# International Finance by dominic.cecilia

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```									International Finance                                  Dr. Angela Ng
FINA 342                                                     HKUST

Class Notes 13

INTERNATIONAL PORTFOLIO
INVESTMENT

I. PORTFOLIO THEORY

 Assumptions

 Nominal returns are normally distributed.

 Investors want higher return and less risk in their functional
currency.

 Return and Risk:

Let Xi = proportion of wealth devoted to asset i, such that Xi
= 1.

 Expected return on a portfolio is simply a weighted average
of the expected returns on the securities in the portfolio, i.e.,
E[R p ]   X i E[R i ]
i

 Portfolio variance:
Var[R p ]   p   Xi X j ij
2

i   j

where ij = ijij

 Portfolio variance depends on the correlation between

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assets. The correlation does not impact the expected return
on a portfolio.

 Exercises:
Correlations
E[Ri]     (Ri)       A       B         J
American (A)     11.5%     15.8%       1.000 0.616       0.334
British (B)      17.1%     31.9%       0.616 1.000       0.262
Japanese (J)     21.9%     35.1%       0.334 0.262       1.000

 Calculate the expected returns on the following portfolios.

(1) Equal weights of A and J

(2) Equal weights of A, B, and J

 Calculate the portfolio variances.

(1) Equal weights of A and J

(2) Equal weights of A, B, and J

 Key results of portfolio theory

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 The extent to which risk is reduced by portfolio
diversification depends on correlation of assets in the
portfolio.

High correlations yield few diversification benefits.
Low correlations yield lots of diversification benefits.

 With a single security, portfolio variance equals the
variance of that single security. As the number of assets
increases, portfolio variance becomes more dependent on
the covariances and less dependent on variances.

In the limit as N, portfolio variance depends only on
covariance.

 The risk of an asset when held in a large portfolio, depends
on its return covariance with other securities in the portfolio
and not on its return variance.

 Diversification and Correlation Coefficient

 Risk is reduced by portfolio diversification when a portfolio
is extended to include new investments whose returns are
imperfectly correlated with the original portfolio.

 How does one measure the relative independence of asset
returns?

Correlation coefficient between returns of assets A and B is
the covariance scaled by the standard deviations of returns
of the two assets, i.e., AB = AB/AB.

1  AB  +1

 The less the correlation between two assets, the greater the
potential for risk reduction through portfolio diversification.

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(See Exhibit 13.1)

II. INTERNATIONAL PORTFOLIO DIVERSIFICATION

 A globally diversified stock/bond portfolio offers higher
expected return at lower portfolio risk than a purely domestic
portfolio. (See Exhibit 13.2)

 Higher expected return – Developing economies are much
more likely to experience above-average economic growth.
This leads to higher expected returns in emerging markets.

 Lower portfolio risk – National economies do not move in
unison, and stock and bond returns vary widely across
national markets. Diversifying across international markets
can greatly reduce portfolio risk because of the relatively
low correlation between national debt and equity market
indices.

 Can we achieve the same diversification benefits by selecting
only a few issues in the domestic market?

See Exhibit 13.3

 The benefits of international diversification are the greatest for
residents of those countries with the least diversified
economies.

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 The degree of independence of a stock market is linked to the
independence of a nation’s economy and government policies.

Constraints and regulations imposed by national governments,
technological specialization, independent fiscal and monetary
policies, and cultural and sociological differences all
contribute to the degree of a capital market’s independence.

Conversely, when there are close economic and government
policies, like among the members of the European Union, one
observes more commonality in capital market behavior.

 Correlation between national markets tend to increase when
market volatility increases.

III. RETURN AND RISK ON FOREIGN INVESTMENT

 Notations:

St = Spot exchange rate, in \$/FC

Ptf = Price of foreign asset in foreign currency units

Ptd = Price of foreign asset in domestic currency (\$) units

Rtf = Return on foreign asset in foreign currency units

Rtd = Return on foreign asset in domestic currency units

 What is the price of the foreign equity in domestic currency?

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 Domestic currency return on foreign asset:
Rtd = (Ptd / Pt-1d) – 1
= (Ptf St / Pt-1f St-1) – 1
= (Ptf / Pt-1f) (St / St-1) – 1
= (1 + Rtf) (1 + std/f) – 1
= Rtf + std/f + Rtf std/f

Hence, domestic currency return on foreign assets has three
parts:
– return in the local currency,
– change in the spot exchange rate,
– an interaction term.

Example 1: The Mexican stock market goes up by 30% in
pesos, but the peso falls 20% against \$. What is the \$ return on
the Mexican market?

Example 2: Pohang Steel of South Korea falls 20% in local
terms. The Japanese yen falls 20% against the Korean won.
What is the yen return on an investment in Pohang Steel?

 Expected return on foreign asset and variance:

E[Rd] = E[Rf] + E[sd/f] + E[Rf sd/f]

Var[Rd] = Var[Rf] + Var[sd/f] + Var[Rf sd/f] + 2Cov[Rf , sd/f]
+ 2Cov[Rf , Rf sd/f] + 2Cov[sd/f , Rf sd/f]
= Var[Rf] + Var[sd/f] + Var[Rf sd/f] + 2Cov[Rf , sd/f]
+ 2(Rf)2Cov[1, sd/f] + 2(sd/f)2Cov[1, Rf]
= Var[Rf] + Var[sd/f] + Var[Rf sd/f] + 2Cov[Rf , sd/f]

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 Variance of return on foreign stocks (Exhibit 13.4)

 The dominant risk in the equity markets is return volatility
in national markets.

 Equity values in foreign currency have a low correlation
with the value of the currency itself.

 Variance of return on foreign bonds (Exhibit 13.5)

 Foreign bonds have two sources of risk:
– Interest rate variability in foreign currency
– Exchange rate variability

 The relative split between Var[Rf] and Var[sd/f] depends on
the relative volatility of interest rates and exchange rates.

 Smaller and less diversified countries typically have even
more volatile returns in the local currency.

foreign assets.

 Currency risk

 Currency risk is smaller than the risk of the corresponding
stock market.

 Market risks and currency risks are not additive.

 The exchange risk of an investment may be hedged.

 The contribution of currency risk should be measured for
the total portfolio rather than for individual markets or
securities.

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 Hedging foreign currency risk does not completely
eliminate risk. It merely substitutes exposure to domestic
purchasing power (i.e., inflation) risk for exposure to
currency risk. To hedge against domestic inflation risk,
contracts must be signed in real, not nominal, terms.

IV. BARRIERS TO INTERNATIONAL PORTFOLIO
DIVERSIFICATION

MARKET SEGMENTATION

 Definition: A national capital market is segmented if the
required rate of return on securities in that market differs from
the required rate of return on securities of comparable
expected return and risk that are traded in other national
securities markets.

 Capital market segmentation is a major market imperfection.
Firms resident in a segmented market need to source capital
abroad to lower their cost of capital and improve their market
liquidity.

More segmented, higher cost of capital, more incentive to
source capital abroad or invest in international equities.

WHAT CAUSES MARKET SEGMENTATION?

 Government controls

 Foreign exchange controls to stabilize cross-border
financial flows.

 Capital inflow and capital outflow controls, i.e.,
prohibitions or limitations on foreign investment by
domestic residents, on domestic investment by foreigners.

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 Prohibitions on domestic share ownership by foreign
investors.

 Taxes

 Capital gain taxes – Capital gains are taxed by the investor’s
home government.

 Stamp taxes – A stamp tax is a tax on a financial transaction.
Transaction taxes can be proportional to the amount of the
transaction.

 Withholding taxes on dividend and interest income
distributions – Countries often impose a withholding tax on
interest and/or dividends paid in their currency and within
their borders. This means that foreign investors may be
taxed twice: once in the country where income is paid and
once in the country where it is received.

 Transaction costs

 Information barriers

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V. INTERNATIONAL INVESTMENT VEHICLES

DIRECT PURCHASE IN FOREIGN MARKETS

 The most direct way to invest internationally is direct
purchases in foreign debt and equity markets.

 Barriers

 High information and transaction costs, foreign taxes.

 Dividends and capital gains are received in foreign
currencies.

DOMESTIC-BASED MULTINATIONAL CORPORATIONS

 An easily accessible way for investors in countries with
developed capital markets is to invest in domestic firms that do

 The diversification benefits depend on the type of foreign
operations conducted by the MNC.

 Whether a MNC provides international diversification benefits
ultimately depends on whether its share price moves with the
domestic stock market or with the foreign markets.

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AMERICAN DEPOSITORY RECEIPTS

 Definition: A receipt representing a number of foreign shares
that are deposited in a US bank.

The bank serves as a transfer agent for the ADRs, which are
traded on the listed exchanges in the US or in the OTC
markets.

Owners of the ADR have the right to redeem their ADR and
obtain the true underlying foreign shares. Arbitrage of this sort
ensures that the price of the ADR and the underlying shares
will be nearly identical.

 The first ADR began trading in 1927 as a means of eliminating
some of the risks, delays, inconveniences, and expenses of

 On the London Stock Exchange, Global Depository Receipts
allow foreign firms to trade, and Singapore Depository
Receipts are traded on the Singapore Stock Exchange.

 Created by a bank at the request of the foreign company
that issued that underlying security.

 Depository fees are paid by the foreign company.

 Created at the request of a US investment banking firm
without direct involvement by the foreign issuing firm.

 Depository fees are paid by the ADR investors.

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1. ADRs are dominated in US dollars, traded on a US stock
exchange, and can be purchased through the investor’s
regular broker.

2. Dividends received on the underlying shares are collected
and converted to US dollars by the custodian and paid to the

whereas settlement practices for the underlying stock vary
in foreign countries.

4. ADR price quotes are in US dollars.

5. ADRs are registered securities that provide for the
protection of ownership rights, whereas most underlying
stocks are bearer securities.

receipt to another investor on the exchange on which it is
traded, or it can be returned to the bank depository for cash.

7. ADRs frequently represent a multiple of the underlying
shares, rather than a one-for-one correspondence, to allow
to trade in a price range customary for US investors.

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MUTUAL FUNDS

 Categories of mutual funds, from the US perspective:

 Global – Investing in US and non-US shares

 International – Investing in non-US shares only

 Regional – Investing in a geographic area

 Country – Investing in a single country

 Specialty – International investment in an industry group

 Closed-end funds versus Open-end funds

 Closed-end funds

 A fixed number of share against an initial capital offering
is issued. The shares of the closed-end fund are then
traded in a secondary market, usually listed on an
exchange, at prices reflecting a premium or discount
relative to the net-asset-value of the underlying foreign
shares.

 Owner earns a return equal to the change in net asset
value on the fund’s underlying assets plus the change in
the fund’s discount (or premium) to net asset value.

 Open-end funds

 Ready to issue and redeem shares at prices reflecting the
net asset value of the underlying foreign share.

– Owner earns a return equal to the change in the net asset
value on the fund’s underlying assets.

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 Closed-end country funds (CECF)

 CECFs invest in a single country’s stocks.

 CECFs often trade at a premium to NAV when there are
limits on foreign ownership.

Why?

– “Portfolio maximization” in the presence of investment
restrictions: investors attempt to maximize the
mean-variance efficiency of their portfolios given
restrictions.

– “Investor    sentiment”:     emphasizes      cross-border
heterogeneity in investor expectations.

– If domestic traders are more bullish on foreign stocks
than their foreign counterparts, they can bid up the price
of CECF shares relative to net asset values.

– Premium/discount reflects the differential between
domestic and foreign sentiment regarding underlying
value of the CECF.

 Restricted CECFs are more highly correlated with domestic
stocks than they are with their own NAVs. As a result,
CECFs may be a poor vehicle for international
diversification.

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HEDGE FUNDS

 Hedge funds are private investment partnerships with a
general manager and a small number (fewer than 100) of
limited partners.

 Hedge funds are unregulated as long as each partner passes
SEC accreditation.

Each partner must have a net worth of at least \$1 million or
income of more than \$200,000.

Entry fees of partnership are as high as \$1 million with a
minimum investment of several years.

 The attraction of hedge funds lies in their historically high
returns and their potential for a lower correlation of returns
with traditional stock and bond investments.

OTHER VEHICLES

 Equity-linked Eurobonds: Eurobonds offered with equity
options attached.

Example: Yen Eurobonds with warrants – purchased by
Japanese investors who have few other vehicles for owning
equity options with Japan.

 Foreign market index futures, options, and swaps

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VI. HOME ASSET BIAS

 Despite the potential benefits of international portfolio
diversification, most investors concentrate their portfolio in
domestic securities. (See Exhibit 13.6)

 Explanations

 Domestic stock portfolios may serve as a hedge against
domestic inflation risk.

 The costs of international portfolio diversification.

 Market imperfections
– cross-border capital flow constraints
– transaction costs
– differential taxes
– possible investor irrationality

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Exhibit 13.1
Portfolio Diversification

Mean annual return

20%

J
= -1
= +0.325
 = +1
A

10%

0%
0%                  10%                 20%               30%       40%

Standard deviation of annual return

Exhibit 13.2
International Diversification

Expected return

W        M

Rf

Standard deviation of return

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Exhibit 13.3
Domestic versus International Diversification

Portfolio risk relative to
the risk of a single asset
(P²/i²)

U.S. diversification only
International diversification
1.0

0.5

5          10           15        20         25
Number of stocks in portfolio

Exhibit 13.4
Variance of Returns on Foreign Stocks

interaction
f                \$/f
Var(R )            +    Var(s ) + terms =                 Var(Rf)
Canada      0.826              +     0.052 + 0.122 =                  1.000
France      0.825              +     0.216 + -0.041 =                 1.000
Germany     0.807              +     0.308 + -0.114 =                 1.000
Japan       0.676              +     0.264 + 0.061 =                  1.000
Switzerland 0.824              +     0.419 + -0.243 =                 1.000
U.K.        0.810              +     0.185 + 0.005 =                  1.000
Average     0.795              +     0.241 + -0.035 =                 1.000

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Exhibit 13.5
Variance of Returns on Foreign Bonds

interaction
f               \$/f
Var(R )               +   Var(s ) + terms =              Var(Rf)
Canada      0.601                 +    0.184 + 0.215 =               1.000
France      0.242                 +    0.823 + -0.065 =              1.000
Germany     0.124                 +    0.818 + 0.058 =               1.000
Japan       0.172                 +    0.701 + 0.126 =               1.000
Switzerland 0.090                 +    0.936 + -0.026 =              1.000
U.K.        0.287                 +    0.599 + 0.114 =               1.000
Average     0.253                 +    0.677 + 0.070 =               1.000

Exhibit 13.6
Home Asset Bias

Market capitalization                Percentage of equity
as a percentage                    portfolio held in
of total                       domestic equities
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%
U.K.                         10.3%                            78.5%
U.S.                         36.4%                            98.0%

Source: Ian Cooper and Evi Kaplanis, “Home Bias in Equity Portfolios, Inflation Hedging, and
International Capital Market Equilibrium,” Review of Financial Studies 7, No. 1, Spring 1994.

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