Question

Mr Munzara is a currency arbitrager for BE Forward, Tokohama. The spot rate this morning is ¥111.22/$ and early indications are that short term interest rates in the USA, 90 – day rates, are about to rise from their current level of 3.125%. The central bank of USA, the Fed, is worried about rising inflation and has been publicly considering raising interest rates 25 basis points (0.25%). The 90 – day forward rate to Munzara by local Japanese banks are roughly the same at ¥111.14/$. The current 90 – day yen euro-deposit rate of interest is 2.156%. Mr Munzara has ¥800 million at his disposal.

(a) How can Munzara make a profit through covered interest arbitrage?


(b) How much in yen can he hope to make in profit in 90 days?


(c) If future spot exchange rates were determined by interest rate differentials alone (that is, if the forward rate was a very good forecast of future spot exchange rates), what would Munzara expect the spot rate to be in 90 days if the USA Federal Reserve Bank does the expected?


(d) If Munzara’s expectation of the future spot rate is that of part (c), what profit could he expect to make from uncovered interest arbitrage?

Answer 1

(a) Munzara can make a profit through covered interest arbitrage by following these steps:

1. Borrowing in yen: Munzara borrows ¥800 million from a Japanese bank at the current interest rate of 2.156% for 90 days.
2. Converting yen to dollars: Munzara converts the borrowed yen to dollars at the spot exchange rate of ¥111.22/$, which gives him approximately $7,188,893.23.
3. Investing in the US: Munzara invests the dollars in a US bank or financial instrument that offers an interest rate higher than the yen interest rate.
4. Converting back to yen: After 90 days, Munzara converts the matured investment and interest earnings back to yen at the 90-day forward rate of ¥111.14/$.
5. Repaying the yen loan: Finally, Munzara repays the yen loan, including interest, to the Japanese bank.

The difference between the amount received in step 4 and the amount repaid in step 5 represents the profit from covered interest arbitrage.

(b) To calculate the profit in yen, we need to consider the interest earned on the dollar investment. Assuming Munzara finds a US investment offering a 90-day interest rate higher than 2.156%, we can estimate the profit after 90 days by subtracting the yen loan repayment from the dollar investment and interest converted back to yen at the 90-day forward rate.

(c) If future spot exchange rates were determined solely by interest rate differentials, and assuming the forward rate is an accurate predictor, Munzara would expect the spot rate in 90 days to be ¥111.14/$. This expectation is based on the assumption that the interest rate differential between the US and Japan would be reflected in the forward rate.

(d) If Munzara's expectation of the future spot rate is ¥111.14/$, and he engages in uncovered interest arbitrage, it means he speculates on the future spot rate without covering his position. If the actual spot rate in 90 days turns out to be ¥111.14/$, there would be no profit or loss from uncovered interest arbitrage, as his speculation aligns with the spot rate.