The money duration of a bond is a measure of the price change in units of the currency in which the bond is denominated, given a change in annual yield to maturity.
Money Duration = AnnModDur x PVFULL
ΔPVFULL≈ -MoneyDur x Δyield
Consider a bond with a par value of $100 million. The current yield to maturity (YTM) is 5% and the full price is $102 per $100 par value. The annual modified duration of this bond is 3. the money duration can be calculated as the annual modified duration (3) multiplied by the full price ($102 million): 3 x $102 million = $306 million. If the YTM rises by 1% (100 bps) from 5% to 6% the decrease in value will be approximately $306 million x 1% = $3.06 million. If the YTM rises by 0.1% (10 bps), the decrease in value will be $306 million x 0.1% = $0.306 million.
An important measure which is related to money duration is the price value of a basis point (PVBP). The PVBP is an estimate of the change in the full price given a 1 bp change in the yield-to-maturity. The formal equation is given below.
where PV_ and PV+ are full prices calculated by decreasing and increasing the YTM by 1 basis point.
A quick way of calculating the price value of a basis point is to take the money duration and multiply by 0.0001. For example, if the money duration of a portfolio is $200,000 the price value of a basis point is $200,000 x 0.0001 = $20. (1 bp = 0.01% = 0.0001)
Example 13: Calculating money duration of a bond
A life insurance company holds a USD 1 million (par value) position in a bond that has a modified duration of 6.38. The full price of the bond is 102.32 per 100 of face value.
Example 14: Calculating PVBP for a bond
Consider a $100, five-year bond that pays coupons at a rate of 10% semi-annually. The YTM is 10% and it is priced at par. The modified duration of the bond is 3.81. Calculate the PVBP for the bond.
Money duration = $100 x 3.81 = $381.00
PVBP = $381 x 0.0001 = $0.0381