Question

Bond price Maturity we find the following Treasury bonds and their prices 5980 2 years 1 year 51 000 $100 10% $100 Coupon rate al Compute the YTMs for the above three bonds b) Suppose that we need the above coupon bond for your cash requirements. However, due to some reasons, we cannot buy the coupon bond. Therefore, instead of the coupon bond, we decide to buy 1 year and 2 year zero coupon bond. If this alternative investment has the same cash flows as the coupon bond, how many bonds we need to buy lie., XX 1 year bonds and CO 2 year bonds)? What is the cost for this alternative bond investment? c) Using your work in question b), is there an arbitrage opportunity? If any, how can we transact for arbitrage? Compute the arbitrage profits for this question, we can assume that we can transact the coupon bond.)

Answer 1

a) YTMs for the 3 bonds:

Price = Coupon/(1+y) + (Coupon + Principal)/(1+y)2 , where y = YTM of the bond

Bond 1: 980 = 100/(1+y) + 1100/(1+y)2 and Solving for y, we get y = 11.1705%

Bond 2: 98 = 100/(1+y) and Solving for y, we get y = 2.04%

Bond 3: 96 = 100/(1+y)2 and Solving for y, we get y = 2.0621%

b) Let’s value this by creating a replicating portfolio. That is, let’s buy some amount of each bond so that the cash flows of our portfolio exactly match the cash flows of the coupon bond. The number of bonds we need to buy are:

	Periodic Cash Flows	Cost
Year	1	2
Coupon Bond	100	1100	$980
	Replicating Cash Flow
1 unit of Bond XX	100	-	1 x 98 = $98
11 unit of Bond OO	-	1100	11 x 96 = $1056
Total Cash Flow	100	1100	$1154

1 unit of Bond 2 and 11 unit of Bond 3 has same cash flow as coupon bond

c) The Coupon bond is under valued relative to the replicating portfolio. To take advantage of the arbitrage opportunity buy the coupon bond and sell the replicating portfolio.

	Periodic Cash Flows
	0	1	2
Buy Coupon Bond	-$980	+$100	+$1100
Replicating Bond
Sell 1 unit of Bond XX	+$98	-$100)	-
Sell 11 unit of Bond OO	+$1056	-	-$1100
Total Cash Flows	$174	0	0

Arbitrage profit = $1056 + $98 - $980 = $174