Journal of Risk

Welcome to Volume 8 Issue 2 of The Journal of Risk. This issue is made up of 4 technical papers: In "Backtesting within the trading book", Stahl,Wehn and Zapp expand the usual backtesting procedure, which is done at the highest level of the institution. This paper provides a battery of tests for backtesting various components within the trading book. Using an actual trading book, the paper shows how to analyze the portfolio's risk forecasts and associated realized gains and losses. An interesting result is that the portfolio distribution converges to a normal distribution at higher levels of aggregation.

The second paper is "Improved duration-based backtesting of value-at-risk", by Haas. It is well known that traditional tests of VAR exceptions, defined as days when the loss exceeds VAR, lack statistical power. In other words, currently used tests often do not reject VAR models even when they are wrong. More recently, some researchers have proposed tests based on the number of days, also called "duration", between exceptions. Such tests can be used to detect clustering in VAR exceptions. Short durations imply clustering, or violation of conditional coverage. This paper provides an improvement over duration-based backtests of VAR using an alternative framework that is shown to have higher power than previous approaches.

Next is "Risk estimation using the multivariate normal inverse Gaussian distribution", by Aas, Haff and Dimakos. This paper proposes use of the multivariate normal inverse Gaussian distribution as the conditional distribution for a multivariate GARCH model when modeling financial returns. Modeling the joint distribution is important because it provides internally consistent risk estimates for a portfolio of assets. When weights change, for example, there is no need to estimate again the statistical model. The paper compares this distribution with traditional alternatives such as the multivariate normal distribution, t-distribution and skew t-distribution. The authors show that this new distribution provides better estimates of portfolio value at-risk than traditional ones.

In "Testing hedge effectiveness for option positions", Kerkhof, Melenberg and Schumacher examine the risk of a hedged option position. This type of position is typical of many option books but creates special problems when measuring risk. Risk is measured using the standard deviation, value at-risk and expected shortfall for the distribution of one-period hedge error. Because expected shortfall cannot be tested with the usual binomial test, the authors present a transformation procedure to compensate for the change in risk characteristics. The results indicate that it is crucial to take changes of volatility into account, via either historical simulation method or a simple vector autoregression model.

The last paper is "Tail approximation for credit risk portfolios with heavy-tailed risk factors", by Kostadinov. This paper builds an approximation to the tails of portfolio credit losses when risk factors have heavy tails. This is an important problem because conventional models based on jointly normal risk factors cannot represent the simultaneous defaults that are frequently observed in practice. The paper derives an upper bound for the tail losses using a mixture of analytic and Monte Carlo simulations.