Carry Trades: Annual interest rates are 2% in Japan and 8% in Australia

Japan Interest Rate = 2%

Australia Interest Rate = 8%

Investment Horizon = 90 Days

a)

As per Uncovered Interest Parity Theory (UIP), the difference in the interest rates of 2 countires would be exactly offset by the relative change in both the currencies over the same period. SImply put, it states that if in a country interest rates are higher (High Yielding Currencies) than other (Lower Yielding Currencies), then one can't just get higher rates by investing in other currency. This was because of the depreciation of the high yielding currency over the same period which will offset the excess returns earned by investor by investing in higher yielding currencies. Thus, higher yielding currencies are expected to depreciate as compared to lower yielding currenies as per the UIP theory.

Now, here,

Australia interest Rate (8%) > Japan Interest rate (2%)

Thus, we can say that AUD is a high yielding currency while JPY is a low yielding currency. Thus, as per UIP, JPY is expected to appreciate as compared to AUD over the 90 days period.

Now, As per UIP,

Expected Exchange Rate = Spot Rate * (1 + Australian Interest Rate / 4) / (1 + Japanese interest Rate / 4)

(Expected Exchange Rate / Spot Rate) - 1 = (1 + 8% / 4) / (1 + 2% / 4) - 1

Expected Appreciation = 1.49%

Thus, as per UIP, the expected appreciation in Yen is 1.49% over the 90 days period as compared to AUD.

b)

Depreciation in Yen = 2%

Required Appreciation for No profit in Carry trade = 1.49%

Thus,

P/L of Carry trade = Required Appreciation - Actual Appreciation

P/L of Carry trade = 1.49% - (- 2%)

P/L of Carry trade = 3.49%

Thus, Profit would be 3.49% in case of this carry trade. The actual profit would be more than that. It is rough multiplication.

Actual Profit / Loss of Carry Trade = (1 + Depreciation / (1 - Depreciation)) * (1 + AUD Interest Rate / 4) - (1 + Yen Interest Rate / 4)

Actual Profit / Loss of Carry Trade = (1 + 2% / (1 - 2%)) * (1 + 8% / 4) - (1 + 2% / 4)

Actual Profit / Loss of Carry Trade = 1.0204 * 1.02 - 1.005

Actual Profit / Loss of Carry Trade = 3.58%

Thus, actual profit / loss on carry trade would be 3.58%.

c)

An Arbitrage Profit is made when the profit is risk less i.e. the profit amount is fully certain and there can be no changes in that. But in this carry trade, the profit or loss depends on the situation of Yen and AUD. If the Yen appreciation would have been more than 1.49%, it would be a loss situation and if it would have been anything less than that, it would be a profitable situation. So, we can't say this situation to be a case of arbitrage as there are also chances of losses and even profits are not certain here. So, it was clearly not a case of arbitrage.