Loss aversion,asymmetric market comovements,and the home bias

Loss aversion has been used to explain why a high equity premium might be consistent with plausible levels of risk aversion. The intuition is that the first-order-different utility impact of wealth gains and losses leads loss-averse investors to behave similarly to investors with high risk aversion. But if so, should those agents not perceive larger gains from international diversification than standard expected-utility investors with plausible levels of risk aversion? They might not, because comovements in international stock markets are asymmetric: correlations are higher in market downturns than in upturns. This asymmetry dampens the gains from diversification relatively more for loss-averse investors. We analyze the portfolio problem of such an investor who has to choose between home and foreign equities in the presence of asymmetric comovement in returns. Perhaps surprisingly, in the context of the home bias puzzle we find that loss-averse investors behave similarly to those with standard expected-utility preferences and plausible levels of risk aversion. We argue that preference specifications that appear to perform well with respect to the equity premium puzzle should be subjected to this “test”.     

Heterogeneous Beliefs, Speculation, and the Equity Premium

Agents with heterogeneous beliefs about fundamental growth do not share risks perfectly but instead speculate with each other on the relative accuracy of their models' predictions. They face the risk that market prices move more in line with the trading models of competing agents than with their own. Less risk‐averse agents speculate more aggressively and demand higher risk premiums. My calibrated model generates countercyclical consumption volatility, earnings forecast dispersion, and cross‐sectional consumption dispersion. With a risk aversion coefficient less than one, agents' speculation causes half the observed equity premium and lowers the riskless rate by about 1%.     

Market incompleteness and the equity premium puzzle: Evidence from state-level data

This paper investigates the importance of market incompleteness by comparing the rates of risk aversion estimated from complete and incomplete markets environments. For the incomplete-markets case, we use consumption data for the 50 US states. We find that the rate of risk aversion under the incomplete-markets setup is much lower. Furthermore, including the second and third moments of the cross-sectional distribution of consumption growth in the pricing kernel lowers the estimate of risk aversion. These findings suggest that market incompleteness ought to be seen as an important component of solutions to the equity premium puzzle.     

Risk premia: Exact solutions vs. log-linear approximations

We derive exact expressions for the risk premia for general distributions in a Lucas economy and show that the errors when using log-linear approximations can be economically significant when the shocks are nonnormal. Assuming growth rates are Normal Inverse Gaussian (NIG) and fitting the distribution to the data used in Mehra and Prescott (1985), the coefficient of relative risk aversion required to match the equity premium is more than halved compared to the finding in their article. We also consider a standard long-run risk model and, by comparing our exact solutions to the log-linear approximations, we show that the approximation errors are substantial, especially for high levels of risk aversion.     

Risk,uncertainty, and asset prices

We identify the relative importance of changes in the conditional variance of fundamentals (which we call “uncertainty”) and changes in risk aversion in the determination of the term structure, equity prices, and risk premiums. Theoretically, we introduce persistent time-varying uncertainty about the fundamentals in an external habit model. The model matches the dynamics of dividend and consumption growth, including their volatility dynamics and many salient asset market phenomena. While the variation in price–dividend ratios and the equity risk premium is primarily driven by risk aversion, uncertainty plays a large role in the term structure and is the driver of countercyclical volatility of asset returns.     

Generalized Disappointment Aversion and Asset Prices

We characterize generalized disappointment aversion (GDA) risk preferences that can overweight lower‐tail outcomes relative to expected utility. We show in an endowment economy that recursive utility with GDA risk preferences generates effective risk aversion that is countercyclical. This feature comes from endogenous variation in the probability of disappointment in the representative agent's intertemporal consumption‐saving problem that underlies the asset pricing model. The variation in effective risk aversion produces a large equity premium and a risk‐free rate that is procyclical and has low volatility in an economy with a simple autoregressive endowment‐growth process.     

From boom ‘til bust: How loss aversion affects asset prices

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.     

Asset Pricing with Garbage

A new measure of consumption, garbage, is more volatile and more correlated with stocks than the canonical measure, National Income and Product Accounts (NIPA) consumption expenditure. A garbage‐based consumption capital asset pricing model matches the U.S. equity premium with relative risk aversion of 17 versus 81 and evades the joint equity premium‐risk‐free rate puzzle. These results carry through to European data. In a cross‐section of size, value, and industry portfolios, garbage growth is priced and drives out NIPA expenditure growth.     

Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players and the interaction between buyers and sellers. In commodities markets this premium is an important indicator of the behavior of buyers and sellers and their views on the market spanning between short-term and long-term horizons. We show that under certain assumptions it is possible to derive explicit solutions that link levels of risk aversion and market power with market prices of risk and the market risk premium. We apply our model to the German electricity market and show that the market risk premium exhibits a term structure which can be explained by the combination of two factors. Firstly, the levels of risk aversion of buyers and sellers, and secondly, how the market power of producers, relative to that of buyers, affects forward prices with different delivery periods.     

The Equity Premium: Consistent with GDP Growth and Portfolio Insurance

We find that the long‐term equity premium is consistent with both GDP growth and portfolio insurance. We use a supply‐side growth model and demonstrate that the arithmetic average stock market return and the returns on corporate assets and debt depend on GDP per capita growth. The implied equity premium matches the U.S. historical average over 1926–2001. Separately, we find that the equity premium tracks the value of a put option on the S&P 500. Our theory predicts a smaller equity premium in the future, assuming that the recent regime shifts in dividend policies, interest rates, and tax rates are permanent.     

Robust portfolio choice with uncertainty about jump and diffusion risk

We analyze the portfolio planning problem of an ambiguity averse investor. The stock follows a jump-diffusion process. We find that there are pronounced differences between ambiguity aversion with respect to diffusion risk and jump risk. Ignoring ambiguity with respect to jump risk causes larger losses in an incomplete market, whereas ignoring ambiguity with respect to diffusion risk is more severe in a complete market. For a deterministic jump size we show that the loss from market incompleteness is always increasing in the level of ambiguity aversion with respect to one risk factor and decreasing in the level of ambiguity aversion with respect to the other risk factor.     

Time-varying risk aversion and asset prices

This paper uses a variant of the consumption-based representative agent model in Campbell and Cochrane [Campbell, J.Y., Cochrane, J.H., 1999. By force of habit: Consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251] to study how investors’ time-varying risk aversion affects asset prices. First, we show that a countercyclical variation of risk aversion drives a procyclical conditional risk premium. Second, we show that with a small value for the volatility of the log surplus consumption ratio, a large value of risk aversion may not determine whether the equity premium and the risk-free rate puzzles can be resolved or not. Third, we show that countercyclical risk aversion may not help explain the predictability of long-horizon stock returns, the univariate mean-reversion of stock prices and the “leverage effect” in return volatility.     

Private Equity Performance and Liquidity Risk

Private equity has traditionally been thought to provide diversification benefits. However, these benefits may be lower than anticipated as we find that private equity suffers from significant exposure to the same liquidity risk factor as public equity and other alternative asset classes. The unconditional liquidity risk premium is about 3% annually and, in a four‐factor model, the inclusion of this liquidity risk premium reduces alpha to zero. In addition, we provide evidence that the link between private equity returns and overall market liquidity occurs via a funding liquidity channel.     

Heterogeneity in the Effect of Managerial Equity Incentives on Firm Value

We document significant heterogeneity in the relation between chief executive officer (CEO) equity incentives and firm value using quantile regression. We show that CEO delta is more effective in the presence of ample investment opportunities, while CEO vega is more beneficial for firms lacking investment opportunities. Further, Tobin's Q increases in CEO delta for more risk‐tolerant firms but increases in CEO vega for more risk‐averse firms. We also observe that higher monitoring intensity after the Sarbanes‐Oxley Act reduces CEO delta's role in compensation. Risk aversion alters the optimal incentive‐value relation, and the nature of this relation also depends on the level of Tobin's Q.     

Idiosyncratic Volatility Covariance and Expected Stock Returns

Given that the idiosyncratic volatility (IDVOL) of individual stocks co‐varies, we develop a model to determine how aggregate idiosyncratic volatility (AIV) may affect the volatility of a portfolio with a finite number of stocks. In portfolio and cross‐sectional tests, we find that stocks whose returns are more correlated with AIV innovations have lower returns than those that are less correlated with AIV innovations. These results are robust to controlling for the stock's own IDVOL and market volatility. We conclude that risk‐averse investors pay a premium for stocks that pay well when AIV is high, consistent with our model.     

Preference heterogeneity and asset prices: An exact solution

We introduce a general equilibrium model of a multi-agent, pure-exchange economy and find a set of conditions that enable us to obtain explicit closed-form solutions to the equilibrium interest rate, stock price, risk premium and stock market volatility when investors have heterogenous risk aversions. Because the market is dynamically complete, full risk sharing obtains and a representative agent can be constructed, though the risk aversion of this agent fluctuates over time with the state of the economy, as the relative wealth distribution of the individual investors changes. We show that preference heterogeneity can cause asset prices to be significantly more volatile than the underlying dividends and that it can lead to leverage-like effects in volatility, in the sense that volatility increases after stock-market declines.     

Luxury Goods and the Equity Premium

This paper evaluates the equity premium using novel data on the consumption of luxury goods. Specifying utility as a nonhomothetic function of both luxury and basic consumption goods, we derive pricing equations and evaluate the risk of holding equity. Household survey and national accounts data mostly reflect basic consumption, and therefore overstate the risk aversion necessary to match the observed equity premium. The risk aversion implied by the consumption of luxury goods is more than an order of magnitude less than that implied by national accounts data. For the very rich, the equity premium is much less of a puzzle.     

Asset Pricing without Garbage

This paper provides an explanation for why garbage implies a much lower relative risk aversion in the consumption‐based asset pricing model than National Income and Product Accounts (NIPA) consumption expenditure: Unlike garbage, NIPA consumption is filtered to mitigate measurement error. I apply a simple model of the filtering process that allows one to undo the filtering inherent in NIPA consumption. “Unfiltered NIPA consumption” well explains the equity premium and is priced in the cross‐section of stock returns. I discuss the likely properties of true consumption (i.e., without measurement error and filtering) and quantify implications for habit and long‐run risk models.     

How loss averse are investors in financial markets?

We investigate loss aversion in financial markets using a typical asset allocation problem. Our theoretical and empirical results show that investors in financial markets are more loss averse than assumed in the literature. Moreover, loss aversion changes depending on market conditions; investors become far more loss averse during bull markets than during bear markets, indicating their more profound disutility for losses when others enjoy gains. Contrary to most previous results, we find that investors are more sensitive to changes in losses than changes in gains.     

Robust general equilibrium under stochastic volatility model

This paper studies the implications of model uncertainty under stochastic volatility model for equilibrium asset pricing. We derive the equilibrium equity premium and risk-free rate in a pure-exchange economy with one representative agent who is averse not only to risk but also to model uncertainty. The results show that robustness increases the equilibrium equity premium while lowers the risk-free rate.