# Duration

1. Define the duration of a bond and discuss its uses
2. Why modified duration is a better measure than maturity when calculating the bond’s sensitivity to change in interest rates
3. Define convexity and explain how modified duration and convexity are used to approximate the bond’s percentage in price, given a change in interest rates

Bond: Price-yield relationship
1. Basic concept: price, yield to maturity, current yield, capital yield, coupon.
Yield to maturity= (current yield+ capital yield)
(Current yield=coupon /current price)
2. Interest rate sensitivity (how interest rate change can affect bond price)-(detailed explanation on PP514, TEXT BOOK)
1) YTM-Price
2) YTM-Price (change rate)
3) Maturity-Interest rate sensitivity
4) Maturity-Interest rate sensitivity (change rate)
5) Coupon- Interest rate sensitivity
6) Current yield-interest rate sensitivity
1)-5): Malkiel’s bond pricing relationship
6): Homer and Martin (1972)
3. Duration (linear approximation of price yield relationship)
a. Why use duration (Pros):
(1) Simple, effective
(2) Tool of immune portfolio
(3) Measure interest rate risk
i. Maturity is the main determinant of bond risk, while time to maturity is not a perfect measure of long term/short term nature, therefore it is important to apply a more accurate one.
ii. Duration is proportion to the price change, but maturity is not.
b. Definition:
Macaulay Duration:
* As a effective maturity concept, weighted average of the time to each coupon or principle payment made by the bonds.
* This form of duration measures the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments received in the future
Modified Duration:
* This measure expands or modifies Macaulay duration to measure the responsiveness of a bond’s price to interest rate changes. It is defined as the percentage change...