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P2.T5.405. Basel Committee on value at risk (VaR), expected shortfall (ES) and other risk measures

Nicole Seaman

Director of FRM Operations
Staff member
AIM: Compare VaR, expected shortfall, and other relevant risk measures.


405.1. In regard to value at risk (VaR) as a risk measure, the Basel Committee asserts each of the following as true, EXCEPT which is of the following is not accurate?

a. VaR measures only the loss quantile, which implies a drawback: by disregarding losses beyond the VaR level, a risk manager who relies strictly and exclusively on VaR may be tempted to avoid losses within the confidence level while increasing losses beyond the VaR level
b. VaR measures only the loss quantile, which implies an advantage ("positive flipside"): it makes backtesting easier (or possible in the first place) simply because empirical quantiles are per se robust to extreme outliers, unlike typical estimators of the expected shortfall
c. Subadditivity reflects the idea that risk can be reduced by diversification: in theory, the use of non-subadditive risk measures in a Markowitz-type portfolio optimisation problem may lead to optimal portfolios that are very concentrated and that would be deemed quite risky by normal economic standards
d. Although VaR is technically not sub-additive (and not coherent), in the trading book and market risk context the literature has produced no instances where VaR's lack of coherence creates an actual, practical problem

405.2. According to the Basel Committee, each of the following is true about expected shortfall (ES) as a risk measure, except for which of the following is the LEAST true?

a. ES corrects three shortcomings of VaR: ES accounts for the severity of losses beyond the confidence threshold; it is always subadditive and coherent; and it mitigates the impact that the particular choice of a single confidence level may have on risk management decisions
b. ES aligns the interests of bank managers and owners to those of the public much better than VaR; and by accounting for the severity of losses beyond the confidence threshold, it appeals to regulators, who are concerned about exactly these losses.
c. Compared to VaR, a key disadvantage of ES, by definition, is virtually impossible to backtest and "no known methods have been yet discovered" to backtest ES
d. The calculation of ES and the marginal contributions of assets to portfolio ES is more challenging than the corresponding calculations for VaR, especially for high confidence levels, because a formula for the alpha-quantiles of the loss distribution is often missing. Simulations need to be done in most cases

405.3. According to Basel, the spectral risk measure (SRM) is formally defined as:

Each of the following statements is true about this SRM, except which statement is false?

a. An advantage of SRM over ES and VaR is that ES is not bound to a single confidence level
b. The main disadvantages of SRM are: SRM is not smooth; and it offers no intuitive link to risk aversion
c. The weight, w, must be (weakly) increasing over [0,1]
d. An increasing weight, w, over [0,1] ensures the SRM is coherent

Answers here:

cash king

New Member
Anyone can give me some clue for question 405.2? I think A and C are true. For B, I think maybe ES is not so appealing to regulator since it can't be backtested. But what about D? I've no idea for it.