Journal of Risk

Stan Uryasev

University of Florida

Risk management typically consists of determining the best course of action in order to optimize a given measure of risk. However, in practice, it is often not trivial to estimate such measures or related parameters that affect the optimization. Typical challenges revolve around the fact that modern risk measures are of the quantile type and that we need to account for correlation and dependence between several tails of probability distributions. This issue contains articles that relate statistical inference to risk management in a variety of problems.

How well can we estimate risk measures, especially those associated with extreme occurrences? The paper of Baysal and Staum provides asymptotically valid confidence intervals and regions for value-at-risk and expected shortfall (conditional value-at-risk) that are based on independent profits with a common distribution. This work continues a strand of recent developments regarding various approaches for quantile estimation along robust statistics, resampling and empirical likelihood techniques.

A major concern regarding worldwide markets is the domino effect, particularly in times of economic distress. In her paper, de Melo Mendes addresses the connection between unconditional extreme dependence and conditional extreme dependence in the context of financial risk management. Using Latin American and Asian market data, the author illustrates how its application leads to implications on interdependencies that go beyond the traditional wisdom.

The two main practical limitations associated with the classical approach to portfolio optimization are the difficulty in obtaining reliable parameter estimates and the sensitivity of the optimal solution to data input. In their paper, Jabbour et al eschew these problems by developing an alternative that relies on current data only, without the need for estimation based on historical observations. Additionally, their approach makes use of a coherent downside measure of risk resulting in a linear programming formulation.

A coherent measure that is particularly useful for stress-testing a portfolio is that of maximum loss, which compares the current value against the minimum over a set of admissible scenarios. A critical factor affecting the quality of this measure is the selection of such a set. In his paper, Breuer proposes a method such that this measure is robust for elliptical distributions. In particular, under certain conditions, the inclusion of risk factors that are either irrelevant or highly correlated with other risk factors will not affect the maximum loss.