Chapter 11 Project Collect Some Monthly Data Over

Chapter 11

Currency Risk Management

Note: In the sixth edition of Global Investments, the exchange rate quotation symbols differ from previous

editions. We adopted the convention that the first currency is the quoted currency in terms of units

of the second currency.

For example, €:$ = 1.4 indicates that one euro is priced at 1.4 dollars. In previous editions we used

the reversed convention $/€ = 1.4, meaning 1.4 dollars per euro.

All problems in this test bank still use the old convention and have not been adapted to reflect the

new quotation symbols used in the 6th edition.

◼ Questions and Problems

1. A German corporation finalized a sale to a Thai client on April 15. The German corporation will

deliver some gardening equipment on May 31 and will be paid 345 million baht on June 30. The

current spot exchange rate is 40 baht/euro. The German corporation is worried about a depreciation

of the baht in the coming two months and wishes to sell those baht forward against euros.

a. Give some reasons why the German corporation should use forward rather than futures currency

contracts.

b. Exactly what contract should the German corporation arrange with its bank?

Chapter 11 Currency Risk Management 159

2. A Japanese investor holds a portfolio of British stocks worth £10 million. The current three-month

dollar/pound forward exchange rate is $/£ = 1.65, and the current three-month yen/dollar forward

exchange rate is ¥/$ = 100. What position should the Japanese investor take to hedge the pound/yen

exchange risk?

3. An Italian investor owns a portfolio of South Korean stocks worth 1.25 billion won. The current spot

and one-month forward exchange rates are 1,250 won/€ (one won = 0.0008 euro). Interest rates are

equal in both countries. You are worried that some rumor about the bankruptcy of a major local bank

could lead to a strong depreciation of the won. You have observed that Korean stocks tend to react

negatively to a depreciation of the local currency (won). A broker tells you that a regression of

Korean stock returns (measured in won) on the €/won percentage exchange rate movements has a

slope of +0.50. In other words, Korean stocks tend to go down by 0.5% when the won depreciates

by 1%.

a. Discuss what your currency hedge ratio should be.

b. A month later, your Korean stock portfolio has gone down to 1.1875 billion won and the spot and

forward exchange rates are now 0.00072 €/won. Analyze the return on your hedged portfolio.

160 Solnik/McLeavey • Global Investments, Sixth Edition

4. An American investor holds a British bond portfolio worth £100 million. The portfolio has a duration

of 7. She fears a temporary depreciation of the pound but wishes to retain the bonds. To cover this

risk, she decides to sell pounds forward. She has observed that the British government tends to adopt

a “leaning-against-the-wind” policy. When the pound depreciates, British interest rates tend to rise to

defend the currency. A regression of “variations in long–term British yields” on “percentage $/£

exchange rate movements” has a slope coefficient of −0.1. In other words, British yields tend to

go up by 10 basis points (0.1%) when the pound depreciates by 1% relative to the dollar.

a. What should be the optimal hedge ratio used by the investor if she wishes to reduce the

uncertainty caused by exchange risk? (The investor uses only forward currency contracts to

hedge this risk, not bond futures contracts.)

b. Detail the factors that could make this hedge imperfect if the depreciation of the pound

materializes.

Solution

Chapter 11 Currency Risk Management 161

5. Back in 1990, East Germany was in the process of merging into West Germany. Its national currency

was to be replaced by the Deutsche mark (DM). A U.S. dollar-based investor has a portfolio worth

DM 100 million in German bonds. The current spot exchange rate is 2 DM/$. The current one-year

market interest rates are 6% in DM and 10% in dollars. One-year currency options are quoted in

Chicago with a strike price of 50 U.S. cents per DM; a call DM is quoted at 1 U.S. cent and a put

DM is quoted at 1.2 U.S. cents; these option prices are for one DM.

You are worried that the integration of East and West Germany will cause inflation in Germany and a

drop in the DM. So, you consider using forward contracts or options to hedge the currency risk.

a. What is the one-year forward exchange rate DM/$?

b. Simulate the dollar value of your portfolio assuming that its DM value stays at DM 100 million;

use DM/$ spot exchange rates equal in one year to: 1.6, 1.8, 2, 2.2, and 2.4. First consider a

currency forward hedge, then a currency-option insurance.

c. What could make your forward hedge imperfect?

Solution

162 Solnik/McLeavey • Global Investments, Sixth Edition

6. Today is April 1st and you’re French. You hold $1 million worth of American securities. You fear a

depreciation of the dollar. The spot exchange rate is 0.80 $/€ or 1.25 €/$. The forward rate maturing

July 1 is 1.255 €/$. Currency options on the euro are traded in Chicago. They are options on 1 euro,

maturing July 1 and whose prices (premium and strike) are given in U.S. cents in the following table:

Strike

Premium

Call

Put

80

2

85

0.2

5.4

If you hedge using a forward contract, the bank requires no deposit. If you buy options, you must sell

some of your U.S. securities in order to buy these options. You assume that your securities will keep

exactly the same value on July 1.

a. You decide to hedge. What will be the euro value of your portfolio on July 1?

b. You decide to insure your portfolio using currency options. Do you need to buy/sell calls €/

puts €?

c. Assume that you use options with a strike of 80 U.S. cents. How many options do you need to

insure perfectly your portfolio?

d. Same question with options with a strike of 85?

e. Simulate the results of your hedge and insurance with the two options if the spot exchange rate

on July 1 is equal to 0.70 $/€, 0.80 $/€, and 0.90 $/€. Fill the following table with the value of the

portfolio in euros:

Portfolio Value in Euros on July 1:

Original Portfolio

With Hedge

With Calls 80

With Calls 85

S = 0.70 $/€

1,428,571

S = 0.80 $/€

1,250,000

S = 0.90 $/€

1,111,111

f. What is the best choice if you think that the chances of the depreciation of the $ are very weak

but still exist.

Unhedged

Chapter 11 Currency Risk Management 163

Solution

7. An American investor believes that the dollar will depreciate and buys one call option on the euro at

an exercise price of 110 cents per euro. The option premium is 1 cent per euro, or $625 per contract

of 62,500 euros (Philadelphia):

a. For what range of exchange rates should the investor exercise the call option at expiration?

b. For what range of exchange rates will the investor realize a net profit, taking the original cost

into account?

c. If the investor had purchased a put with the same exercise price and premium, instead of a call,

how would you answer the previous two questions?

164 Solnik/McLeavey • Global Investments, Sixth Edition

Solution

8. An Italian importer will be paid $1 million in three months (March). He must decide whether to sell

$1 million forward or to buy currency options for that amount.

The current market prices are as follows:

Exchange rates: Spot $/€ = 1.10

Three-month forward: $/€ = 1.11

Call euro March 110 U.S. cents: 1.5 U.S. cents per €.

Put euro March 110 U.S. cents: 1.0 U.S. cents per €.

What are the differences between the strategies of selling currency forward and buying currency

options?

Solution

9. What are the major determinants of the value of a currency option (call and put)?

a. Briefly justify each determinant and its direction.

b. What is the relation between a currency put and a currency call (put–call parity)?

c. In what circumstances would an American-type option be exercised before expiration?

(You may provide an example to illustrate your answers.)

Chapter 11 Currency Risk Management 165

Solution

10. On April 1, an Australian investor decides to hedge a U.S. portfolio worth $10 million against

exchange risk using AUD call options. The spot exchange rate is AUD/$ = 2.5 or $/AUD = 0.40.

The Australian investor can buy November calls AUD with a strike price of 0.40 U.S. cents per

AUD at a premium of 0.8 U.S. cent per AUD. The size of one contract is AUD 125,000. The delta

of the option is estimated at 0.5.

a. How many AUD calls should our investor buy to hedge the U.S. portfolio against the AUD/$

currency risk?

b. A few days later the U.S. dollar has dropped to AUD/$ = 2.463 ($/AUD = 0.406) and the dollar

value of the portfolio has remained unchanged at $10 million. The November 40 AUD call is

now worth 1.2 cents per AUD and has a delta estimated at 0.7. What is the result of the hedge?

c. How should the hedge be adjusted?

166 Solnik/McLeavey • Global Investments, Sixth Edition

Solution

11. An American portfolio manager wishes to increases her exposure to Japanese stocks by $10 million

without taking much foreign exchange risk. The spot exchange rate is ¥100 per dollar. She considers

several alternatives:

• Exchange Traded Funds (ETFs) are listed on the Tokyo stock exchange. The ETF is a traded fund

that tracks the TOPIX index. Each share has a value of ¥1,000.

• Futures contracts are available on the TOPIX index. Each contract is for ¥1,000 times the index.

The current futures price of the TOPIX index is 1,000. The margin deposit per contract is ¥50,000.

• At-the-money call options on the TOPIX index are available. Each contract is for ¥1,000 times the

index. The premium on the call is ¥60 per index or ¥60,000 per contract.

What strategy could she adopt using those contracts?

Chapter 11 Currency Risk Management 167

Solution

12. An asset manager has a mandate to manage a European equity portfolio for a U.S. pension client. The

portfolio size is $100 million. The benchmark is some European equity index with a 50% currency

hedging target. But the currency management is delegated to a currency overlay manager. The

geographical breakdown of the portfolio on January 1 is as indicated below:

By Country

Value

in Local Currency

Value

in Dollars

British Stocks

£10 million

$15 million

Euroland Stocks

€20 million

$23 million

Swiss Stocks

SFr 1.4 million

$1 million

Total

$38 million

a. Assume that the currency overlay manager is neutral on currencies (that is, does not have specific

forecasts on exchange rate). What would you expect the currency overlay manager to do on this

portfolio?

b. Assume now that the currency overlay manager is bullish on the euro and pound but bearish on

the Swiss franc (relative to the dollar). What kind of actions are you expecting from the currency

overlay manager?

168 Solnik/McLeavey • Global Investments, Sixth Edition

Solution

13. Project: Collect some monthly data over ten years for the following prices: Japanese, German, and

British stock and bond indexes; the dollar exchange rates of their respective currencies.

a. Using a regression between asset returns and percentage currency movements, calculate for each

asset class the minimum-risk currency hedge ratio for an American investor.

b. Same question assuming that you are a German investor. Are the conclusions different?

Now collect some data on Argentinean, Chilean, and Brazilian stock indexes and their respective

currencies.

c. Using a regression, calculate for each asset class the minimum-risk currency hedge ratio

assuming that you are an American investor.

d. Are your conclusions similar to those obtained for developed markets? Why?