Josef Hadar

Diversification of interdependent prospects

Abstract This paper extends the stochastic dominance approach to the problem of diversification of interdependent prospects. One basic result is that a risk averter should always mix any two identically distributed prospects, regardless of the nature of the interdependence between them. A similar result holds for the case of n prospects, provided all the joint distribution functions of dimension n − 1 are identical. When the n -dimensional joint distribution function is symmetric, then the optimal strategy is to put an equal amount into each prospect. The paper also provides conditions which make diversification optimal in the absence of identical marginal distributions.

Asset diversification in Yaari's dual theory

Abstract This paper presents an application of the dual theory of choice under uncertainty to the problem of asset diversification. It is shown that when there are two or more risky assets, conditions which are sufficient for expected-utility maximizers to diversify among n assets, are also sufficient for dual agents to do so. This result is in contrast to the case of one risky and one safe asset in which dual agents invest all their funds in only one of the assets, while expected-utility maximizers usually diversify.

Decision making with stochastic dominance: An expository review

This paper surveys the use of stochastic dominance to decision making under uncertainty. The first part presents the relevant definitions and some properties of distributions satisfying one of the stochastic dominance conditions. These properties include restrictions on moments, an invariance property, and properties of random variables related by an exact formula. The second part contains some applications of the stochastic dominance method and especially the problem of selecting optimal portfolios. Most of the results in this section deal with conditions that make diversification an optimal strategy.

Gains from Diversification

By now it has been firmly established that, under a variety of circumstances, risk averters should follow a policy of diversifying their investments. Several different theorems dealing with the conditions for diversification have recently appeared in the literature; for example [2], [3], [6]. The most general of these results says that if n assets are independently distributed, have equal means, and positive finite variances, the optimal portfolio for each risk averter includes some positive amount of each asset. The attractiveness of this theorem derives from the fact that optimality follows despite only weak conditions imposed on the distributions. The disadvantage is that it cannot identify any specific diversified portfolio which all risk averters would prefer to specialized ones. For unanimous ranking of portfolios stronger conditions are required, such as those used in the diversification theorems given in [2], [3]. For example, when two assets are identically distributed, any mixture of the two assets is preferred to a specialized portfolio by every risk averter. And in the case where the joint distribution of the individual assets is symmetric, the portfolio with an equal amount of each asset is the optimal portfolio for every risk averter. In this paper we consider the case where risk averters unanimously judge a particular asset to be superior to all other assets. Somewhat surprisingly, it turns out that risk averters will unanimously prefer certain diversified portfolios to specializing in the superior asset. This result holds if and only if the independently distributed prospects have equal means and the same range.

A Note on Beneficial Changes in Random Variables

This paper is an extension of Jack Meyers paper titled “Beneficial Changes in Random Variables Under Multiple Sources of Risk and Their Comparative Statics” published in the June 1992 issue of this journal. The extension consists of showing which of the sufficient conditions in Meyers Theorems 1 and 3 are also necessary, and which are not. In addition, conditions are provided which are necessary and sufficient for general beneficial changes to imply a decrease in the demand for insurance.

A Note on Increased Probability of Loss and the Demand for Insurance

It is shown that the effect of increased probability of loss on the demand for insurance depends on whether both insured and insurer are aware of the change. When both insurer and insured share the same beliefs about the probability of loss (symmetric information), an increase in the loss probability may lead risk-averse agents to demand less insurance.

Stochastic dominance for ranking ventures: Comments and extensions

This paper suggests some extensions to Tilley and Eilons paper on ranking ventures. Tilley and Eilon consider concave utility functions consisting of two linear segments and this allows all rectangular distributions to be ordered. Such utility functions have a wide scope and allow other distributions to be ordered.

Consistent planning with changing tastes

Abstract This paper proposes an approach to achieving a consistent consumption plan which is free of the shortcomings that characterize earlier proposals in the literature. Specifically, our consumption plan exists, is coherent, and most important, is Pareto-optimal.

Consistent Planning Under Uncertain Lifetime

This paper considers the problem of intertemporal planning when changing tastes result in inconsistent plans. This problem has been considered in the literature under the assumption of a lifetime certainty. Some of the solutions proposed in the literature exhibit certain undesirable properties such as incoherence and lack of Pareto-optimality. This paper proposes a procedure for solving the intertemporal dilemma when lifetime is uncertain. The proposed solution is coherent and Pareto-optimal, and is, in fact, valid for the case of certain as well as uncertain lifetime. [020]