Allocating Assets in Climates of Extreme Risk: A New Paradigm for Stress Testing Portfolios

Abstract

The authors extended the standard paradigm for portfolio stress testing in two ways. First, they introduced a toolkit that enables investors to envision and administer extreme scenarios. The risk model is integral to the stress test. They demonstrated the substantial impact of using historical and hypothetical covariance matrices in scenario construction. Second, they used a scenario-constrained optimization to incorporate the output of a portfolio stress test directly into an investment decision.

Over the past five years, financial markets have been dealt a steady series of blows, including the implosion of massive and seemingly invulnerable investment banks, the collapse of the U.S. housing market, the sovereign debt crisis in Europe, and the downgrade of U.S. debt. As unprecedented scenarios continue to unfold, investors face the daunting task of positioning their portfolios to perform well in extreme situations. As a result, stress testing has become an important facet of the investment process.

Investors stress test their portfolios to analyze the impact of extreme events, which tend to lie outside the purview of statistical risk measures. Stress tests can detect a portfolio’s vulnerabilities and assess its expected reaction to market scenarios and, consequently, can add significant value to an investment process. No prescription exists, however, for determining the most salient scenarios or for translating scenario profits and losses into an investment decision. We addressed both of these issues.

First, consider that most stress tests are based on shocks to a core set of factors. For example, an investor concerned about the impact of inflation may want to stress interest rates and spreads between nominal and real rates. However, an inflation shock may propagate to equities, exchange rates, and other risk factors in different ways. A covariance matrix is commonly used to infer shocks to those risk factors for which an investor does not have a view. In this way, a risk model plays a central role in specifying a scenario. We demonstrated the importance of using a stressed covariance matrix in combination with explicit shocks to a core set of factors, and we provided a simple framework for generating both historical and hypothetical stressed covariance matrices. Stressed historical covariance matrices can be easily generated by sampling from periods of market instability and by varying the responsiveness of the estimation process. Stressed hypothetical covariance matrices can be created by modifying volatilities and shocking correlations. The latter can be done safely with a latent variable methodology that does not compromise the statistical integrity of the matrix.

Second, we showed how to incorporate an exogenous market shock in an investment decision, which amounts to a trade-off between the competing objectives of minimizing risk and maximizing return. Using a constrained mean–variance optimization, we perturbed portfolio weights to mitigate losses under the specified shock. To do this, we reverse optimized expected returns that are consistent with the optimality of an investor’s starting portfolio. Then, we ran a constrained optimization yielding perturbed portfolio weights that are optimal given that losses are capped if the shock occurs.

Although precisely measuring the likelihood of an extreme event may not be possible, assessing the impact of such events on a portfolio is nevertheless a valuable exercise. We introduced a new paradigm for translating extreme events into asset class scenarios and highlighted the integral role that the covariance matrix plays in the translation. With memories of autumn 2008 still vivid and the market still reeling from subsequent shocks and ensuing periods of high volatility, investors are increasingly concerned about extreme events and have begun to quantify the losses that they can withstand. Investors who are cognizant that bouts of turbulence are endemic to markets can use our paradigm to perturb allocations so as to be better positioned for what may lie ahead.