Question

Last week, the spot rate for Australian Dollars was 0.7306 USD/ 1 AUD. The 180-day (6 month) forward rate quoted in the market was for 0.7340 USD/1 AUD and the risk-free rate on 180-day securities was 2.90 percent APR for United States LIBOR and 1.96 percent APR for Australian LIBOR. (LIBOR rates are widely used as a reference rate for financial instruments.) Assume that the US is the home country.

Are the quotes for AUD above relative to the USD direct or indirect quotations?

Choose one: direct or indirect

Is the USD expected to appreciate or depreciate relative to the AUD given the forward rate quoted above?

Choose one: appreciate or depreciate

What is the implied forward rate if interest rate parity holds in this case? Does interest rate parity hold here? Use 4 decimal places for accuracy.

What is the Implied forward rate?

Which country’s risk free security offers the highest expected $ profit for a US investor, or are the $ profits the same?

Determine the $ profit for both investments using a beginning amount of 1,000 USD. What is the $ profit of US LIBOR and what is the $ profit for Australian LIBOR

Answer 1

Part 1: Direct/ Indirect quote

A currency pair (in this case USD/AUD) has two currencies involved in which one is the Base currency which is equal to a single unit in the quote and other is the quoted currency which gives the price of one unit of the base currency. In the given question, AUD is the base currency and USD is the quoted (price) currency implying that the price of one AUD is expressed in terms of USD.

Definition:

Direct quote: In a currency quote, when the domestic currency is the quoted (price) currency, it is a direct quote

Indirect quote: In a currency quote, when the domestic currency is the base currency, it is a indirect quote

In the given question, US is the home country, therefore, USD is the domestic currency. As explained above, when the domestic currency is the (quoted) price currency, it is a direct quote, therefore, given quote of 0.7306 USD / 1 AUD is a direct quote.

Part 2: USD is expected to appreciate or depreciate

Spot rate = USD 0.7306 / 1 AUD

Forward rate = USD 0.7340 / 1 AUD

Appreciation (Depreciation) of a currency A to currency B occurs if the price of the currency A in the future is lower (higher) than price of currency B.

In the given question, the forward market which implies expectations of the future has a higher rate of USD per AUD than the current spot rate, that is, 0.734 > 0.7306 implying that the USD is expected to depreciate relative to the AUD.

Part 3: Implied forward rate as per interest rate parity

Interest rate parity is the theory under which the difference in interest rates of the countries should be equal to the difference between their forward and spot rates.

Forward rate _(A/B) = Spot rate _(A/B) * Interest rate _(A) / Interest rate of _(B)

In this question, Currency A = USD and Currency B = AUD

Spot _(USD/AUD) = 0.7306

Since the provided rates are APR for a 180-day period, so the usable rates are:

Interest rate _(A) = 2.9% *180/360 = 1.45%

Interest rate _(B) = 1.96% * 180/360 = 0.98%

Forward rate _(A/B) = 0.7306 * 0.0145/0.0098 = 1.0810

Therefore, the forward rate implied by the Interest rate parity is USD 1.0810 / 1 AUD.

Since, the forward market quote (USD 0.734 / 1 AUD) is not equal to the forward rate implied by the Interest rate parity (USD 1.0810 / 1 AUD), Interest rate parity does not hold in this case.

Part 4: Implied forward rate

Implied forward rate is the difference between the forward market quote and spot quote adjusted for the period of the forward contract.

Implied forward rate = ((Forward rate_(A/B) / Spot rate_(A/B))^{(1/period of forward contract)}) - 1

= ((0.734 / 0.7306)^(1/180/360)) - 1

Implied forward rate = 0.93%