A New Approach to Tail Risk

Abstract

One of the fundamental requirements of investment management is the ability to assess risk and to adjust exposure to control tail risk, the risk of larger than acceptable losses. Since the onset of the recent credit crisis, the effects of widespread failure of standard techniques for tail risk management have been an almost daily feature in the financial news.

The most widely used approach to risk assessment by large financial institutions is the statistical tool known as Value at Risk (VaR). In fact, VaR is the risk measure commonly accepted by bank regulators in the banks’ internal models for regulatory capital calculations (International Money Fund 2007). Conventional VaR and Conditional Value at Risk (CVaR) are useful, however, only if their implementation is consistent with the nature of the data. Conventional VaR and CVaR assume that data come from a normal distribution. We examine some of the failings of using this approach with tail risk in a number of examples from 2007 and 2008.

To make VaR and CVaR work, it is important to correctly identify the nature of the tails that these techniques try to estimate. For this we introduce tail risk bands, a practical risk measurement tool that categorizes risk levels and identifies assets and market conditions for which conventional VaR cannot be expected to adequately represent downside risk.

We illustrate our approach on daily data from equity markets and monthly data from hedge funds. In particular we show that this analysis provided warning of the riskiness of AIG, JPMorgan Chase, Lehman Brothers, the S&P 500 Index, and other equity indexes well in advance of the credit crisis. For the cases where tail risk bands indicate that the conventional VaR model cannot work, we provide a simple, easy-to-implement alternative. This is appropriate in the case of moderately heavy tails, which are common in financial data. This alternative is easily substituted for the standard approach and, as we show in a number of examples, provides a more realistic estimate of risk. We show that this can be used to make risk-adjusted comparisons of assets, using Berkshire Hathaway and JPMorgan Chase shares and the S&P 500 Index as examples.

Finally, we provide evidence that during periods of unusual market turmoil only specialized techniques designed to deal with the statistics of extremes are likely to adequately assess the probability or the size of large losses.

Keywords: Tail Risk

JEL Classification: G11, G12, G14