University of California at Irvine
This extended issue of The Journal of Risk reflects the variety of topics covered in financial risk management. It contains four papers on market risk and one on credit risk. The first two papers deal with portfolio optimization. This is the next step after risk measurement and takes into account expected returns as well.
In “Value-at-risk in portfolio optimization: properties and computational approach”, Gaivoronski and Pflug compare three methods of portfolio optimization using alternative risk measures, VAR, conditional VAR (CVAR), and standard deviation. The paper shows that VAR optimization is a non-trivial problem and proposes a useful solution to smooth out the irregularities in the historical VAR measure. In addition, the authors demonstrate that the optimized portfolios can be quite different across risk measures. VAR-based optimization appears feasible and successfully lowers risk, based on in-sample and out-of sample experiments.
A related paper is “Analytical portfolio value-at-risk”, by Kaplanski. The paper develops analytical tools to calculate the VAR of a portfolio composed of generally distributed assets. This analytical VAR can then be used to construct optimal portfolios when the objective function or a constraint is expressed in terms of VAR. The proposed method makes it straightforward to calculate the optimal portfolio and leads to interesting insights on the effect of higher moments on the portfolio composition.
Next is “Conditional value-at-risk estimation using non-integer values of degrees of freedom in Student’s t-distribution”, by Andreev and Kanto. This short paper presents closed-form solutions for computing the conditional VAR for a Student t-distribution. This is an interesting contribution to the literature given the increased emphasis on fattailed distributions and conditional VAR measures. The analytical formulas can be used to analyze how kurtosis affects CVAR.
The fourth paper is “Efficient filtering of financial time series and extreme value theory”, by Nyström and Skoglund. The authors provide a state-of-the-art application of Garch and EVT to estimate the tails of a time series. The model is based on an ARMA–asymmetric Garch(1,1) process. The mode is estimated using a GMM method, which is shown to be more efficient than the usual quasi-maximum likelihood. After this filtering, the paper proceeds to estimate the shape of the scaled residuals using extreme value theory. The authors report that a maximum likelihood method produces more precise estimates than the usual Hill estimator.
Finally, “Calculating credit risk capital charges with the one-factor model”, by Emmer and Tasche, deals with credit risk. The authors examine the risk contribution of individual credits in the context of a one-factor credit risk model. Such models assume that defaults depend on a common factor and are otherwise conditionally independent, which considerably simplifies the portfolio analysis for well-diversified portfolios. The paper extends the granularity approach presented by Gordy to provide a decomposition of the approximate capital charge for each asset in the portfolio. In addition, the paper presents closed form formulas for the capital charge when there is concentration in one asset.
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.
Conditional value-at-risk estimation using non-integer values of degrees of freedom in Student's t-distribution