LECTURE 6 : INTERNATIONAL PORTFOLIO DIVERSIFICATION / PRACTICAL ISSUES

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LECTURE 6 INTERNATIONAL PORTFOLIO
DIVERSIFICATION / PRACTICAL ISSUES

• (Asset Pricing and Portfolio Theory)

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Contents

• International Investment
• Is there a case ?
• Importance of exchange rate
• Hedging exchange rate risk ?
• Practical issues
• Portfolio weights and the standard error
• Rebalancing

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Introduction

• The market portfolio
• International investments
• Can you enhance your risk return profile ?
• Some facts
• US investors seem to overweight US stocks
• Other investors prefer their home country
• ? Home country bias
• International diversification is easy (and
  cheap)
• Improvements in technology (the internet)
• Customer friendly products Mutual funds,
  investment trusts, index funds

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Relative Size of World Stock Markets (31st Dec.
2003)
US Stock Market 53
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International Investments
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Benefits of International Diversification
Risk ()
Non Diversifiable Risk
domestic
international
Number of Stocks
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Benefits and Costs of International Investments

• Benefits
• Interdependence of domestic and international
  stock markets
• Interdependence between the foreign stock returns
  and exchange rate
• Costs
• Equity risk could be more (or less than
  domestic market)
• Exchange rate risk
• Political risk
• Information risk

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The Exchange Rate
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International Investment
Investment horizon 1 year
rUS / ERUSD
Domestic Investment (e.g. equity, bonds, etc.)


rEuro / EREuro
Euro
Euro
International Investment (e.g. equity, bonds,
etc.)


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Example Currency Risk

• A US investor wants to invest in a British firm
  currently selling for 40. With 10,000 to
  invest and an exchange rate of 2 1
• Question
• How many shares can the investor buy ? A 125
• What is the return under different scenarios ?
• (uncertainty what happens over the next year
  ?)
• Different returns on investment (share price
  falls to 35, stays at 40 or increases to 45)
• Exchange rate (dollar) stays at 2(/),
  appreciate to 1.80(/), depreciate to 2.20
  (/).

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Example Currency Risk (Cont.)
Share Price () -Return -Return S1.80(/) -Return S2.00(/) -Return S2.20(/)
35 -12.5 -21.25 -12.5 3.75
40 0 -10 0 10
45 12.5 1.25 12. 5 23.75
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How Risky is the Exchange Rate ?

• Exchange rate provides additional dimension for
  diversification if exchange rate and foreign
  returns are not perfectly correlated
• Expected return in domestic currency (say ) on
  foreign investment (say US)
• Expected appreciation of foreign currency (/)
• Expected return on foreign investment in foreign
  currency (here US Dollar)
• Return E(Rdom) E(SApp) E(Rfor)
• Risk Var(Rdom) var(SApp) Var(Rfor)
  2Cov(SApp, Rfor)

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Variance of USD Returns
Country Ex. Rate Local Ret. 2 Cov
Canada 4.26 84.91 10.83
France 29.66 61.79 8.55
Germany 38.92 41.51 19.57
Japan 31.85 47.65 20.50
Switzerl. 55.17 30.01 14.81
UK 32.35 51.23 16.52
Eun and Resnik (1988)
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Practical Considerations
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Portfolio Theory Practical Issues (General)

• All investors do not have the same views about
  expected returns and covariances. However, we
  can still use this methodology to work out
  optimal proportions / weights for each individual
  investor.
• The optimal weights will change as forecasts of
  returns and correlations change
• Lots of weights might be negative which implies
  short selling, possibly on a large scale (if this
  is impractical you can calculate weights where
  all the weights are forced to be positive).
• The method can be easily adopted to include
  transaction costs of buying and selling and
  investing new flows of money.

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Portfolio Theory Practical Issues (General)

• To overcome the sensitivity problem
• choose the weights to minimise portfolio
  variance (weights are independent of badly
  measured expected returns).
• choose new weights which do not deviate from
  existing weights by more than x (say 2)
• choose new weights which do not deviate from
  index tracking weights by more than x (say 2)
• do not allow any short sales of risky assets
  (only positive weights).
• limit the analysis to only a number (say 10)
  countries.

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No Short Sales Allowed (i.e. wi gt 0)
E(Rp)
Unconstraint efficient frontier (short selling
allowed)

• Constraint efficient frontier
• (with no short selling allowed)
• always lies within unconstraint
• efficient frontier or on it
• - deviates more at high levels of ER and s

?p
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Jorion, P. (1992) Portfolio Optimisation in
Practice, FAJ
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Jorion (1992) - The Paper

• Bond markets (US investors point of view)
• Sample period Jan. 1978-Dec. 1988
• Countries
• USA, Canada, Germany, Japan, UK, Holland, France
• Methodology applied
• MCS, optimum portfolio risk and return
  calculations
• Results
• Huge variation in risk and return
• Zero weights
• US 12 of MCS
• Japan 9 of MCS
• other countries at least 50 of the MCS

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Monte Carlo Simulation and Portfolio Theory

• Suppose k assets (say k 3)
• (1.) Calculate the expected returns, variances
  and covariances for all k assets (here 3), using
  n-observations of real data.
• (2.) Assume a model which forecasts stock
  returns
• Rt m et
• (3.) Generate (nxk) multivariate normally
  distributed random numbers with the
  characteristics of the real data (e.g. mean
  0, and variance covariances).
• (4.) Generate for each asset n-simulated
  returns using the model above.

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Monte Carlo Simulation and Portfolio Theory
(Cont.)

• (5.) Calculate the portfolio SD and return of
  the optimum portfolio using the simulated
  returns data.
• (6.) Repeat steps (3.), (4.) and (5.) 1,000
  times
• (7.) Plot an xy scatter diagram of all 1,000
  pairs of SD and returns.

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Jorion (1992) - Monte Carlo Results
True Optimal Portfolio
UK
Annual Returns()
Germany
US
Volatility ()
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Britton-Jones (1999) Journal of Finance
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Britton-Jones (1999) The Paper

• International diversification Are the optimal
  portfolio weights statistically significantly
  different from ZERO ?
• Returns are measured in US Dollars and fully
  hedged
• 11 countries US, UK, Japan, Germany,
• Data monthly data 1977 1996 (two subperiods
  19771986, 19861996)
• Methodology used
• Regression analysis
• Non-negative restrictions on weights not used

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Britten-Jones (1999) Optimum Weights
1977-1996 1977-1996 1977-1986 1977-1986 1987-1996 1987-1996
weights t-stats weights t-stats weights t-stats
Australia 12.8 0.54 6.8 0.20 21.6 0.66
Austria 3.0 0.12 -9.7 -0.22 22.5 0.74
Belgium 29.0 0.83 7.1 0.15 66 1.21
Canada -45.2 -1.16 -32.7 -0.64 -68.9 -1.10
Denmark 14.2 0.47 -29.6 -0.65 68.8 1.78
France 1.2 0.04 -0.7 -0.02 -22.8 -0.48
Germany -18.2 -0.51 9.4 0.19 -58.6 -1.13
Italy 5.9 0.29 22.2 0.79 -15.3 -0.52
Japan 5.6 0.24 57.7 1.43 -24.5 -0.87
UK 32.5 1.01 42.5 0.99 3.5 0.07
US 59.3 1.26 27.0 0.41 107.9 1.53
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Summary

• A case for International diversification ?
• Empirical (academic) evidence Yes
• Need to consider the exchange rate
• Portfolio weights
• Very sensitive to parameter inputs
• Seem to have large standard errors
• Suggestions to make portfolio theory workable in
  practice.

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References

• Cuthbertson, K. and Nitzsche, D. (2001)
  Investments Spot and Derivatives Markets,
  Chapter 18

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References

• Jorion, P. (1992) Portfolio Optimization in
  Practice, Financial Analysts Journal, Jan-Feb,
  p. 68-74
• Britton-Jones, M. (1999) The Sampling Error in
  Estimates of Mean-Variance Efficient Portfolio
  Weights, Journal of Finance, Vol. 52, No. 2, pp.
  637-659
• Eun, C.S. and Resnik, B.G. (1988) Exchange Rate
  Uncertainty, Forward Contracts and International
  Portfolio Selection, Journal of Finance, Vol
  XLII, No. 1, pp. 197-215.

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END OF LECTURE