Arbitrage question for FX

Would anyone be kind enough to go through the process of explaining to me how you derive, step-by-step an arbitrage profit here: The Eur currently trades at \$1.0231. The USD rfr is 4% and the Eur rfr is 5%. 6 mths fwd contracts are quoted at \$1.0225. Thank you,

The risk free rate is greater in europe, so the Euro should depreciate (it will take less dollars to buy 1 euro). The arbitrage free exchange rate in 6m would be 1.0231 X (1-[(0.05-0.04)/2]) = \$1.018 The euro is more expensive thru the forward than it is thru the arbitrage, hence, you buy it thru the arbitrage and you sell it thru the forward Now: You start with \$1 1) You go short thru the forward contract (you enter into the obligation to sell euros in 6m) 2) You buy 0.9774 euros. 1/1.0231 = 0.9774 3) You invest for 6 month In 6 months: 1) You collect 0.9774 X 0.05/2 = 0.0244 euros of interest. You now have 0.9774 + 0.0244 = 1.0018 euros 2) You sell these euros theu the forward contract and you get 1.0244 dollars. 1.0018 X 1.0225 = 1.0244 You had a return of 4.88% (annualized), which is more than the US risk free rate. If you would have borrowed the original buck, you would have had to pay \$0.02 of interest. You would be left with 0.0044 pure arbitrage profit. That may not sound like much, but if you did it with \$1million, you would be left with \$4,400 of pure arbitrage profit.

I found the answer in the Q-BANK—0.004399 for 1 investment but maybe it’s wrong.

cfafrank Wrote: ------------------------------------------------------- > I found the answer in the Q-BANK—0.004399 for \> 1 investment but maybe it’s wrong. This is correct. See my explaination. I’ve round it to 0.0044

Geez, we will not tolerate such sloppiness. You were off by \$0.000001 due to egregious rounding.

olivier Wrote: ------------------------------------------------------- > cfafrank Wrote: > -------------------------------------------------- > ----- > > I found the answer in the Q-BANK—0.004399 \> for \> \> 1 investment but maybe it’s wrong. > > > This is correct. See my explaination. I’ve round > it to 0.0044 Mr. JoeyD said you should be punished because of this.

Thank you Olivier.