Answer both questions
A).The treasurer of a German firm has €5 million to invest for three months. The annual interest rate in the Germany is 4 percent: the interest rate in the United Kingdom is 2 percent. The spot rate of exchange is €1.1/£ and the three-month forward rate is €1.2/£. Ignoring transactions costs, in which country would the treasurer want to invest the company’s capital using the forward market? Explain your answer.
B)Suppose the spot rate of exchange between Germany and the UK at time t is $1.50/£. If the interest rate in the US is 13 percent and it is 8 percent in the UK, what would you expect the one-year forward rate to be if no immediate arbitrage opportunities exist?
A) The treasurer would want to invest the company's capital using the forward market in the United Kingdom. This is because the forward rate in the UK (€1.2/£) is higher than the spot rate (€1.1/£), indicating that the market expects the pound to appreciate against the euro.
By investing in the UK using the forward market, the company can lock in a higher exchange rate for converting pounds back to euros in three months compared to the spot rate. This means that when the investment is converted back to euros, the treasurer will receive a larger amount of euros compared to investing in Germany.
B) To determine the expected one-year forward rate, we can use the concept of interest rate parity. According to interest rate parity, the forward exchange rate should incorporate the interest rate differential between the two countries.
The formula for interest rate parity is:
Forward rate = Spot rate × (1 + domestic interest rate) / (1 + foreign interest rate)
In this case, the domestic interest rate is the interest rate in the US (13%) and the foreign interest rate is the interest rate in the UK (8%). The spot rate is given as $1.50/£.
Substituting the values into the formula, we get:
Forward rate (one-year) = $1.50/£ × (1 + 0.13) / (1 + 0.08)
= $1.50/£ × 1.13 / 1.08
= $1.57/£
Therefore, if no immediate arbitrage opportunities exist, we would expect the one-year forward rate to be around $1.57/£.
A) To determine in which country the treasurer would want to invest the company's capital using the forward market, we need to compare the returns from investing in Germany versus investing in the United Kingdom.
In Germany, the annual interest rate is 4 percent, and since the investment is for three months, we need to calculate the quarterly interest rate.
Quarterly interest rate in Germany = (1 + Annual interest rate)^(1/4) - 1
= (1 + 0.04)^(1/4) - 1
= 0.009902
In the United Kingdom, the annual interest rate is 2 percent, but we need to convert it to the quarterly interest rate using the following formula:
Quarterly interest rate in the UK = (1 + Annual interest rate)^(1/4) - 1
= (1 + 0.02)^(1/4) - 1
= 0.004872
Now, let's calculate the returns from investing in Germany using the forward market. The forward rate is given as €1.2/£. However, the treasurer wants to invest in pounds, so we need to calculate the forward rate in pounds. The reciprocal of €1.2/£ gives us £0.833/€.
Now, let's calculate the return when investing in Germany using the forward market:
Return from Germany = €5 million * (1 + Quarterly interest rate in Germany)
= €5 million * (1 + 0.009902)
= €5,049,510
If we convert this back to pounds using the forward rate of £0.833/€, we get:
€5,049,510 * £0.833/€ = £4,201,829
Next, let's calculate the returns from investing in the United Kingdom:
Return from the UK = €5 million * (1 + Quarterly interest rate in the UK)
= €5 million * (1 + 0.004872)
= €5,024,360
If we convert this back to pounds using the spot rate of €1.1/£, we get:
€5,024,360 * £1.1/€ = £4,526,800
Comparing the returns, £4,201,829 from investing in Germany using the forward market is less than £4,526,800 from investing in the UK using the spot market. Therefore, the treasurer would want to invest the company's capital in the United Kingdom using the forward market.
B) To estimate the one-year forward rate between Germany and the UK, we can use the Interest Rate Parity (IRP) formula. According to IRP, the one-year forward rate should be equal to the spot rate multiplied by the ratio of interest rates between the two countries.
Let's apply this formula to the situation:
Forward rate = Spot rate * (1 + Interest rate in the UK) / (1 + Interest rate in the US)
= $1.50/£ * (1 + 0.08) / (1 + 0.13)
= $1.50/£ * 1.08 / 1.13
= $1.429/£
Therefore, if no immediate arbitrage opportunities exist, we would expect the one-year forward rate between Germany and the UK to be $1.429/£.