Consider investing in three different bonds. All maturity values are $100. All interest rates are expressed per annum with semi-annual compounding and coupons are paid semi-annually as in the US Treasury bond market.
Bond A: a 6-month zero-coupon bond. The current price is $99. Bond B: a 2-year coupon bond with 4 % coupon. Bond C: a 5-year zero-coupon bond.
The yield curve is currently flat.
1. Compute the yield to maturity on these bonds.
2. What must the price of the 2-year coupon bond (Bond B) be?
3. What is the price of the Bond C?
4. Compute the Modified durations of the three bonds.
[Note: bonds pay semiannual coupons and period of time is 6 months. You will calculate duration in half-years first, and then divide the result by 2 to find D in years. To find Modified Duration, divide Duration (in years) by (1+rate per year/2).]
5. Suppose you want to create a portfolio of bonds A and C with the same Dm as that of Bond B, what should the portfolio weights be?
6. You expect interest rates to increase by 50 bp (0.5%). What percentage price change does the Dm concept predict for the three bonds?
7. Given these percentage price changes, is there any advantage to being invested in Bond B, as compared to being invested in the portfolio of Bonds A and C as computed in part (5)?