Money duration & price value of basis point (PVBP)

Bond duration is a measure of a bond’s interest rate risk. It is typically expressed as a number but can be quantified with reference to a bond using either the money duration of the price value of basis point.

Money duration

Money duration (also called dollar duration in the US) of a bond is a measure of price change of the bond in response to a 1% change in its yield in the currency in which the bond denominated either on a 100 of par basis or the actual size of the bond.

Money duration equals the product of the annual modified duration and the full price of the bond.

\[ MoneyDur=AnnModDur\times{PV}^F \]

The absolute change in the price of a bond equals the negative product of the money duration and percentage change in yield:

\[ ∆PV^F=-MoneyDur×∆Yield \]

Price value of a basis point

Another version of the money duration is the price value of a basis point (PVBP) which equals the change in full price given a one basis point change in the yield to maturity. It is also called PV₀₁ (and DV₀₁), i.e. price/dollar value of 01 bp. It is calculated as the difference between the bond price when yield decreases by one basis point (PV−) and bond price when yield increases by one basis point (PV+) divided by 2:

\[ PVBP=\frac{PV_- – PV_+}{2} \]

A related statistic is called basis point value which equals money duration multiplied by 0.0001.

Test

Which of the following is incorrect about money duration and price value of a basis point?

1. Money duration is a type of yield duration.
2. Money duration is calculated based on the flat price of the bond.
3. The price value of a basis point is also referred to as PV₀₁ and DV₀₁.

Show answer

B is correct. All yield calculations are based on the full price of the bond, i.e. price inclusive of accrued interest and not the flat price.

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A 10-year $1,000,000 par value zero-coupon bond currently priced at $630,000 would have a price value of a basis point of:

1. $601.48
2. $1,202.95
3. Insufficient information

Show answer

A is correct. The first step is to find the yield to maturity of the bond, which is 4.73%. Next, we need to decrease the yield by 1 basis point, i.e. to 4.72% to get a price of $630,601.87. Similarly, if we increase the yield by 1 basis point to 4.74%, the price would be $629,398.76. The price value of a basis point then equals $601.48 (=($630,601.87 − $629,398.76)/2).