3. A company issues a leveraged floating-rate note with a face value of $5,000,000 that pays a coupon of 2.5 times Libor. The company plans to generate a profit by selling the notes, using the proceeds to purchase a bond with a fixed coupon rate of 7 percent a year, and hedging the risk by entering into an appropriate swap. A swap dealer provides a quote with a fixed rate of 6 percent and a floating rate of Libor. Discuss whether the company should enter into a swap involving paying fixed, receiving floating or paying floating, receiving fixed. Calculate the amount of the arbitrage profit the company can earn by entering into the appropriate swap. In your answer, indicate the cash flows generated at each step. Also explain what additional risk the company is taking on by doing the swap.
(Institute 407)
答案
Because the company has a floating-rate obligation on the floating-rate note, it should enter into a swap involving receiving a floating rate. Accordingly, the appropriate swap to hedge the risk and earn a profit would be a pay-fixed, receive-floating swap. Let Libor be L. Cash flows generated at each step are as follows:
Issue leveraged floating-rate notes and pay coupon =
L(2.5)($5,000,000) = $12,500,000L
Buy bonds with a face value = (2.5)($5,000,000) = $12,500,000
Receive a coupon = (0.07)($12,500,000) = $875,000
Enter into a pay-fixed, receive-floating swap:
Pay = (0.06)(2.5)($5,000,000) = $750,000
Receive = L(2.5)($5,000,000) = $12,500,000L
Net cash flow = –$12,500,000L + $875,000 – $750,000 + $12,500,000L = $125,000
疑问：关于这个leveraged floating rate我还是不太理解，是不是这样的：一上来发行这个leveraged notes比如说融资100元，libor是1%，那么他实际支付利息是2.5%（2.5倍libor）即，2.5元，然后他购买一个固定利率债券，面值是250元，但价格是100元，收到固定利率7%，即17.5元，然后他又做了一个付固定收浮动的swap，名义本金250元？
面值250，价格100，这样的债券实际存在吗，为什么本来本金是100元，后面所有的交易都可以达到名义本金250？他全部的交易和他一开始就发行一个面值250，利率是1倍libor的普通债券差别在哪里？
