Economics - Interest rate/forward rates

[CFAHouston]

Suppose that the current interest rates in the U.S. and Japan are 13.665 percent and 8.5000 percent, respectively. Also, the spot rate for the dollar is 1.1975 US$/Yen, and the 1-year forward rate is 1.2545 US$/Yen. If $100 is invested, what is the total arbitrage profit that a U.S. investor could earn?

A) $23.06700.

B) $5.70000.

C) No arbitrage profit can be made.

D) $0.23067.

 

[satyaa]

I think the answer is (C).

F = S * (1+domestic rate) / (1 + Foreign Rate)

or (1 + Domestic Rate) = F * (1 + Foreign Rate)/(Spot Rate)

1.13665 = 1.2545 * (1.085)/1.1975

1.13665 = 1.136645

So, no arbitrage

 

[cheredayko]

I agree with satyaa - no arbitrage profit.

However, if interest rate in U.S. were 14% (instead of 13.655% as indicated in the question), then using interest rate parity formula (see above at satyaa), the 1-year forward rate would be 1.2582$/yen - cheaper dollar.

Then borrow yen in Japan, buy dollars at spot rate, put them in deposit for 1 year in U.S., then sell dollars for yen and pay back initial loan:

1,000 yen --> 835$ ---> deposit
in one year 952$ ---> 1,197.79 yen - 1,085 yen (paying back loan) = 113 yen arbitrage profit