Question

Bond A has the following:
20 years left to maturity
7.5% Coupon Rate
Semiannual payments

Bond B has the following:
5 years left till maturity
7.5% Coupon Rate
​​​​​​​Semiannual payments

Both bonds are similar to each other in all other features and risk. If the current market rate of interest suddenly drops from 7% to 5%, which of these bonds will change more in value? Please show calculations of each bond valuation at 7% as well as 5% and compute percentage change in price to arrive at your answer. Also include a short paragraph explaining two kinds of interest rate risk.

​​​​​​​Thank you very much!

Answer 1

It is seen from above that Bond A changes more in value than Bond B for a given change in interest rate. This is due to a measure called Convexity. The convexity is the change in price for a given change interest rate and it is higher for longer duration bonds.

The two kinds on interest rate risk are Price risk and Reinvestment risk. Price risk is the change in Price of a bond which can change the underlying change in interest rates. A change in interest rate can also lead to non availability of opportunity to reinvest with the current investment rate.

Formulae

Formulae as above...