Problems

• Consider the following Bond Structure

Face Value Interest Rate (%)

Maturity (Years)

Current Price

100000 0 1 91000

100000 10.5 2 99000

100000 11 3 99500

100000 11.5 4 99900

Solutions

• r1 = 9.89%

• r2 = 12.41% (1 year forward rate)

• r3 = 11.51% (2 year forward rate)

• r4 = 12.78% (3 year forward rate)

Interest rate Sensitivity

• Consider a bond whose with Coupon 10% and maturing in 1 year and FV of 100. Its current market price should be:– 110/1.1 = 100– If the required YTM is 9% then 110/1.09 =100.92– If the required YTM is 11% then 110/1. =99.10– Increase in Bond price for 1% fall in YTM is 0.92– Decrease in Bond price for a 1% increase in YTM is

0.9

Interest rate Sensitivity

• There is an inverse relation between bond prices and yields

• An increase in yield causes a proportionately smaller price change than a decrease in yield of the same magnitude

• Prices of long term bonds are more sensitive to interest rates changes than prices of short term bonds

• As maturity increases, interest rate increases but at a decreasing rate

• Prices of low coupon bonds are more sensitive to interest changes than prices of high coupon bonds

Immunisation: A Hybrid Strategy

• As interest rates tend to change, bondholders are exposed to interest rate risk.– Price risk (Change in bond prices owing to interest

rate changes)– Reinvestment risk arising from the rate at which

interest income can be reinvested in future– Price risk and reinvestment risk move in opposite

directions

Lets understand the risk through some numbers

• I buy a 10 year 10% coupon bond at par value of 100.

• I sell the bond after two years. – If at the point of sale interest rates hadn’t changed

then I can sell for Rs100– If at the point of sale interest rates had increased

(say to 12%) then I can sell for Rs90.06– If at the point of sale interest rates had decreased

(say to 8%) then I can sell for Rs111.49

How does the Bondholder immunise this risk

• Simple!• Choose a bond whose duration is equal to the

investment horizon• Changes in interest rates, losses (or gains) in

capital values will be offset by gains (or losses) on reinvestments

• As a manager you will have to manage by equating the duration of the portfolio of asset with that of the liability

Interest rate Swaps

• An interest rate swap is a transaction involving an exchange of one stream of interest obligations for another.– Exchange Fixed and Floating– Exchange on Floating rate with another– Swaps are interest rate risk mitigating strategies

Next Class

• Equity Valuation