International Portfolio Investment

1
International Portfolio Investment

• Reading Chapter 15

2
Lecture Outline

• Basics of diversification
• Benefits of international diversification
• Measuring foreign investment performance
• The home bias puzzle

3
Why Go Global?

• In a nutshell Diversification!!!
• Potential for higher expected returns for same
  risk.
• Potential for lower portfolio risk for same
  return.

International investing
4
International Correlations Diversification

• Security returns are much less correlated across
  countries than within a country.
• This is because economic, political,
  institutional and even psychological factors
  affecting security returns tend to vary across
  countries, resulting in low correlations among
  international securities.
• Types of companies in each country can also vary
  significantly.

5
International Stock Returns (70 04)
Mean () Std. Dev. () Std. Dev. (, LC) ßW (1970-2004)
Australia 12.33 24.03 10.98 1.005
France 12.62 21.02 21.04 1.042
Germany 8.91 23.39 28.36 0.950
Japan 5.14 24.40 16.78 1.017
Netherlands 13.45 17.97 22.33 0.974
Switzerland 12.96 17.90 15.78 0.879
UK 11.94 17.73 15.54 1.065
USA 12.22 15.86 16.44 0.920
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International Correlation Structure (70 04)

7
Domestic vs. International Diversification
100
Portfolio Risk ()
U.S. stocks
27
12
International stocks
1 10 20 30 40 50
Number of Stocks
8
International Investing

• The tools are Mean/Variance Analysis same as in
  previous finance units.
• However, there are many important cross-country
  differences that matter when we invest
  internationally
• Country Risk
• Currency Risk
• We start out with the mathematics of portfolio
  optimization

9
Portfolio Theory

• Assumptions
• Nominal returns are normally distributed.
• Investors want more return and less risk as
  denominated in their home currency.
• Let wi proportion of wealth devoted to asset i
  such that Si wi 1
• Expected return on a portfolio
• Portfolio Variance

where sij rij si sj
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Expected Return on a Portfolio

• ERi si
• A American 14.3 16.4
• B British 17.6 29.9
• J Japanese 17.7 35.7
• Example Equal weights (50) of A and J
• ERp wA ERA wJ ERJ
• (0.5x0.143)(0.5x0.177)
• 0.16 or 16

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Portfolio Variance

Correlation ERi si
A B J A American 14.3
16.4 1 0.557 0.325 B British
17.6 29.9 0.557 1 0.317 J
Japanese 17.7 35.7 0.325 0.317
1 Example Equal weights of A and
J sP2 wA2 sA2 wJ2 sJ2 2 wA wJ rAJ sA
sJ (0.5)2(0.164)2 (0.5)2(0.357)2
2(0.5)(0.5)(0.325)(0.164)(0.357) 0.0481 sP
(0.0481)1/2 0.2190 or 21.9 percent
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Diversification Risk

• The risk of a portfolio is measured by the ratio
  of the variance of a portfolios return relative
  to the variance of the market return (portfolio
  beta).
• As an investor increases the number of securities
  in a portfolio, the portfolios risk declines
  rapidly at first, then asymptotically approaches
  the level of systematic risk of the market.

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Diversification Risk

• 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.

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Diversification Risk
Total Risk Diversifiable Risk
Market Risk
(unsystematic) (systematic)
Portfolio of US stocks
By diversifying the portfolio, the variance of
the portfolios return relative to the variance
of the markets return (beta) is reduced to the
level of systematic risk -- the risk of the
market itself.
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Limitations of Domestic Investment

• If we only invest in domestic shares, then we are
  limited by the types of companies on offer in our
  home market.
• For example, the Australian market is overweight
  in mining companies and underweight in technology
  companies compared to the US and other markets.
• If we want to invest in IT or electronics
  companies, how do we do that in Australia?
• By investing internationally, we have a more
  diverse range of investment opportunities.

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Internationalizing a Domestic Portfolio
An investor may choose a portfolio of assets
enclosed by the Domestic portfolio opportunity
set. The optimal domestic portfolio is found at
DP, where the Capital Market Line is tangent to
the domestic portfolio opportunity set. The
domestic portfolio with the minimum risk is MRDP.
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Internationalizing a Domestic Portfolio
An investor may choose a portfolio of assets
enclosed by the international portfolio
opportunity set. The optimal international
portfolio is found at IP, where the Capital
Market Line is tangent to the international
portfolio opportunity set.
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Domestic vs. International Diversification
100
Portfolio Risk ()
U.S. stocks
27
12
International stocks
1 10 20 30 40 50
Number of Stocks
19
Key Results of Portfolio Theory

• The extent to which risk is reduced by portfolio
  diversification depends on the correlation of
  assets in the portfolio.
• As the number of assets increases, portfolio
  variance becomes more dependent on the
  covariances (or correlations) and less dependent
  on variances.
• The risk of an asset when held in a large
  portfolio depends on its return covariance (or
  correlation) with other assets in the portfolio.
• Example MSCI World Index MSCI Emerging
  Markets Index

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Two Asset Case
21
Combinations of the two portfolios if correlation
1
22
Combinations of the two portfolios if correlation
1
Amount of risk reduction
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Are Correlations Constant?

• Longin Solnik estimated national stock market
  correlations during periods of high and low
  market volatility assuming constant correlations
  (ri,us) between index i and the U.S. market.
• While, movements in volatility of various market
  indices are not synchronized, they nevertheless
  conclude that volatility is contagious.
• This means that stock markets tend to move
  together during BAD times. Which is not good, as
  it is during bad times that we really want
  differences across markets.

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The Bad News On Correlations
De Santis and Gerard (1997)
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Exchange Rate Risk

• The realized dollar return for an Australian
  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 Australian dollar and the
  foreign currency, i.e.
• Uncertainty about what will happen to the foreign
  stock market (rforeign market).
• Uncertainty about what will happen to the
  exchange rate (g/FC).

27
Exchange Rate Risk

• The realized dollar return for an Australian
  resident investing in a foreign market is given
  by

Where, Ri is the local currency return in the
ith market. ri is the rate of change in the
exchange rate between the local currency and
the dollar.
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Exchange Rate Risk

• An example with Japanese shares
• US investor takes 1,000,000 on 1/1/2002 and
  invests in shares traded on the Tokyo Stock
  Exchange (TSE)
• On 1/1/2002, the spot exchange rate was 130/
• The investor purchases 6,500 shares valued at
  20,000 for a total investment of 130,000,000
• At the end of the year, the investor sells the
  shares at a price of 25,000 per share yielding
  162,500,000
• On 1/1/2003, the spot exchange rate was 125/
• The investor receives a 30 return on investment
  (1,300,000/1,000,000) - 1 30

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Exchange Rate Risk

• An example with Japanese shares
• The total return reflects not only the rise in
  the yen stock price but also the appreciation of
  the yen.
• The formula for the total return is

Where (1/125)/(1/ 130)-1 0.04
25,000/20,000-1 0.25
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Exchange Rate Risk

• The risk for an Australian resident investing in
  a foreign market will depend not only on the risk
  in the foreign market but also on the risk of the
  exchange rate between the Australian dollar and
  the foreign currency

This equation demonstrates that exchange rate
fluctuations contribute to the risk of foreign
investment through two channels 1. Its own
volatility - Var(gi). 2. Its covariance with the
local market returns - Cov(Ri,gi).
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Where to Invest?
Country Index '07 Return
China SSEC 96.66
India BSE 47.15
Brazil Bovespa 43.65
Hong Kong HSI 39.31
South Korea Seoul Comp. 32.25
Germany DAX 30 22.29
Singapore ST Index 16.63
Mexico IPC 11.68
U.S. Nasdaq 9.81
Canada TSE 7.16
U.S. DJIA 6.43
U.K. FTSE 100 3.80
U.S. SP 500 3.53
France CAC 40 1.31
Italy MIBTEL -7.81
Japan Nikkei -11.13
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Where to Invest?
2006 returns
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How to Invest?

• Direct share investment purchase shares in
  foreign markets using foreign currencies. Can be
  hard to do!
• ADRs/GDRs purchase shares in foreign companies
  that are traded on your home exchange in local
  currency. Limited number!
• MNCs why cant we just buy shares in
  multinational companies to diversify
  internationally? Diversification benefits not as
  good as investing internationally!
• So what are the easy ways?

34
International Mutual Funds

• An Australian investor can easily achieve
  international diversification by investing in an
  Australian-based international mutual fund.
• The advantages include
• Savings on transaction and information costs.
• Circumvention of legal and institutional barriers
  to direct portfolio investments abroad.
• Professional management and record keeping.

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Country Funds

• 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 country. This allows investors to
• Speculate in a single foreign market with minimum
  cost.
• Construct their own personal international
  portfolios.
• Diversify into emerging markets that might be
  inaccessible to individual investors.

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Other Avenues

• Exchange Traded Funds ETFs are investment
  companies, registered with the SEC with assets
  consisting of baskets of securities included in
  an index fund.
• One share in an ETF provides an investor
  diversification to all the constituents of the
  relevant index and its price and yield track the
  indices performance.
• World Equity Benchmark Shares (WEBS)/iShares
  Country specific baskets of stocks designed to
  replicate indices of 14 countries.
• Low cost, convenient way for investors to hold
  diversified investments in several different
  countries.

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Home Bias Puzzle

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

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Home Bias Puzzle Possible Explanations

• Barriers to international investment (e.g.
  foreign investment not allowed in a lot of
  countries).
• restrictions on capital flows have fallen over
  time
• can use country funds
• International trading frictions turnover taxes,
  other taxes, limited liquidity
• Not a huge problem for larger markets, yet home
  bias remains
• Domestic equities may provide a superior
  inflation hedge.
• Sovereign risk - repatriation of funds
• Exchange rate risk
• Information asymmetries
• Psychological impediments

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Conclusions
Low correlations across international markets may
increase the risk-return trade off
1

• Important time variations may exist that can
  challenge these benefits. Time horizon matters.

2
Investors might not be taking full advantage of
the benefits of international diversification.
This is known as the home bias puzzle.
3