# Arbitrage pricing

There is a Schweser question at the end of LOS36 that I am really confused on.

Bond Issue [Maturity] Coupon Par () Price ()

Bond A: [2 years] 10% \$1,000 1,170.12

Bond B: [1 year] 0% \$1,000 985.22

Bond C: [2 years] 0% \$11,000 10,667.28

It gave the above information, and also that the yield curve is flat at 1.50%. Then it proceeded to ask if you are able to make an arbitrage gain by selling 1 Bond A and simultaneously purchasing 10 Bond B and 10 Bond C. How do I solve for this?

You’re trying to equate the future cash flows.

I believe that you want to buy only 1 bond C, not 10.

I believe it says 10, but I’ll check and update.

@s2000magician it says 10… idk what to do.

It’s wrong.

You should sell 10 A bonds, buy 1 B bond, and buy 1 C bond.

The net cash flow today is +\$11,701.20 from the A bonds, −\$985.22 from the B bond, and −\$10,667.28 for the C bond, or +\$48.70.

The net cash flow in 1 year is −\$1,000 from the A bonds and +\$1,000 from the B bond, or \$0.

The net cash flow in 2 years is −\$11,000 from the A bonds and +\$11,000 from the C bond, or \$0.

Yes ran into that in the reading. I think the 10 is a typo, like S2000 said.

CFready, the way I solved for it is that you know either bond A or Bond B has to be a factor of 10, because Bond C is 10x more. Alternatively, bond A and bond B could both be a factor of 10 and you could have 2 of bond C. Then I just plugged in numbers brute force and see which one produces a profit. Maybe that way is slowest but it actually isnt too bad. And its easier because you have multiple choice so you just have to try 3 calcuations.

For example:

• Buy 10A, sell 1B sell 1 C ==> no profit
• Sell 1A, buy 10B, sell 1 C ==> no profit