Price Value of a Basis Point

Modified duration expresses interest rate sensitivity as an approximate percentage price change per one percentage point change in yield. PVBP converts that percentage into money by scaling it twice: first by the bond's full price, which produces money duration, and then by 0.0001, which shrinks the move from one hundred basis points to one. The result is a currency amount per basis point for whatever quantity of bonds the price refers to, whether that is one bond quoted per 100 of par or an entire inventory position.

Because of the second scaling, PVBP inherits everything that drives duration, including time to maturity, coupon level, yield level and any embedded options, but it also inherits price level and position size. A deep-discount bond and a high-coupon premium bond can share a duration figure and still carry very different money exposures per basis point.

The alternative route is direct revaluation. Price the bond at its current yield to maturity, then reprice it with the yield raised by one basis point and again with the yield lowered by one basis point. Take the difference between the low-yield price and the high-yield price and halve it. That average of the upside and downside price movements is PVBP, and the same symmetric procedure underlies the approximate modified duration formula, simply left in currency terms rather than divided by price.

Averaging the two sides matters conceptually because the price-yield relationship is curved: the gain from a yield fall slightly exceeds the loss from an equal yield rise. Over a single basis point that asymmetry is negligible for an option-free bond, which is why PVBP is treated as a pure first-order measure and convexity adjustments are reserved for larger yield shifts.

PVBP is the working language of interest rate risk because currency amounts aggregate cleanly while percentage durations do not. A desk can add the basis point values of bonds, futures, swaps and repo positions across the book to obtain a single net exposure, then express it as profit or loss for a one basis point parallel shift. Hedge sizing follows directly: divide the exposure to be neutralised by the basis point value of the hedging instrument to obtain the required number of contracts or the notional of the swap.

Risk reports rarely stop at one number. Splitting total basis point value into partial or key rate contributions along the maturity spectrum reveals curve exposure that a single duration figure conceals, so a book can be flat in aggregate while remaining long the front end and short the long end.

Expect to move fluently in both directions. Given annual modified duration and a full price, produce PVBP; given PVBP, recover money duration by multiplying by ten thousand, or recover modified duration by dividing money duration by the full price. Expect also to translate PVBP into the estimated profit or loss on a stated yield move by multiplying by the number of basis points, remembering the sign convention that prices fall when yields rise.

Two details cause avoidable errors. The relevant price is the full price including accrued interest, not the quoted flat price, and the quantity being measured must match the position: PVBP quoted per 100 of par must be scaled by par value in hundreds before it describes a real holding. Confirm both before comparing figures or computing a hedge ratio.