Set Of Risky Assets Research Articles

Delegated Portfolio Management Under Ambiguity Aversion

We examine the problem of setting optimal incentives for a portfolio manager hired by an investor who wants to induce ambiguity-robust portfolio choices with respect to estimation errors in expected returns. We consider a one-period model with a set of risky assets (with multivariate normal returns) whose expected returns are estimated with uncertainty and a linear sharing rule between a risk-neutral investor and a risk averse portfolio manager. The manager accepts the contract if the compensation off ered is at least as large as a minimum compensation he determines from his minimum acceptable utility level. Adopting a worst-case max-min approach we obtain in closed-form the optimal compensation in various cases where the investor and the manager, respectively adopt or relinquish an ambiguity averse attitude. We apply our result to compute the compensation fees for an investment strategy restricted by Socially Responsible rules. The application shows, for instance, that the additional premium requested by a manager for restricting the investment set should decrease when the aversion to ambiguity increases.

Covariance complexity and rates of return on assets

This paper considers the estimation of the expected rate of return on a set of risky assets. The approach to estimation focuses on the covariance matrix for the returns. The structure in the covariance matrix determines shared information which is useful in estimating the mean return for each asset. An empirical Bayes estimator is developed using the covariance structure of the returns distribution. The estimator is an improvement on the maximum likelihood and Bayes–Stein estimators in terms of mean squared error. The effect of reduced estimation error on accumulated wealth is analyzed for the portfolio choice model with constant relative risk aversion utility.

Differential taxation and the encouragement of risk-taking

In the framework of expected utility maximization with risk aversion it is shown that the standard result about the tax encouragement of risk taking in a two-asset model, can be extended to the case of many risky assets. There are no tax substitution effects within the set of risky assets; in particular there is no substitution from less to more risky assets. It is also demonstrated that the qualitative response pattern is independent of the assumed existence of a safe asset. The by now common conclusion that capital income taxation encourages risk-taking must therefore be interpreted with some care.

An Algorithm for Deriving the Capital Market Line

This paper examines the problem of deriving the tangent (or market) portfolio from a given set of risky assets and a specified risk-free borrowing and lending rate. Deriving the tangent portfolio involves solving a mathematical programming problem which can be specified as the minimization of a quadratic objective function with linear constraints. The complementary pivot algorithm has previously been shown to be capable of deriving the optimal solution to certain quadratic programming problems, subject to a nonnegativity constraint. This paper demonstrates that the algorithm can be used to derive the tangent portfolio and that the nonnegativity constraint does not pose any serious handicap. Furthermore, it is shown that the algorithm can efficiently solve large-scale problems of this nature.

A Dual Concept and Associated Algorithm in Mean-Variance Portfolio Analysis

We consider in this paper the problem of allocation by an investor of his funds between a set of risky assets and a single safe asset, under conditions in which the separation theorem holds. Focussing in particular on the computationally more difficult case where no short sales are permitted, we exhibit a dual problem which arises naturally out of the saddle-point property implied in the Kuhn-Tucker optimising conditions. By showing how to solve this dual we derive a computationally straightforward method of solution for the optimum portfolio proportions and obtain a condition for every security to be held. We show briefly how the treatment can be extended to general homogeneous restrictions on portfolio proportions.