A B-rated bond has yield to maturity of 10%. The default probability for B-rated bonds is 5%, and if default happens, investors expect to lose 60% of the bond value. What is the expected average return of this bond?

Question

BlackTom AI · Accepted Answer

Expected loss = default probability × loss given default, so adjust the promised yield by that expected loss.

1) Relevant concepts
- Yield to maturity (10%) is the promised return if no default occurs.
- Default probability (p = 5% or 0.05) is the chance the bond defaults.
- Loss given default (LGD = 60% or 0.60) is the fraction of bond value lost if default occurs.
- Expected return = promised yield minus the expected loss due to default (expected loss measured in percentage points of principal).

2) Step-by-step reasoning and calculations
- Compute expected loss in percentage points: expected loss = p × LGD = 0.05 × 0.60.
- Multiply: 0.05 × 0.60 = 0.03, i.e., 3 percentage points.
- Subtract expected loss from the promised yield: expected average return = 10% − 3% = 7%.

All intermediate steps:
- p = 5% = 0.05
- LGD = 60% = 0.60
- expected loss = 0.05 × 0.60 = 0.03 = 3%
- expected return = 10% − 3% = 7%

3) Why this is correct
This method treats the promised yield as the return conditional on no default and reduces it by the average (probability-weighted) loss of principal from default. The expected loss in percent points directly lowers the expected percentage return, yielding 7%.

4) Briefly why other common answers would be incorrect
- 10% ignores default risk and thus overstates the realistic average return.
- A computation that weights final dollar outcomes like 0.95×1.10 + 0.05×0.40 − 1 gives 6.5%; that approach treats recovery as a final gross payoff mix but mixes principal recovery and promised yield inconsistently with the problem’s statement of a 60% loss of bond value. The standard and intended interpretation is the expected loss in percentage points (3%), so 7% is correct.
  
Conclusion: The expected average return is 7%, which matches the provided answer.

A B-rated bond has yield to maturity of 10%. The default probability for B-rated bonds is 5%, and if default happens, investors expect to lose 60% of the bond value. What is the expected average return of this bond?单项选择题

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