What is money duration and how does it differ from modified duration in practical risk management?

Question

AcadiFi · Accepted Answer

Money duration (also called dollar duration) measures the absolute dollar change in a bond or portfolio's market value for a given yield change, as opposed to percentage change. It equals:

Money Duration = Modified Duration × Market Value

For a $30M position with MD = 6.0, money duration = 6.0 × $30M = $180M per 100% (1 full percentage point of yield change). For a 1bps change, scale down: $180M × 0.0001 = $18,000. That's the BPV (Basis Point Value) or PVBP.

For your system reporting $1.8M 'per percentage point':
- That's $1.8M per 100 bps
- Per 1 bp: $1.8M / 100 = $18,000
- So a 25bp yield rise would cost ~$450,000 (before convexity adjustment)

**Why money duration for risk management?**

1. **Position-size-aware**: Modified duration of 6.5 means nothing without knowing the notional. Money duration directly answers 'how many dollars do I lose per bp?'

2. **Hedging ratios**: To hedge one position with another, you equalize money durations (or BPVs):
 Hedge ratio = BPV_asset / BPV_hedge
 If your $30M bond has BPV $18,000 and a Treasury future has BPV $120 per contract, you need 150 contracts to hedge.

3. **Aggregation across currencies**: Convert everything to a common currency; money duration adds linearly across a multi-currency book.

4. **VaR inputs**: Money duration × yield volatility × z-score gives a first-order parametric VaR. Essential for trading desk risk.

**Money Convexity**: The dollar analog of convexity:
Money Convexity = Convexity × Market Value

Full dollar P&L estimate:
$ΔP = −MoneyDur × Δy + ½ × MoneyConv × (Δy)²

**BPV vs PVBP vs DV01**: These are the same concept at 1bp — conventions differ by desk. BPV and PVBP typically use + or − 1bp bump in the yield; DV01 (Dollar Value of 01) is the change for a 1bp yield move. Same number, different marketing.

**Rule for practitioners**: Never discuss 'duration' without the dollar context. A PM saying 'I'm long 5 years of duration' means they have $5 of BPV per basis point, not modified duration of 5 — terminology varies by shop.

What is money duration and how does it differ from modified duration in practical risk management?

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