0 - 2 Sample Topics for MS&E 247S International Investments MWF 1

MS&E247s International Investments Handout #4 Page 1 of 23July 1, 2002

MWF 1:15-2:05 Skilling 193

Course web page:http://www.stanford.edu/class/msande247s

Handout #4Sample Topics for International Investments

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Sample Topics forMS&E 247S International Investments

July 1, 2002

Topic 1: The Hamburger Standard

Topic 2: Arbitrage

Topic 3: A Macroeconomic Theory of the Open Economy

Topic 4: Building Blocks of The Parity Framework

Topic 5: Monetary Policy, Interest, and Exchange Rates

Topic 6: Swaps & Linkage Across International Capital Markets

Topic 7: CFA Exam Questions

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Mankiw / Macroeconomics 5E (good optionalbackground reading)

Chapter 5 Open-Economy Macroeconomics

http://www.bfwpub.com/pdfs/mankiw/0716752379_12.pdf

http://www.bfwpub.com/pdfs/mankiw/0716752379_05.pdf

Chapter 12 Aggregate Demand in the Open Economy

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Investors’ Dictionaries (Use them Often!)

http://www.duke.edu/~charvey/Classes/wpg/glossary.htm

http://www.individualinvestor.com/investor_university/inv_glos.asp

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Sample Slides for

MS&E 247S International Investments

0 - 6Building Blocks of International Investments

International Investments

Exchange RateDetermination and KeyRelationships

International FinancialInstitutions andInstruments

International CorporateFinance: Currency Riskand Taxes

International PortfolioManagement: Allocationand Currency Risk

International FinancialInnovation and RiskManagement


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The Hamburger Standardhttp://www.economist.com/editorial/justforyou/f

ocus/big_mac_index.html

THE BIG MAC INDEXhttp://www.economist.com/markets/Bigmac/Index.cfm

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BIG MAC INDEXBurgernomics is based on the theory of purchasing-power parity, the notion that a dollar should buy thesame amount in all countries. Thus in the long run,the exchange rate between two countries shouldmove towards the rate that equalises the prices of anidentical basket of goods and services in eachcountry. In other words, a dollar should buy the sameamount everywhere. Our "basket" is a McDonald'sBig Mac, which is produced in about 120 countries.The Big Mac PPP is the exchange rate that wouldmean hamburgers cost the same in America asabroad. Comparing actual exchange rates with PPPsindicates whether a currency is under- or overvalued.

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Evidence: The Law of One Price• One test of the Law of One Price is the Big

Mac index, which has been publishedannually in The Economist since 1986.

• The Big Mac index was devised as a light-hearted guide to whether currencies are attheir “correct” level, based on PPP.– Our “basket” is a McDonalds’ Big Mac, which

is produced and consumed in variouscountries around the world.

– The Big Mac PPP is the exchange rate thatwould leave hamburgers costing the same inAmerica as abroad.

The Economist 4-34

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Evidence: The Law of One Price

¤ Comparing actual exchange rates with PPPssignals whether a currency is under- or over-valued.

• The result of the 2000 survey suggested thatthe average price of a Big Mac in the U.S. was$2.51, but was as little as $1.19 in Malaysia,and as much as $3.58 in Israel.

• Hence the Israeli shekel is the mostovervalued currency (by 43%), while theMalaysian ringgit is the most undervalued (by53%).

The Economist 4-35

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The Economist convert into dollars at the spot rate

Big MacPPP rate(of theUS$)

foreign-currency priceUS($) price

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=25/04/00 0 - 12

4-37The Economist

25/04/00


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Big Mac PPP rate(of the foreign

currency)

US($) priceforeign currency price=

Big Mac PPP rate(of the foreign currency)

x 100spot rate

(of foreign currency)Big Mac PPP rate

(of the foreign currency)–Under (-) / Over (+)

valuation againstthe dollar, %

=

Big Mac PPP rate(of the US$)

foreign currency priceUS($) price=

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Example 1. Canada

Purchasing power of C$2.85= Purchasing power of $2.51= a Big Mac

Hence Big Mac PPP implies 1 C$ = $ (2.51/2.85)

However from the market spot rate, 1 C$ = $ (1/1.47)

(-)/(+) valuation against $, % (based on Big Mac PPP)(1/1.47) - (2.51/2.85)

(2.51/2.85)=

= - 22.8%


=(1/1.47)

(2.51/2.85)= - 1

4-38

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Example 2. Denmark

Purchasing power of 24.75 DKr= Purchasing power of $2.51= a Big Mac

Hence Big Mac PPP implies 1 DKr = $ (2.51/24.75)

However from the market spot rate, 1 DKr = $ (1/8.04)

(-)/(+) valuation against $, % (based on Big Mac PPP)(1/8.04) - (2.51/24.75)

(2.51/24.75)=

= + 22.6%


(1/8.04)(2.51/24.75)= - 1

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The Economist

• The Big Mac index is not a perfect measure ofPPP. Price differences may be distorted bytrade barriers on beef, sales taxes, localcompetition and changes in the cost of non-traded inputs such as rents.

• But despite its flaws, the Big Mac indexproduces PPP estimates close to thosederived by more sophisticated methods.¤ A currency can deviate from PPP for long

periods, but several studies have found thatthe Big Mac PPP is a useful predictor of futuremovements.

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The Economist

¤ Indeed, the Big Mac has had severalforecasting successes.

¤ When the euro was launched at the start of1999, most forecasters predicted that it wouldrise. But the euro has instead tumbled -exactly as the Big Mac index had signaled. Atthe start of 1999, euro burgers were muchdearer than American ones.

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0 - 1817/04/01


0 - 1917/04/01 0 - 2017/04/01

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The first column of the table shows local-currencyprices of a Big Mac; the second converts them intodollars. The average price of a Big Mac in America is$2.54 (including sales tax). In Japan, Big Macscoffers have to pay ¥294, or $2.38 at currentexchange rates. The third column calculates PPPs.Dividing the yen price by the dollar price gives a BigMac PPP of ¥116. Comparing that with this week’srate of ¥124 implies that the yen is 6% undervalued.

(1/124 - 1/116)/(1/116) = -0.0645 = -6% (yen is 6%undervalued)

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The cheapest Big Macs are found in China,Malaysia, the Philippines and South Africa, and allcost less than $1.20. In other words, these countrieshave the most undervalued currencies, by morethan 50%. The most expensive Big Macs are foundin Britain, Denmark and Switzerland, which byimplication have the most overvalued currencies.Sterling, for example is 12% overvalued against thedollar—less than two years ago, it was overvaluedby 26%.

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The greatest triumph of the Big Mac index hasbeen in tracking the euro. When Europe’s newcurrency was launched in January 1999, virtuallyeverybody predicted that it would rise against thedollar. Everybody, that is, except the Big Macindex, which suggested that the euro started offsignificantly overvalued. One of the best-knownhedge funds, Soros Fund Management, admittedthat it chewed over the sell signal given by the BigMac index when the euro was launched, but thendecided to ignore it. The euro tumbled; Soros wascheesed off.

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The average price today in the 12 euro countries iseuro2.57, or $2.27 at current exchange rates. Theeuro’s Big Mac PPP against the dollar iseuro1=$0.99, which shows that it has now undershotMcParity by 11%. That, in turn, implies that sterlingis 26% overvalued against the euro.


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Overall, the dollar has never looked so overvaluedduring 15 years of burgernomics. In the mid 1990sthe dollar was cheap against most currencies; now itlooks dear against all but three. The mostundervalued of the rich-world currencies are theAustralian and New Zealand dollars, which are both40-45% below McParity. They need to ketchup.All the emerging-market currencies are undervaluedagainst the dollar on a Big Mac PPP basis. That, inturn, means that a currency such as Argentina’speso, which is undervalued only a tad against thedollar, is massively overvalued compared with othercurrencies, such as the Brazilian real and virtually allof the East Asian currencies.

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Some of our readers find the Big Mac index hard toswallow. Not only does the theory of purchasing-power parity hold only for the very long run, buthamburgers are a flawed measure of PPP. Localprices may be distorted by trade barriers on beef,sales taxes, or big differences in the cost of propertyrents. Nevertheless, some academic studies of theBig Mac index have concluded that betting on themost undervalued of the main currencies each yearis a profitable strategy.

Please update the Big Mac index (Apr 25th 2002) from thefollowing urls:http://www.economist.com/markets/Bigmac/Index.cfmhttp://www.economist.com/opinion/PrinterFriendly.cfm?Story_ID=1098872

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Arbitrage: Transactions intended to take advantage ofobserved pricing discrepancies, and earn profits with little orno exposure to risk (have arbitrage opportunities diminisheddue to the issue of the single European currency €?)· Spatial arbitrageFor a single currency, spatial arbitrage refers to pricedifferences across market locations or dealers.$/DM (NY) ≠ $/DM (London) or$/DM (Dealer A) ≠ $/DM (Dealer B)· Triangular arbitrageFor three currencies, triangular parity implies:SF/MP = SF/$ x $/MP MP: Mexican PesoImportance of triangular parity for constructing “cross rates”Direct markets in DM/£ were observed, but prices constrainedby DM/£ = DM/$ x $/£

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Triangular Arbitrage

$

£¥

Credit Lyonnais

S(£/$)=1.50

Credit Agricole

S(¥/£)=85

Barclays

S(¥/$)=120

Suppose weobserve thesebanks postingthese exchangerates.

First calculate theimplied cross ratesto see if anarbitrage exists.

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$

£¥

Credit Lyonnais

S(£/$)=1.50

Credit Agricole

S(¥/£)=85

Barclays

S(¥/$)=120

80¥1£

120¥1$

1$50.1£

=×

The implied S(¥/£) crossrate is S(¥/£) = 80

Credit Agricole hasposted a quote ofS(¥/£)=85 so there is anarbitrage opportunity.

So, how can we make money?

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$

£¥

Credit Lyonnais

S(£/$)=1.50

Credit Agricole

S(¥/£)=85

Barclays

S(¥/$)=120

80¥1£

120¥1$

1$50.1£

=×

As easy as 1 – 2 – 3:

1. Sell our $ for £,

2. Sell our £ for ¥,

3. Sell those ¥ for $.


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Triangular ArbitrageSell $100,000 for £ at S(£/$) = 1.50

receive £150,000Sell our £ 150,000 for ¥ at S(¥/£) = 85

receive ¥12,750,000

Sell ¥ 12,750,000 for $ at S(¥/$) = 120receive $106,250

profit per round trip = $ 106,250- $100,000 = $6,250

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The Bid-Ask Spread

• The bid price is the price a dealer iswilling to pay you for something.

• The ask price is the amount the dealerwants you to pay for the thing.

• The bid-ask spread is the differencebetween the bid and ask prices.

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Taking Advantage of aTriangular Arbitrage Opportunity

• A cross-rate trader at Bankers Trust notices that :– Credit Lyonnais is buying dollars at S(FF/$b)=5.0515, the

same as Bankers Trust’s bid price (bank’s $ buying price)– Barclays is offering (selling) dollars at S($/£b)=1.5573, also

the same as Bankers Trust’s selling price– Credit Agricole is making a direct market between the franc

and the pound, with a current FF bid price of S(£/FFb)=0.1273 (which implies a reciprocal £ ask price (offeringprice, bank’s currency selling price) of S(FF/£a)=7.8555)

• The FF/£ bid price should be no lower than S(FF/£b) = 1.5573 ×5.0515 = 7.8667. Yet Credit Agricole is offering to sell Britishpounds at a rate of only 7.8555! Opportunity knocks!

Eun/Resnick 4.3

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Eun/Resnick 4.3

S

£ FFCredit Agricole

S(FF/£a) = 7.8555

BarclaysS($/£b) = 1.5573

Credit LyonnalsS(FF/$b) = 5.0515


1.5573($/£b) x 5.0515(FF/$b) = 7.8667(FF/£b)

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$ 5,000,000× 5.0515FF 25,257,500÷ 7.8555£ 3,215,263× 1.5573$ 5,007,129$ 5,000,000$ 7,129

Bankers Trust Arbitrage Strategy

Sell U.S. dollars to Credit Lyonnaisfor French francsSell French francs to Credit Agricolefor British poundsSell British pounds to Barclaysfor U.S. dollars

Arbitrage profit

Eun/Resnick 4.3


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• Credit Agricole must raise its asking price aboveFF7.8555/£1.00.– The cross exchange rates gave FF/£ bid-ask prices (bank’of

FF7.8667-FF7.8717. These prices imply that Credit Agricolecan deal inside the spread and sell for less than FF7.8717, butnot less than FF7.8667.

– An ask price of FF7.8700, for example, would eliminate thearbitrage profit. At that price, the FF25,257,500 would beresold for FF25,257,500/7.8700=£3,209,339, which in turnwould yield only £3,209,339×1.5473=$4,965,810, or a loss of$34,190.

Eun/Resnick 4.3



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Cross-Rate Foreign Exchange Transactions

a. Bank Customer wants to sell £1,000,000 for French franks. The Bankwill sell U.S. dollars (buy British pounds) for $1.5573. The sale yieldsBank Customer: £1,000,000 x 1.5573 = $1,557,300.The Bank will buy dollars (sell French franks) for FF5.0515. The sale ofdollars yields Bank Customer: $1,557,300 x FF5.0515 = FF7,866,701Bank Customer has effectively sold British pounds at a FF/£ bid price ofFF7,866,701/£1,000,000 = FF7.8667/£1.00

American Terms ($/FC) European Terms (FC/$)Bank Quotations Bid Ask Bid AskBritish pounds 1.5573 1.5578 .6419 .6421French franks 0.1979 0.1980 5.0515 5.0531

0.1980 x 5.0515 = 1.000 and 0.1979 x 5.0531 = 1.000

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Cross-Rate Foreign Exchange Transactions

b. Bank Customer wants to sell FF10,000,000 for British pounds. TheBank will sell U.S. dollars (buy French franks) for FF5.0531. The saleyields Bank Customer: FF10,000,000 /5.0531 = $1,978,983.The Bank will buy dollars (sell British Pounds) for $1.5578. The sale ofdollars yields Bank Customer: $1,978,983 / $1.5578 = £1,270,370.Bank Customer has effectively bought British pounds at a FF/£ ask priceof FF10,000,000/£1,270,370 = FF7.8717/£1.00.

From parts (a) and (b), we see the currency against currency bid-askspread for British pounds is FF7.8667-FF7.8717.

American Terms ($/FC) European Terms (FC/$)Bank Quotations Bid Ask Bid AskBritish pounds 1.5573 1.5578 .6419 .6421French franks 0.1979 0.1980 5.0515 5.0531

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A Macroeconomic Theory of theOpen Economy

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The Market for Loanable Funds

Saving = Domesticinvestment

Net foreigninvestment+

S = I + NF I

Net foreign investment is the purchase offoreign assets by domestic residents minusthe purchase of domestic assets by foreigners.

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Some Important IdentitiesY (GDP, gross domestic product) =

C (consumption) + I (investment) + G (government purchases) + NX (net export)(for open economies)

Y=C+I+G (for a closed economy)

Y-C-G=IY-C-G is called the national saving, or just saving, and is denoted S

S=I (For economy as a whole, saving must be equal to investment.)

S=Y-C-G=(Y-T-C) + (T-G) where T is the net tax amount collectedby the government, Y-T-C is called private saving, and T-G iscalled public saving.

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Equilibriumquantity

Quantity ofLoanable Funds

RealInterest

Rate

Equilibriumreal interest

rate

Supply of loanable funds(from national saving)

Demand for loanable funds(for domestic investment

and net foreigninvestment)

A MACROECONOMIC THEORY OF THE OPEN ECONOMYA MACROECONOMIC THEORY OF THE OPEN ECONOMY

The Market for Loanable Funds

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The Market for Loanable FundsThe interest rate in an open economy, as in aclosed economy, is determined by the supplyand demand for loanable funds.National saving is the source of the supply ofloanable funds. Domestic investment and netforeign investment are the sources of thedemand for loanable funds.At the equilibrium interest rate, the amount thatpeople want to save exactly balances theamount that people want to borrow for thepurpose of buying domestic capital and foreignassets.

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The Market for Foreign Currency Exchange

Net foreign investment = Net exports

NF I = NX

Suppose that Boeing sells some planes to aJapanese airline for yens. This sale increasesU.S. net exports and U.S. net foreign investmentby the same amount. Boeing then exchanges itsyen for dollars with a U.S. mutual fund that wantsthe yen to buy stock in Sony (Japan). NX andNFI rise by an equal amount again!

6-130

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The Market for Foreign-CurrencyExchange...

Quantity of Dollars Exchangedinto Foreign Currency

RealExchange

Rate Supply of dollars(from net foreign investment)

Demand for dollars(for net exports)

Equilibriumquantity

Equilibriumreal exchange

rate

Copyright © 2001 by Harcourt, Inc. All rights reserved 0 - 46

Real and Nominal ExchangeRates

International transactions are influenced byinternational prices.The two most important internationalprices are the nominal exchange rate andthe real exchange rate.

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Nominal Exchange Rates

The nominal exchange rate is the rate atwhich a person can trade the currency ofone country for the currency of another.

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The nominal exchange rate is expressedin two ways:

In units of foreign currency per one U.S. dollar.And in units of U.S. dollars per one unit of theforeign currency.


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Assume the exchange rate between theJapanese yen and U.S. dollar is 80 yen toone dollar.

One U.S. dollar trades for eighty yen.One yen trades for 1/80 (=0.0125) of a dollar.

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If a dollar buys more foreign currency,there is an appreciation of the dollar.If it buys less there is a depreciation ofthe dollar.

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Real Exchange Rates

The real exchange rate is the rate atwhich a person can trade the goodsand services of one country for thegoods and services of another.

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Real Exchange Rates

The real exchange rate compares theprices of domestic goods and foreigngoods in the domestic economy.

If a case of German beer is twice as expensiveas American beer, the real exchange rate is 1/2case of German beer per case of American beer.

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Real Exchange Rates

The real exchange rate depends on thenominal exchange rate and the pricesof goods in the two countriesmeasured in local currencies.

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Real Exchange Rates

The real exchange rate is a keydeterminant of how much acountry exports and imports.

price Foreignprice Domestic x rate exchange Nominal =

RealExchange

Rate


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Real Exchange Rates

A depreciation (fall) in the U.S. realexchange rate means that U.S. goods havebecome cheaper relative to foreign goods.This encourages consumers both at homeand abroad to buy more U.S. goods andfewer goods from other countries.

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Real Exchange Rates

As a result, U.S. exports rise, and U.S.imports fall, and both of these changes raiseU.S. net exports.Conversely, an appreciation in the U.S. realexchange rate means that U.S. goods havebecome more expensive compared toforeign goods, so U.S. net exports fall.

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Purchasing-Power Parity

The purchasing-power parity theory isthe simplest and most widely acceptedtheory explaining the variation ofcurrency exchange rates.

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Purchasing-Power Parity

According to the purchasing-powerparity theory, a unit of any givencurrency should be able to buy the samequantity of goods in all countries.

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Basic Logic ofPurchasing-Power Parity

The theory of purchasing-power parity isbased on a principle called the law of oneprice.According to the law of one price, a goodmust sell for the same price in alllocations.

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If the law of one price were not true,unexploited profit opportunities wouldexist.The process of taking advantage ofdifferences in prices in different marketsis called arbitrage.


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If arbitrage occurs, eventually prices thatdiffered in two markets would necessarilyconverge.According to the theory of purchasing-power parity, a currency must have the samepurchasing power in all countries andexchange rates move to ensure that.

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Implications ofPurchasing-Power Parity

If the purchasing power of the dollar isalways the same at home and abroad, thenthe exchange rate cannot change.The nominal exchange rate between thecurrencies of two countries must reflect thedifferent price levels in those countries.

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Implications ofPurchasing-Power Parity

When the central bank prints large quantitiesof money, the money loses value both interms of the goods and services it can buyand in terms of the amount of othercurrencies it can buy.

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10,000,000,000

1,000,000,000,000,000

100,000

1

.00001

.00000000011921 1922 1923 1924 1925

Exchange rate

Money supply

Price level

Indexes(Jan. 1921 = 100)

Money, Prices, and the Nominal ExchangeRate During the German Hyperinflation

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Limitations ofPurchasing-Power Parity

Many goods are not easily traded orshipped from one country to another.Tradable goods are not always perfectsubstitutes when they are produced indifferent countries.

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The Market for Foreign Currency ExchangeThe real exchange rate is determined by the supplyand demand for foreign-currency exchange.The supply of dollars comes from net foreigninvestment (NFI). Because NFI does not depend onthe real exchange rate, the supply curve is vertical.The demand for dollars comes from net exports.Because a lower real exchange rate stimulates netexports (and thus increases the quantity of dollarsdemanded to pay for these net exports), the demandcurve is downward sloping.At the equilibrium real exchange rate, the number ofdollars people supply to buy foreign assets exactlybalances the number of dollars people demand to buynet exports.


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Net Foreign Investment :The Link Between the Two Markets

S = I + NF I

NF I = NX

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6-134

0 Net ForeignInvestment

Net foreign investmentis negative.

Net foreign investmentis positive.

RealInterest

Rate

A MACROECONOMIC THEORY OF THE OPEN ECONOMYA MACROECONOMIC THEORY OF THE OPEN ECONOMY

How Net Foreign Investment Depends on the Interest Rate

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How Net Foreign InvestmentDepends on the Interest Rate

Because a higher domestic real interest ratemakes domestic assets more attractive, itreduces net foreign investment.Note the position of zero on the horizontal axis:Net foreign investment can be either positive ornegative.

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Principles of Macroeconomics Figure 18.4

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The Real Equilibrium in an Open Economy

In panel (a), the supply and demand forloanable funds determine the real interest rate.In panel (b), the interest rate determines netforeign investment, which provides the supply ofdollars in the market for foreign-currencyexchange. In panel (c), the supply and demandfor dollars in the market for foreign-currencyexchange determine the real exchange rate.

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The Effects of a Government Budget Deficit

When the government runs a budget deficit, itreduces the supply of loanable funds from S1 to S2in panel (a). The interest rate rises from r1 to r2 tobalance the supply and demand for loanable funds.In panel (b), the higher interest rate reduces netforeign investment. Reduced net foreigninvestment, in turn, reduces the supply of dollars inthe market for foreign-currency exchange from S1 toS2 in panel (c). This fall in the supply of dollarscauses the real exchange rate to appreciate fromE1 to E2. The appreciation of the exchange ratepushes the trade balance toward deficit.


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The Effects of an Import QuotaWhen the U.S. government imposes a quota on theimport of Japanese cars, nothing happens in themarket for loanable funds in panel (a) or to netforeign investment in panel (b). The only effect is arise in net exports (exports minus imports) for anygiven real exchange rate. As a result, the demandfor dollars in the market for foreign-currencyexchange rises, as shown by the shift from D1 to D2in panel (c). This increase in the demand for dollarscauses the value of the dollar to appreciate from E1to E2. This appreciation of the dollar tends to reducenet exports, offsetting the direct effect of the importquota on the trade balance.

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The Effects of Capital FlightIf people in Mexico decide that Mexico is a risky place tokeep their savings, they will move their capital to saferhavens such as the United Sates, resulting in an increase inMexican net foreign investment.Consequently, the demand for loanable funds in Mexicorises from D1 to D2, as shown in panel (a), and this drives upthe Mexican real interest rate from r1 to r2. Because netforeign investment is higher for any interest rate, that curvealso shifts to the right from NFI1 to NFI2 in panel (b). At thesame time, in the market for foreign-currency exchange, thesupply of pesos rises from S1 to S2, as shown in panel (c).This increase in the supply of pesos causes the peso todepreciate from E1 to E2, so the peso becomes less valuablecompared to other currencies.

0 - 78Building Blocks of The Parity Framework

The Parity Framework

Four Definitions: S, F, r, I

Four Derived KeyTerms: rF - rD, IF - ID,f, s

Purchasing PowerParity + UncoveredInterest Parity (FisherInternational Effect)

Forward Rate UnbiasedProperty + Interest RateParity

Key Interest – ExchangeRates Linkages


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Four DefinitionsThe spot exchange rate, S. The rate of exchange of twocurrencies tells us the amount of foreign currency that one unitof domestic currency can buy. Spot means that we refer to theexchange rate for immediate delivery.The forward exchange rate, F. The rate of exchange of twocurrencies set on one date for delivery at a future specifieddate, the forward rate is quoted today for a delivery takingplace at a future date.The interest rate, r. The rate of interest for a given timeperiod is a function of the length of the time period and thedenomination of the currency. Interest rates are usuallyquoted in the market place as an annualized rate.The inflation rate, I. This is equal to the rate of consumerprice increase over the period specified. The inflationdifferential is equal to the difference of inflation rates betweentwo countries.

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The interest rate differential, rF - rD. The interest ratedifferential is equal to the difference in interest rates betweentwo countries.

The inflation differential, IF - ID. The inflation differential isequal to the difference of inflation rates between two countries.

The forward discount or premium, f. This is often calculatedas an annualized percentage deviation from the spot rate:

The exchange rate movement, s. This is equal to the spotexchange rate movement over the period specified.f = (F-S0)/S0 and s = (S1-S0)/S0

Four Derived Key Terms

annualizedforwardpremium(discount)

forward rate - spot ratespot rate

= × × 100 %12no. months forward

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t = 0 1 2 3 n……

S1S0

F0,1

F0,2

F1,1

F1,2

S2 S3

Forward exchange rate premium f = (F-S0)/S0

Exchange rate movement over the period specified

s = (S1-S0)/S0

Spot rate: S0 = S current time

Forward rate: F0,1 = F contract signing time, time to maturity

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· Parity conditions are useful when parity holds· Parity conditions are useful when parity does not hold

Key Interest Rate-Exchange Rate Linkages:The Parity Framework

Please note that parity conditions are long-termequilibrium conditions. It might not happen in thenear future (e.g., in three months) but it morelikely to happen in the long-run (e.g., in six years).

0 - 83Four International Parity ConditionsPurchasing Power Paritylinking spot exchange rates and inflationAbsolute PPP: The price of a market basket of U.S. goodsequals the price of a market basket of foreign goods whenmultiplied by the exchange rate.Relative PPP: The percentage change in the exchange rateequals the percentage change in U.S. goods prices less thepercentage change in foreign goods prices.Uncovered Interest Paritylinking interest rates and inflationFisher Effect: For a single economy, the nominal interest rateequals the real interest rate plus the expected rate of inflation.International Fisher Effect: For two economies, the U.S. interestrate minus the foreign interest rate equals the expecteddifference in inflation rates between the two countries.

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Interest Rate Paritylinking forward exchange rates and expected spotexchange rateThe forward exchange rate premium equals (approximately)the U.S. interest rate minus the foreign interest rate.

Forward Rate Unbiased Propertylinking forward exchange rates and expected spotexchange ratesForeign Exchange Expectations: Today’s forward premium (fordelivery in n days) equals the expected percentage change inthe spot rate (over the next n days).

Four International Parity Conditions


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International Parity Relations Linear Approximationwhere Spot Rate S are in indirect quote (FC/DC or FC/$)

Solnik 2.1

Interest RateParity

Forward RateUnbiasedProperty

Uncovered Interest Parityor Fisher InternationalEffect

Purchasing PowerParity (relativeversion) PPP

IRPFIE

FRU

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An Example of Interest Rate Parity

Suppose an investor with $1,000,000 to invest for90 days is trying to decide between investing inU.S. dollars at 8% per annum (2% for 90 days) orin DM at 6% per annum (1.5% for 90 days).The current spot rate is DM 1.5311/$ and the 90-day forward rate is DM 1.5236/$.As shown in the next slide, regardless of theinvestor’s currency choice, his hedged returnwill be identical.

Multinational Financial Management 6-136

0 - 87

An Example of Interest Rate Parity

Multinational Financial Management Ex 5.7

Alternative investment:Invest $1,000,000 in

New York for 90 days at 2%and receive $1,020,000 in 90 days

New York

Start$1,000,000

Finish$1,020,000

Convert $1,000,000to DM at DM 1.5311/$ for DM 1,531,100

1.

DM 1,531,100Frankfurt: today

DM 1,554,066.50Frankfurt: 90 days

Invest DM 1,531,100 at 1.5%for 90 days, yielding DM 1,554,066.50 in 90 days

2.

Simultaneously with the DMinvestment, sell the DM 1,554,066.50 forward at arate of DM 1.5236/$ for delivery in 90 days, &receive $1,020,000 in 90 days

3.

6-137

0 - 88

Korean Won: Depreciation versus Interest Rate Differential(in % per year)

Solnik 2.3

0 - 89

From 1991 to 1996, the won had a much higherinterest rate than the dollar (an annual differentialaround 10%), but the exchange rate with thedollar remained stable. In 1997, the Asian crisishit many currencies in the region and the wonwas devalued by some 50%.

Averaging over the 1991-97 period, we find thatthe interest rate differential roughly matches thecurrency depreciation. So any investor applyingthe strategy to invest in this high-interest-ratecurrency would have made a profit for severalyears and lost all of it in 1997.

Solnik 2.3

0 - 90

An Example of Covered Interest ArbitrageSuppose the interest rate on pounds sterling is 12% inLondon, and the interest rate on a comparable dollarinvestment in New York is 7%. The pound spot rate is$1.75 and the one-year forward rate is $1.68. These ratesimply a forward discount on sterling of 4% [(1.68 - 1.75) /1.75] and a covered yield on sterling approximately equalto 8% (12% - 4%). Because there is a covered interestdifferential in favor of London, funds will flow from NewYork to London.To illustrate the profits associated with covered interestarbitrage, we will assume that the borrowing and lendingrates are identical and the bid-ask spread in the spot andforward markets is zero.

Multinational Financial Management 6-138


0 - 91

An Example of Covered Interest Arbitrage

Multinational Financial Management Ex 5.8

New Yorktodayone year

Borrow $1 million at an interestrate of 7%, owing $1,070,000at year end

1.

London : todayLondon: one year

Start:

Convert the $1 million to pounds at $1.75/£ for£571,428.57

2.

Invest the £571,428.57in London at 12%,generating £640,000 by year end

3.

Simultaneously, sell the£640,000 in principal plusinterest forward at a rate of$1.68/£ for delivery in year,yielding $1,075,200 at year end

4.

Net profit equals$5,200

7.Finish:

Repay the loan plus interest of $1,070,000 out of the $1,075,200

6.

Collect the £640,000 and deliver it to the bank’s foreign exchange department in return for $1,075,200

5.

6-139

0 - 92

Monetary Policy, Interest Rates,and Exchange Rates

In an open economy with flexible exchange rates, assumethat there is no inflation (so, nominal rates = real rates)and that initially, domestic and foreign interest rates areexpected to be constant and equal to each other.

The central bank announces that one-year interest rateswill be 2% lower for each of the next five years, after whichthey will return to normal. Financial markets fully believethis announcement.

What is the effect on the exchange rate today?

B21 - 22

0 - 93

0 1 2 3 4 50

2

4

6

8

10%

0 1 2 3 4 5- 2

0%

Years

Years

Interest rate, i

Exch

ange

rate

, E (D

C/F

C)

depreciation

expectedappreciation

The announcement does not affectthe interest rates (and hence,exchange rates) beyond the firstfive years.

Interest parity: For the five years,the domestic currency is expectedto appreciate by 2% each year, sothat the rates of return on domesticand foreign bonds are equal.

So, a 2% decrease in interest ratesexpected to last for five years leadsto a depreciation of 5x2%=10%today, followed by expectedappreciation of 2% a year over thenext five years.

Monetary Policy, Interest Rates,and Exchange Rates

B21 - 23

0 - 94

The long run is a misleading guide to currentaffairs. In the long run we are all dead.Economists set themselves too easy, toouseless a task if in tempestuous seasonsthey can only tell us when the storm is longpast, the ocean will be flat.

- John Maynard Keynes

7-48

Long-Run versus Short-Run

0 - 95

Technical analysis vs. Fundamental Analysis

Technical analysis is the form of chartinginvolves the search of current and predictablepatterns in stock prices to enhance returns.

Fundamental analysis uses earnings anddividend prospects of the firm, expectations offuture interest rates, and risk evaluation of thefirm to determine the stock prices.

0 - 96


0 - 97 0 - 98

0 - 99

International Financial Innovation:

(1) Constructing Outright Forward Contract

(2) Exotic Swap

0 - 100

t = 0 1 2 3 n……

S1S0

F0,1

F0,2

F1,1

F1,2

S2 S3

Forward exchange rate premium f = (F-S0)/S0

Exchange rate movement over the period specified

s = (S1-S0)/S0

Spot rate: S0 = S current time

Forward rate: F0,1 = F contract signing time, time to maturity

0 - 101

Suppose you need DM in 180 days.Option 1buy DM in the spot market - and earn interest in DM (money market hedging)Option 2buy DM in the forward market (hedging withforward) - will have to pay 1.3022% more than the spot price

Option 3buy DM in the spot market 180 days later - but is exposed to foreign exchange rate risk

Spot v.s. Forward0 - 102

D

A

Foreign Exchange MarketProducts and Activities

time dimension

curr

ency

dim

ensi

on

Jan 1 Jul 1US$

DM

A managerwishes toown DMon July 1.

buy DMforward

at F

sell DMforward

at F

Option 2

The Relationship between Spot and Forward Contracts


0 - 103

D

Foreign Exchange MarketProducts and Activities

time dimension

curr

ency

dim

ensi

on

Jan 1 Jul 1US$

DM

A managerwishes toown DMon July 1.

A

The Relationship between Spot and Forward Contracts

Bborrow US$ at i$

lend US$ at i$

Option 1

C

buy DMspot at S

sell DMspot at S

borrow DM at iDM

lend DM at iDM

0 - 104

time dimension

curr

ency

dim

ensi

on

Jan 1 Jul 1US$

DM

B A

C D

Spot v.s. Forward

Levich Figure 3.2 Pg. 78

borrow DM at iDM

lend DM at iDM

borrow US$ at i$

lend US$ at i$

buy DMspot at

S

sell DMspot at

S

buy DMforward

at F

sell DMforward

at F

0 - 105

Subject: Regarding the "Box" Diagram(1) An arrow from DM to US$, can be thought of asSELLING DM or BUYING US$.(2) The reverse arrow from US$ to DM represents thereverse transaction, SELLING US$ or BUYING DM.(3) An arrow from right to left (from the future to thepresent), can be thought of as borrowing - taking cashfrom the future and bringing it to the present.(4) The reverse arrow from left to right (from the present tothe future), can be thought of as investing - taking cashthat you have now and putting it away until the future.

0 - 106

Note: A forward purchase of DM (equivalent to aforward sale of US$) is shown by the arrow AD.This outright forward contract can be replicatedby (1) borrowing US$ (arrow AB), (2) buying DMin the spot market (arrow BC), and (3) lending theDM (arrow CD).

The borrowing and lending are carried out as asingle transaction – a foreign exchange swap.The maturity of the forward contracts is identicalto the maturity of the borrowing and lendingcontracts.

A forward sale of DM can be described byreversing the direction of the arrows.

0 - 107

Using Figure 3.2:Constructing Outright Forward Contracts

Forward Purchase of DM on January for Value on July 1Line segment AD (price F, forward rate $/DM)Can be replicated by:Borrowing $, line segment AB (price i$)Buying DM spot, line segment BC (price S)Lending DM, line segment CD (price iDM)

Forward Sale of DM on January 1 for Value on July 1Line segment DA (price F) Can be replicated by:Borrowing DM, line segment DC (price iDM)Selling DM spot, line segment CB (price S)Lending $, line segment BA (price i$)

0 - 108

Implication:In the absence of transaction costs, price offorward contract = price of three replicatingcontracts.F ($/DM) = S ($/DM) × (1 + i[$]) (1 + i[DM])

Further Implications:Forward contracts are 'redundant'; that is, aforward contract can be replicated by a spotcontract and a swap (a simultaneous borrowingand lending in the money market).


0 - 109

A corporation that uses an outright forwardcontract has a contingent, off-balancesheet liability. No cash changes hand so there isno direct effect on the firm's balance sheet. Theforward contract uses part of the firm's scarcecredit capacity at its bank.

A bank that constructs or hedges a forwardposition by using a ‘spot and a swap’ alters theasset and liability exposure of the bank. In otherwords, the trader’ s position must be funded.

0 - 110

Swaps & Linkages Across International Capital Markets

Cross Currency Interest Rate Swap

Interest Rate Swap

Interest Rate Swap Floating-Floating Currency Sw

apFixe

d-Fi

xed

Cur

renc

y Sw

ap

A B

C D

Cur

renc

y X

Cur

renc

y Y

Fixed RateAsset or Liability

Floating RateAsset or Liability

Interest Rate Base

Currency ofDenomination

Figure 13.8 Pg 469

ExamplesA Dollar-denominated straight EurobondB Eurodollar floating- rate note (FRN)C Samurai bondD Euroyen floating- rate note (FRN)

13-32

Cross Curre

ncy In

teres

t Rate

Swap

0 - 111

13-36

Price Quoting Conventions in the Swap Market

CounterParty A

SwapDealer

CounterParty B

Swap dealerreceives

floating rate

Swap dealerpays fixed

rate

Swap dealerpays

floating rate

Swap dealerreceivesfixed rate

Bid Quote Offer QuoteSwap Quotes

Quotes are given from the perspective of the swap dealer.The convention is to quote only the fixed side of the swap.All fixed quotes are against LIBOR unless otherwise stated.

Panel C of Table 13.5 Pg 470

0 - 112

Applications of Swaps:Magnifying Risk and Return

Many of the illustrations in this chapter have linked aswap with a bond issue, but these decisions areseparable. A firm can issue a bond in one year andthen decide to swap later, using the swap as a riskmanagement tool. However, a firm could enter into aswap without a prior bond issue. This transaction isthe same as a pure speculation on the direction ofexchange rates or interest rates.

0 - 113

An Unsuccessful Exotic Swap

Procter and Gamble (P&G) (based in Cincinnati andwith $30 billion in annual sales) lost $157 million onan exotic swap whose payments (“in most cases”)were defined by the formula:

17.0415 x (5-year Treasury rate)- (price of 6.25 percent Treasury due 8/2023)- 0.75%

The amount of interest that P&G would pay under thisformula is shown in Table 13.7.

0 - 114

30-Year Interest Rate5-year Int 6% 7% 8%

5% -0.75% -0.75% 4.20%6% -0.75% 10.80% 21.20%7% 15.10% 24.90% 38.20%

Table 13.7 Interest Cost (Premium over the CP Rate) in the Procter & Gamble/Bankers Trust Interest Rate Swap


0 - 115

International Risk Management

How Leeson Broke Barings

0 - 116

The activities of Nick Leeson on the Japanese and Singaporefutures exchanges, which led to the downfall of his employer,Barings, are well-documented.Barings collapsed because it could not meet the enormous tradingobligations, which Leeson established in the name of the bank.When it went into receivership on February 27, 1995, Barings, viaLeeson, had outstanding notional futures positions on Japaneseequities and interest rates of US$27 billion: US$7 billion on theNikkei 225 equity contract and US$20 billion on Japanesegovernment bond (JGB) and Euroyen contracts. Leeson also sold70,892 Nikkei put and call options with a nominal value of $6.68billion. The nominal size of these positions is breathtaking; theirenormity is all the more astounding when compared with the banksreported capital of about $615 million.

0 - 117

The size of the positions can also be underlined by the fact that inJanuary and February 1995, Barings Tokyo and London transferredUS$835 million to its Singapore office to enable the latter the meetits margin obligations on the Singapore International MonetaryExchange (SIMEX).

0 - 118

0 - 119 0 - 120

The Building Blocks of Contingent Decisions

(a) Purchase of Right to Buy at a Fixed Price

(b) Purchase of Right to Sell at a Fixed Price

Opt

ion

Payo

ff

Value of Underlying Asset at Decision Date

(c) Sell Right to Buy at a Fixed Price

(d) Sell Right to Sell at a Fixed Price

$0 $0

Real Options: Amram & Kulatilaka Figure 4.1


0 - 121

The Building Blocks of Noncontingent Decisions(e) Forward Purchase (long position)(e) = (a) + (d)

(f) Forward Sale (short position)(f) = (b) + (c)

Payo

ff

Value of Underlying Asset at Decision Date

$0 $0

Real Options: Amram & Kulatilaka Figure 4.2

A forward contract is the right to buy or sell an asset ata specified date in the future at a specified price. Thepayoffs to a forward are not contingent on a futuredecision (hence there is no kink) but do depend on therealized value of an uncertain asset (the line is sloped).

0 - 122

A Short Straddle (sale both a call and a put)in the $/£

0.10

0.05

0.00

-0.05

-0.10

-0.15

-0.201.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75

Prof

it or

Los

s in

$

$/£

Profit and Loss Positions

Sell Call

Sell Put

ShortStraddle

Box 12.1 Figure A

0 - 123 0 - 124

About the CFA Program• The Chartered Financial Analyst (CFA) Program is a

globally recognized standard for measuring thecompetence and integrity of financial analysts.

• Its curriculum develops and reinforces a fundamentalknowledge of investment principles.

• Three levels of examination measure a candidate’sability to apply these principles at a professional level.

• The CFA exam is administered annually in more than 70nations worldwide.

• http://www.aimr.org/cfaprogram/

0 - 125

a. Explain the following three concepts ofpurchasing power parity (PPP):i. The law of one price.ii. Absolute PPP.iii.Relative PPP.

b. Evaluate the usefulness of relative PPP inpredicting movements in foreign exchangerates on a:i. Short-term basis (e.g., three months).ii. Long-term basis (e.g., six years).

CFA (level III, 1997)

CFA-1

0 - 126

i. The law of one price is that, assuming competitive markets andno transportation costs or tariffs, the same goods should havethe same real prices in all countries after converting prices toa common currency.

ii. Absolute PPP, focusing on baskets of goods and services, statesthat the same basket of goods should have the same price in allcountries after conversion to a common currency. Underabsolute PPP, the equilibrium exchange rate between twocurrencies would be the rate that equalizes the prices of abasket of goods between the two countries. This rate wouldcorrespond to the ratio of average price levels in the countries.Absolute PPP assumes no impediments to trade and identicalprice indexes that do not create measurement problems.


CFA-2


0 - 127

CFA (level III, 1997)iii.Relative PPP holds that exchange rate movements reflect

differences in price changes (inflation rates) betweencountries. A country with a relatively high inflation ratewill experience a proportionate depreciation of itscurrency’s value vis-à-vis a country with a lower rate ofinflation. Movements in currencies provide a means formaintaining equivalent purchasing power levels amongcurrencies in the presence of differing inflation rates.Relative PPP assumes prices adjust quickly and priceindexes properly measure inflation rates. Because relativePPP focuses on changes and not absolute levels, relativePPP is more likely to be satisfied than the law of one priceor absolute PPP.

CFA-3

0 - 128

CFA (level III, 1997)i. Short-term basis (e.g., three months). Relative PPP is not

consistently useful in the short run because: (1) Relationshipsbetween month-to-month movements in market exchangerates and PPP are not consistently strong, according toempirical research. Deviations between the rates can persistfor extended periods; (2) exchange rates fluctuate minute byminute because they are set in the financial markets. Pricelevels, in contrast, are sticky and adjust slowly; and, (3) manyother factors can influence exchange rate movements ratherthan just inflation.

ii. Long-term basis (e.g., six years). Research suggests that overthe long term a tendency exists for market and PPP rates tomove together, with market rates eventually moving towardlevels implied by PPP.

CFA-4

0 - 129

Even though the investment community generally believesthat country M’s recent budget deficit reduction is“credible, sustainable, and large,” analysts disagree abouthow it will affect country M’s foreign exchange rate. JuanDaSilva, CFA, states “the reduced budget deficit will lowerinterest rates, which will immediately weaken country M’sforeign exchange rate.”


a. Discuss the direct (short-term) effects of a reduction incountry M’s budget deficit on:i. Demand for loanable funds.ii. Nominal interest rates.iii.Exchange rates.

CFA-5

0 - 130

CFA (level III, 1998)b. Helga Wu, CFA, states, “Country M’s foreign

exchange rate will strengthen over time as a result ofchanges in expectations in the private sector incountry M.” Support Wu’s position that country M’sforeign exchange rate will strengthen because of thechanges a budget deficit reduction will cause in:i. Expected inflation rates.ii. Expected rates on return on domestic securities.

CFA-6

0 - 131

CFA (level III, 1998)i. Demand for loanable funds. The immediate effect of reducing

the budget deficit is to reduce the demand for loanable fundsbecause the government needs to borrow less to bridge the gapbetween spending and taxes.

ii. Nominal interest rates. The reduced public sector demand forloanable funds has the direct effect of lowering nominalinterest rates because lower demand leads to lower cost ofborrowing.

iii.Exchange rates. The direct effect of the budget deficitreduction is a depreciation of the domestic currency and theexchange rate. As investors sell lower yielding country Msecurities to buy the securities of other countries, country M’scurrency will come under pressure and country M’s currencywill depreciate.

CFA-7

0 - 132

CFA (level III, 1998)i. Expected inflation rates. In the case of a credible,

sustainable, and large reduction in the budget deficit,reduced inflationary expectations are likely because thecentral bank is less likely to monetize the debt by printingmoney. Purchasing power parity and international Fisherrelationships suggest that a currency should strengthenagainst other currencies when expected inflation declines.

ii. Expected rates on return on domestic securities. A reductionin government spending would tend to shift resources intoprivate sector investments, where productivity is higher.The effect would be to increase the expected return ondomestic securities.

CFA-8


0 - 133

CFA (level III, 1996)The HFS Trustees have decided to invest in internationalequity markets and have hired Jacob Hind, a specialistmanager, to implement this decision. He hasrecommended that an unhedged equities position betaken in Japan, providing the following comment anddata to support his views:

“Appreciation of a foreign currency increases thereturns to a U.S. dollar investor. Since appreciation ofthe yen from 100¥/$ to 98 ¥/$ is expected, the Japanesestock position should not be hedged.”

CFA-9

0 - 134

CFA (level III, 1996)Market Rates and Hind’s Expectations

Spot rate (direct quote)Hind’s 12-month currency forecast1-year Eurocurrency rate (% per annum)Hind’s 1-year inflation forecast (% per annum)

n/an/a6.003.00

100 98 0.80 0.50

U.S. Japan

Assume that the investment horizon is one year and thatthere are no costs associated with currency hedging.State and justify whether Hind’s recommendation shouldbe followed. Show any calculations.

CFA-10

0 - 135

CFA (level III, 1996)Appreciation of a foreign currency will, indeed, increase thedollar returns that accrue to a U.S. investor. However, theamount of the expected appreciation must be compared withthe forward premium or discount on that currency in order todetermine whether hedging should be undertaken or not.

In the present example to yen is forecast to appreciate from100 to 98 (2 percent). However, the forward premium on theyen as given by the differential in one-year eurocurrencyrates, suggests an appreciation of over 5 percent:

Forward premium = [(1.06)/(1.008)] -1 = 5.16%

CFA-11

0 - 136

CFA (level III, 1996)Thus, the manager’s strategy to leave the yen unhedged is notappropriate. The manager should hedge because by doing so,a higher rate of yen appreciation can be locked in. Given theon-year eurocurrency rate differentials, the yen positionshould be left unhedged only if the yen is forecast toappreciate to over 95 yen per US dollar.

CFA-12

0 - 137

Good Sources of Information onInternational Investments

· Datastream is an extremely rich source ofinternational financial data (currencies, stocks,bonds, macro statistics, etc.).

· International Financial Statistics, published monthlyby The International Monetary Fund, contains muchfinancial and macroeconomic data for IMF membercountries.

· The Economist's Intelligence Unit publishesquarterly Country Reports and annual CountryProfiles. These are good, for example, for detailson countries’ foreign exchange regimes.

0 - 138

· Commercial and investment banks: most producevaluable research on current developments (e.g.,Bank of America's monthly Currency Review).

· Euromoney is a periodical that focuses on issuesrelevant to this class; occasionally, a particular topicwill be treated in depth in a EuromoneySupplement.

· The National Bureau of Economic Research(NBER) produces a working paper series thatcontains current academic articles on internationaltopics (check http://www.nber.org).

· See my web page for links to useful sites ininternational financehttp://www.stanford.edu/~ffuy/weblinks.htm

Documents

0 - 2 Sample Topics for MS&E 247S International Investments MWF 1