Chapter%2022%20International%20Portfolio%20Diversification

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Chapter 22International Portfolio Diversification

• 22.1 The Algebra of Portfolio Diversification
• 22.2 Mean-Variance Efficiency
• 22.3 The Benefits of International Portfolio
  Diversification
• 22.4 Variances on Foreign Stock and Bond
  Investments
• 22.5 Home Asset Bias
• 22.6 Barriers to International Portfolio
  Diversification
• 22.7 Summary

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Perfect financial markets...a starting point

• Frictionless markets
• no government intervention or taxes
• no transaction costs or other market frictions
• Rational investors with equal access to costless
  information and market prices
• All investors rationally price financial
  securities
• All investors have equal access to costless
  information
• All investors have equal access to market prices,
  so that buyers and sellers are price takers

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The algebra of portfolio theory

• Assumptions
• Nominal returns are normally distributed
• Investors want more return and less risk in their
  functional currency
• Let Xi proportion of wealth devoted to asset
  i
• such that Si Xi 1
• Expected return on a portfolio ERP Si Xi
  ERi
• Portfolio variance Var(RP) sP2 Si Sj Xi Xj
  sij
• 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 of A and J
• ERp XA ERA XJ ERJ
• (1/2)(0.143)(1/2)(0.177)
• 0.160, or 16.0 percent.

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Portfolio variance

• Correlation
• ERi si A B C
• A American 14.3 16.4 1.000 0.557 0.325
• B British 17.6 29.9 0.557 1.000 0.317
• J Japanese 17.7 35.7 0.325 0.317 1.000
• Example Equal weights of A and J
• sP2 XA2 sA2 XJ2 sJ2 2 XA XJ rAJ sA sJ
• (½)2(0.164)2 (½)2(0.357)2
• 2(½)(½)(0.325)(0.164)(0.357)
• 0.0481
• sP (0.0481)1/2 0.2190, or 21.9 percent

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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.

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Diversification
Mean annual return
J
r -1
r 0.325
r 1
A
Standard deviation of annual return
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Mean-variance efficiency
Mean annual return
B
J
A
Standard deviation of annual return
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International portfolio diversification

• Potential for higher returns
• Potential for lower portfolio risk

Expected return
M
W
Rf
Standard deviation of return
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Domestic versus international diversification

Portfolio risk relative to the risk of a single
asset (sP²/si²)
U.S. diversification only
International diversification
1.0
0.5
5
10
15
20
25
Number of stocks in portfolio
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Historical stock market performance(1970-1998)
Source Morgan Stanley Capital International
Perspectives
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International stock returns (Annual returns to
U.S. investors from 1970-1998)

• Mean Stdev bW SI
• Canada 0.108 0.167 0.866 0.240
• France 0.166 0.290 0.836 0.338
• Germany 0.158 0.295 0.631 0.305
• Japan 0.177 0.357 0.833 0.305
• Switzerland 0.173 0.253 0.750 0.415
• U.K. 0.176 0.299 0.958 0.361
• U.S. 0.143 0.164 0.892 0.457
• World 0.136 0.161 1.000 0.422
• bW versus the MSCI world stock market index
• Sharpe Index (SI) (RP - RF) / sP

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International stock market correlations(Annual
returns to U.S. investors from 1970-1998)

• CN FR DM JP SW UK US
• FR 0.471
• DM 0.363 0.567
• JP 0.310 0.339 0.330
• SW 0.526 0.564 0.659 0.374
• UK 0.539 0.516 0.406 0.317 0.552
• US 0.732 0.484 0.420 0.325 0.587 0.557
• W 0.725 0.569 0.493 0.629 0.609 0.624 0.833

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Efficiency gains through international
diversification
Adapted from Asset Allocation with Hedged and
Unhedged Foreign Stocks and Bonds by Philippe
Jorion, Journal of Portfolio Management, Summer
1989, p. 49-54.
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Returns on foreign assets

• Recall Ptd Ptf Std/f
• (Ptd / Pt-1d) (1 Rd )
• and (Std/f / St-1d/f) (1 sd/f )
• The return on a foreign asset in the domestic
  currency is then
• Rd (Ptd / Pt-1d)-1
• (Ptf Std/f / Pt-1fSt-1d/f)-1
• (Ptf/Pt-1f)(Std/f /St-1d/f)-1
• (1 Rf )(1 sd/f ) - 1
• Rf sd/f Rf sd/f (22.7)

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Return statistics on foreign assets

• Expected return
• ERd ERfEsd/fERf sd/f
• Variance
• Var(Rd)
• Var(Rf)Var(sd/f)Var(Rfsd/f)
• 2Cov(Rf,sd/f)2Cov(Rf,Rfsd/f)2Cov(sd/f,
  Rfsd/f)
• Var(Rf)Var(sd/f)(interaction terms)

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Variance of return on foreign stocks(from the
perspective of U.S. investors)

• interaction
• Var(Rf) Var(s/f) 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
• The dominant risk in foreign stock markets is
  return variability in the local currency
• Exchange rate variability is of secondary
  importance

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Variance of return on foreign bonds(from the
perspective of U.S. investors)

• interaction
• Var(Rf) Var(s/f) 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
• The dominant risk in foreign bond markets is
  exchange rate variability
• Return variability in the local currency is of
  secondary importance

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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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Home asset bias

• Despite the potential benefits of international
  portfolio diversification, most investors
  concentrate their portfolios in domestic
  securities. Why?
• Domestic stock portfolios may serve as a hedge
  against domestic inflation risk
• The costs of international portfolio
  diversification

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Barriers to international portfolio investment

• Market frictions
• Government controls
• Taxes
• Transactions costs
• Unequal access to market prices
• Investor irrationality
• Unequal access to information