How do you decompose a bond's total risk into spread risk and interest rate risk?

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AcadiFi · Accepted Answer

A corporate bond's total yield is the sum of the benchmark risk-free rate and the credit spread. Total price risk can be decomposed into the portion driven by benchmark...

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**Decomposition Framework:**

Total yield change = Δ(benchmark rate) + Δ(credit spread)

Total price change ≈ -D_IR × Δ(benchmark) - D_CS × Δ(spread)

**Worked Example -- Triton Energy Bond Portfolio (fictional)**

Triton holds $50M face value of investment-grade corporate bonds with an average effective duration of 6.0 years.

Over Q1, the portfolio experienced:
- Benchmark (Treasury) yield: +75 bps
- Credit spread: +25 bps
- Total yield change: +100 bps

| Risk Component | Duration | Yield Change | Price Impact | % of Total Loss |
|---|---|---|---|---|
| Interest rate risk | 6.0 | +75 bps | -6.0 × 0.75% = **-4.50%** | 75% |
| Spread risk | 6.0 | +25 bps | -6.0 × 0.25% = **-1.50%** | 25% |
| **Total** | | +100 bps | **-6.00%** | **100%** |

Dollar loss = $50M × 6.00% = **$3.0M**

Of which: $2.25M from rates, $0.75M from spreads.

**Risk Budgeting Application:**

| Portfolio Segment | Weight | IR Duration Contribution | Spread Duration Contribution |
|---|---|---|---|
| Treasuries | 40% | 3.2 | 0.0 |
| IG Corporate | 35% | 2.1 | 2.1 |
| HY Corporate | 15% | 0.5 | 1.8 |
| EM Sovereign | 10% | 0.8 | 1.0 |
| **Total** | **100%** | **6.6** | **4.9** |

This tells the PM that 57% of their duration-weighted risk comes from interest rates and 43% from credit spreads. The high-yield allocation contributes disproportionately to spread risk (1.8/4.9 = 37% of spread risk from only 15% of the portfolio).

**Hedging Implications:**
- Treasury futures or interest rate swaps hedge the IR component
- CDS indices (CDX IG, CDX HY) hedge the spread component
- Neither instrument hedges the other's risk, so both are needed for full immunization

How do you decompose a bond's total risk into spread risk and interest rate risk?

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