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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A risk analyst at a bank estimates the one-year default probability of a BBB-rated corporate issuer in two ways: (1) from historical default experience for BBB issuers, and (2) by backing it out of the issuer's bond spread over the risk-free rate. The bond-implied estimate is considerably higher than the historical estimate. Which statement best explains this pattern?

Bond-spread-implied default probabilities are risk-neutral, so they include compensation for risk and other spread components such as liquidity and taxes. Historical default frequencies are real-world estimates. Therefore the spread-implied probability is typically higher than the historical one for the same issuer.

  1. AThe bond-implied estimate is a risk-neutral probability, which embeds compensation for risk and other spread components, so it typically exceeds the real-world probabilityCorrect
  2. BThe historical estimate is risk-neutral and therefore overstates true default likelihood
  3. CThe bond-implied estimate is a real-world probability and the historical estimate ignores recovery
  4. DThe difference arises only because historical data covers more years than the bond's maturity

Explanation

Probabilities backed out of bond spreads are risk-neutral and reflect risk premia, liquidity and tax effects as well as expected loss. Historical default rates are real-world estimates. Hence the spread-implied figure is usually higher. The option calling the historical figure risk-neutral reverses the definitions.

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