The prospect theory of Kahneman and Tversky (in Econometrica 47(2), 263–291, 1979) and the cumulative prospect theory of Tversky and Kahneman (in J. Risk uncertainty 5, 297–323, 1992) are descriptive models for decision making that summarize several violations of the expected utility theory. This paper gives a survey of applications of prospect theory to the portfolio choice problem and the implications for asset pricing. We demonstrate that prospect theory (and similarly cumulative prospect theory) has to be re-modelled if one wants to apply it to portfolio selection. We suggest replacing the piecewise power value function of Tversky and Kahneman (in J. Risk uncertainty 5, 297–323, 1992) with a piecewise negative exponential value function. This latter functional form is still compatible with laboratory experiments but it has the following advantages over and above Tversky and Kahneman’s piecewise power function:
1. The Bernoulli Paradox does not arise for lotteries with finite expected value.
2. No infinite leverage/robustness problem arises.
3. CAPM-equilibria with heterogeneous investors and prospect utility do exist.
4. It is able to simultaneously resolve the following asset pricing puzzles: the equity premium, the value and the size puzzle.
In contrast to the piecewise power value function it is able to explain the disposition effect.
Resolving these problems of prospect theory we show how it can be combined with mean–variance portfolio theory.
This paper studies an overlapping generations model with stochastic production and incomplete markets to assess whether the introduction of an unfunded social security system leads to a Pareto improvement. When returns to capital and wages are imperfectly correlated a system that endows retired households with claims to labor income enhances the sharing of aggregate risk between generations. Our quantitative analysis shows that, abstracting from the capital crowding-out effect, the introduction of social security represents a Pareto improving reform, even when the economy is dynamically effcient. However, the severity of the crowding-out effect in general equilibrium tends to overturn these gains.
Both institutional and private investors often have only limited flexibility in timing their investment decision. They look for investments that will ideally be independent of the timing decision. In this article, a new class of derivative products whose payoff is linked to the trend of the underlying instrument is introduced. By linking the trend to the payoff, the timing of the decision becomes less important. Therefore, trend derivatives offer some time-diversification benefits. How trend derivatives are designed and priced is shown. Due to their peculiar features, trend derivatives offer some interesting applications such as executive stock option plans.
We apply the recurrent reinforcement learning method of Moody, Wu, Liao, and Saffell (1998) in the context of the strategic asset allocation computed for sample data from US, UK, Germany, and Japan. It is found that the optimal asset allocation deviates substantially from the fixed-mix rule. The investor actively times the market and he is able to outperform it consistently over the almost two decades we analyze.
