Work out a bond's PVBP (value change per basis point) and explain it
The idea
The price value of a basis point (PVBP) is the change in a bond's price for a one basis point change in its yield, stated as a money amount rather than a percentage. It is estimated by repricing the bond one basis point lower and one basis point higher and averaging the difference: PVBP = (price at the lower yield - price at the higher yield) / 2. It can also be approximated as modified duration x full price x 0.0001, and it is one ten-thousandth of money duration. Because it is in currency, it scales directly with position size and adds across a portfolio, which makes it the working measure for hedging: the par amount of a hedge is set so its PVBP offsets the portfolio's. For an option-free bond, PVBP falls as yields rise, since both price and duration decline.
A practice question
The price value of a basis point (PVBP) of a bond is best described as the:
- change in yield for a 1% change in priceWhy not: Reverses the relationship. PVBP measures the price response to yield, not the yield response to price.
- change in price for a 1 bp change in yield — correct
- percentage price change for a 1% yield changeWhy not: That is close to modified duration, which is a percentage measure, not a money amount per basis point.
PVBP is the money change in price for a one basis point change in yield. Being in currency, it scales with position size and is used for hedging.
A harder one
A 5-year, 4% annual-coupon bond yields 5% and is priced at 95.6705. At yields of 4.99% and 5.01% its prices are 95.7126 and 95.6284. Its PVBP per 100 par is closest to:
- 0.0421 — correct
- 0.0842Why not: Takes the full difference between the two prices without dividing by 2.
- 0.0004Why not: Divides by the price, giving a fractional price change rather than a money amount.
PVBP = (95.7126 - 95.6284) / 2 = 0.0842 / 2 = 0.0421 per 100 par.
The hardest tier
A portfolio has a PVBP of 30,000. A hedging bond has a PVBP of 0.0750 per 100 par. To neutralise the portfolio's rate exposure, the manager should:
- buy 40 million parWhy not: Adds to the exposure. A long bond position gains and loses alongside the portfolio.
- short 400,000 parWhy not: Forgets that the hedge bond's PVBP is quoted per 100 par.
- short 40 million par — correct
Hedge par = portfolio PVBP / (hedge PVBP per 100 / 100) = 30,000 / 0.00075 = 40,000,000. Shorting it offsets the portfolio's gain or loss per basis point.
In the app: 6 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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