Reading 29 - EOC 3
Summary of question:
Issue bond with 5M face value paying 2.5%xLIBOR. Use proceeds to purchase a bond with a fixed coupon rate of 7%. Enter into a swap where the dealer quotes a fixed rate of 6% and floating rate of LIBOR.
It asks you to calculate the arbitrage profit.
But in the solution it says to issue a floating rate bond with face value of 5M paying 2.5%xLIBOR and take the proceeds to purchase a fixed rate bond with face value of 2.5x(5M)=12.5M and paying a 6% coupon. Then enter into a swap with notional principle of 12.5M where you pay 7% and receive LIBOR.
Doesn’t arbitrage imply no net negative cash flow at any period? But if you issue a bond for 5M and then purchase a bond for 12.5M it’s not arbitrage anymore?
Another question:
Reading 29 EOC 9
Where does the 4% come from in the solution if FS(2,5) < exercise rate?
I know this doesn’t help anyone who doesn’t have the text but any help is appreciated from those who do!
Face value is not equal to price. The question is assuming credit/default risk etc. is the same for all parties, so the yield achieved should be the same. Say the 12.5M nominal yielding L face value bond sells for $12.5m, the 5M nominal yielding 2.5L should sell for 2.5*5 = 12.5M
Sell 2.5L bond for 12.5M and buy fixed bond receiving 7%. Now each year you pay 12.5M*L and receive 12.5M * 0.07.
Buy a pay fixed swap for 12.5M @ 6%. In this you pay 12.5M*0.06 and receive 12.5M*L
Total net outlay = 12.5M - 12.5M = 0
Total annual net earings = 12.5M * 0.07 - 12.5M * 0.06 + 12.5M*L-12.5M*L = 12.5M * 0.01
I’ve assumed the price is 12.5M but we don’t know that, so total annual profit here is Price * 0.01.
I’ve just had a look at that question 9, and the 4% is an example. The question is asking what would happen is the swap rate at expiry is now cheaper than the swaption rate. In this case, don’t exercise the swaption, enter into a swap at the new rate. The answer has given an example of 4%, but it could be anything less than 5%.
P.S - I feel this is a terribly worded question.“If FS(2,5) is below the exercise rate” to me means if the payer swaption (2,5) rate of 5% is below the new swap rate, which means the swap should be entered into. In fact it means if the new rate is below the entered into rate.
That makes a lot more sense. Thanks a lot mattmania. Hope your studies are going well.