# Exchange rates

1) Suppose the current spot rate is 100 Japanese Yen to 1 US dollar. You expect the spot rate in 30 days to be 98 Yen to the US dollar. Furthermore, (at an annualized rate) you can borrow US dollars at 5.2% and lend them at 5.0% and you can borrow the Japanese Yen at 5.7% and lend them at 5.5%. You can borrow or lend or lend USD 1,000,000 or Yen 100,000,000 and there are no transaction costs. If your expectation of the spot rate in 30 days is correct, answer the following:

a) Which currency would you borrow?

b) How much interest would you pay (in the currency that you borrow)?

c) How much interest would you make (in the currency that you lend)?

d) What would be your net profit (in USD)?

2. Suppose the current spot rate is 1 Euro to 1 US dollar. You expect the spot rate in 60 days to be 0.97 Euros to the 1 US dollar. Furthermore (at an annualized rate) you can borrow US dollars at 7.0% and lend them at 6.7% and you can borrow Euros at 6.3% and lend them at 6.0%. Assume you can borrow or lend USD 1,000,000 or Euro 1,000,000 and there are no transaction costs. If your expectation of the spot rate in 60 days is correct, answer the following:

a) Which currency would you borrow?

b) How much interest would you pay (in the currency that you borrow)?

c) How much interest would you make (in the currency that you lend)?

d) What would be your net profit (in USD)?

3. You purchase a call option on pounds for a premium of $0.03 per unit, with an exercise price of $1.64; the option will not be exercised until the expiration date, if at all. If the spot rate on the expiration date is $1.65, what is your net profit or loss per unit?

(round to the nearest penny)

4. The premium on a pound put option is $0.03 per unit. The exercise price is $1.60. the break-even point is _________________for the buyer of the put, and _______________ for the seller of the put. (assume zero transaction costs and round to the nearest penny)

5. Assume the spot rate of the Swiss Franc is $0.62 and the one-year forward rate is $0.66. Does the forward rate exhibits a premium or a discount? What is the premium or discount percentage?

6. A company will receive 1,000,000 euros in 30 days, and is certain that the euro will depreciate substantially over time. Assuming the firm is correct, what is the best strategy? (ex: sell euros forward, remain unhedged, purchase euro currency call options, purchase euros forward, purchase euros put option--choose all that apply)

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#### Solution Preview

1) Suppose the current spot rate is 100 Japanese Yen to 1 US dollar. You expect the spot rate in 30 days to be 98 Yen to the US dollar. Furthermore, (at an annualized rate) you can borrow US dollars at 5.2% and lend them at 5.0% and you can borrow the Japanese Yen at 5.7% and lend them at 5.5%. You can borrow or lend or lend USD 1,000,000 or Yen 100,000,000 and there are no transaction costs. If your expectation of the spot rate in 30 days is correct, answer the following:

a) Which currency would you borrow?

b) How much interest would you pay (in the currency that you borrow)?

c) How much interest would you make (in the currency that you lend)?

d) What would be your net profit (in USD)?

Interest rate on USD

lend= 5% annualized

borrow= 5.2% annualized

Interest rate on JPY

lend= 5.5% annualized

borrow= 5.7% annualized

Current spot rate= 100 JPY= 1 USD

Spot rate in 30 days= 98 JPY= 1 USD

a) Which currency would you borrow?

The Yen is appreciating

Current spot rate= 100 JPY= 1 USD

Or $1 will buy 100 Yens

Spot rate in 30 days= 98 JPY= 1 USD

Or $1 will buy 98 Yens only after 30 days

Which means that after 30 days the value of Yen would be more than what it is today in USD terms

However Yen has a higher interest rate= 5.6% (average of lending and borrowing rates)

when compared to USD rate= 5.1% (average of lending and borrowing rates)

From the interest rate parity the currency with a higher interest rate should depreciate

If it does not then there is arbitrage opportunity which can be exploited as is the case here

We buy the cheaper currency and sell the dearer currency

Since currently Yen is cheaper than what it would be 30 days from now

We borrow $ and convert it to Yen now

b) How much interest would you pay (in the currency that you borrow)?

Principal= $1,000,000

Borrowing rate= 5.2% annualized=

Time = 30 days= 1/12 years

Therefore Interest paid= Principal x Rate x Time= $4,333 =1000000*5.2%* 1/12

c) How much interest would you make (in the currency that you lend)?

We convert the dollars to Yen at the current spot rate

Current spot rate= 100 JPY= 1 USD

$1,000,000 = JPY 100,000,000 =1000000*100

Principal= $100,000,000

Lending rate= 5.5% annualized=

Time = 30 days= 1/12 years

Therefore Interest paid= Principal x Rate x Time= JPY 458,333 =100000000*5.5%* 1/12

d) What would be your net profit (in USD)?

Principal and interest at the end of 30 days for the amount lent=

JPY 100,458,333 =100000000+458333

We convert this into $ at 30 days spot rate

Spot rate in 30 days= 98 JPY= 1 USD

Amount in $ received= $1,025,085 =100458333/98

Principal and interest that has to ...

#### Solution Summary

Answers questions on currency exchange rates.