Hi, everyone.
Be careful with the Question ID: 724659 in the Schweser QBank.
If the one-year forward exchange rate is DC/FC 2 and the spot rate is DC/FC 1.9 when the foreign rate of return is 12% and the domestic return is 10%, which of the following statements would be most accurate? A) The arbitrage possibilities cannot be determined with the data given. B) Arbitrage is possible here, investors should borrow domestic, lend foreign. C) Arbitrage is possible here, investors should borrow foreign, lend domestic.
Narrative:
Question 1: Is there an arbitrage opportunity? If the result of the following formula (derived from rearranging the interest rate parity condition) is not equal to 0, there is an arbitrage opportunity. (1 + rdomestic) − [((1 + rforeign) × ForwardDC/FC)) / SpotDC/FC] = ? Here, ( 1 + 0.10 ) − [(( 1 + 0.12 ) × 2.0DC/FC) / 1.9DC/FC] = ( 1.10 − 1.18 ) = −0.08, which is not equal to 0. Arbitrage opportunities exist. Question 2: Borrow Domestic (local) or Foreign? Here are some “rules” regarding where to start the arbitrage (where to borrow). These rules only work if there are no transaction costs and only if the currency is quoted in DC/FC terms. Rule 1: If the sign on the result of question 1 is negative, borrow domestic. If the sign is positive, borrow foreign. Here, the sign is negative, so borrow domestic. Rule 2: (rd − rf) < (Forward − Spot) / Spot then Borrow Domestic (rd − rf) > (Forward − Spot) / Spot then Borrow Foreign Here, borrow domestic: (rd − rf) = ( 0.10 − 0.12 ) = −0.02 < (Forward − Spot) / Spot = ( 2.0DC/FC − 1.9DC/FC ) / 1.9DC/FC = 0.05 −0.02 < 0.05 Summary: To take advantage of arbitrage opportunities, borrow domestic and lend foreign.
The rule # 2 is false. Suppose, we have the following inputs: spot = 1.900, forward = 1.862, rdomestic = 10%, rforeign = 12%.
According to the rule # 2 we get (0.1 - 0.12) = (1.862 - 1.900) / 1.900 => -0.02 = -0.02, i. e. the choice is ambivalent.
However, if we apply the rule # 1, we’ll get 1.100 - 1.120 x 1.862 / 1.900 = 0.0024, i. e. we’d rather borrow in the foreign currency while lend in the domestic currency.