and has a utility function that, as in prospect theory, is concave over gains and convex over losses, then he will exhibit a disposition effect. Shefrin and Statman (1985) justify their emphasis on realized gains and losses by reference to “mental accounting,” a term used to describe how people think about, organize, and evaluate their financial transactions. In their view, when an investor sells a stock, he is closing a mental account that was opened when he first bought the stock. The moment of sale is therefore a natural time at which to evaluate the transaction: a realized gain is seen as a good outcome and a realized loss as a poor outcome. Realized gains and losses thereby become carriers of utility in their own right. Although described using different language, this motivation for realization utility is similar to our own.1 More recently, Barberis and Xiong (2009) use a two-period model to study the trading behavior of an investor who derives utility from realized gains and losses with a utility function that is concave over gains and convex over losses. They observe that, consistent with Shefrin and Statman (1985), the investor often exhibits a disposition effect. They do not study any other implications of realization utility, nor do they link it to any other applications.2 In this paper, we offer a more comprehensive analysis of realization utility. We construct a richer model—an infinite horizon model that allows for transaction costs and a stochastic liquidity shock. We derive an analytical solution for the investor's optimal trading strategy. We show how realization utility can be incorporated into both a model of trading behavior and a model of asset pricing. We document several basic implications of realization utility. And we discuss many potential applications, rather than just one. In Section 2, we present a partial equilibrium model of realization utility, one that also assumes a linear functional form for the realization utility term. In Section 3, we use a piecewise-linear functional form. In Section 4, we show how realization utility can be embedded in a model of asset prices. Section 5 discusses a range of applications and testable predictions, while Section 6 concludes.

A number of authors have suggested that investors derive utility from realizing gains and losses. We present a model of this “realization utility,” study its predictions, and show that it can shed light on a number of puzzling facts. There are several possible directions for future research. First, while many of our model's implications match the observed facts, some do not. For example, our model predicts too strong a disposition effect: in our framework, investors never voluntarily sell stocks at a loss, while, in reality, they clearly do. It would be useful to see whether an extension of our model—one that modifies our preference specification in some way, or that allows for richer beliefs about expected stock returns—can make more accurate predictions.17 Another natural research direction involves testing the implications of realization utility. To do this, we can use field data on investor trading behavior; or experimental data, as in Weber and Camerer (1998). Another type of data that has recently become available is neural data. For example, Frydman, Barberis, Camerer, Bossaerts, and Rangel (2011) use functional magnetic resonance imaging (fMRI) technology to monitor the brain activity of 28 subjects while they trade stocks in an experimental market. The authors use the neural data to test some theories of investor behavior, including the one presented in this paper. Finally, it would be useful to think about other applications of realization utility. These applications may again concern the trading and pricing of financial securities, or they may be drawn from quite different areas of study. After all, the core idea that, in our view, underlies realization utility—that people break their experiences down into episodes and receive a burst of utility when an episode comes to an end—strikes us as one that may be relevant in many contexts, not just the financial market context that we have focused on in this paper.