The Loss Aversion / Narrow Framing Approach to the Equity Premium Puzzle

We review a recent approach to understanding the equity premium puzzle. The key elements of this approach are loss aversion and narrow framing, two well-known features of decision-making under risk in experimental settings. In equilibrium, models that incorporate these ideas can generate a large equity premium and a low and stable risk-free rate, even when consumption growth is smooth and only weakly correlated with the stock market. Moreover, they can do so for parameter values that correspond to sensible attitudes to independent monetary gambles. We conclude by suggesting some possible directions for future research.

What Drives the Disposition Effect? An Analysis of a Long-Standing Preference-Based Explanation

One of the most striking portfolio puzzles is the %u201Cdisposition effect%u201D: the tendency of individuals to sell stocks in their portfolios that have risen in value since purchase, rather than fallen in value. Perhaps the most prominent explanation for this puzzle is based on prospect theory. Despite its prominence, this explanation has received little formal scrutiny. We take up this task, and analyze the trading behavior of investors with prospect theory preferences. We find that, at least for the simplest implementation of prospect theory, the link between these preferences and the disposition effect is not as obvious as previously thought: in some cases, prospect theory does indeed predict a disposition effect, but in others, it predicts the opposite. We provide intuition for these results, and identify the conditions under which the disposition effect holds or fails. We also discuss the implications of our results for other disposition-type effects that have been documented in settings such as the housing market, futures trading, and executive stock options.

Comovement

A number of studies have identifed patterns of positive correlation of returns, or comovement, among different traded securities. We distinguish three views of such comovement. The traditional “fundamentals†view explains the comovement of securities through positive correlations in the rational determinants of their values, such as cash flows or discount rates. “Category-based†comovement occurs when investors classify different securities into the same asset class and shift resources in and out of this class in correlated ways. A related phenomenon of “habitat-based†comovement arises when a group of investors restricts its trading to a given set of securities, and moves in and out of that set in tandem. We present models of each of the three types of comovement, and then assess them empirically using data on stock inclusions into and deletions from the S&P 500 index. Index changes are noteworthy because they change a stock’s category and investor clientele (habitat), but do not change its fundamentals. We find that when a stock is added to the index, its beta and R-squared with respect to the index increase, while its beta with respect to stocks outside the index falls. The converse happens when a stock is deleted. These results are broadly supportive of the category and habitat views of comovement, but not of the fundamentals view. More generally, we argue that these non-traditional views may help explain other instances of comovement in the data.

Prospect Theory and Asset Prices

We propose a new framework for pricing assets, derived in part from the traditional consumption-based approach, but which also incorporates two long-standing ideas in psychology: prospect theory, and evidence on how prior outcomes affect risky choice. Consistent with prospect theory, the investor in our model derives utility not only from consumption levels but also from changes in the value of his financial wealth. He is much more sensitive to reductions in wealth than to increases, the ``loss-aversion'' feature of prospect utility. Moreover consistent with experimental evidence, the utility he receives from gains and losses in wealth depends on his prior investment outcomes; prior gains cushion subsequent losses -- the so-called 'house-money' effect -- while prior losses intensify the pain of subsequent shortfalls. We study asset prices in the presence of agents with preferences of this type, and find that our model reproduces the high mean, volatility, and predictability of stock returns. The key to our results is that the agent's risk-aversion changes over time as a function of his investment performance. This makes prices much more volatile than underlying dividends and together with the investor's loss-aversion, leads to large equity premia. Our results obtain with reasonable values for all parameters.

Prospect Theory and Asset Prices

We study asset prices in an economy where investors derive direct utility not only from consumption but also from fluctuations in the value of their financial wealth. They are loss averse over these fluctuations and the degree of loss aversion depends on their prior investment performance. We find that our framework can help explain the high mean, excess volatility and predictability of stock returns, as well as their low correlation with consumption growth. The design of our model is influenced by prospect theory and by experimental evidence on how prior outcomes affect risky choice.

Comovement

A number of studies have identifed patterns of positive correlation of returns, or comovement, among different traded securities. We distinguish three views of such comovement. The traditional 'fundamentals' view explains the comovement of securities through positive correlations in the rational determinants of their values, such as cash flows or discount rates. 'Category-based' comovement occurs when investors classify different securities into the same asset class and shift resources in and out of this class in correlated ways. A related phenomenon of 'habitat-based' comovement arises when a group of investors restricts its trading to a given set of securities, and moves in and out of that set in tandem. We present models of each of the three types of comovement, and then assess them empirically using data on stock inclusions into and deletions from the S&P 500 index. Index changes are noteworthy because they change a stock's category and investor clientele (habitat), but do not change its fundamentals. We find that when a stock is added to the index, its beta and R-squared with respect to the index increase, while its beta with respect to stocks outside the index falls. The converse happens when a stock is deleted. These results are broadly supportive of the category and habitat views of comovement, but not of the fundamentals view. More generally, we argue that these non-traditional views may help explain other instances of comovement in the data.

A Model of Casino Gambling

We show that prospect theory offers a rich theory of casino gambling, one that captures several features of actual gambling behavior. First, we demonstrate that, for a wide range of preference parameter values, a prospect theory agent would be willing to gamble in a casino even if the casino only offers bets with no skewness and with zero or negative expected value. Second, we show that the probability weighting embedded in prospect theory leads to a plausible time inconsistency: at the moment he enters a casino, the agent plans to follow one particular gambling strategy; but after he starts playing, he wants to switch to a different strategy. The model therefore predicts heterogeneity in gambling behavior: how a gambler behaves depends on whether he is aware of the time inconsistency; and, if he is aware of it, on whether he can commit in advance to his initial plan of action.

Style Investing

We study asset prices in an economy where some investors classify risky assets into different styles and move funds back and forth between these styles depending on their relative performance. Our assumptions imply that news about one style can affect the prices of other apparently unrelated styles, that assets in the same style will comove too much while assets in different styles comove too little, and that high average returns on a style will be associated with common factors for reasons unrelated to risk. They also lead to a rich pattern of own- and cross-autocorrelations, sample premia that can be very different from true premia, and imply that style momentum strategies will be profitable. We use our model to shed light on many puzzling features of the data.

Mental Accounting, Loss Aversion, and Individual Stock Returns

We study equilibrium firm-level stock returns in two economies: one in which investors are loss averse over the fluctuations of their stock portfolio and another in which they are loss averse over the fluctuations of individual stocks that they own. Both approaches can shed light on empirical phenomena, but we find the second approach to be more successful: in that economy, the typical individual stock return has a high mean and excess volatility, and there is a large value premium in the cross-section which can, to some extent, be captured by a commonly used multifactor model.