Question

With $2,000,000 to invest, a spot rate of 71.635kr/$, a three-month forward rate of 72.9127kr/$, an expected spot of 70kr/$, a US$ three-month interest rate of 4.80%, and an Icelandic krona three-month interest rate of 12.020%, using uncovered interest arbitrage, can a position yield a return in excess of 4%?

No, it is not possible.

Yes, the yield is 4.21%

Yes, the yield is 4.80%

Yes, the yield is 5.41%

Answer 1

Answer is: Yes, the yield is 4.21%.

For uncovered interest arbitrage, we need to borrow low interest rate currency and invest this in high interest rate currency by converting it with spot exchange rate. in uncovered interest arbitrage, we don't use any forward or futures to hedge currency exchange risk. so, we will not use three-month forward rate of 72.9127kr/$ in the yield calculation.

So, we will borrow $2,000,000 at 4.8% interest for 3-months. then convert it to Icelandic krona using spot exchange rate of 71.635kr/$. invest this Icelandic krona at 12.020% for 3-months and convert it back to dollars using expected spot rate of 70kr/$.

Interest on dollar loan for 3-months = ($2,000,000*4.80%)*3/12 = $288,000/12 = $24,000

Amount of Icelandic krona to be invested = $2,000,000*71.635kr/$ = 143,270,000 Kr

interest earned on investment = (143,270,000 Kr*12.020%)*3/12 = 17,221,054 Kr*3/12 = 4,305,264 Kr

Total value of investment = investment value + interest earned = 143,270,000 Kr + 4,305,264 Kr = 147,575,264 Kr

now convert this total value of investment back to dollars using expected spot rate after 3-months.

Total value of investment in dollars = 147,575,264 Kr/70kr/$ = $2,108,218

Net return in dollars = Total value of investment in dollars - dollar loan interest = $2,108,218 - $24,000 = $2,084,218

Yield on investment = (Net return in dollars/amount borrowed) - 1 = ($2,084,218/$2,000,000) - 1 = 1.0421 - 1 = 0.0421 or 4.21%