Diversification Preferences in the Theory of Choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper studies axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion

Portfolio Selection with Narrow Framing: Probability Weighting Matters

This paper extends the model with narrow framing suggested by Barberis and Huang (2009) to also account for probability weighting and a convex-concave value function in the specification of cumulative prospect theory preferences on narrowly framed assets. We show that probability weighting is needed in order that investors reduce their holding of narrowly framed risky assets in the presence of negative skewness and high Sharpe ratios, which are typical characteristics of stock index returns. The model with framing and probability weighting can thus explain the stock participation puzzle under realistic assumptions on stock market returns. We also show that a convex-concave value function generates wealth effects that are consistent with empirical observations on stock market participation. Finally, we address the asset pricing implications of probability weighting in the model with narrow framing and show that in the case of negative skewness the equity premium of narrowly framed assets is much higher than when probability weighting is not taken into account.Narrow framing, cumulative prospect theory, probability weighting function,negative skewness, simulation methods

Loss aversion with a state-dependent reference point

This study investigates loss aversion when the reference point is a state-dependent random variable. This case describes, for example, a money manager being evaluated relative to a risky benchmark index rather than a fixed target return level. Using a state-dependent structure, prospects are more (less) attractive if they depend positively (negatively) on the reference point. In addition, the structure avoids an inherent aversion to risky prospects and yields no losses when the prospect and the reference point are the same. Related to this, the optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) when the reference point is selected completely endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. For example, the typical investment benchmark index is externally fixed by the investment principal for the duration of the investment mandate. We develop a choice model where adjustment costs cause stickiness relative to an initial exogenous reference point.Reference-dependent preferences, stochastic reference point, loss aversion, disappointment theory, regret theory.

Loss aversion with multiple investment goals

This paper presents a time-continuous portfolio selection model with loss averse investors, who possess multiple investment goals at different time horizons. The model assumes partial narrow framing. Investors follow a two-step approach. First, they optimally allocate wealth among investment goals. Second, they determine an optimal investment strategy for each investment goal separately. We show that when loss aversion is according to the experimental findings, investors mainly invest their wealth to reach long-term goals and adopt investment strategies with high leverage to reach short-term goals. The overall strategy also display high leverage. The same patterns is observed when loss aversion is extreme and goals are very ambitious. By contrast, when loss aversion is extreme but goals are not too ambitious, investors mainly invest to reach short-term goals and adopt safe investment strategies for this purpos

A Satisficing Alternative to Prospect Theory

In this paper, we axiomatize a target-based model of choice that allows decision makers to be both risk averse and risk seeking, depending on the payoff's position relative to a prespecified target. The approach can be viewed as a hybrid model, capturing in spirit two celebrated ideas: first, the satisficing concept of Simon (1955); second, the switch between risk aversion and risk seeking popularized by the prospect theory of Kahneman and Tversky (1979). Our axioms are simple and intuitive; in order to be implemented in practice, our approach requires only the specification of an aspiration level. We show that this approach is dual to a known approach using risk measures, thereby allowing us to connect to existing theory. Though our approach is intended to be normative, we also show that it resolves the classical examples of Allais (1953) and Ellsberg (1961).satisficing; aspiration levels; targets; prospect theory; reflection effect; risk measures; coherent risk measures; convex risk measures; portfolio optimization

Dual representation of choice and aspirational preferences

We consider choice over a set of monetary acts (random variables) and study a general class of preferences. These preferences favor diversification, except perhaps on a subset of sufficiently disliked acts, over which concentration is instead preferred. This structure encompasses a number of known models in this setting. We show that such preferences can be expressed in dual form in terms of a family of measures of risk and a target function. Specifically, the choice function is equivalent to selection of a maximum index level such that the risk of beating the target function at that level is acceptable. This dual representation may help to uncover new models of choice. One that we explore in detail is the special case of a bounded target function. This case corresponds to a type of satisficing and has descriptive relevance. Moreover, the model results in optimization problems that may be efficiently solved in large-scale.

Making prospect theory fit for finance

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 theor

Loss Aversion with a State-Dependent Reference Point

This study investigates reference-dependent choice with a stochastic, state-dependent reference point. The optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) if the reference point is selected fully endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. We develop a choice model in which adjustment costs can cause stickiness relative to an initial, exogenous reference point. Using historical U.S. investment benchmark data, we show that this model is consistent with diversification across bonds and stocks for a wide range of evaluation horizons, despite the historically high-risk premium of stocks compared to bonds

The α-beauty contest: Choosing numbers, thinking intervals

We present a model for the ?-beauty contest that explains common patterns in experimental data of one-shot and iterative games. The approach is based on two basic assumptions. First, players iteratively update their recent guesses. Second, players estimate intervals rather than exact numbers to cope with incomplete knowledge of other players' rationality. Under these assumptions we extend the cognitive hierarchy model of Camerer et al. [Camerer, C., Ho, T., Chong, J., 2003b. A cognitive hierarchy model of one-shot games. Quart. J. Econ. 119, 861–898]. The extended model is estimated on experimental data from a newspaper experiment