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Explain the Basel 2.5 stressed VaR measure, work out its value, and then determine the market risk capital charge.

FRM® Part II · Operational Risk and Resilience · Solvency, Liquidity, and Other Regulation After the Global Financial Crisis · FRM2.ORR.22.a

The idea

Basel 2.5 added a stressed VaR because ordinary VaR, calibrated on a recent calm window, left banks thinly capitalised just before the crisis. Stressed VaR is the same 10-day, 99 percent VaR run on the bank's current portfolio, but using market data from a continuous 12-month period of significant financial stress. The multipliers mc and ms are at least 3, plus an add-on of 0 to 1 that grows with backtesting exceptions. Let VaR and sVaR be the previous day's figures, each with its average over the previous 60 days. The market risk capital charge for VaR and stressed VaR is then the sum of two terms: Charge = max(VaR, mc × average VaR) + max(sVaR, ms × average sVaR). Typical errors are applying the multiplier to the latest day, dropping the max rule, and replacing the VaR term with the stressed term instead of adding both. Incremental and comprehensive risk charges sit on top.

Formulas

Basel 2.5 market risk charge for VaR and stressed VaR

Charge = max(VaR, mc × VaRavg) + max(sVaR, ms × sVaRavg)

VaR
the previous day's 10-day 99 percent VaR
mc
the VaR multiplier, 3 plus an add-on of 0 to 1
VaRavg
the average VaR over the previous 60 days
sVaR
the previous day's stressed VaR
ms
the stressed VaR multiplier, 3 plus an add-on of 0 to 1
sVaRavg
the average stressed VaR over the previous 60 days

Each term takes its own maximum and the two are added. Applying the multiplier to the latest day is the usual slip.

A practice question

From the question bank, with the reason each wrong option is wrong.

Under Basel 2.5, the stressed VaR is calculated using which market data?

  1. A continuous 12-month stress period of market data, applied to the bank's current portfolio - correct
  2. The most recent 12 months of data with all volatilities doubled, applied to the current portfolioWhy not: Confuses stressed VaR with an arbitrary scaling of recent volatility; the calibration uses an actual historical stress period.
  3. Data from the period of the bank's largest past losses, applied to the positions held in that periodWhy not: Applies the stress to the old portfolio; stressed VaR revalues today's positions using stress-period market moves.
  4. Data from a 12-month stress period, measured at a 99.9% confidence level over a one-year horizonWhy not: Imports the IRC and CRM parameters (99.9%, one year); stressed VaR keeps the 99%, 10-day VaR specification.

Stressed VaR keeps the VaR specification (10-day, 99%) and the current portfolio but replaces the calibration window with a 12-month period of significant financial stress. Its purpose was to stop capital falling when markets are calm.

A harder one

A bank's supervisor sets mc = ms = 3.4 after backtesting. VaR (10-day, 99%) was USD 18 million yesterday and averaged USD 15 million over the previous 60 days. Stressed VaR was USD 40 million yesterday and averaged USD 35 million over the previous 60 days. The market risk capital charge for VaR plus stressed VaR is closest to:

  1. USD 58 millionWhy not: Takes the larger of latest and average with no multiplier, ignoring the multiplication factors on the 60-day averages.
  2. USD 51 millionWhy not: Omits the stressed VaR term; Basel 2.5 adds the stressed term to the VaR term.
  3. USD 170 million - correct
  4. USD 150 millionWhy not: Uses a multiplier of 3 and ignores the 0.4 backtesting add-on.

VaR term = max(18, 3.4 x 15) = 51. Stressed term = max(40, 3.4 x 35) = 119. Charge = 51 + 119 = 170. The multiplier applies to the 60-day average, and the two terms are added.

The hardest tier

A bank's 1-day 99% stressed VaR was USD 4.2 million yesterday, and the average of the previous 60 daily 1-day stressed VaR figures was USD 3.8 million. Assume the bank scales to a 10-day horizon by the square root of 10, and ms = 3. The stressed VaR component of the Basel 2.5 charge is closest to:

  1. USD 36.0 million - correct
  2. USD 11.4 millionWhy not: Applies the multiplier but forgets to scale the 1-day figure to a 10-day horizon.
  3. USD 13.3 millionWhy not: Takes yesterday's figure and ignores that the multiplier on the 60-day average is larger, so the max rule picks the average term.
  4. USD 114.0 millionWhy not: Scales by 10 instead of the square root of 10 when moving from 1 day to 10 days.

10-day yesterday = 4.2 x sqrt(10) = 13.28. 10-day average = 3.8 x sqrt(10) = 12.02, times 3 = 36.05. The larger is 36.0.

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