Leverage Aversion and Portfolio Optimality

Portfolio volatility is the only source of risk in mean–variance optimality, but it fails to capture all the risks faced by leveraged portfolios. These risks include the possibility of margin calls and forced liquidations at adverse prices and losses beyond the capital invested. To recognize these risks, the authors incorporated leverage aversion into the optimization process and examined the effects of volatility and leverage aversion on optimal long–short portfolios.Mean–variance optimization considers only portfolio volatility; it fails to capture all the risks incurred by leveraged portfolios, including long–short portfolios. Leverage introduces such risks as the possibility of margin calls and forced liquidations at adverse prices, as well as potential losses beyond the capital invested. We believe that many investors are averse to these sources of risk, as well as to volatility. That is, risk aversion—or its inverse, risk tolerance—is multidimensional. An investor’s tolerance for leverage should play a role alongside the investor’s tolerance for volatility in selecting an optimal leveraged portfolio. It may restrain the investor’s appetite for leverage (and potential lenders’ willingness to underwrite it) and be able to explain the difference between the apparent optimality of leveraged portfolios from a conventional mean–variance perspective and their suboptimal nature from the investor’s perspective. We examine leverage aversion in the context of leveraged portfolios that contain short positions. An enhanced active equity (EAE) portfolio relaxes the long-only constraint to allow for short sales equal to some percentage of capital and for use of the short-sale proceeds to buy additional securities long while maintaining a 100% exposure to an underlying benchmark. For example, short sales equal to 30% of capital provide for a 30% expansion of long positions, giving rise to an enhanced active 130–30 long–short portfolio. We define a parameter that measures leverage tolerance and determine what amount of short selling as a percentage of capital (the enhancement) is optimal given various levels of investor leverage tolerance.We posit that an investor’s risk tolerance includes a component of leverage tolerance in addition to volatility tolerance and develop a leverage tolerance term that can be added to the conventional mean–variance utility function. Given estimates for securities’ expected active returns and covariances for the stocks in the S&P 100 Index, we find EAE portfolios that maximize this augmented utility function for a range of volatility and leverage tolerances. We find that as volatility tolerance increases, the optimal level of enhancement increases, rapidly at first. As leverage tolerance increases, the optimal enhancement increases at a slower rate. The optimal enhancement levels off more slowly in the case of leverage tolerance than in the case of volatility tolerance. When leverage tolerance is added to the investor’s utility function, optimizations yield EAE portfolios that seem reasonable given the levels of leverage of actual EAE portfolios. For example, a leverage tolerance of 1 combined with a volatility tolerance of 1 results in an optimal enhancement of about 25%. We found that the optimal level of enhancement is highly dependent upon the investor’s particular level of leverage tolerance. For a volatility tolerance of 1 and leverage tolerances between 0 and 2, the optimal level of enhancement ranges from less than 5% to more than 45%. Leverage introduces sources of risk that are not captured by traditional mean–variance optimization. We suggest the inclusion of leverage tolerance in investor utility functions. The explicit recognition of leverage aversion by investors might curtail some of the outsized levels of leverage and consequent market disruptions that have been experienced in recent years.