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1、LECTURE 6 : INTERNATIONAL PORTFOLIO DIVERSIFICATION / PRACTICAL ISSUES,(Asset Pricing and Portfolio Theory),Contents,International Investment Is there a case ? Importance of exchange rate Hedging exchange rate risk ? Practical issues Portfolio weights and the standard error Rebalancing,Introduction,
2、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) Cus
3、tomer friendly products : Mutual funds, investment trusts, index funds,Relative Size of World Stock Markets (31st Dec. 2003),US Stock Market 53%,10%,International Investments,Risk (%),Number of Stocks,Non Diversifiable Risk,domestic,international,Benefits of International Diversification,Benefits an
4、d 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,The Ex
5、change Rate,Investment horizon : 1 year,$,rUS / ERUSD,$,Domestic Investment (e.g. equity, bonds, etc.),$,rEuro / EREuro,$,International Investment (e.g. equity, bonds, etc.),Euro,Euro,International Investment,Example : Currency Risk,A US investor wants to invest in a British firm currently selling f
6、or 40. With $10,000 to invest and an exchange rate of $2 = 1 Question : How many shares can the investor buy ? A : 125 What is the return under different scenarios ? (uncertainty : what happens over the next year ?) Different returns on investment (share price falls to 35, stays at 40 or increases t
7、o 45) Exchange rate (dollar) stays at 2($/), appreciate to 1.80($/), depreciate to 2.20 ($/).,Example : Currency Risk (Cont.),How Risky is the Exchange Rate ?,Exchange rate provides additional dimension for diversification if exchange rate and foreign returns are not perfectly correlated Expected re
8、turn 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),Variance of USD Ret
9、urns,Eun and Resnik (1988),Practical Considerations,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 op
10、timal 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 i
11、nclude transaction costs of buying and selling and investing new flows of money.,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 whic
12、h 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.,No Short Sales Al
13、lowed (i.e. wi 0),E(Rp),p,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,Jorion, P. (1992) Portfolio Optimisation in Practice,
14、 FAJ,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
15、: US 12% of MCS Japan 9% of MCS other countries at least 50% of the MCS,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 forec
16、asts 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.,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.,
