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Set out the elements that make up credit risk

CFA® Level I · Fixed Income · Credit Risk · FI.5.a

The idea

Credit risk has two parts: the probability that the borrower fails to pay, and the loss suffered if it does. Expected loss is the product of the probability of default and the loss given default, which is one minus the recovery rate, applied to the amount exposed. The credit spread is the compensation demanded for bearing that risk, and it moves on the market price of risk as well as on the borrower's fundamentals — spreads widen in a crisis even for issuers whose own position is unchanged. Seniority decides who recovers first, which is why two bonds from the same issuer with the same default probability can still carry very different spreads.

A practice question

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

Expected loss is the probability of default multiplied by:

  1. the loss given default — correct
  2. the coupon rateWhy not: The coupon determines what is promised, not what is lost when the promise fails. The loss depends on exposure and recovery.
  3. the bond's durationWhy not: Duration measures sensitivity to rates. It plays no part in what a default costs.

One component is how likely the failure is, the other is how much is actually lost when it happens.

A harder one

Default probability is 4% and the recovery rate is 60%. Expected loss on $1,000 of exposure is:

  1. $24Why not: 0.04 x 0.60 x 1,000 — the *recovery* rate used as the loss rate. What is lost is the 40% not recovered.
  2. $16 — correct
  3. $40Why not: 0.04 x 1,000 — recovery ignored entirely, as though a default cost the whole exposure. This is the upper bound rather than the answer.

Loss given default is 40%, so 0.04 multiplied by 0.40 multiplied by 1,000 gives 16.

The hardest tier

Spread duration measures a bond's price sensitivity to a change in:

  1. its credit spread — correct
  2. the benchmark yieldWhy not: That is ordinary modified or effective duration. Spread duration isolates the risk premium instead.
  3. its couponWhy not: The coupon is fixed by the bond's terms and does not change.

It is the same mathematics as duration applied to the risk premium rather than to the risk-free rate.

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