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?
- Money duration is a type of yield duration.
- Money duration is calculated based on the flat price of the bond.
- 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.
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:
- $601.48
- $1,202.95
- 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).