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Contrast credit spread risk with credit default risk.

FRM® Part I · Financial Markets and Products · Corporate Bonds · FRM1.FM.17.d

The idea

Credit default risk is the risk that the issuer fails to make a promised payment of interest or principal, so the investor loses part or all of the amount owed. With PD the probability of default and LGD the loss given default, the expected loss is EL = PD × LGD × exposure. Credit spread risk is the risk that the bond's price falls because the spread over the benchmark widens, even though the issuer is still paying. Spreads widen when the market sees weaker credit quality, after a downgrade, or when liquidity or risk appetite deteriorates. The price effect is roughly minus modified duration times the change in spread, so long-duration bonds suffer most. Spread risk is a mark-to-market loss that matters if the position is marked, financed or sold. Default risk is a realised credit loss. The exam trap is to call every price decline from credit worries a default loss.

Formulas

Expected loss from default

expected loss = PD × LGD × exposure

PD
the probability of default over the period
LGD
loss given default, 1 minus the recovery rate
exposure
the amount owed at default

Measures default risk only. A price fall from a wider spread is spread risk, a separate mark-to-market loss.

Price change from a change in credit spread

percentage price change = −D × Δs

D
modified duration
Δs
the change in the credit spread, in decimals

A mark-to-market loss with no default. Long-duration bonds suffer most.

A practice question

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

Which statement correctly describes credit spread risk?

  1. The risk that the issuer fails to make a promised payment of interest or principal on time.Why not: Defines credit default risk, not spread risk.
  2. The risk that the bond is called by the issuer before maturity.Why not: Confuses spread risk with call risk.
  3. The risk that benchmark Treasury yields rise, lowering all bond prices.Why not: Describes interest rate risk, which is independent of the spread.
  4. The risk of a price fall as the spread over the benchmark widens, without a default. - correct

Spread risk is the mark-to-market loss from a wider spread to the benchmark. Default risk is the loss from non-payment.

A harder one

A holder owns USD 10 million face of a bond with a one-year probability of default of 2% and an expected recovery of 40% of face. What is the expected default loss over the year (ignoring discounting and accrued interest)?

  1. USD 120,000 - correct
  2. USD 80,000Why not: Multiplies by the recovery rate instead of the loss given default (1 minus recovery).
  3. USD 200,000Why not: Ignores recovery and treats the full face as lost on default.
  4. USD 6,000,000Why not: Uses the loss given default alone and forgets the default probability.

Expected loss = PD x (1 - recovery) x exposure = 0.02 x 0.60 x 10,000,000 = USD 120,000. This is default risk; spread risk is separate.

The hardest tier

A pension fund holds a corporate bond it intends to hold to maturity. The issuer's spread widens by 100 bp, but the issuer pays every coupon on time and repays principal at maturity. Which statement is correct?

  1. The fund suffers a default loss equal to the price decline, because wider spreads imply default.Why not: Confuses spread widening with default; no payment has been missed.
  2. A mark-to-market loss from spread risk, not a default loss; realised only on a sale. - correct
  3. The fund suffers no loss of any kind, because holding to maturity eliminates both spread risk and default risk.Why not: Holding to maturity does not remove default risk, and the mark-to-market loss is still a loss in reported value.
  4. The fund's loss is interest rate risk, since spreads are part of the risk-free yield curve.Why not: Spreads are the credit component above the risk-free curve and are a different risk from rate movements.

Spread widening cuts the market price but not the contractual cash flows. The loss is unrealised and may reverse, and becomes real if the bond is sold or if the issuer later defaults.

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