International Finance

International Portfolio Investments

Security X & Y with the following attributes

Security Return RiskX 20% 10%Y 30% 16%

Correlation coefficient (ρX,Y) = 0.540% of funds invested on XCalculate the portfolio return & risk

Ep = ∑ Wi Ei

= (.40)(.20) + (.60)(.30) = 0.26 = 26%σ2

p = w21 σ2

1 + w22 σ2

2 + 2w1w2 ρ1,2 σ1*σ2 = (40%)2(10%)2+(60%)2(16%)2+2(40%)(60%)(0.5)(10%)(16%) = 12.1%

International Correlation Structure and Risk Diversification

• Security returns are much less correlated across countries than within a country.– This is so because economic, political, institutional, and

even psychological factors affecting security returns tend to vary across countries, resulting in low correlations among international securities.

– Business cycles are often high asynchronous across countries.

U.S based investor takes US$1000000 on January 1, 2002, and invests in a share traded on the Tokyo Stock Exchange (TSE). On January 1, 2002, the spot exchange rate is ¥130.00/$. The investor uses his funds to acquire shares on the TSE at ¥20000 per share, and holds the shares for one year. At the end of one year, the investor sells the shares at the market price, which is ¥25000. On January 1, 2003, the spot rate is ¥125.00/$.Calculate the total return on the investment

(US$1300000 – US$1000000)/ US$1000000 = 30%

The total return is a combination of the return on the Japanese Yen and the return on the shares listed on the TSE

R$ = [(1 + r¥/$)(1 + rshares,¥)] – 1

rshares,¥ = Percentage change in the share pricer¥/$ = Percentage change in the currency value

R$ = [(1 + 0.2500)(1 + 0.0400)] – 1 =30%

If a U.S. resident just sold shares in a British firm that had a 15% return (in pounds) during a period when the pound depreciated 5%, his dollar return is

Effects of Changes in the Exchange Rate

• The realized dollar return for a U.S. resident investing in a foreign market will depend not only on the return in the foreign market but also on the change in the exchange rate between the U.S. dollar and the foreign currency.

International Correlation Structure

Stock Market AU FR GM JP NL SW UK US

Australia (AU) .586              

France (FR) .286 .576            

Germany (GM) .183 .312 .653          

Japan (JP) .152 .238 .300 .416        

Netherlands (NP)

.241 .344 .509 .282 .624      

Switzerland (SW)

.358 .368 .475 .281 .517 .664    

United Kingdom (UK)

.315 .378 .299 .209 .393 .431 .698  

United States (US)

.304 .225 .170 .137 .271 .272 .279 .439

Relatively low international correlations imply that investors should be able to

reduce portfolio risk more if they diversify internationally

rather than domestically.

Domestic vs. International Diversification

0.44

0.27

0.12

Portf

olio

Ris

k (%

)

Number of Stocks1 10 20 30 40 50

Swiss stocks

U.S. stocks

International stocks

When fully diversified, an international portfolio can be less than half as risky as a

purely U.S. portfolio.

A fully diversified international portfolio is only 12 percent as risky as holding a single

security.

Optimal International Portfolio Selection

• The correlation of the U.S. stock market with the returns on the stock markets in other nations varies.

• The correlation of the U.S. stock market with the Canadian stock market is 70%.

• The correlation of the U.S. stock market with the Japanese stock market is 24%.

• A U.S. investor would get more diversification from investments in Japan than Canada.

Summary Statistics for Monthly Returns ($U.S.)

Stock Market Correlation Coefficient Mean (%)

SD (%)

CN FR GM JP UK

Canada (CN)           .79 5.83 0.90

France (FR) 0.38         1.42 7.01 1.02

Germany (GM)

0.33 0.66       1.23 6.74 0.87

Japan (JP) 0.26 0.42 0.36     1.47 7.31 1.22

United Kingdom

0.58 0.54 0.49 0.42   1.52 5.41 0.90

United States 0.70 0.45 0.37 0.24 0.57 1.33 4.56 0.80

.79% monthly return = 9.48% per year

Summary Statistics for Monthly Returns ($U.S.)

Stock Market Correlation Coefficient Mean (%)

SD (%)

CN FR GM JP UK

Canada (CN)           .79 5.83 0.90

France (FR) 0.38         1.42 7.01 1.02

Germany (GM)

0.33 0.66       1.23 6.74 0.87

Japan (JP) 0.26 0.42 0.36     1.47 7.31 1.22

United Kingdom

0.58 0.54 0.49 0.42   1.52 5.41 0.90

United States 0.70 0.45 0.37 0.24 0.57 1.33 4.56 0.80

measures the sensitivity of the market to the world market.

Clearly the Japanese market is more sensitive to the world

market than is the U.S.

The Optimal International Portfolio

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8

Standard Deviation (monthly)

Mea

n R

etur

n (m

onth

ly)

US

CN

GM

UKJP

FR

4.2%

1.53OIP Efficient set

Rf

1.53%

1.33%

Gains from International Diversification

• For a U.S. investor, the risk-return tradeoff for the optimal international portfolio and optimal domestic portfolio are shown below and at right.

  OIP ODP

Mean Return

1.53% 1.33%

Standard Deviation

4.27% 4.56%risk

retu

rn

4.27% 4.56%

OIP

ODP

An investor is considering investing in two different risky assets, an index of the U.S equity markets and an index of the German equity markets.

Expected return Expected riskU.S equity index 14% 15%German equity index 18% 20%Correlation coefficient (ρUs-GER) 0.3440% of investment on U.S

Calculate the return & risk on international portfolio

Country E(Ri) σi Wi A 0.12 0.20 0.60 B 0.08 0.10 0.30 C 0.04 0.03 0.10ρAB = 0.25ρAC = -0.08ρBC = 0.15Calculate the international portfolio expected return & risk

E(Rp) = (0.60)(0.12) + (0.30)(0.80) + (0.10)(0.04) = 10%

σ2p = ∑W2

i σ2j + ∑∑WiWjCovij

σ2p = [W2

Aσ2A+W2

Bσ2B+W2

Cσ2C]+[2WAWBσAσBρAB+2WAWCσAσCρAC

+ 2WBWC σBσCρBC] = 13.6%

Investors should examine returns by the amount of return per unit of risk accepted, rather than in isolation. To consider both risk and return in evaluating portfolio performance,

Sharpe measure (SHP)Treynor measure (TRN)

SHPi = ( Ri – Rf ) / σi

Where, Ri = Average return for portfolio i during a specified time period Rf = Average risk free rate of return σi = risk of portfolio i

TRNi = (Ri – Rf) / βi

Assume that the risk free is 5% per year for Hong Kong, calculate SHP and TRN

Assume the U.S dollar returns (monthly averages) shown below for three Baltic republics. Calculate the SHP and TRN measures of market performance.

Country M.Ret SD Rf BetaEstonia 1.12% 16% 0.42% 1.65Latvia 0.75% 22.8% 0.42% 1.53Lithuania 1.6% 13.5% 0.42% 1.20

International Mutual Funds: A Performance Evaluation

• A U.S. investor can easily achieve international diversification by investing in a U.S.-based international mutual fund.

• The advantages include:1. Savings on transaction and information costs.2. Availability of legal and institutional barriers to

direct portfolio investments abroad.3. Professional management and record keeping.

The Capital Asset Pricing Model – CAPM

The CAPM is an equation that expresses the equilibrium relationship between a security’s expected return and it’s systematic risk.

E(ri) = rf + βi(rM - rf)

Nestle, is a Swiss-based multinational firm. A prospective Swiss

investor might assume a risk-free return of 3.3% (index of Swiss

government bond issues), an average return on a portfolio of Swiss

equities of 10.2% (Financial Times Swiss Index), and a βNestle of 0.885.

Calculate the expected rate of return on Nestle equity.

9.41%

The International Capital Asset Pricing Model

The international version of the CAPM includes risk premium for multi-country exposure. The general form of international CAPM is given as:

E(ri) – rf = βi[E(rM) – rf] + ∑ γi,k[E(Sn) + rnf – rf]

rf = Continuous compounded risk-free rate in the domestic countrySn = Exchange rate of country krn

f = Continuous compounded risk-free rate in country kn = Number of countries consideredβi and γi = regression coefficients

In the case of Nestle, for the same period as before, a global portfolio

index such as the Financial Times index would show a market return of

13.7%. In addition, a beta for Nestle estimated on Nestle’s returns

versus the global portfolio index would be 0.585. Calculate the

expected return of an internationally diversified Swiss investor.

Why Home Bias in Portfolio Holdings?

• Home bias refers to the extent to which portfolio investments are concentrated in domestic equities.

The Home Bias in Equity Portfolios

Country Share in World Market Value

Proportion of Domestic Equities in Portfolio

France 2.6% 64.4%

Germany 3.2% 75.4%

Italy 1.9% 91.0%

Japan 43.7% 86.7%

Spain 1.1% 94.2%

Sweden 0.8% 100.0%

United Kingdom 10.3% 78.5%

United States 36.4% 98.0%

Total 100.0%  

Why Home Bias in Portfolio Holdings?

• Three explanations come to mind:1. Domestic equities may provide a superior

inflation hedge.2. Home bias may reflect institutional and

legal restrictions on foreign investment.3. Extra taxes and transactions/information

costs for foreign securities may give rise to home bias.