Portfolio Choice with Stochastic Investment Opportunities: a User's Guide

This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using tools from stochastic control, and how to rigorously verify their optimality by means of convex duality. Special emphasis is placed on long-horizon asymptotics, that lead to particularly tractable results.Comment: 31 pages, 4 figure

Volatility Trends and Optimal Portfolios: the Case of Agricultural Commodities

While the financial world is experiencing a crisis, the prices of most agricultural commodities have remained high, although exhibiting extreme volatilidy. Motivated by evidence showing that volatility trends are present in agricultural commodity prices, we analyze stochastic processes whose unconditional variance changes with time. This analysis suggests a semi-parametric model for capturing the trending behavior of second moments, in which these moments are polynomial-like functions of time. Based on this model, we formulate the portfolio problem faced by an investor when the variances and the covariances of the returns of the available assets are trending. Then, we obtain an approximate solution of the problem, which is based on the consistent estimation of the order of variance-covariance growth and apply it for the construction of an optimal portfolio of agricultural commodities. It is shown that the performance of this portfolio is superior to those of alternative portfolios which are formed by employing methods not accounting for the presence of volatility trends in commodity returns.

Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ($CVaRD$) based Sharpe ratio for measuring risk-adjusted performance of a dynamic portfolio. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 Index and we evaluate and analyze the dependence of the $CVaRD$-based Sharpe ratio on the utility function and the associated risk aversion level