Modified duration

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%.
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