Portfolio Leverage in Asset Allocation Problems

In the classical portfolio optimization framework, the leverage of a portfolio is not taken into account and, by assumption, the risk of a portfolio is totally described by the volatility of its returns. As a consequence, the portfolios on the classical mean-variance efficient frontier are not indifferent in terms of leverage. The introduction of leverage measurement in portfolio theory permits to consider other kinds of risk, like margin calls, forced liquidations at undesired prices and losses beyond the total capital. The literature on this topic is very limited while portfolio leverage is of central importance, in particular to set up operative investment strategies. In this paper we propose a simple definition of leverage and we try to introduce it in the classical portfolio selection scheme. We define the concept of leverage free equivalent portfolios in order to compare different investment alternatives for given levels of leverage. The central result of the paper is that the leverage free equivalent of the classical mean-variance efficient portfolios do not preserve the original mean-variance dominance structure. This permits to discriminate if an increase in the expected return of a portfolio totally depends on the leverage effect or is a consequence of a more efficient allocation.