University of California at Irvine
This issue of the Journal of Risk contains four long papers dealing with market risk management.
The first paper, “Risk estimation using the normal inverse Gaussian distribution”, by P. J. de Jongh and J. H. Venter, proposes practical methods for estimating a conditional normal inverse Gaussian (NIG) density. This is part of the search for density functions with fatter tails than the normal probability density function (PDF). Much attention has been recently devoted to the NIG density as it allows for fat tails and has the nice property that the sum of independent NIG random variables is still NIG. A traditional alternative is the conventional extreme value theory (EVT) tail distribution. This requires, however, very long periods for precise estimates. The author shows that the NIG approach is more robust than the EVT approach for reasonable sample sizes under a variety of conditions.
The second paper is “Robust conditional variance estimation and value-at-risk”, by C. Guermat and R. D. F. Harris. The paper examines an alternative to traditional exponentially weighted moving averages (EWMA) estimators for risk. The drawback of the standard estimator is its use of squared returns, which makes it very sensitive to extreme observations. Instead, the authors propose an investigation of a class of power EWMA. They show that using the absolute value of returns rather than the square leads to a more robust estimator, which in addition is more efficient in the sense of generating lower capital charges.
Next, “Portfolio optimization with conditional value-at-risk objective and constraints”, by P. Krokhmal, J. Palmquist and S. Uryasev, extends previous work published by Rockafeller and Uryasev in this journal (Journal of Risk, 2(3)). Conditional value-at-risk (CVAR) is defined as the expected loss beyond the value-at-risk (VAR), and has better properties than traditional VAR measures. The authors develop an optimization technique for maximizing expected returns under CVAR constraints.
Finally, the paper by A. Johansen and D. Sornette, “Large price drawdowns are outliers”, provides an intriguing analysis of the behavior of extreme returns. The authors argue that returns exhibit strong correlations at times of extreme events, which would invalidate the usual extreme value theory (EVT) approach that assumes independent returns. This explains their focus on “drawdowns”, or cumulative losses, from the recent high. The authors demonstrate that the very largest drawdowns are outliers, notwithstanding the fact that very large daily drops are not outliers. As a result, extrapolating long-horizon VAR from short-term data is likely to underestimate risk.
The mission of the Journal of Risk is to further our understanding of risk management. Contributions to the journal are welcome from academics, practitioners, and regulators in the field. With this in mind, authors are encouraged to submit full-length papers. See “Guidelines for Authors” for further details.