a. Suppose the Japanese yen exchange rate is ¥118=$1, and the British pound exchange rate is £1=$1.81. i. What is the cross rate in terms of yen per pound? ii. Suppose the cross rate is ¥204 = £1.…

a. Cross-Rate and Arbitrage Opportunity

i. Cross-Rate Calculation (¥ per £)

The cross-rate between two currencies can be derived using the given exchange rates. Here, we need to find the exchange rate of yen per pound (¥/£) using the given rates:

• Given:
  • ¥118 = $1
  • £1 = $1.81

Step 1: Convert $1 to £ using the second rate. $$1\text{ USD}=\frac{1}{1.81}\text{ GBP}\approx 0.5525\text{ GBP}$$

Step 2: Since ¥118 = $1, we can express $1 in yen and then convert it to pounds. $$1\text{ USD}=118\text{ JPY}$$ $$1\text{ USD}=0.5525\text{ GBP}$$

Step 3: To find ¥ per £, we rearrange the relationship: $$1\text{ GBP}=\frac{118}{0.5525}\text{ JPY}\approx 213.55\text{ JPY}$$

Final Answer: The cross-rate is ¥213.55 per £1.

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ii. Arbitrage Opportunity Analysis

Given:

• Market cross-rate: ¥204 = £1
• Calculated cross-rate: ¥213.55 = £1

Since ¥204 < ¥213.55, the market rate is undervaluing the yen relative to the pound. This creates an arbitrage opportunity.

Arbitrage Strategy:

1. Buy £1 using $1.81 (since £1 = $1.81).
2. **Convert $1.81toyen\ast \ast at\yen 118/$: $$1.81\times 118=213.55\text{ JPY}$$
3. Sell yen for £ at the market rate (¥204 = £1): $$\frac{213.55}{204}\approx 1.0468\text{ GBP}$$
4. Profit: You end up with 1.0468 GBP instead of the initial 1 GBP, making a 4.68% profit without risk.

Conclusion: Yes, there is an arbitrage opportunity. An investor can exploit the mispricing by buying pounds with dollars, converting to yen, and then selling yen back for pounds at a higher rate.

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b. Forward Exchange Rate Analysis

i. Premium or Discount?

The spot rate is Can$1.15/$, and the 6-month forward rate is Can$1.19/$.

• If the forward rate > spot rate, the domestic currency (USD) is selling at a premium (i.e., it costs more Canadian dollars to buy one USD in the future).
• If the forward rate < spot rate, the domestic currency is selling at a discount.

Here, Can$1.19/$ (forward) > Can$1.15/$ (spot), meaning the USD is selling at a premium relative to the Canadian dollar.

Final Answer: The US dollar is selling at a premium relative to the Canadian dollar.

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ii. Expected Currency Appreciation

When a currency is selling at a premium in the forward market, it implies that the domestic currency (USD) is expected to appreciate against the foreign currency (Canadian dollar).

Reasoning:

• If the USD is selling at a premium (forward > spot), it means that in 6 months, 1 USD will buy more Canadian dollars than it does today.
• This suggests that the USD is expected to strengthen (appreciate) relative to the Canadian dollar.

Final Answer: The US dollar (USD) is expected to appreciate in value.