Question

1. It is the end of September and the current AUD/USD exchange rate is 1.9230, the Australian and US three-month interest rates are 6 and 4.5% p.a. respectively. A forecast indicates that the exchange rate at the end of the year will be 1.8750.

(a) What would you do on the basis of this information? (b) If the actual exchange rate turns out to be 1.9370, calculate the percentage forecasting error. (c) Is there an error of direction in this forecast? (d) What is the outcome of acting on this forecast? (a) The forecast indicates that the US dollar would depreciate by 2.5%, making it an opportunity to take a short position on the currency. By borrowing US dollars at 4.5% or 1.125% for three months and investing in Australian assets for three months at 1.5%, the expected net return will be 2.875% (the sum of the interest differential and the percentage change in the exchange rate). (d) The exchange rate rose by 0.73%. PLS TELL ME HOW DID THE VALUES OF ANS (A) AND (D) ARRIVED PLS.... I NEED DETAILED WORKINGS PLS

Answer 1

(A)

The value of 1 USD earlier = 1.9230 AUD

The value of 1 USD later (as per the forecast) = 1.8750 AUD

We can clearly see from the above values that it is expected that the USD will diminsh in value over this period. Hence, as per the forecast, the USD would depreciate (value of 1 USD decreases) by = (1.9230 - 1.875)/1.9230 = 2.5%

We can borrow from the US markets at 4.5% annually or 4.5%/4 = 1.125% per quarter. Hence, we must pay back 1+(1.125%) = 1.0125 to the US lender at the end of the 3 months.

Similarly, we can borrow from the AUS markets at 6% annually or 6%/4 = 1.5% per quarter.

The interest rate differential is 1.5% - 1.125% = 0.375%. Hence, borrowing in the US markets is cheaper. However, we can gain from arbitrage only if (on borrowing in the cheaper market i.e. US and deploying it in an expensive market i.e. AUS) the depreciation of the borrowing currency does not wipe out the differential interest rate benefit.

Let's say we borrow 1USD (at 1.125% per quarter), buy 1.9230 AUD (current rates) and invest their to generate 1.9230*(1+6%/4) = 1.9518 AUD at the end.

Converting it back to USD at the forecast rate, we have 1.041 USD. After paying to the US lender, we have = 1.041 - 1.0125 = USD 0.0285

Therefore, the returns are 0.0285/1.0 = 2.85%

(D) Value of 1 USD at the beginning = 1.923 AUD

Value of 1 USD at the end of the period (as it actually turns out to be) = 1.937

We can clearly see that the USD has increased in value (it is worth more AUDs than it was in the beginning of the period). Hence, the rise = (1.937 - 1.923)/1.923 = 0.73%