The following U.S. Treasury bonds pay coupons semi-annually and have a face value of $1,000 (the coupon rate in the table is the annual coupon rate).

Bond	Maturity	Coupon	Price
A	6 months	8%	$936.00
B	12 months	6%	$871.60

The cash flow of the bond is

Bond	6 months	12 months
A	1040
B	30	1030

1. Using the principle of no arbitrage, calculate the prices of one-dollar zero-coupon bonds that mature in 6 and 12 months. That is, fill in the missing prices in the following table. [Hint: these prices are the same as the 6- and 12-month discount factors]

Bond	Price	6 months	12 months
Z1		1	0
Z2		0	1

b. There is another U.S. Treasury bond with the following cash flows. Show that there is an arbitrage opportunity. Should you buy or sell Bond C to take advantage of the arbitrage?

Bond	Price	6 months	12 months
C	$1,249.21	$496.50	$978.50

c. How would you trade to take advantage of the arbitrage opportunity? That is, describe the portfolio of bonds A and B that can be used to offset the future cash flows generated by trading 1 unit of bond C. How much would you earn from trading 1 unit of bond C?

Bond	Units	Today	6 months	12 months
A
B
C
Net