international investing

International Investing

Department of Banking and Finance

SPRING 2007-08

by

Asst. Prof. Sami Fethi

2

Ch 18: International Investment

Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

BackgroundBackground

Global Market – US Market is approx. 50% of all markets– Improved access & technology– New Instruments

Emphasis for our investigation– Risk Assessment– Diversification

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IssuesIssues

What are the risks involved in investment in foreign securities?

How do you measure benchmark returns on foreign investments?

Are there benefits to diversification in foreign securities?

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Risks in International Investing: Foreign ExchangeRisks in International Investing: Foreign Exchange

Exchange rate: The rate at which domestic currency can be converted into foreign currencyExchange Rate Risk

Variation in return related to changes in the relative value of the domestic and foreign currency

Total Return = Investment return plus return on foreign exchange

Not possible to completely hedge a foreign investment

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Example 1-Exchange rate riskExample 1-Exchange rate risk

Consider an investment in risk-free government bill paying 10% annual interest in British pounds. Suppose the current exchange rate is $ 2 per pound, and the US investor starts with $20,000.

What happens if the dollar-pound exchange rate varies over the year?

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Solution 1-Exchange rate riskSolution 1-Exchange rate risk

The amount can be exchanged for £10,000 and invested at a riskless 10% rate in the UK to provide £11,000 in one year. The depreciation of pound to dollar is 1.80.

10000(10%)=1000 total; £11000

11000(1.80)=£19800

$ 200 relative to $20000

200/20000=0.01 or 1%.

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Example 2-Exchange rate riskExample 2-Exchange rate risk

Using the figures in example 1, calculate the rate of return in dollars to a US investor holding the British bill if the year-end exchange rate is;

A) E1=$2.00/£

B) E1=$2.20/£

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Solution 2-Exchange rate riskSolution 2-Exchange rate risk

The following formula can be applied:

(1 + rUS) = [1 + rUK]E1 /Eo

A) (1 + rUS) = [1 + 0.1]2 /2

rUS=1.1-1.0=0.1 or 10%

B) (1 + rUS) = [1 + 0.1]2.20 /2

rUS=1.21-1.0=0.21 or 21%

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Example 3-Hedging Exchange rate riskExample 3-Hedging Exchange rate risk

Suppose the future exchange rate was $1.93/£ when the investment was made. The US investor could have assured a riskless dollar-denominated return by locking in the year-end exchange rate at $ 1.93/£. Referring to example 1 and

A) Calculate the riskless US return B) Calculate total amount of end-year proceeds in

dollar.

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Solution 3-Hedging Exchange rate riskSolution 3-Hedging Exchange rate risk

The following formula can be applied:

(1 + rUS) = [1 + rUK]Fo/Eo

A) (1 + rUS) = [1 + 0.1]1.93 /2.00

rUS=0.0615 or 6.15% B) (11000) (1.93)

$21,230

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Example 4-covered interest rateExample 4-covered interest rate

Suppose rf(US) is 6.15%, futures price is $1.90/£ rather than being $1.93/£

What are the arbitrage strategy and associated profits?

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Solution 4-covered interest rateSolution 4-covered interest rate

Action ICF CF in one Year

Borrow 1 UK pound. Repay in one year.

$2.00 -E1(1.10)

Convert the pound to $2 and lend in USA

$-2.00 2.00(1.0615)

Enter a contract to purchase 1.10 pound at a future price of

$1.90/£

0 1.10(E1-1.90)

total $ 0 $ 0.033

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Example 5-covered interest rateExample 5-covered interest rate

Suppose rf(US) is 6.15%, futures price is $1.95/£ rather than being $1.93/£

What are the arbitrage strategy and associated profits?

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Solution 5-covered interest rateSolution 5-covered interest rate

Action ICF CF in one Year

Borrow $2 USA pound..

$2.00

Convert the dollar to $2 and lend in UK at 10

% interest rate$-2.00

-E1(1.10)

Enter a contract to sell 1.10 pound at a

future price of $1.95/£

0 1.10(E1-1.90)

total $ 0 $ 0.022

-2.00(1.0615)

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Returns with FXReturns with FX

Return in US is a function of two factors

1. Return in the foreign market

2.Return on the foreign exchange

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Returns with FXReturns with FX

(1 + rUS) = (1 + rFM) (1 + rFX)

rUS = return on the foreign investment in US Dollars

rFM = return on the foreign market in local currency

rFX = return on the foreign exchange

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Return Example-6: Dollar Depreciates Return Example-6: Dollar Depreciates

Relative to the PoundRelative to the Pound Initial Investment : $100,000

Initial Exchange: $2.00/ Pound Sterling

Final Exchange:$2.10/ Pound Sterling

Return in British Security: 10%

Return in US Dollars

(1 + rUS) = (1.10) (1.05) = (1.155)

rUS = 15.5%

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Return Example-7: Dollar Appreciates Relative Return Example-7: Dollar Appreciates Relative to the Poundto the Pound

Initial Investment : $100,000Initial Exchange: $2/ Pound SterlingFinal Exchange: $1.85/ Pound SterlingReturn in British Security: 10%Return in US Dollars

(1 + rUS) = (1.10) (.9250) = (1.0175)

rUS = 1.75%

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Example 8-Sell ForwardExample 8-Sell Forward

How many pounds would the investor in example 3 need to sell forward to hedge exchange rate risk if

A) r(uk)=20% B) r(uk)=30%

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Solution 8-Sell ForwardSolution 8-Sell Forward

Sell in the forward as an amount of foreign currency equal to (INV) [1+r(foreign)]

A) (10000) (1.20)= 12000 pounds B) (10000) (1.30)= 13000 pounds

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Other Risks in International InvestingOther Risks in International Investing

Country - SpecificComposition

– Political– Financial– Economic

Composite Ratings

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Int’l Investment ChoicesInt’l Investment Choices

Direct Stock PurchasesMutual Funds

– Open End– Closed End– WEBS

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Diversification BenefitsDiversification Benefits

Evidence shows international diversification is beneficial

Possible to expand the efficient frontier above domestic only frontier

Possible to reduce the systematic risk level below the domestic only level

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Efficient Frontier with International DiversificationEfficient Frontier with International Diversification

ReturnReturn

RiskRisk

* *

*

**

* *

*DomDom

Int’lInt’l Evidence shows international diversification is beneficial

Possible to expand the efficient frontier above domestic only frontier

Possible to reduce the systematic risk level below the domestic only level

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Systematic Risk Level with International Systematic Risk Level with International DiversificationDiversification

RiskRisk

SecuritiesSecurities

Int’lDomDom

This figure suggests that international diversification can reduce the standard deviation of domestic portfolio by as much as half

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Constructing benchmark portfolio of Constructing benchmark portfolio of foreign assetsforeign assets

Active or passive international investing requires a benchmark portfolio. One widely used index of non-US stock is European, Australian, Far East (EAFE) index. This index is constructed or computed by Morgan and Stanley.

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Factors in Assessing Active International Factors in Assessing Active International Investment PerformanceInvestment Performance

Currency SelectionCountry SelectionStock SelectionCash / Bond Selection

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Currency SelectionCurrency Selection

This measures the contribution to total portfolio performance attributable to exchange rate fluctuations relative to the investor’s benchmark currency, which we will take to be the US dollar. We might use a benchmark like the EAFE index to compare a portfolio’s currency selection for a particular period to a passive benchmark.

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Country SelectionCountry Selection

This measures the contribution to performance attributable to investing in better-performing stock markets of the world. It can be measured as weighted average of equity index returns of each country using as weights the share of the manager’s portfolio in each country

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Stock Selection-Cash / Bond SelectionStock Selection-Cash / Bond Selection

Stock Selection: choice of specific stocks within a country’s equity market.

Cash / Bond Selection: choice between money market and longer-term bonds.

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Example 9- performance AttributionExample 9- performance Attribution

EAFE Weight

Return on Equity Index

Currency.App E1/E0-

1

Manager’s

Weight

Manager’s Return

Europe 0.30 10% 10% 0.35 8%

Australia 0.10 5% -10% 0.10 7%

Far East 0.60 15% 30% 0.55 18%

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Using the information given in the above table. Here, all exchange rates are expressed as unit of foreign currency that can be purchased with one U.S. dollar.

a) Calculate the overall performance for both EAFE and Manager and state the situation whether there exists loss or contribution relative to EAFE.

b) Calculate the currency selection for both EAFE and Manager and state the situation whether there exists loss or contribution relative to EAFE.

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c) Calculate the country selection for both EAFE and Manager and state the situation whether there exists loss or contribution relative to EAFE.

d) Calculate the stock selection for both EAFE and Manager and state the situation whether there exists loss or contribution relative to EAFE.

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Solution 9- performance AttributionSolution 9- performance Attribution

OP: Dollar return=return on index+ curr. Appri. a) EAFE: .30(10+10)+.10(5-10) + .60(15+30)=32.5%

MANAGER: .35(8+10)+.10(7-10) + .55(18+30)=32.4%

Conclusion: Loss of .10% relative to EAFE CS: Dollar return=(weight) (curr. Appri.) b) EAFE: (.30x10%)+(.10x-10%) + (.60x30)=20%

MANAGER: (.35x10%)+(.10x-10%) + (.55x30)=19%

Conclusion: Loss of 1% relative to EAFE

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CS: Dollar return=(return on index) (weight.) c) EAFE: (.30x10%)+(.10x5%) + (.60x15%)=12.5%

MANAGER: (.35x10%)+(.10x5%) + (.55x15%)=12.25%

Conclusion: Loss of 0.25% relative to EAFE

SS: MW(MR-ROEI) d) (8%-10%) .35+ (7%-5%) .10+ (18%-15%) .55=1.15%

Conclusion: contribution of 1.15 % relative to EAFE

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Using the same data given in the previous table as portfolio weights change to 40% in Europe, 20% in Australia, and 40% in the far East and repeat all parts in the example 9.

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OP: Dollar return=return on index+ curr. Appri. a) EAFE: .30(10+10)+.10(5-10) + .60(15+30)=32.2%

MANAGER: .40(8+10)+.20(7-10) + .40(18+30)=25.8%

Conclusion: Loss of 6.7% relative to EAFE CS: Dollar return=(weight) (curr. Appri.) b) EAFE: (.30x10%)+(.10x-10%) + (.60x30)=20%

MANAGER: (.40x10%)+(.20x-10%) + (.40x30)=14%

Conclusion: Loss of 6% relative to EAFE

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CS: Dollar return=(return on index) (weight.) c) EAFE: (.30x10%)+(.10x5%) + (.60x15%)=12.5%

MANAGER: (.40x10%)+(.20x5%) + (.40x15%)=11%

Conclusion: Loss of 1.5% relative to EAFE

SS: MW(MR-ROEI) d) (8%-10%) .40+ (7%-5%) .20+ (18%-15%) .40=0.8%

Conclusion: contribution of 0.8 % relative to EAFE

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Example 11- Buying & SellingExample 11- Buying & Selling

What is the cost of buying Mexican peso 100000? What is the cost of purchasing $ 1million? How much do we received from selling $ 150000? How much do we received from the sale of

Mexican peso 10 million? Note: MP/$ is 2.5010/2.5075

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Solution 11- Buying & SellingSolution 11- Buying & Selling

MP 100000/2.5010=$ 39984 $ 1mnx2.5070= MP 2.5075mn $ 150000x2.5010= MP 375150 MP 10mn/2.5075=$ 3988036

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Example & Solution 12- Cross ratesExample & Solution 12- Cross rates

Suppose you want the £/$ cross rate and you are given: Y/$=154.33; Y/£=235.20, what is the £/$ cross rate ?

Y/$/ Y/£=Y/$x£/Y=154.33/235.20=0.6562

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Example 13- Discounts and premiumsExample 13- Discounts and premiums

Suppose that the following data are given as a rate of discount on the spot rate:

$/£ spot 1.5840-1.5860 1 month forward 4.50c-4.75c discount 3 month forward 6.85c-7.0c discount What is the actual forward rate for both 1 and 3

months?

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Solution 13- Discounts and premiumsSolution 13- Discounts and premiums

Spot 1.5840 1.5860 + 450 475 1 month forward= 1.6290 1.6335 Spot 1.5840 1.5860 + 685 700 3 month forward= 1.6525 1.6560

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Example 14- Depreciation-AppreciationExample 14- Depreciation-Appreciation

Suppose you have the following information: $/£ spot 1.5345 12 months forward5c premium Calculate the 12 months forward rate? Calculate the forward rates for the next five years? If depreciation 5% for the next two years and

Appreciation 7% for the rests. Note: spot $/£ x (1-rate of appreciation)= forward $/£

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Solution 14- Depreciation-AppreciationSolution 14- Depreciation-Appreciation

Forward rate appreciation in dollar is: 5/1.6580=3.25% Spot $ 1.5345x(1-0.0325)=$ 1.4846 12 month

forward 1.5345x(1+0.05)=$ 1.6112 one year fwd 1.6112x(1+0.05)=$ 1.6918 two year fwd 1.6918 x(1-0.07)=$ 1.5734 three year fwd 1.5734x(1-0.07)=$ 1.4632 four year fwd 1.4632 x(1-0.07)=$ 1.3608 five year fwd

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Example 15- interest ratesExample 15- interest rates

Suppose that you have the spot $/£ is 1.5840-1.5860 and 12 months forward $/£ is 1.5370-1.5400. Also, UK and US treasury bills are 8% and 5% respectively.

What is the percentage change in the $ Calculate the 12 month forward rate.

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Solution 15- interest ratesSolution 15- interest rates

$ interest-£ interest/(1+£ interest) (0.05-0.08)/(1.08)=2.78%. This is appreciation in

the $ (- represents app. and + represents dep.) 1.5840(1-0.0278)=1.5400 This 12 months forward $/£.

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Example 16- forecasting exchange ratesExample 16- forecasting exchange rates Suppose the current Y/£ spot rate for buying Y is

224.20 and estimates of UK and Japanese inflation rates over the next three years are as follows:

Inflation rates UK Japan Year 1 3% 5% Year 2 4.5% 2% Year 1 3% 3% Calculate the forecasting exchange rates for the

relevant years.

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Solution 16- forecasting exchange ratesSolution 16- forecasting exchange rates

At Year 1 (0.05-0.03)/(1.03)=0.0194 Y will depreciate by 1.94 %

Y 224.2(1+0.0194)=Y 228.55 year 1 spot. At Year 2 (0.02-0.045)/(1.045)=-0.023 Y will

appreciate by 2.3% Y 228.55(1-0.023)=Y 223.81year 2 spot. At Year 3 (0.03-0.03)/(1.03)=0: No change in

the Y/£ spot rate Y 223.81 Year 3 spot.

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Purchasing power parity and Interest rate parityPurchasing power parity and Interest rate parity

PPP (1+IF)/(1+ ID)

IRP (1+rF)/(1+ rD)

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The EndThe End

Thanks

international investing

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