Suppose you buy four assets on February 1, 2018, hold them for one year, and then resell them on February 1, 2019 if they have not matured. The four assets are:
i. a one year discount bond with face value of $1,000.
ii. a two year discount bond with face value of $1,000.
iii. a ten year coupon bond with a face value of $1,000 and a coupon rate of 10%.
iv. A consol bond with an annual coupon of $100.
(a) Calculate the price for each of the four assets on February 1, 2018 if the initial interest rate on that date is 10 %. [Hint about coupon bond: Think about the price of the coupon bond if the interest rate is equal to the coupon rate]
(b) Calculate the price for each of the four assets after one year on February 1, 2019 assuming that the interest rate has changed to 7.13 %. Do the same for 8.48%, 10%, 11.75% and 13.81%. [Hint: After one year, the 2 year and 10 year bonds have one year less time remaining to maturity. And, the one-year bond has no price because it matured]
(c) Compute the rate of return from holding each of the four assets for one year, under each of the five interest rate scenarios. [Remember to include capital gains/losses and coupon and face value payments]
(d) Which asset's rate of return is most sensitive to shocks to interest rates? Which asset is least sensitive to interest rate risk? Rank the four assets in terms of exposure to interest rate risk.