Lisa R. Goldberg and Michael Y. Hayes
We discuss a practical and effective extension of portfolio risk management and construction best practices to account for extreme events. The central element of the extension is (expected) shortfall, which is the expected loss given that a value-at-risk limit is breached. Shortfall is the most basic measure of extreme risk, and unlike volatility and value at risk, it probes the tails of portfolio return and profit/loss distributions. Consequently, shortfall is (in principle) a guide to allocating reserve capital. Since it is a convex measure, shortfall can (again, in principle) be used as an optimization constraint either alone or in combination with volatility. “In principle” becomes “in practice” only if shortfall can be forecast accurately. A recent body of research uses factor models to generate robust, empirically accurate shortfall forecasts that can be analyzed with standard risk management tools such as betas, risk budgets and factor correlations. An important insight is that a long history of returns to risk factors can inform short-horizon shortfall forecasts in a meaningful way.