Horizon Problems and Extreme Events in Financial Risk Management

Central to the ongoing development of practical financial risk management methods is recognition of the fact that asset return volatility is often forecastable. Although there is no single horizon relevant for financial risk management, most would agree that in many situations the relevant horizon is quite long, certainly longer than a few days. This fact creates some tension, because although short-horizon asset return volatility is clearly highly forecastable, much less is known about long-horizon volatility forecastability, which we examine in this paper. We begin by assessing some common model-based methods for converting short-horizon volatility into long-horizon volatility; we argue that such conversions are problematic even when done properly. Hence we develop and apply a new model-free methodology to assess the forecastability of volatility across horizons and find, surprisingly, that forecastability decays rapidly as the horizon lengthens. We conclude that for managing risk at horizons longer than a few weeks, attention given to direct estimation of extreme event probabilities may be more productive than attention given to modeling volatility dynamics, and we proceed to assess the potential of extreme value theory for estimating extreme event probabilities. Acknowledgments : Prepared for Federal Reserve Bank of New York Economic Policy Review (1998). We thank Beverly Hirtle for insightful and constructive comments, but we alone are responsible for remaining errors. The views in this paper are those of the authors and do not necessarily reflect those of the International Monetary Fund. Christoffersen, P., Diebold, F.X., and Schuermann, T. (1998), "Horizon Problems and Extreme Events in Financial Risk Management," Economic Policy Review, Federal Reserve Bank of New York, October, 109-118.