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This article studies the impact of heterogeneous loss averse investors on asset prices. In very good states loss averse investors become gradually less risk averse as wealth rises above their reference point, pushing up equity prices. When wealth drops below the reference point the investors become risk seeking and demand for stocks increases drastically, eventually leading to a forced sell-off and stock market bust in bad states. Heterogeneity in reference points and initial wealth of the loss averse investors does not change the salient features of the equilibrium price process, such as a relatively high equity premium, high volatility and counter-cyclical changes in the equity premium.

The aim of this paper is to analyze the impact of loss averse investors on asset prices in a continuous-time version of the Lucas (1978) pure-exchange economy with heterogeneous agents. We link the equilibrium outcomes to the optimal dynamic investment strategy of the investors, to understand how myopic loss averse agents influence stock prices and volatility. We first consider an economy populated by a group of regular risk averse agents and a group of myopic loss averse agents. Both groups of agents have a power utility function over intertemporal consumption. The first group of agents also evaluate their wealth at the end of the first evaluation period with a power utility function, measuring total expected utility from future consumption during their remaining lifetime. The myopic loss averse agents, on the other hand, evaluate changes in their wealth at the end of the evaluation period with the value function of prospect theory, while ignoring all events beyond that first period. For loss averse investors it matters a lot whether wealth is above or below the reference point. We therefore also study a second economy with heterogeneous loss averse agents that have different levels of initial wealth and reference points. We are particularly interested to see whether this type of heterogeneity smooths the demand for stocks, potentially reducing the equity premium and volatility compared to a representative agent economy with one loss averse agent. This paper contributes to the growing literature on loss aversion and asset pricing, including amongst others Benartzi and Thaler, 1995, Barberis et al., 2001 and McQueen and Vorkink, 2004. Benartzi and Thaler (1995) introduce the concept of myopic loss aversion and argue that it can explain the equity premium puzzle. Barberis et al. (2001) fit the historical equity premium in an infinite-horizon consumption-based equilibrium model with one aggregate loss averse investor, while McQueen and Vorkink (2004) show that a similar model can replicate the asymmetric GARCH properties of monthly US stock market data. The basic features of our Lucas exchange economy are similar to Barberis et al. (2001), except that our setup has a finite horizon, which improves the tractability of the model. The setup allows us to analyze the impact of investor heterogeneity in an economy populated by loss averse agents with different levels of initial wealth and different reference points. In our opinion this type of investor heterogeneity is an important issue, as the investment strategy of loss averse agents changes drastically depending on the level of wealth relative to the reference point. Other relevant related papers are Berkelaar et al., 2004 and Gomes, 2005. Berkelaar et al. (2004) derive the optimal dynamic investment strategy of loss averse investors in a continuous-time complete market setting, providing the foundation for the equilibrium results in this paper. Gomes (2005) analyzes portfolio choice of loss averse investors in a discrete-time model with finite horizon and asset prices in a heterogeneous agent economy with both regular agents and loss averse agents. While Gomes (2005) focuses more on the implications for trading volume, in this paper we study asset prices and volatility, using an approach that gives more closed-form expressions, including results for economies with heterogeneous loss averse investors. The outline of the paper is as follows. In Section 2 we introduce the continuous-time economy and we derive the main result, an expression for the equilibrium stock price in an economy with loss averse investors, both homogeneous and heterogeneous. In Section 3 we calibrate the model with US consumption data and present the main properties of the equilibrium stock price, the equity premium and volatility. We compare our results to the literature. Section 4 concludes the paper.

This article studies the impact of myopic loss averse investors on asset prices. We find that the stock price function in an economy with loss averse agents resembles a path from boom ’til bust. Loss averse investors have relatively low demand for stocks when wealth is just above the reference point, but relatively high demand when wealth is sufficiently far above the reference point to make future losses unlikely, leading to stock market booms in very good states of the world. When wealth drops below the reference point the investors become risk seeking and the demand for stocks increases drastically, eventually leading to a ‘bust’ in bad states of the world when the loss averse investor are forced to sell stocks to avoid bankruptcy. The equity premium and stock market volatility in an economy with loss averse agents are considerably higher on average than in a standard economy with CRRA agents. Further, changes in the equity premium and volatility are counter-cyclical, depending on whether the wealth of the loss averse agents is above or below their reference point. Our relatively simple continuous-time complete market model with a finite horizon allows us to derive expressions for asset prices for an economy with heterogeneous loss averse agents having different reference points and levels of initial wealth. We show that heterogeneous loss averse agents cannot be represented by one aggregate loss averse agent, as is the case in a standard CRRA economy. Interestingly, we that find heterogeneity in reference points and initial wealth does not reduce the equity premium and volatility on average compared to an economy with one aggregate loss averse investor as studied previously by Barberis et al. (2001). However, investor heterogeneity does smooth out some of the extreme sensitivity to initial parameter values that we observe in a representative agent economy.