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 %
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.
The formula of Forward rate
F = S + swap rate
Here, F = Forward rate
S = Spot rate = $ 1.5700
F = 1.5700 + 0.01
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%
In forward rate:
If the trader wants invest in the trader will earn
=10 million * 3%
If the trader wants to invest in forward rate then the trader will earn
= 10 million * 1.5800 * 0.4%
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.
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 %.
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.
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