1. LECTURE 6 : INTERNATIONAL PORTFOLIO DIVERSIFICATION / PRACTICAL ISSUES (Asset Pricing and Portfolio Theory)

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

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

4. Relative Size of World Stock Markets (31 st Dec. 2003) US Stock Market 53% 10%

7. International Investments

8. Risk (%) Number of Stocks Non Diversifiable Risk domestic international Benefits of International Diversification

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

10. The Exchange Rate

11. Investment horizon : 1 year $ r US / ER USD $ Domestic Investment (e.g. equity, bonds, etc.) $ r Euro / ER Euro $ International Investment (e.g. equity, bonds, etc.) Euro International Investment

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

13. Example : Currency Risk (Cont.) Share Price (£) £-Return$-ReturnS=1.80($/£)$-ReturnS=2.00($/£)$-ReturnS=2.20($/£) £ 35 -12.5%-21.25%-12.5%3.75% £ 40 0%-10%0%10% £ 45 +12.5%1.25% 12. 5% 23.75%

14. How Risky is the Exchange Rate ? Exchange rate provides additional dimension for diversification if exchange rate and foreign returns are not perfectly correlated 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 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(R dom ) = E(S App ) + E(R for ) Risk : Var(R dom ) = var(S App ) + Var(R for ) + 2Cov(S App, R for )

15. Variance of USD Returns Country Ex. Rate Local Ret. 2 Cov Canada4.2684.9110.83 France29.6661.798.55 Germany38.9241.5119.57 Japan31.8547.6520.50 Switzerl.55.1730.0114.81 UK32.3551.2316.52 Eun and Resnik (1988)

16. Practical Considerations

17. 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. 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 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). 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. The method can be easily adopted to include transaction costs of buying and selling and investing ‘new’ flows of money.

18. Portfolio Theory : Practical Issues (General) To overcome the sensitivity problem : 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.

19. No Short Sales Allowed (i.e. w i > 0) E(R p ) p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 

20. Jorion, P. (1992) ‘Portfolio Optimisation in Practice’, FAJ

21. Jorion (1992) - The Paper Bond markets (US investor’s point of view) Sample period : Jan. 1978-Dec. 1988 Sample period : Jan. 1978-Dec. 1988 Countries : Countries : USA, Canada, Germany, Japan, UK, Holland, France Methodology applied : Methodology applied : MCS, optimum portfolio risk and return calculations Results : 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

22. Monte Carlo Simulation and Portfolio Theory Suppose k assets (say k = 3) 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 : R t =  +  t (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.

23. 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.

24. Jorion (1992) - Monte Carlo Results Annual Returns(%) Volatility (%) UK Germany US True Optimal Portfolio

25. Britton-Jones (1999) – Journal of Finance

26. Britton-Jones (1999) – The Paper International diversification : Are the optimal portfolio weights statistically significantly different from ZERO ? International diversification : Are the optimal portfolio weights statistically significantly different from ZERO ? Returns are measured in US Dollars and fully hedged Returns are measured in US Dollars and fully hedged 11 countries : US, UK, Japan, Germany, … 11 countries : US, UK, Japan, Germany, … Data : monthly data 1977 – 1996 (two subperiods : 1977–1986, 1986–1996) Data : monthly data 1977 – 1996 (two subperiods : 1977–1986, 1986–1996) Methodology used : Methodology used : –Regression analysis –Non-negative restrictions on weights not used

27. Britten-Jones (1999) : Optimum Weights 1977-19961977-19861987-1996 weightst-statsweightst-statsweightst-stats Australia12.80.546.80.2021.60.66 Austria3.00.12-9.7-0.2222.50.74 Belgium29.00.837.10.15661.21 Canada-45.2-1.16-32.7-0.64-68.9-1.10 Denmark14.20.47-29.6-0.6568.81.78 France1.20.04-0.7-0.02-22.8-0.48 Germany-18.2-0.519.40.19-58.6-1.13 Italy5.90.2922.20.79-15.3-0.52 Japan5.60.2457.71.43-24.5-0.87 UK32.51.0142.50.993.50.07 US59.31.2627.00.41107.91.53

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

29. References Cuthbertson, K. and Nitzsche, D. (2001) ‘Investments : Spot and Derivatives Markets’, Chapter 18 Cuthbertson, K. and Nitzsche, D. (2001) ‘Investments : Spot and Derivatives Markets’, Chapter 18

30. References Jorion, P. (1992) ‘Portfolio Optimization in Practice’, Financial Analysts Journal, Jan- Feb, p. 68-74 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 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. 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.

31. END OF LECTURE