Warrington College of Business Administration, University of Florida
Given that credit risk has played a critical role in economics in the past two decades, there is a continued need for improved models related to it. Empirical aspects of credit risk are just as important, and this issue contains results pertaining to the estimation of correlated extreme events. In recent years we have also witnessed the significant impact that hedge funds have had on financial markets, and it is quite fitting that this issue also addresses related optimization problems.
The subprime credit crisis has revealed several risk management weaknesses, such as the underestimation of default probabilities and correlations of mortgage pools. Given the difficulties inherent in portfolio model validation in general, and especially in benign economic times, more powerful statistical tests would be helpful. The first paper in this issue, “Evaluation of credit portfolio models: test statistics for densitybased tests”, by Plank and Walter, makes a contribution in this direction. The authors compare the power characteristics of several test statistics for density-based tests. They find significant differences in their small-sample characteristics and give their conclusions on which statistics are more and less appropriate from a conservative risk management perspective. More specifically, they find that the commonly used likelihood ratio test is not necessarily the best choice. Furthermore, their results indicate that the Lagrange multiplier statistic leads to a more conservative assessment of credit risk, while theWald statistic tends to its underestimation.
Hedge fund risk is typically style-specific and investors often allocate capital to different hedge funds. However, the simultaneous collapse of several hedge funds during the 2008–9 financial crisis raises questions regarding such strategies. In the second paper, “Modeling extreme returns and asymmetric dependence structures of hedge fund strategies using extreme value theory and copula theory”, Viebig and Poddig apply extreme value theory and copula theory to the modeling of the multivariate daily returns of hedge fund strategy indexes. They show that time series outliers are clustered when volatilities and credit spreads increase. These phenomena are attributed to “flight to quality” and investors seeking liquidity. As such, these indexes exhibited a strong “domino effect” during the recent financial crisis. Viebig and Poddig show that the generalized Pareto distribution copula approach is an appropriate modeling choice for approximating multivariate hedge fund distributions that exhibit extreme return observations and asymmetric dependence structures.
The third paper, “High-conviction equity portfolio optimization”, by Crezée and Swinkels, develops an algorithm to optimize a recently introduced measure of port folio diversification – the so-called Portfolio Diversification Index – applied to highconviction equity hedge funds. While the optimization is conducted in-sample, the authors are the first to investigate the out-of-sample properties of this risk measure. Their sample period covers the years from 2000 to 2009 and their method appears to be robust with respect to both the investment opportunities and the time period under consideration. Their results are particularly enlightening given the preference of many investors for naive diversification.
Short positions are generally perceived to be very risky and are often excluded from the set of strategies available to many investment professionals. However, given the popularity of long–short strategies among hedge funds, assessing the impact of short sales through an empirical study is of great interest. The fourth paper, “Long–short portfolio optimization in the presence of discrete asset choice constraints and two risk measures”, by Kumar, Mitra and Roman, shows that, by using short selling in an integrated optimization approach, the risk of the chosen financial portfolios can be considerably reduced and controlled. Both the volatility and the conditional value-atrisk (CVaR) are (simultaneously) lower than those found in long-only counterparts. Most notably, it is the CVaR (and, generally, the downside risk) that can be dramatically reduced. Thus, by relaxing the “no-short-selling” constraint, portfolios with superior Sharpe and Sortino ratios can be obtained.
Long–short portfolio optimization in the presence of discrete asset choice constraints and two risk measures
Modeling extreme returns and asymmetric dependence structures of hedge fund strategies using extreme value theory and copula theory