Tae Kun Seo

The Effects of Shifts in a Return Distribution on Optimal Portfolios

When the distribution of the returns of a risky asset undergoes a stochastically dominating shift, a risk-averse investor may not necessarily increase the investment in that asset. This paper provides restrictions on the investors utility function that are necessary and sufficient for a dominating shift to bring about no decrease in the investment in the respective asset if there are two risky assets in the portfolio. These conditions are also necessary if there are n > 2 assets, and are necessary and sufficient if the utility function exhibits constant absolute risk aversion. Copyright 1990 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Asset Proportions in Optimal Portfolios

The paper is concerned with conditions under which the proportion of a given asset in the optimal portfolio of a risk averse agent is at least as large as some given proportion. The paper provides a condition that is necessary and sufficient for such a result to hold. The analysis is then confined to portfolios in which the distributions of assets differ by either a first-degree stochastic dominance shift or by a mean-preserving shift. Examples are provided to show that under some conditions a risk averter may invest a smaller proportion of his wealth in the dominating asset than in the dominated asset. The paper then provides conditions that are necessary and sufficient for a risk averter to invest more in the dominating asset.

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.

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.

Minimal Efficient Portfolio Sets for Non-Specialization

The usefulness of the stochastic dominance approach to portfolio selection arises from its ability to indicate unanimous ranking by risk averters. That is, we know from the stochastic dominance theorem that all risk averters prefer one portfolio to another if and only if the second degree stochastic dominance (SSD) condition holds (Hadar and Russell [1], Hanoch and Levy [5], and Rothschild and Stiglitz [6]). By employing this rule a variety of special diversification theorems have been established (see Hadar and Russell [2, 3] and Hadar, Russell and Seo [4]). These results emphasize the gains that are derived from diversification.

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]