International Portfolio
Theory and Diversification
A. Review: Diversification and portfolio
theory
B. Home Bias
C. International diversification
D. How to diversify internationally
E. Cases against international
diversification
International Financial Markets
2
REVIEW:
DIVERSIFICATION AND
PORTFOLIO THEORY
3
4
Historical returns and risks of
various instruments
Series
Large-company
stocks
Small-company
stocks
Average Standard
Return Deviation
13.3%
20.1%
*
17.6
33.6
5.9
8.7
5.5
9.3
5.4
5.8
U.S. Treasury
bills
3.8
3.2
Inflation
3.2
4.5
Long-term
corporate bonds
Long-term
government
Intermediate-term
government
Distribution
-90%
0%
5
90%
Stocks are Inherently Risky!
The Historical Record of
Total Returns on Large-Company Stocks
6
Stocks are Inherently Risky!
7
Diversification
• Portfolio diversification is the investment in
several different asset classes or sectors
– Diversification can substantially reduce the
variability of returns
– This reduction in risk arises because worse than
expected returns from one asset are offset by better
than expected returns from another
• Diversification is not just holding a lot of
assets
– For example, if you own 50 internet stocks, you are
not diversified
– However, if you own 50 stocks that span 20
different industries, then you are diversified
8
Why Diversification Works
• Portfolio risk depends on the correlation between the
returns of the assets in the portfolio
• Correlation (or covariance)
– The tendency of the returns on two assets to move together.
– Imperfect correlation is the key reason why diversification
reduces portfolio risk as measured by the portfolio standard
deviation.
• Positively correlated assets tend to move up and down together.
• Negatively correlated assets tend to move in opposite directions.
• Imperfect correlation, positive or negative, is why
diversification reduces portfolio risk.
9
Covariance and Correlation
• Covariance:
n


COV ( RA , RB )   ( RAi  R A )( RBi  R B ) Pi
i 1
• Correlation Coefficient
– Correlation is a standardized covariance scaled by the
product of two standard deviations, so that it can take a
value between -1 and +1.
– The correlation coefficient is denoted by Corr(RA, RB) or
simply, A,B.
 A, B 
COV ( RA , RB )
 A B
10
Correlation
11
Combining Negatively Correlated
Assets to Diversify Risk
12
Investing on Metals in Different
Stage of Business Cycle
13
Diversification
• Financial economists suggest that there are two
types of risks investors should be aware of.
– Systematic or market risk
– Unsystematic or asset-specific risk
• Diversification is about reducing asset-specific risk
by combining many uncorrelated assets.
– If we hold only one asset, or assets in the same industry,
then we are exposing ourselves to risk that we could
diversify away
– Diversifiable Risk = Unsystematic Risk
– For well diversified portfolios, unsystematic risk is very
small
– Consequently, the total risk for a diversified portfolio is
essentially equivalent to the systematic risk.
14
Systematic and Unsystematic Risk
• Systematic risk is risk that influences a large
number of assets. Also called market risk, so it is
non-diversifiable.
– Example: Labor strike, CEO resignation, Produce liability
lawsuit, Earnings reports.
• Unsystematic risk is risk that influences a single
company or a small group of companies. Also
called unique risk or firm-specific risk, so it is
diversifiable.
– Example: Variability of growth in the money supply,
Interest rate changes, GDP changes.
• Total risk = Systematic risk + Unsystematic risk
15
Pop Quiz:
Systematic Risk or Unsystematic Risk?
• The government announces that inflation unexpectedly
jumped by 2 percent last month.
•
Systematic Risk
• One of Big Widget’s major suppliers goes bankruptcy.
•
Unsystematic Risk
• The head of accounting department of Big Widget announces
that the company’s current ratio has been severely
deteriorating.
•
Unsystematic Risk
• Congress approves changes to the tax code that will increase
the top marginal corporate tax rate.
•
Systematic Risk
16
Average annual
standard deviation (%)
Risk
Reduction
49.2
Diversifiable risk
23.9
19.2
Nondiversifiable
risk
1
10
20
30
40
Number of stocks
1,000 in portfolio
17
Measuring Systematic Risk
• To be compensated for risk, the risk has to be special.
– Unsystematic risk is not special.
– Systematic risk is special.
• The Beta coefficient () measures the relative systematic risk
of an asset.
– Assets with Betas larger than 1.0 have more systematic risk than
average.
– Assets with Betas smaller than 1.0 have less systematic risk than
average.
• Because assets with larger betas have greater systematic
risks, they will have greater expected returns.
• Note that not all Betas are created equally.
18
Estimating Beta
19
Two-Security Portfolio: Risk
  w   w   2wD wE Cov  rD , rE 
2
p
2
D
2
D
2
E
2
E
or
 p2  wD2  D2  wE2 E2  2wD wE D E Corr  rD , rE 
 D2
 E2
= Variance of Security D
= Variance of Security E
CovrD , rE  = Covariance of returns for Security D and Security E
20
Example: Correlation and the
Risk-Return Trade-Off, Two Risky Assets
Inputs
Return
Deviation
Risky Asset 1
14.0%
20.0%
Risky Asset 2
8.0%
15.0%
Correlation
Risk-Return Profile
-0.20
80
Percentage
in Risky
Standard Expected
Asset 1
Deviation Return
-60.0%
28.9%
4.4%
-50.0%
26.4%
5.0%
-40.0%
23.9%
5.6%
-30.0%
21.5%
6.2%
-20.0%
19.2%
6.8%
Exp Ret
Portfolio
18.0%
16.0%
14.0%
12.0%
10.0%
8.0%
6.0%
4.0%
2.0%
0.0%
0.0%
20.0%
SD
40.0%
21
Correlation and the
Risk-Return Trade-Off, General case
22
Efficient Frontier with Intel and
Coca-Cola
23
Efficient Frontier with Ten Stocks
Versus Three Stocks
24
Efficient Frontier with Multiple
Assets
25
HOME BIAS
26
“Home Bias” in Portfolio Holdings:
Definition
• Home bias refers to the extent to which portfolio
investments are concentrated in domestic equities.
Share in World
Market Value
Proportion of
Domestic Equities in
Portfolio64.4%
France
2.6%
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%
27
Why Home Bias in
Portfolio Holdings?
• Some explanations come to mind:
– Domestic equities may provide a superior
inflation hedge.
– Home bias may reflect institutional and legal
restrictions on foreign investment.
– Extra taxes and transactions/information costs
for foreign securities may give rise to home
bias.
28
INTERNATIONAL
DIVERSIFICATION
29
Stock Market Returns in U.S. Dollars
and Local Currencies for 2009
30
Average Returns and Volatilities in
Emerging Markets
31
Market Sizes of Developed Markets Billions of
U.S. dollars, end of 2006
32
Sizes of Emerging Markets Billions
of U.S. dollars, end of 2006
• At the end of 2006 emerging markets had a total market cap of
approximately $6.8 trillion.
• Emerging markets have grown rapidly since 1980s and represented
over 13% of the world stock market capitalization at the end of
33
2006.
International Diversification
and Risk
• The case for international diversification of
portfolios can be decomposed into two
components,
– Potential risk reduction benefits of
holding international securities.
– Potential foreign exchange risk of
holding international securities
34
Portfolio Risk Reduction Through
Diversification
35
Potential Risk Reduction of Holding
International Securities
• The risk of a portfolio is measured by the ratio of the variance of a
portfolio’s return relative to the variance of the market return
(portfolio beta).
• The total risk of any portfolio is therefore composed of systematic
risk (the market) and unsystematic risk (the individual securities).
• Increasing the number of securities in the portfolio reduces the
unsystematic risk component leaving the systematic risk
component unchanged.
• As an investor increases the number of securities in a portfolio, the
portfolio’s risk declines rapidly at first, then asymptotically
approaches the level of systematic risk of the market.
36
Portfolio Risk Reduction Through
International Diversification
37
Potential Risk of Holding
International Securities
• The second component of the case for
international diversification addresses foreign
exchange risk.
– Purchasing assets in foreign markets, in foreign currencies may
alter the correlations associated with securities in different
countries (and currencies).
– This provides portfolio composition and diversification
possibilities that domestic investment and portfolio construction
may not provide.
– The risk associated with international diversification, when it
includes currency risk, is very complicated when compared to
domestic investments.
38
Foreign Exchange Risk and
International Diversification
• Japanese yen return=?
• Dollar return =?
39
Characteristics of Foreign Equity Returns,
1980–2010
40
Internationalizing the Domestic
Portfolio
• Classic portfolio theory assumes a typical investor is riskaverse.
– This means an investor is willing to accept some risk but
is not willing to bear unnecessary risk.
• The typical investor is therefore in search of a portfolio that
maximizes expected portfolio return per unit of expected
portfolio risk.
• The near-infinite set of portfolio combinations of domestic
securities form the domestic portfolio opportunity set (next
exhibit).
• The set of portfolios along the extreme left edge of the set is
termed the efficient frontier.
• This efficient frontier possess the minimum expected risk for
each level of expected portfolio return.
41
Optimal Domestic Portfolio Construction
42
Internationalizing the Domestic
Portfolio
• The portfolio with the minimum risk along all those
possible is the minimum risk domestic portfolio (MRDP).
• The individual investor will search out the optimal
domestic portfolio (DP), which combines the risk-free
asset and a portfolio of domestic securities found on
the efficient frontier.
• He or she begins with the risk-free asset (Rf) and
moves out along the security market line until reaching
portfolio DP.
• This portfolio is defined as the optimal domestic
portfolio because it moves out into risky space at the
steepest slope.
43
International Diversification
and Risk
• The next exhibit illustrates the impact of allowing the investor
to choose among an internationally diversified set of potential
portfolios.
• The internationally diversified portfolio opportunity set shifts
leftward of the purely domestic opportunity set.
• The investor can now choose an optimal portfolio that combines
the same risk-free asset as before with a portfolio from the
efficient frontier of the internationally diversified portfolio
opportunity set.
• The optimal international portfolio, IP, is again found by locating
that point on the capital market line (internationally diversified)
which extends from the risk-free asset return of Rf to a point of
tangency along the internationally diversified efficient frontier.
• The benefits are obvious in that a higher expected portfolio
return with a lower portfolio risk can be obtained when
compared to the domestic portfolio alone.
44
The Gains from International Portfolio
Diversification
45
International Diversification
and Risk
• It is critical to be clear as to exactly why the
internationally diversified portfolio opportunity set is of
lower expected risk than comparable domestic
portfolios.
• The gains arise directly from the introduction of
additional securities and/or portfolios that are of less
than perfect correlation with the securities and
portfolios within the domestic opportunity set.
• An investor can reduce investment risk by holding risky
assets in a portfolio.
• As long as the asset returns are not perfectly positively
correlated, the investor can reduce risk, because some
of the fluctuations of the asset returns will offset each
other.
46
Alternative Portfolio Profiles Under
Varying Asset Weights
47
National Markets
and Asset Performance
• Asset portfolios are traditionally constructed using both
interest bearing risk-free assets and risky assets.
• For the 100 year period ending in 2000, the risk of
investing in equity assets has been rewarded with
substantial returns.
• The true benefits of global diversification, however,
arise from the fact that the returns of different stock
markets around the world are not perfectly positively
correlated.
• This is because the are different industrial structures in
different countries, and because different economies do
not exactly follow the same business cycle.
48
National Markets
and Asset Performance
• Interestingly, markets that are contiguous or
near-contiguous (geographically) seemingly
demonstrate the higher correlation coefficients for
the past century.
• It is often said that as capital markets around the
world become more and more integrated over
time, the benefits of diversification will be
reduced.
• Analysis of market data supports this idea
(although the correlation coefficients between
markets are still far from 1.0).
49
Real Returns and Risks on the Three Major Asset
Classes, Globally, 1900–2000
50
Correlation Coefficients between World
Equity Markets, 1900–2000
51
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 80%.
• The correlation of the U.S. stock market with the
Japanese stock market is 21%.
• A U.S. investor would get more diversification
from investments in Japan than Canada.
52
Market Performance Adjusted for Risk:
The Sharpe and Treynor Performance
Measures
• To consider both risk and return in evaluating
portfolio performance, we introduce two measures:
The Sharpe Measure (SHP)
= SHPi = Ri – Rf
σi
The Treynor Measure (TRN)
= TRNi = Ri – Rf
βi
53
Market Performance Adjusted for Risk:
The Sharpe and Treynor Performance
Measures
• Though the equations of the Sharpe and Treynor
measures look similar, the difference between them is
important.
• If a portfolio is perfectly diversified (without any
unsystematic risk), the two measures give similar
rankings, because the total portfolio risk is equivalent to
the systematic risk.
• If a portfolio is poorly diversified, it is possible for it to
show a high ranking on the basis of the Treynor measure,
but a lower ranking on the basis of the Sharpe measure.
• As the difference is attributable to the low level of
portfolio diversification, the two measures therefore
provide complimentary but different information.
54
Summary Statistics of the Monthly Returns for 18 Major Stock
Markets, 1977–1996 (all returns converted into U.S. dollars and
include all dividends paid)
55
Hong Kong Example
56
Mutual Funds, ADRs, and ETFs
HOW TO DIVERSIFY
INTERNATIONALLY
57
Concentration
• Investors need to know whether a national market is
made up of a diversity of firms or concentrated in a
few large firms.
• A market that is dominated by a few large firms
provides fewer opportunities for risk diversification.
• However, if the market concentration is high, investors
may be able to mimic the market easily by owning a
small number of firms by owning the ADRs.
• On the NYSE and Tokyo Stock Exchange., the top 10
firms represent less than 20% of total market cap.
• Conversely, in Switzerland, the top 10 firms account
for approx. 70% of total market cap.
58
Share of the Ten Largest Listed Companies
in the National Market Capitalization
59
International Investment Vehicles:
American Depository Receipts
• Foreign stocks often trade on U.S. exchanges as
ADRs.
– It is a receipt that represents the number of foreign
shares that are deposited at a U.S. bank.
– After a U.S. bank has taken custody of foreign shares in
its foreign office, ADRs can be issued as claims against
the foreign shares.
– The issuing bank services the ADRs by collecting all
dividends, rights offerings, etc., and distributing the
proceeds in US$ to the ADR owners.
• The bank serves as a transfer agent for the ADRs
• Adding ADRs to domestic portfolios has a
substantial risk reduction benefit.
60
International Investment Vehicles
ADRs
• There are many advantages to trading
ADRs as opposed to direct investment in
the company’s shares:
– ADRs are denominated in U.S. dollars, trade on
U.S. exchanges and can be bought through any
broker.
– Dividends are paid in U.S. dollars.
– Most underlying stocks are bearer securities,
the ADRs are registered.
61
International Investment Vehicles
• Mutual funds
– Mutual funds that invest in foreign stocks can
be grouped into several categories from a U.S.
perspective:
•
•
•
•
•
Global - Investing in U.S. and non-U.S. shares.
International - Investing in non-U.S. shares only.
Regional - Investing in a geographic area.
Country - Investing in a single country.
Specialty - International investments in an industry
group such as telecommunications, or special themes
such as newly privatized firms.
62
International Mutual Funds
• A U.S. investor can easily achieve international
diversification by investing in a U.S.-based
international mutual fund. The advantages include
– Speculate in a foreign market with minimum transaction
and information cost.
– Circumvention of legal and institutional barriers to direct
portfolio investments abroad.
– Diversify into emerging markets that are otherwise
practically inaccessible.
– Professional management and record keeping.
• Recently, country funds have emerged as one of the
most popular means of international investment.
– A country fund invests exclusively in the stocks of a single
county or specific regions.
63
International Mutual Funds: A
Performance Evaluation
As can be seen below, a sample of U.S. based international mutual
funds has outperformed the S&P 500 during the period 1977-1986,
with a higher standard deviation. US
Mean
Annual
Return
18.96%
Standard
Deviation
US
R2
5.78%
0.69
0.39
S&P 500
14.04%
4.25%
1.00
1.00
U.S. MNC
Index
16.08%
4.38
.98
.90
U.S. Based
International
Mutual Funds
International Mutual Funds: A
Performance Evaluation
U.S. stock market movements account for less than 40% of the
fluctuations of international mutual funds, but over 90% of the
movements in U.S. MNC shares. This means that the shares of U.S.
MNCs behave like those of domestic firms, without providing
effective international diversification.
Mean Annual
Return
Standard
Deviation
US
R2
U.S. Based
International
Mutual Funds
18.96%
5.78%
0.69
0.39
S&P 500
14.04%
4.25%
1.00
1.00
U.S. MNC Index
16.08%
4.38
.98
.90
A Typical Headline about Country Fund
in Financial Press
• Over the past three years as of March 9, 2005,
Vanguard European Stock Index fund VEURX
gained 12.5 percent annually,
• Vanguard Pacific Stock Index fund VPACX rose
12.1 percent and
• Vanguard Emerging Markets Index fund VEIEX
gained 22.3 percent.
• All three funds have outpaced the S&P 500stock index over the same period.
66
New Trend
• Increasingly, exchange-traded funds (ETFs)
become popular to diversify internationally,
along with traditional mutual funds.
• Examples:
–
–
–
–
Brazil: EWZ
Asia 50 ADRs: ADRA
China: FXI
South Africa: EZA
67
Growth of U.S. ETFs over time
68
Exchange Traded Funds, ETFs
•
An exchange traded fund, or ETF,
– A relatively recent innovation – since 1993.
– Is basically an index fund but it is not a mutual fund.
– Trades like a closed-end fund (without the discount phenomenon).
•
An area where ETFs seem to have an edge over the more traditional index
funds is the more specialized indexes.
•
A well-known ETF is the “Standard and Poor’s Depositary Receipt” or SPDR.
– This ETF mimics the S&P 500 index.
– It is commonly called “spider."
•
Another well-known ETF mimics the Dow Jones—it is called "Diamond.“
•
A list of ETFs can be found at www.amex.com.
–
•
SPY, DIA, QQQQ, VNQ, EWZ, EFA, FXI, and others
Major sponsors include Barclays Global Investors, State Street Global
Advisor, PowerShares, Vanguard, and others.
69
ETFs
Creation
• An ETF sponsors files a plan with the SEC.
• Arranges to set aside the shares representing the
basket of securities that forms the ETF index.
• These few million shares are placed into a trust.
• Create an unit shares that represent claims on the
bundles of shares held in the trust.
• These unit shares are then traded in exchanges.
70
ETFs
Characteristics
• ETF is like an index fund but not exactly a
mutual fund because
– Advantage
• Can be sold short or purchased on margin
• It can have options.
• Can be bought and sold continuously during the day like
stocks or closed-end funds.
• Generally have very low expense: .10% or one-tenth of 1
percent.
• Tax efficient
– Disadvantage
• Prices can depart by small amounts from NAV
• Must be purchased from a broker. Must pay a
commission.
71
ETF Sponsors and Products
72
ETFs,
Performance
73
CASES AGAINST
INTERNATIONAL
DIVERSIFICATION
74
Case Against International
Diversification
• International correlations have trended upward over the past
decade.
• Correlation seems to increase dramatically in periods of high
market volatility like financial crises.
– So the benefits of international risk diversification disappears when they
are most needed.
– A phenomenon referred to as “correlation breakdown”.
• The increases in correlations have been due to such factors
as deregulation, capital mobility, free trade, and the
globalization of corporations.
– Capital mobility has increased especially among developed countries.
• Markets that used to be segmented are moving towards
global integration.
75
Correlations Between Foreign and U.S.
Equity Market Returns
76
Comparison of Selected Correlation Coefficients
between Stock Markets
for Two Time Periods (dollar returns)
77
Internationalization
of Financial Markets
78
Foreign
Exchange
Market:
Exchange
Rates
Current foreign exchange rates
http://www.federalreserve.gov/releases/
H10/hist
79