Margin Requirements and Portfolio Optimization: A Geometric Approach

Abstract

Using geometric illustrations, we investigate what implications of portfolio optimization in equilibrium can be generated by the simple mean-variance framework, under margin borrowing restrictions. First, we investigate the case of uniform marginability on all risky assets. It is shown that changing from unlimited borrowing to margin borrowing shifts the market portfolio to a riskier combination, accompanied by a higher risk premium and a lower price of risk. With the linear risk-return preference, more stringent margin requirements lead to a riskier market portfolio, contrary to the conventional belief. Second, we investigate the effects of differential marginability on portfolio optimization by allowing only one of the risky assets to be pledged as collateral. It is shown that the resulting optimal portfolio is not always tilted towards holding more of the marginable asset, when the margin requirement is loosened.

Keywords: portfolio optimization, margin, collateral, borrowing constraint, mean-variance, efficient frontier, asset allocation

JEL Classification: G11