Fixed Income
coreMoney Duration & PVBP
Builds onModified Duration — if this page feels steep, start there.
- modified duration: the position's % price change per unit of yield change
- the position's full market value (price times holdings)
- money (dollar) duration: dollars of value change per unit of yield change
- one basis point written as a decimal — the trader's natural increment
- price value of a basis point (a.k.a. DV01): dollars gained or lost per 1bp yield move
Reading the notation
Why it must be true
Modified duration answers in percentages; a risk manager's phone call demands dollars. Money duration is the conversion: multiply the percentage sensitivity by the position's market value, and you get dollars of P&L per unit of yield move.
Scale it to the trader's natural increment — one basis point (0.01%) — and you have the PVBP ("price value of a basis point," also DV01): the dollars this position gains or loses when yields tick once. Desks live in this unit: "I'm running $40k of DV01" says exactly how much a one-tick rate move costs, position sizes are set by it, and hedges are built by matching it — equal and opposite PVBPs cancel.
The derivation
Start from modified duration's definition as a percentage response:
Multiply through by the position's value to convert percent into dollars:
Set to one basis point ():
Duration, money duration and PVBP are one fact in three units: percent per yield, dollars per yield, dollars per basis point.
When to reach for it
Converting duration into dollar terms for a specific position — sizing rate risk, setting limits, or matching a hedge in DV01.
Listen for
Back-of-the-envelope
Estimate it in your head first — then the calculator only confirms.
- ≈
Decimal shuffle: PVBP = ModDur × P × 10⁻⁴. A $1m position with duration 5 → 5 × 1{,}000{,}000 / 10{,}000 = $500 per bp. Divide by ten thousand, done.
- ≈
Scale check: PVBP is SMALL relative to the position (basis points are small). If your 'PVBP' is 1% of the position, you computed money duration instead.
- ≈
Linear in both inputs: double the position or double the duration, double the PVBP — hedge ratios are just PVBP ratios.
Traps in applying it
- ✗Quoting money duration when PVBP was asked (off by the 10⁻⁴ factor) — the most common slip.
- ✗Using the face value instead of the market value of the position.
- ✗Forgetting the sign convention in use: PVBP is quoted as a positive magnitude, but yields up means value DOWN for a long.
Limits & criticisms
PVBP inherits duration's linearity: exact for one basis point, drifting for large moves where convexity takes over — a 100bp scenario is not 100 PVBPs. It also prices only parallel shifts of the position's own yield; curve twists need key-rate PVBPs, and the measure must be recomputed as prices and durations drift — yesterday's DV01 is stale after a big rally.
Where it came from
Dollar-based risk measures grew up on 1970s–80s bond desks, when Volcker-era volatility made "how many dollars do we lose per basis point?" the daily survival question — dealers hedging with the new Treasury futures needed DV01-matching to size the hedge. Today PVBP is the native language of every rates desk, risk report and futures hedge ratio: regulators aggregate bank rate-risk in DV01 terms, and swap desks quote hedges by matching it.
One identity, 2 questions
The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.
Money duration
The unit conversion: percent-per-yield into dollars-per-yield — duration priced for THIS position.
Dollars per tick
The desk's unit: what one basis point costs. Hedging = finding the position with equal and opposite PVBP.
On the BA II Plus
Worked example: A portfolio of $500,000.00 carries modified duration 9.5. Compute its DV01 (PVBP).
- 1.9.5 [×] 500000 [=]money duration first
- 2.[×] 0.0001 [=]scale to one basis point
→ $475.00