Question

12. a. How is “bond risk” measured?

b. If a bond has modified duration of 5, how will a 1% increase in interest rates affect the price?

Answer 1

a) A bond generally makes payment of coupon rate of interest at pre-defined intervals of time and finally the face value on maturity whether at par, discount or premium. There are also other kinds of bonds like zero coupon bonds and the like, but bonds in general are in the nature discussed above.

And risk of bond can be considered as the failure of the bond writer or seller to pay the interest or the principal (face value). And hence the bonds issued by various issuers are rated by several agencies, viz Standards and Poor, Moody's etc based on various factors, like performance, economic cycles, stability etc.

Generally bonds issued by US Government or any generally stable western government have the highest ratings. Treasury Bills are considered even risk free, but as usual carry very low rate of interest.

Duration of a bond, invented by F. Macaulay, also called Macaulay's duration, is used to measure the sensitivity of price of the bond to changes in interest rates, Albiet having it's limitations, duration did a good job in finding interest rate sensitivity based in the market expectations and return and risk free rate and comparing it with the coupon rate of the bond.

To compute Macaulay Duration, weighted average of the times to each coupon or principal payment made by the bond.

Modified duration is also used as a measure of sensitivity of price to the interest rate changes.

However both of them fail as they consider price and interest rate to have a linear relation when in actuality they have a kind of curvilinear relationship, so convexity is also used to measure the sensitivity to the interest rate changes. It measures the changes in duration in relation to the changes in interest rate.

b) If modified duration of a bond is x, that means the price of the bond moves -x% if the interest rate changes by 1%

So, if bond has modified duration is 5, for 1% increase in interest rates, the price of the bond would move -5% or it would decrease by 5%.