USD/INR spot is 83.00, one-year rupee rates 7% and dollar rates 5%, and the one-year forward is quoted at 85.50. Is that consistent with covered interest parity, and if not, build the arbitrage for USD 10 million.

Parity puts the forward at about 84.58, so 85.50 is too high and the arbitrage is to sell dollars forward against dollars you hold. Borrow Rs 83 crore at 7%, buy USD 10 million at 83, invest it at 5% to have USD 10.5 million in a year, and sell that forward at 85.50 for Rs 89.775 crore. Repay Rs 88.81 crore. The difference, about Rs 96.5 lakh, is locked on day one with no exchange rate exposure.

Two routes to the same destination must cost the same or someone will take the cheaper one and sell the dearer. Rs 83 invested for a year at 7% becomes Rs 88.81; one dollar invested at 5% becomes USD 1.05; the forward that makes the two equal is 88.81 over 1.05, about 84.58. That is covered interest parityThe condition that the forward exchange rate equals spot adjusted for the two interest rates, so that borrowing in one currency and lending in the other, with the exchange risk covered forward, earns nothing.. A quote of 85.50 says a dollar in a year costs more rupees than its interest advantage justifies, so the dollar is overpriced forward, and the trade is to be a seller of dollars forward and a holder of dollars now.

Write the loop so that every leg is covered. Borrow Rs 83 crore for one year at 7%, owing Rs 88.81 crore; buy USD 10 million spot at 83; place the dollars for one year at 5%, which returns USD 10.5 million; and sell exactly USD 10.5 million forward at 85.50, which will bring in Rs 89.775 crore. In a year the forward settles, the rupee loan is repaid, and the bank keeps Rs 96.5 lakh. Nothing in the loop depends on where spot is in a year, which is what makes it an arbitrage and not a bet.

In practice the quote would not survive a minute, so the interviewer wants the frictions that let small gaps persist. Bid-offer in spot, forward and both deposit markets eats part of the rupee; the rupee borrowing uses the bank's balance sheet and liquidity lines; the forward and the deposit both carry counterparty exposure for a year; and onshore rupee funding is not freely available to every participant, which is why onshore and offshore forwards can differ. A gap of almost a rupee would still be traded. Say the limits: the rates are simple annual, so a quoted money-market rate on a different day count would move the parity forward by a few paise, and the arbitrage as written assumes the same rate for borrowing and lending in each currency.