Allocating Assets in Climates of Extreme Risk

Abstract

In this article, we extend the standard paradigm for portfolio stress testing in two ways. First, we introduce a structured set of tools that enable investors to envision and administer extreme scenarios. We show how to take account of historical and hypothetical covariance matrices in scenario construction, and we provide examples that demonstrate the substantial impact of doing so. In short, the risk climate can and should be incorporated in a stress test. Second, we provide a means to incorporate the output of a portfolio stress test directly into an investment decision, which ultimately boils down to a trade-off between the competing objectives of minimizing risk and maximizing return. We achieve this with a scenario-constrained mean-variance optimization that can incorporate extreme risk and other non-Gaussian effects. We illustrate our methods in the context of an asset allocation problem. However, our methods our quite general, and can be applied to different types of investment processes.

Keywords: Allocating Assets Climates of Extreme Risk portfolio stress testing extreme scenario sset Allocation Stress Testing Risk Management Portfolio Construction investment processes