Modified duration is a measure of the price sensitivity of a bond to yield-to-redemption movements. In Math terms, it represents the first-order derivative of a price function from the yield. It is important to note that modified duration shows volatility not of the net price, but of the full price inclusive of AI
. Its connection with duration can be proved by the formula:
MD – modified duration
D – Macaulay duration
r – yield-to-maturity
With small values the equation will be as follows:
P – price (inclusive of AI)
P – price change
r – yield change
Suppose modified duration equals 4, the bond is traded at a price of 90% and yield of 8%, AI
is 0. How will the price change if the yield grows to 8.5% (by 0.005%).
Price movement can be calculated the following way: -4*0.005*90 = -1.8. I.e. the bond price will decrease by 1.8 to 88.2%.