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Explain the steps that produce the incremental risk capital charge on trading book positions held by a bank.

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

The idea

The incremental risk charge (IRC) from Basel 2.5 captures default and credit migration risk on unsecuritized credit positions in the trading book, such as corporate bonds and credit default swaps, which a 10-day VaR cannot see. The bank simulates, usually by Monte Carlo, joint rating transitions and defaults of issuers using a correlation model. It revalues the positions in every scenario, builds the distribution of losses over one year, and takes the 99.9 percent quantile. Each position has a liquidity horizon of at least three months. The constant level of risk assumption says positions are rebalanced back to their initial risk at the end of each horizon, so a defaulted exposure is replaced and can default again. Securitizations are excluded. The usual mistake is treating positions as held unchanged for the whole year. IRC is added to VaR and stressed VaR.

Formulas

Chance of at least one default over the IRC year with rebalancing

P = 1 − (1 − p)ⁿ

p
the default probability in one liquidity horizon
n
the number of liquidity horizons in the year

Assumes independent horizons under the constant level of risk. Rebalancing gives a new chance of default each horizon.

A practice question

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

Which description of the Basel 2.5 incremental risk charge (IRC) is correct?

  1. A 99% 10-day measure of credit spread changes on all bonds and credit derivatives held for tradingWhy not: Describes ordinary VaR on credit spreads; IRC targets default and migration over a much longer horizon and higher confidence.
  2. A 99.9% one-year measure of default and migration losses on unsecuritized trading book credit positions - correct
  3. A 99.9% one-year measure of every market risk factor on all securitization positions held for tradingWhy not: Securitizations are excluded from IRC, and IRC covers default and migration, not every market risk factor.
  4. A 97.5% expected shortfall measure of default losses on loans held in the banking bookWhy not: Confuses IRC with the later FRTB expected shortfall and applies it to the banking book; IRC is a trading book charge at 99.9%.

IRC fills a gap in VaR: jump-to-default and rating migration risk on trading book credit positions, measured at 99.9% over one year, with securitizations handled elsewhere.

A harder one

Which sequence best describes how a bank would derive the IRC from a Monte Carlo model?

  1. Simulate correlated migrations and defaults, revalue after rebalancing, build the one-year loss distribution, take the 99.9th percentile - correct
  2. Take each issuer's own 99.9% one-year loss and add the amounts across the whole portfolio of issuersWhy not: Adding stand-alone tail losses assumes perfect default correlation and ignores the simulated joint distribution.
  3. Fit a normal distribution to daily credit spread changes and read off the 99.9% quantile for one yearWhy not: A Gaussian spread model misses jump-to-default and rating migration, which is what IRC is designed to capture.
  4. Apply average one-year default probabilities from a rating table and sum the expected losses of all issuersWhy not: Expected loss is not a 99.9% tail measure and ignores correlation between issuers.

IRC is a tail quantile of a simulated loss distribution that reflects default correlation. Summing stand-alone losses or using expected losses answers a different question.

The hardest tier

A high-yield bond has a three-month liquidity horizon and a 5% probability of default in any three-month period, independent across periods. Under the constant level of risk assumption with a one-year IRC horizon, the probability that the position, or its replacement, defaults at least once during the year is closest to:

  1. 5.00%Why not: Counts only the first liquidity horizon, ignoring that the position is rolled and can default in later quarters.
  2. 18.55% - correct
  3. 9.75%Why not: Uses two rebalancing periods instead of four quarterly periods.
  4. 14.26%Why not: Uses three periods (the number of rebalancing dates) instead of four quarterly exposure periods.

Four independent quarters: 1 - (1 - 0.05)^4 = 18.55%. With a rebalanced position every quarter brings a new default chance, unlike a constant position held for the year.

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