 # arbitrage opportunity

Assume that there are no transaction costs and that securities are infinitely divisible. If an 8 percent coupon paying bond (with semi-annual coupon payments) that has six months left to maturity trades at 97.54, and there is a zero-coupon bond with six months remaining to maturity that is correctly priced using a discount rate of 9 percent, is there an arbitrage opportunity? A) No, the coupon bond is correctly priced. B) Yes, the coupon bond price is too low. C) Yes, the coupon bond price is too high. D) The coupon bond is not correctly priced but no arbitrage trade can be set up using the zero-coupon bond.

C) Yes, the coupon bond price is too high. I went about this as For the 0 coupon bond N=1, I/Y=4.5, PMT=0, FV=100, PV=? PV=95.69 For the 8% coupon with 6 months left–it is 97.54 so coupon bond is priced higher.

B) coupon bond should be priced at 104/1.045=99.52 > 97.54

CPK, Did you take into account that the coupon bond still has an additional coupon payment at maturity? I would agree more with B

I second maratikus, if you buy @ 97.54 and get 104 the HPR is 6.62% => price on the coupon bond too high

doesn’t the fact that the coupon bond is priced at 97.54 take into account the fact that a coupon is still left to be paid…?

If zero coupon is priced correctly, it will yield 9%? Solving for I/Y on the coupon bond is 6.62%, therefore coupon should be higer to improve the yield. C, price should be lower

Here is the given answer (which I am having a hard time wrapping my head around): Your answer: D was incorrect. The correct answer was B) Yes, the coupon bond price is too low. The coupon bond has a cash flow at maturity of 104, which discounted at 9% results in a bond price of 99.52. Therefore, the bond is underpriced. An arbitrage trade can be set up by short-selling 1.04 units of the zero-coupon bond at 99.52 and then using the proceeds to buy 1.02 units of the coupon bond. The arbitrage profit at maturity calculated as follows: Arbitrage Profit = 1.02 x 104 – 1.04 x 100 = \$2.08 I knew it was mispriced, but I totally blew the arb opp

.

100 + 4 coupon at the end… par = 100

Yeh i went for B aswell… the price of the coupon bond (97.54) cant be compared to the price of the zero-coupon bond (95.69) since they have different cash flows (104 vs 100)

how did they setup the arbitrage opp again? Im lost in that explanation. Why would i want to short sell

ancientmtk Wrote: ------------------------------------------------------- > how did they setup the arbitrage opp again? Im > lost in that explanation. Why would i want to > short sell I think for arbitrage, you short the overpriced and buy underpriced asset. The value of zero coupon bond is 95.69 discounted from 100. Short 1.04 * 95.69 = 99.52. You can buy 1.02 share coupon bond with the proceed. 99.52 / 97.54 = 1.02

B for me as well

>Assume that there are no transaction costs and that securities are infinitely divisible. And that there are no funding costs, no margin requirements, you live in cloud cuckoo land… etc…