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Compare credit VaR with market risk value at risk (VaR) by how each is defined, the horizon it covers and the tools used to measure it.

FRM® Part II · Credit Risk Measurement and Management · Credit Value at Risk · FRM2.CR.10.a

The idea

Market VaR and credit VaR answer the same question, how much could we lose at a given confidence level, but they are built differently. Market VaR covers a short horizon, typically one to ten days, because positions are liquid and can be closed or hedged. Its P&L is roughly symmetric and is measured with historical simulation, variance-covariance or Monte Carlo on observed prices. Credit VaR covers a long horizon, usually one year, because loans are illiquid and defaults are slow to resolve. Losses are driven by rare, lumpy defaults, so the distribution is skewed with a fat right tail. It must be modelled from default probabilities, recovery rates, exposures and default correlation, often at 99.9 percent. Square-root-of-time scaling and normality do not carry over. Credit VaR is usually quoted relative to expected loss.

A practice question

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

Which pairing best contrasts the usual horizons of market VaR and credit VaR in a bank?

  1. Market VaR covers one year; credit VaR covers one to ten days.Why not: Reverses the horizons: it is market VaR that is short because positions can be closed or hedged quickly.
  2. Both cover one day, because both are estimated from daily price data.Why not: Assumes loans have daily prices; credit VaR is driven by default events and is normally set over a one-year horizon.
  3. Market VaR covers one day; credit VaR covers the full maturity of each loan.Why not: Confuses the VaR horizon with instrument maturity; the credit VaR horizon is conventionally one year, not loan tenor.
  4. Market VaR covers one to ten days; credit VaR typically covers one year. - correct

Trading positions are liquid, so market VaR uses one to ten days. Loans are illiquid and default risk unfolds slowly, so credit VaR conventionally uses a one-year horizon.

A harder one

A bank wants a one-year economic capital figure for a book of unrated, illiquid middle-market loans for which no price history exists. Which measurement approach fits the data available?

  1. A portfolio credit model using estimated default probabilities, recoveries, exposures and default correlation. - correct
  2. Historical simulation of the daily price changes of the loans.Why not: Needs observed daily prices, which illiquid loans do not have; this is a market VaR tool.
  3. Variance-covariance VaR from the volatility of daily loan returns.Why not: Needs a return volatility from market data and assumes normal returns; neither suits a loan book with no prices.
  4. A parametric VaR on a listed equity index, scaled to one year by the square root of time.Why not: Uses an unrelated market proxy and square-root scaling; it ignores default, recovery and the skewed loss distribution.

With no market prices the risk has to be modelled from default probability, recovery, exposure and default correlation, as in CreditMetrics, CreditRisk+ or Vasicek-type models.

The hardest tier

A bank backtests a 99.9% one-year credit VaR using annual loss observations and wants at least 5 expected exceedances in the sample to make the test meaningful. Assuming independent years, the number of years of data needed is closest to:

  1. 500 yearsWhy not: Uses a 1% exceedance probability (99% confidence) instead of 0.1%: 5 / 0.01 = 500.
  2. 5,000 years - correct
  3. 1,000 yearsWhy not: Gives only one expected exceedance (1 / 0.001) and ignores the requirement of five.
  4. 50,000 yearsWhy not: Uses a 0.01% exceedance probability (99.99% confidence): 5 / 0.0001 = 50,000.

Expected exceedances = years x (1 - 0.999). For 5 exceedances: 5 / 0.001 = 5,000 years. Annual horizons and extreme confidence levels make credit VaR very hard to backtest, unlike daily 99% market VaR with 2.5 exceptions a year.

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