# Forward rate lower than IRP, how to arbitrage?

Bowman begins his task by gathering the following current market statistics: 1 year U.S. Interest Rates = 8% 1 year U.K. Interest Rates = 10% 1 year /₤ forward rate = 1.70 Current /₤ spot rate = 1.85 Bowman knows that if the forward rate is lower than what interest rate parity indicates, the appropriate strategy would be to borrow: A) pounds, convert to dollars at the forward rate, and lend the dollars. B) dollars, convert to pounds at the forward rate, and lend the pounds. C) dollars, convert to pounds at the spot rate, and lend the pounds. D) pounds, convert to dollars at the spot rate, and lend the dollars. For some reason I can’t seem to understand the logic behind this. I’d appreciate a walk through of the intuition behind the process. I didn’t post the answer in case anyone wants to take a shot…i’ll post it in a bit. Thanks all.

D? You can this three ways: 1) do the math, 2) memorize the forumla/relationship, 3)think your way through it. I can never remember the formula, so I do 3 and verify with 1 if I have time. So here’s how I think through it: IRP tells you that the forward rate should be 1.816 /P, when in fact the market rate is 1.7 /P. This tells you that the market is undervaluing P’s and overvaluing \$ in the forward market (it will only take \$1.7 to buy one pound when IPR tells you it should cost 1.816). Therefore you want to hold and convert to P at the market forward rate (think buy low, sell high. you want to sell your while they are overvalued). In order to do this, you borrower pounds, convert to today, lend dollars, and then convert them back at the forward rate.

i get D also.

i thought i had it, but i also got confused… sell pounds, invest in \$\$\$\$. sell forward the \$\$\$… i’d say D but i think it leaves out the final step… question is really unclear as to what you are actually trying to accomplish - lower borrowing costs??, arbitrage?, etc?? but the basic principle is almost exactly the same.

lol, you beat me to it! i was doing it by your # 1 to make sure it worked. you’d borrow pounds, convert them to \$USD at the spot and lend \$\$ so you borrow 100pounds, convert it to \$USD x 1.85 at the spot. you have 185 dollars. invest that in the US at 8% for a year (or here it says lend them i guess to pick that yield up?), you have \$199.8. convert it back at the fwd rate so divide by 1.7 = 117.529412 pounds. now, you borrowed those 100 pounds and you pay 10% interest so you pay back 110 pounds. looks to me like the arbitrage is 7.52 and change pounds. yes, no, even close on my calcs? these are easy to get turned around and backwards.

Banni - looks good to me.

Ozzy is correct…the answer is D. Thank you for explaining it that way…it makes sense now. I was so hung up on the implied UK rate i didn’t bother to think that 's were overvalued. Sell dollars now while they are overpriced and borrow UK as it's currently cheaper than the implied (~17%). I guess in practice you'd close the position when forward rates are back to IRP....since everyone else is doing this trade to devalue 's and bring the P’s back up, hence arbitrage. Appreciate it guys, thank you.