You are working for an Australian corporate exporting goods to United Kingdom. Your supervisor asks you to estimate the potential hedging cost for a sale which will be settled in one year. You observe the following data from the international market: Spot RateExpected Future Spot RateInterest RateAUD/USD1.331.37AUD2%USD/GBP1.211.18USD3.50%GBP3%Assuming covered interest parity holds, what is the implied forward premium/discount of the pound relative to the Australian dollar from the bank’s quote?
Question
You are working for an Australian corporate exporting goods to United Kingdom. Your supervisor asks you to estimate the potential hedging cost for a sale which will be settled in one year. You observe the following data from the international market: Spot RateExpected Future Spot RateInterest RateAUD/USD1.331.37AUD2%USD/GBP1.211.18USD3.50%GBP3%Assuming covered interest parity holds, what is the implied forward premium/discount of the pound relative to the Australian dollar from the bank’s quote?
Solution
To calculate the implied forward premium/discount, we first need to calculate the forward rate using the formula for covered interest parity:
F = S * (1 + i_d) / (1 + i_f)
where: F is the forward rate S is the spot rate i_d is the interest rate of the domestic currency (in this case, AUD) i_f is the interest rate of the foreign currency (in this case, GBP)
First, we need to convert the AUD/USD and USD/GBP spot rates to AUD/GBP:
AUD/USD = 1.33 USD/GBP = 1.21
So, AUD/GBP = AUD/USD * USD/GBP = 1.33 * 1.21 = 1.6093
Next, we plug the values into the formula:
F = 1.6093 * (1 + 0.02) / (1 + 0.03) = 1.6093 * 1.02 / 1.03 = 1.5935
The expected future spot rate is given as 1.37.
The forward premium/discount is calculated as (F - E(F)) / E(F), where E(F) is the expected future spot rate.
So, the forward premium/discount = (1.5935 - 1.37) / 1.37 = 0.1632 or 16.32%
Therefore, the pound is at a forward premium of 16.32% relative to the Australian dollar from the bank’s quote.
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