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Question:

You are working in the foreign currency desk of a British bank in the UK. Your superior believes that the currency market has not correctly incorporated the recently announced USA annual inflation rate into the forward exchange * between the US dollar a. the British pound. At present the inter. rate to be earned on £ 10 million for a month would be 5% per annum in the UK and 0.5% per annum in the USA. You have a. gathered the following information:

Exchange rates: Spot $1.5700 per £ 30-Day Forward rate at premium (swap $0.01 per £). Annual inflation rates: UK (£) 3% pa; USA (£) 0.1% pa.

Required:

A) Given the present inflation an exchange rates above calculate expected spot rate in 30 days' time for the market to be in equilibrium. What do relative *rest rates suggest should be the direction of the forward  rate? Compare the quo. forward rate and the expected spot*. Is. market in equilibrium.?

(b) If the market is not equilibrium in part (a) above, .ate what an UK trader* £10 million at her disposal should da to take dva.ge of the situation. Calculate total (arbitrage and opportunity) gain made by the trader if she follows your advice.

(C) Briefly discuss the risk of the above strategy in deriving the total gain. What would be the breakeven exchange rate for this strategy?
 
 

Answer:

(a) Calculation of expected spot rate:-

The formula of expected spot rate is

            E = S * (rf / rd)

   Here, E = Expected spot rate

 S = Spot rate = $ 1.5700

             rd = domestic currency interest rate = 3.5 %

             rf  = foreign currency interest rate = 0.5 %

Therefore,E=1.5700*(0.5%/3.5%)

                                    = 0.2242

We know that if the rate of interest is high in a country, then the country currency is a lot stronger. This is because the investors from the foreign countries will invest more for the country’s high rate of interest. If this happens then the direction of the forward rate will also increase.  

 

(b) The calculation of Forward rate:

The formula of Forward rate

F = S + swap rate

             Here, F = Forward rate

             S = Spot rate = $ 1.5700

             F = 1.5700 + 0.01

                = 1.5800

The forward rate is 1.5800

No, the market is not in equilibrium.

1. If the market is not at equilibrium, then according to the given question the UK trader should invest her 10 million pound in the UK market because the interest rate of the country (UK) is much higher than the USA interest rate. It is known that if the rate of interest is high in a country, then the country currency is a lot stronger. This is because the investors from the foreign countries will invest more for the country’s high rate of interest.

In spot rate:

If the trader wants to invest in UK in spot rate then the trader will earn

= 10 million * 3.5 %

= 35000 pound

Therefore if the trader invest in UK the trader will earn = 30000 pound

If the trader wants to invest in USA the trader will earn

=10 million * 1.5700 * 0.5%

=$ 7850

In forward rate:

If the trader wants invest in the trader will earn

=10 million * 3%

=30000

If the trader wants to invest in forward rate then the trader will earn

= 10 million * 1.5800 * 0.4%

= $6320

Therefore, the arbitrage gain earned by the trader is = $ (7900 – 7800)

= $ 1530

If the trader earns $ 1530 more if she invests in forward market then the trader should invest in the forward rate.

(c) The risk of the above strategy in deriving the total gain is when the trader invests in the forward market the country’s interest rate may fall down for the economic conditions of the country. The inflation rate may rise due to the economic condition of the country. If this occurs then the trader will face loss from her earning.

Break Even Exchange Rate:

The USA interest rate is 0.5 % and the UK interest rate is 3.5 %, it may happen that US dollar can be change into the UK pound and can invest in 3.5 %. If this process is done without doing forward coat, then the interest profit of 3 % can be derived. Then the investor can face a loss of 3 %.

 

Reference:

Bajlum, C. and Tind Larsen, P. (2008). Capital structure arbitrage. Aarhus: University of Aarhus. Aarhus School of Business.

Bragg, S. (2007). Business ratios and formulas. Hoboken, N.J.: Wiley.
Dubil, R. (2004). An arbitrage guide to financial markets. Chichester, West Sussex, England: John Wiley & Sons.

Whistler, M. (2004). Trading pairs. Hoboken, NJ: John Wiley & Sons
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