The authors’ research differs from previously published research in three respects. First, they consider both value at risk (VaR) and stress-testing constraints, whereas previous research considers only one type of constraint (i.e., either VaR or stress testing). Second, the authors explore the extent to which both types of constraints lead to the selection of a portfolio with minimum tail risk for a given required expected return. Third, the authors estimate VaR using historical simulation, whereas prior research estimated VaR parametrically. Finally, they also examine the pro-cyclical effects of the Basel II capital framework.

The authors draw on a considerable amount of previously published work done over more than a decade in the areas of quantitative risk measurement, VaR, conditional VaR (CVaR), portfolio optimization under risk constraints, and analysis of the efficacy of the Basel framework.

They suggest three alternatives to the Basel VaR and stress-testing methodology. First, regulators could base capital requirements on CVaR instead of VaR. Second, regulators could base capital requirements on VaR at multiple confidence levels (e.g., 99% and 99.5%). Third, regulators could base the requirements on VaR at higher confidence levels (99.5% instead of 99%). Not surprisingly, the authors conclude that these alternatives are less pro-cyclical than the Basel framework because their relatively higher capital requirements would presumably reduce the need to raise new capital during times of stress.

The research would be of interest to regulators, risk managers, portfolio managers, traders, and academics interested in VaR, CVaR, stress testing of bank trading books, and the pro-cyclical effects of minimum capital requirements during times of stress.

Central to the authors’ methodology are the concepts of an efficient CVaR frontier, the measurement of expected return versus CVaR, and loss efficiency (e.g., the increased CVaR required of an inferior portfolio relative to the efficient portfolio that has the same expected return). They examine the effectiveness of three sets of constraints—VaR, stress tests, and VaR and stress tests combined—using a six-step process:

1. Confidence level and constraint bounds are selected based on the requirements of the Basel framework.
2. Minimum and maximum required expected returns are identified.
3. Percentile returns are calculated for the range of expected returns.
4. Expected returns are calculated.
5. The minimum and maximum efficiency loss is computed for each expected return.
6. The average efficiency loss, largest maximum efficiency loss, and relative efficiency loss for each expected return are determined for each expected return.

This process enables an impartial assessment of the effectiveness of the constraints controlling CVaR. If the constraints eliminate all portfolios with material efficiency losses, then they are effective in controlling CVaR. Thus, any portfolio that meets the constraints will have tail risk that is similar in magnitude to that of the portfolio with the same expected return that minimizes CVaR.

This research builds on work previously done by the authors dating back more than a decade on the topics of bank supervision and regulation under the Basel framework, VaR, CVaR, and portfolio optimization techniques. In my opinion, commentary on the efficacy of the 2006 Basel framework post-crisis is an area that has already been thoroughly covered. The proposed alternatives to the Basel framework are not controversial; increasing the VaR threshold, using CVaR, and applying multiple VaR levels are all well within the mainstream of defending banks’ books from tail risk events.