The yields on zero-coupon bonds of different maturities are:
Time to Maturity; Yield
2 years; 4%
5 years; 8%
10 years; 4%
You find the hump-shaped yield curve to be very surprising and expect that the yield curve will become flat.
1. Calculate the modied durations and convexities of the three bonds.
2. If you believe that the yield curve will atten out, but do not know whether the overall level of the yield curve will increase or decrease, which bond(s) do you short? Which bond(s) do you long? Provide an answer for all three bonds.
3. Construct a strategy using the 2yr, 5yr, and 10yr bonds that takes advantage of your view that the yield curve will atten out. Long or short $1000 in face value of the 5yr bond. The position should be nearly insensitive to level shifts in the yield curve, even shifts as big as 3 or 4%.
4. What is the value of your position if you're are right and yields in the 2- and 5-year bond stay the same but yield for the 10-year bond increases to 6%.