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Explain how CreditMetrics is applied to estimate economic capital, outlining how the model is built.

FRM® Part I · Valuation and Risk Models · Measuring Credit Risk · FRM1.VR.6.h

The idea

CreditMetrics estimates the distribution of a loan portfolio's value one year ahead and derives economic capital from it. Each borrower has a rating with one-year transition probabilities, including default. Correlation between borrowers comes from a factor model for their asset or equity returns, applied through a Gaussian copula. A simulated normal variable for each borrower is compared with thresholds to decide its new rating. The thresholds are N⁻¹ of the cumulative transition probabilities. In each Monte Carlo trial every loan is revalued at the horizon. A defaulted loan is worth its recovery value, and other loans are valued by discounting remaining cash flows at the spread for the new rating. Summing gives a portfolio value per trial. Economic capital is the mean portfolio value minus the value at the chosen percentile, for example 99.9 percent. Unlike a default-only model, it captures losses from downgrades.

Formulas

CreditMetrics economic capital

economic capital = mean portfolio value − portfolio value at the percentile

mean portfolio value
the average simulated value one year ahead
portfolio value at the percentile
the simulated value at the chosen confidence level, for example the 10th lowest of 10,000 trials at 99.9 percent

Measured in value, so losses from downgrades count as well as defaults. Read the percentile from the bottom of the value distribution.

A practice question

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

Which statement best describes how CreditMetrics estimates economic capital?

  1. It simulates correlated rating changes and defaults over a year, revalues the loans, and sets capital from a high percentile of portfolio value. - correct
  2. It applies historical simulation to ten days of daily bond price changes and scales by the square root of time.Why not: That is a market risk VaR approach; CreditMetrics uses one-year rating migrations and revaluation.
  3. It counts only defaults, so a downgrade without default has no effect on portfolio value.Why not: CreditMetrics is a migration model: downgrades change loan values through the spread for the new rating.
  4. It estimates capital as a fixed percentage of the notional amount of each loan, with the percentage set by regulators for each rating.Why not: That is a regulatory ratio approach; CreditMetrics derives capital from a simulated loss distribution.

CreditMetrics: transition matrix + correlated factor model to simulate rating changes, loan revaluation at the horizon, portfolio value distribution, and capital as the shortfall from the mean at the chosen percentile.

A harder one

A 4-year loan with face value 100 pays an annual coupon of 6. In a CreditMetrics simulation, one year from now the first coupon has just been received and the borrower has been downgraded, so the three remaining cash flows (coupons of 6 at the end of years 2, 3 and 4, plus principal of 100 at the end of year 4) are discounted at 7.5%. The horizon value of the position including the coupon received is closest to:

  1. 96.10Why not: Leaves out the coupon of 6 already received at the horizon.
  2. 102.10 - correct
  3. 106.00Why not: Discounts at the original 6% rate, ignoring the downgrade.
  4. 94.98Why not: Treats four years as still remaining and discounts four cash flows, ignoring that one year has passed.

Horizon value = 6 + 6/1.075 + 6/1.075² + 106/1.075³ = 102.10. The loss versus 106.00 (no downgrade) shows how migration, not only default, moves loan value.

The hardest tier

A CreditMetrics-style simulation of a loan portfolio runs 10,000 trials. The mean portfolio value is 1,010; the lowest value is 790; the 10th lowest value is 880; and the 100th lowest value is 925. The bank defines economic capital as the mean portfolio value minus the portfolio value at the 99.9% confidence level. Economic capital is closest to:

  1. 220Why not: Uses the single worst outcome rather than the 99.9% percentile, which sits at the 10th lowest of 10,000 trials.
  2. 85Why not: Uses the 100th lowest value, which is the 99% level, instead of the 10th lowest for 99.9%.
  3. 130 - correct
  4. 120Why not: Subtracts from the initial portfolio value of 1,000 instead of from the mean value of 1,010.

99.9% of 10,000 trials leaves 10 trials below, so the percentile value is the 10th lowest, 880. Economic capital = 1,010 - 880 = 130.

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