Empirically, co-skewness of asset returns seems to explain a substantial part of the cross-sectional variation of mean return not explained by beta. This finding is typically interpreted in terms of a risk averse representative investor with a cubic utility function. This paper questions this interpretation. We show that the empirical tests fail to impose risk aversion and the implied utility function takes an inverse S-shape. Unfortunately, the first-order conditions are not sufficient to guarantee that the market portfolio is the global maximum for this utility function, and our results suggest that the market portfolio is more likely to represent the global minimum. In addition, if we do impose risk aversion, then co-skewness has minimal explanatory power.

This paper analyzes the optimal investment strategy for loss averse investors, assuming a complete market and general Ito processes for the asset prices. The loss-averse investor follows a partial portfolio insurance strategy. When the investor's planning horizon is short (less than 5 years), he or she considerably reduces the initial portfolio weight of stocks compared to an investor with smooth power utility. The empirical section of the paper estimates the level of loss aversion implied by historical U.S. stock market data, using a representative agent model. We find that loss aversion and risk aversion cannot be disentangled empirically.

We provide theoretical and empirical arguments in favor of a diminishing marginal premium for market risk. In capital market equilibrium with binding portfolio restrictions, investors with different risk aversion levels generally hold different sets of risky securities. Whereas the traditional linear relation breaks down, equilibrium can be described or approximated by a concave relation between expected return and market beta, and a concave relationship between market alpha and market beta. An empirical analysis of U.S. stock market data confirms the existence of a significant concave cross-sectional relation between average return and estimated market beta. We estimate that the market risk premium is at least four to six percent per annum, substantially above traditional estimates. A practical implication for active portfolio managers is that the alpha of “betting against beta” strategies seems dominated by the medium-minus-high-beta spread rather than the low-minus-medium-beta spread. The success of such strategies thus largely depends on underweighting or short selling high-beta stocks.

We examine the risky choices of contestants in the popular TV game show "Deal or No Deal" and related classroom experiments. Contrary to the traditional view of expected utility theory, the choices can be explained in large part by previous outcomes experienced during the game. Risk aversion decreases after earlier expectations have been shattered by unfavorable outcomes or surpassed by favorable outcomes. Our results point to reference-dependent choice theories such as prospect theory, and suggest that path-dependence is relevant, even when the choice problems are simple and well defined, and when large real monetary amounts are at stake.