Asset Selection with Margin Constraints and Income

Abstract

We consider the problem of optimal asset allocation and consumption of an investor whose investment opportunity set includes both a riskless asset and multiple risky assets. The investor receives an income stream that is spanned by the risky assets and faces a margin requirement for holding the risky assets based on his current wealth. When the investor has constant relative risk aversion, using the dual formulation of the optimization problem, we characterize the investor's investment strategy in terms of thresholds in the ratio of current wealth to income. We find that, for large values of the ratio, the investor behaves similar to an investor that does not receive an income. When the investor's current wealth is low, relative to his income we find that the investor shifts from a diversified portfolio towards portfolios with fewer assets that offer higher expected returns. This asset substitution effect is more pronounced when the margin requirement is binding. In the case of deterministic income, and when future earnings are much larger than current wealth, asset substitution leads the investor to hold the single risky asset in his portfolio that provides the highest expected return. We also present numerical simulations illustrating the asset allocations of investors that face margin requirements, as well as wealth equivalent costs of the margin requirement.