We outline a method of portfolio selection incorporating asymmetric dependency structures using copula functions. Assuming normally distributed marginal returns, we illustrate how asymmetric return correlations affect the efficient frontier and subsequent portfolio performance under a dynamic rebalancing framework. Implementing this methodology within the context of tactically allocating a small set of market indices, we demonstrate several key findings. First, we establish the manner by which the efficient frontier constructed under asymmetric dependence differs from a mean-variance frontier. By establishing a paper portfolio based on these differences, we find that asymmetric correlation structures do have real economic value. The primary source of this economic value is the ability to better protect portfolio value and reduce the size of any erosion in return relative to the normal portfolio when asymmetric return correlations are accounted for. Copyright (c) The Authors Journal compilation (c) 2007 AFAANZ.

We examine the relative importance of asymmetric dependence (AD) and systematic risk in the cross-section of US equities. Using a β-invariant AD metric, we demonstrate a lower-tail dependence premium that is only 35% of the market risk premium, compared with an upper-tail dependence discount that is 41% of the market risk premium. Lower tail dependence displays a constant price between 1989-2009. Subsequently, we find that return changes in US equities between 2007-2009 reflected changes in systematic risk and upper-tail dependence. This suggests that both systematic risk and AD should be managed in order to reduce the return impact of market downturns.

No abstract