What is one-sided duration for callable bonds and why does it reveal asymmetric risk?

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AcadiFi · Accepted Answer

One-sided duration calculates the price sensitivity separately for yield increases and yield decreases. For callable bonds, these two values differ significantly because...

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**One-Sided Duration Formulas:**

Up-Duration = [P(0) - P(+Δy)] / [P(0) × Δy]
Down-Duration = [P(-Δy) - P(0)] / [P(0) × Δy]
Two-Sided (Standard) EffDur = [P(-Δy) - P(+Δy)] / [2 × P(0) × Δy]

**Worked Example -- Ridgecrest Power Authority Bond (fictional)**

Ridgecrest 4.75% coupon, 15-year maturity, callable at par in 3 years. Current price $101.50.

| Scenario | Yield Change | Price |
|---|---|---|
| Down 50 bps | -0.50% | $102.80 |
| Current | 0% | $101.50 |
| Up 50 bps | +0.50% | $96.20 |

**Up-Duration** = ($101.50 - $96.20) / ($101.50 × 0.005) = $5.30 / $0.5075 = **10.44**

**Down-Duration** = ($102.80 - $101.50) / ($101.50 × 0.005) = $1.30 / $0.5075 = **2.56**

**Two-Sided EffDur** = ($102.80 - $96.20) / (2 × $101.50 × 0.005) = $6.60 / $1.015 = **6.50**

| Measure | Value | Interpretation |
|---|---|---|
| Up-duration | 10.44 | High sensitivity to rate increases (full downside) |
| Down-duration | 2.56 | Low sensitivity to rate decreases (call caps upside) |
| Two-sided EffDur | 6.50 | Average -- misleading, hides asymmetry |

The standard two-sided effective duration of 6.50 masks the fact that the bond loses 4x more per basis point of rate increase than it gains per basis point of rate decrease. A risk manager using only the two-sided figure would underestimate downside risk.

**When One-Sided Duration Matters Most:**
- Callable bonds trading near the call price (at-the-money call)
- Mortgage-backed securities (prepayment is like a call)
- Any bond where optionality creates asymmetric payoffs

Portfolio stress testing should use one-sided durations for scenarios. A +200 bps shock should use up-duration (10.44 here), giving a much larger estimated loss than the two-sided figure would suggest.

What is one-sided duration for callable bonds and why does it reveal asymmetric risk?

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