3 You are given the following information: Spot exchange rate (AUD/EUR) One-year

Question

3 You are given the following information: Spot exchange rate (AUD/EUR) One-year forward rate (AUD/EUR) One-year interest rate on the Australian dollar One-year interest rate on the euro 1.60 1.62 8.5% 6.5% (a) Calculate the forward premium and interest differential to show whether there is any violation of CIP? 5 (b) Explain the rule of thumb to make covered arbitrage profit. What strategy should apply so that you can make profit on covered arbitrage? 10 (c) Calculate the interest parity forward rate (AUD/Euro) and compare it with the actual forward rate (AUD/Euro). Calculate interest parity and actual forward rates in euro per one Australian dollar. 5 (d) If arbitrage is initiated, suggest some values for the interest and exchange rates after it has stopped and equilibrium has been reached. 10

Explanation / Answer

(a)

Spot Exchange Rate = 1.6 USD/EUR, Forward Exchange Rate = 1.62 USD/EUR.

Australian One Year Interest Rates = 8.5% and Euro One Year Interest Rate = 6.5%

The Ausrtalian currency is assumed to be the domestic currency and European currency is assumed to be the foreign currency so that the given exchange rates are in the direct quote format.

Let the future expected spot rate calculated using the CIP be F.

Therefore, by CIP or Covered Interest Parity we get

F = 1.6 x (1+0.085) / (1+0.065) = 1.63 AUD/EUR

Therefore, the forward premium = Future Expected Spot Rate - Current Spot Rate = 1.63 - 1.6 = 0.03 and Interest Rate differential is 0.085 - 0.065 = 0.02 or 2 percentage points.

Although the actual forward premium = 1.62 - 1.6 = 0.02 which is equal to the interest rate differential, in reality the interest differential is only an approximation of the forward premium (or discount).Also the future spot rate calculated using the CIP is assumed to be the correct (one that ensures no abritrage profits) forward exchange rate.

Since the CIP rate of 1.63 AUD/EUR is different from the stated rate of 1.62 AUD/EUR the CIP principle is definitely violated.

(b) The general strategy to execute a covered interest arbitrage would be as given below:

NOTE: We have used the spot rate, forward rate and interest rate values given in the problem to illustrate the process of covered interest arbitrage. Also, bid-ask spread has been ignored and lending borriwng rates have been assumed to be equal.

Borrow 1000 EUR at the european interest rate of 6.5%.This borrowing would create a liability of 1000 x (1.065) = 1065 EUR after one year.

Convert the 1000 EUR at the spot exchange rate of 1.6 AUD/EUR into AUD. The proceeds received after conversion would be 1000 x 1.6 = 1600 AUD.

Lend the 1600 AUD at the Australian Interest Rate of 8.5%.

After on year the lent money becomes 1600 x (1.085) = 1736 AUD

The lending proceeds will be received back and converted into euros at the forward rate of 1.62 AUD/EUR. This proceed becomes 1736 / 1.62 = 1071.6 EUR

This amount will be used to payoff the original euro loan of 1000 EUR which has now become 1065 EUR owing to the european interest rates.

Amount left after repaying borrowing principal and interest = 1071.6 - 1065 = 6.60 EUR

This amount left is a riskless profit made and hence is an arbitrage profit.

(c) The Interest Parity Forward Rate is 1.63 AUD/ EUR as calculated in part (A). The actual forward rate of 1.62 AUD/EUR is mispriced and can be exploited to make arbitrage profit as demonstrated in part (B).

Spot Rate in AUD = 1 / 1.6 = 0.625 EUR/AUD

Therefore, interest parity forward rate = 0.625 x (1.065 / 1.085) = 0.6135 EUR/AUD

Actual Forward Rate in AUD = 1/1.62 = 0.6173 EUR/AUD

(d) If arbitrage is initiated, the value of the forward exchange rate at which it would stop is 1.63 AUD/EUR, the exchange rate calculated using the CIP formula. If the exchange rate were to go above this value a similar riksless profit making venture is possible, just that the initial borrowing will have to made at AUD (in place of EUR) and the same process repeated as discussed in part (B).The same exchange rate can be also quoted as (1/1.63) =0.6135 EUR/AUD.

In order to calculate the interest rate (for Europe) which would reduce riskless CIP arbitrage profit to zero one needs to do the following:

Let the required euro interest rate be r

Hence, when 1000 EUR is borrowed the amount becomes a liability of 1000 x (1+r) EUR after on year.

1000 EUR converted at spot rate to AUD and lent at 8.5% becomes 1000 x 1.6 x 1.085 = 1736 AUD

When converted to EUR at the quoted (and not CIP) spot rate of 1.62 AUD/EUR we get (1736 / 1.62) = 1071.6 EUR

This euro value should equal the euro borrowing liability so as to remove the CIP arbitrage profit.

Therefore, 1071.6 = 1000 x (1+r)

r = (1071.6 / 1000) - 1 = 0.0716 OR 7.16 % for Europe

Repeating the same process for an initial borrowing of 1600 AUD (for ease of calculation) the required AUD interest rate can be calculated as given below

Amount borrowed in AUD and lent at the EUR interest rate becomes = [1600 / 1.6] x 1.065 = 1065 EUR

This when converted at the qoted forward spot rate becomes 1065 x 1.62 = 1725.3 AUD

This should equal the liability created by the initial AUD borrowing of 1600 AUD to avoid riskless CIP arbitrage.

Let the Australian Interest Rate be r

Therefore, (1+r) x 1600 = 1725.3

r = [1725.3/1600] - 1 = 0.0.783 OR 7.83 % (for Australia)

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