To hedge the currency risk of an expected increase in the value of the UK pound against the US dollar over the next year, you should use a short forward contract on the UK pound. The reason for this is that by taking a short position in the forward contract, you are committing to sell British pounds in the future at a predetermined exchange rate, which locks in the current exchange rate of $1.50/£. This means that even if the pound strengthens, you will be able to exchange your pounds at the agreed-upon rate of $1.50/£, protecting your import costs from currency fluctuations.

The no-arbitrage 1-year forward rate can be calculated using the interest rate parity formula:

F = S * (1 + Rb) / (1 + Ra)

Where:

F is the forward exchange rate

S is the current spot exchange rate ($1.50/£)

Rb is the interest rate in the UK (2.8% or 0.028)

Ra is the interest rate in the US (3.6% or 0.036)

Plugging in the values:

F = 1.50 * (1 + 0.028) / (1 + 0.036) F = 1.50 * 1.028 / 1.036 F ≈ 1.4934/£

So, the no-arbitrage 1-year forward rate should be approximately $1.4934/£.

b. To determine the future spot exchange rate at which you would be indifferent between the forward and option hedges, you need to consider the total cost of the option hedge.

The option strike price is $1.46/£, and the premium is $0.03/£. So, the total cost of the option hedge is $1.46/£ (strike price) + $0.03/£ (premium) = $1.49/£.

This means that if the future spot exchange rate 1 year from now is $1.49/£ or higher, you would be indifferent between the two hedges because the option hedge would cost the same as the forward hedge (based on the previously calculated forward rate of $1.4934/£).

c. Based on the solutions to parts a. and b., you should choose the forward hedge alternative. This is because the forward hedge locks in a better exchange rate of $1.50/£ compared to the option hedge’s breakeven point of $1.49/£. With the forward contract, you are guaranteed to exchange pounds at a more favorable rate, which provides better protection against the expected increase in the pound’s value.

d. It is now 6 months since you entered into the forward contract. The spot rate is $1.53/£, and interest rates are the same as before. To calculate the value of your forward position, you need to consider the difference between the contracted forward rate and the current spot rate.

The contracted forward rate is $1.50/£, and the current spot rate is $1.53/£. Since you have a short forward position, you would have a gain because you can sell pounds at a lower rate than the current market rate.

Value of forward position = (Forward rate – Spot rate) * Amount of pounds in the contract Value of forward position = ($1.50/£ – $1.53/£) * Amount of pounds in the contract Value of forward position = (-$0.03/£) * Amount of pounds in the contract

If you have, for example, £10,000 in the contract:

Value of forward position = (-$0.03/£) * £10,000 = -$300

So, the value of your forward position is -$300, indicating a loss due to the unfavorable movement in the exchange rate.

e. It is now 6 months since you entered into the option contract, and the spot rate is $1.53/£. To calculate the value of your option position if you choose to exercise it, you need to compare the spot rate with the option’s strike price.

The option’s strike price is $1.46/£, and the current spot rate is $1.53/£. Since the spot rate is higher than the strike price, it is advantageous to exercise the option.

Value of option position if exercised = (Spot rate – Strike price) * Amount of pounds in the option Value of option position if exercised = ($1.53/£ – $1.46/£) * Amount of pounds in the option Value of option position if exercised = $0.07/£ * Amount of pounds in the option

If you have, for example, an option on £10,000:

Value of option position if exercised = $0.07/£ * £10,000 = $700

So, the value of your option position if you choose to exercise it is $700, representing your profit from the option hedge.