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Answer: 3.17%.
## Expected Return Calculation **Step 1: Calculate Expected Price Change Due to Rating Migration** Expected return = YTM + Expected price change due to rating migration Price change ≈ -Modified Duration × Change in credit spread **Step 2: Calculate Expected Change in Credit Spread** Expected Δspread = Σ[Probability × (New spread - Current spread)] Current BB spread = 3.20% Expected Δspread = - To A: 2.66% × (1.00% - 3.20%) = 0.0266 × (-2.20%) = -0.05852% - To BBB: 4.20% × (1.40% - 3.20%) = 0.0420 × (-1.80%) = -0.07560% - To BB: 85.24% × (3.20% - 3.20%) = 0.8524 × 0% = 0% - To B: 7.90% × (7.00% - 3.20%) = 0.0790 × 3.80% = 0.30020% Total Expected Δspread = -0.05852% - 0.07560% + 0% + 0.30020% = 0.16608% **Step 3: Calculate Expected Price Change** Expected price change ≈ -6.52 × 0.16608% = -1.082% **Step 4: Calculate Expected Return** Expected return = 4.25% - 1.082% = 3.168% ≈ 3.17% The expected return is closest to 3.17%, which matches option A.
Author: LeetQuiz Editorial Team
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An analyst gathers the following information on the following partial 1-year transition matrix for BB rated bonds and credit spread data:
| Probability (%) | A | BBB | BB | B |
|---|---|---|---|---|
| 2.66 | 4.20 | 85.24 | 7.90 | |
| Credit spread | 1.00% | 1.40% | 3.20% | 7.00% |
Assuming no default, the 1-year expected return on a BB rated bond with a YTM of 4.25% and a modified duration of 6.52 is closest to:
A
3.17%.
B
4.25%.
C
5.33%.
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