You have borrowed money by selling a liability that requires that you make a $1,000,000.00 payment in exactly one year (at t = 1) and a $500,000.00 payment in exactly 2 years (at t = 2). With the money you raised with the sale of this liability, you are thinking about investing in the following two bonds.
Bond Coupon Rate Time to Maturity Payments per Year Face Value
1 8 % 4 1 $1000
2 0 1 0 $1000
Assume that you can buy fractions of these bonds. Also, for each bond there is a very active secondary market so you can sell them if you need cash. The current yield curve is flat at an effective annual rate of 6 percent and the rates apply to both your liability and to the above bonds. You expect that the yield curve will shift sometime between now (t = 0) and the first payment (at t = 1). You expect that it will either shift up to 7 percent or down to 5 percent. You don't expect any further shifts after that, however. Also assume that at any point in time (e.g., t = 1) there will always be a one-year zero-coupon bond for sale at the prevailing rate at that time.
Question:
1. What is the duration of your liability and of the two bonds?