Duration Measures

LOS

69.e. distinguish among the alternative definitions of duration, and explain why effective duration is the most appropriate measure of interest rate risk for bonds with embedded options;


DURATION MEASURES
 Macaulay Duration: The weighted average time to full recovery of principal and interest payments.

= [ΣC_t*t/(1+i)^t]/[ΣC_t/(1+i)^t]

 Characteristics of Macaulay Duration:
1. The duration of a bond with a coupon is always less than the term to maturity.
2. The larger the coupon, the smaller the duration.
3. There is normally a positive relationship between term to maturity and duration. As term to maturity increases, so does duration, but at a decreasing rate.
4. There is an inverse relationship between the yield to maturity and duration.
5. Sinking funds and call features can reduce the duration significantly.



 Modified duration: an adjusted measure of duration called modified duration can be used to approximate the interest rate sensitivity of a noncallable bond. Modified duration equals Macaulay duration divided by 1 plus the current yield to maturity divided by the no. of payments in a year.

Modified Duration = Macaulay duration[1+(ytm/number of payments per year)]


 The percentage change in the price of a bond for a given change in interest rates can be approximated by:

100*ΔP/P = -D_mod*Δi

ΔP = change in price
Δi = change in interest rate
D_mod = Modified duration


For More
http://www.duke.edu/~charvey/Classes/ba350/bondval/duration.htm