Question

a) Given that annual inflation in the UK is 1.7%, annual inflation in the US is 1.81% and the current spot rate is S(GBP/USD) = 1.2644 what is the spot rate – S(GBP/USD) – in 12 months.

b) Explain what is meant by a fixed exchange rate regime.

c) The current spot rate for British pound to the Australian dollar is S(GBP/AUD) = $1.8717/£. Additionally the current spot rate for the British pound to the euro is S(GBP/EUR) = €1.1479/£.

i. Calculate the spot rate for Australian dollar to the euro S(AUD/EUR)

ii. Given that there is a broker in the market quoting S(GBP/EUR) = 1.200 demonstrate the potential arbitrage opportunity

Answer 1

a currency pair compares the value of one currency against another one and shows how much of the quoted currency is needed to buy one unit of the base currency. The base currency is always fixed at one unit, while the quoted currency (foreign currency) is the equivalence of one base unit when traded into the other currency.

GBP/USD = 1.2644 means, 1 GBP is trading for the equivalent of 1.2644 dollar . So our base currency = GBP and foreign currency = USD

a.

inflation rate - annual

UK =  1.7%, US = 1.81%

spot rate,S, = GBP/USD = 1.2644

Using the relative purchasing power parity, forward exchange rate can be calculated using the following formula:

f = S * [(1 + Id) /(1+If)] * n

Where,
f is forward exchange rate in terms of units of domestic currency per unit of foreign currency;
S is spot exchange rate, in terms of units of domestic currency per unit of foreign currency;
Id domestic inflation rate;
If is foreign inflation rate; and
n is Number of days per year for each currency (360, 365 or 366 depending on day-count convention). In our case we have to find the 12 -month forward rate. so n = 1 (i.e. 360 / 360)

=1.2644 * [(1+ 1.7%)/(1+1.81%)] *1 = 1.2630

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b. Explain what is meant by a fixed exchange rate regime

An exchange rate regime is how a nation manages its currency in the foreign exchange market. This is one of the key economic decisions that a country has to take and this decision is closely related to that country’s monetary policy. There are three basic types of exchange regimes: floating exchange, fixed exchange, and pegged float exchange.

A fixed exchange rate, also referred to as pegged exchanged rate is a regime in which a country’s government decides the worth of its currency in terms of either a fixed weight of an asset, another currency, or a basket of other currencies. A country’s monetary authority determines the exchange rate and commits itself to buy or sell the domestic currency at that price. To ensure that a currency will maintain its “pegged” value, the country’s central bank maintain reserves of foreign currencies and gold.They can sell these reserves in order to intervene in the foreign exchange market to make up excess demand or take up excess supply of the country’s currency.

Fixed exchange regimes usually bring stabilization to the real economic activity as it reduces volatility and fluctuations in relative prices. It eliminates the exchange rate risk.

However there a few disadvantages too, like preventing adjustments for currencies that become under- or over-valued and
Requiring a large pool of reserves to support the currency.
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c.

Spot S1 (GBP/AUD) = $1.8717/£.

Spot S2 (GBP/EUR) = €1.1479/£.

i. Calculate the spot rate for Australian dollar to the euro S(AUD/EUR)

This type of currency rate calculation is called as cross rates.The idea of cross rates implies two exchange rates with a common currency, which enables you to calculate the exchange rate between the remaining two currencies.

The cross rate is the currency exchange rate between currency X and currency Y derived from exchange rate between currency X and currency A and between currency Y and currency A.

should give us the exchange rate for AUD/EUR  

=1.1479 / 1.8717 = 0.6133

ii. Given that there is a broker in the market quoting S(GBP/EUR) = 1.200 demonstrate the potential arbitrage opportunity

Currency arbitrage involves the earning from the differences in quotes rather than movements in the exchange rates of the currencies.

Current spot market price => 1 GBP = 1.1479 Euro

Broker's price => 1 GBP = 1.2 Euro

So in this can a person can buy 1 GBP  from the spot market paying 1.1479 euros, and sell that GBP to the broker in exchange for 1.2 Euros. So making an immediate profit of around 4.5%

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