LECTURE 9 : INTERNATIONAL PORTFOLIO DIVERSIFICATION / PRACTICAL ISSUES

1. LECTURE 9 :INTERNATIONAL PORTFOLIO DIVERSIFICATION / PRACTICAL ISSUES (Asset Pricing and Portfolio Theory)

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

3. 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

4. Mean-Variance Portfolio Theory • Risk of the portfolio (measured by the standard deviation) tends to fall when more stocks are included. However, some risk remains (systematic or undiversifiable risk) Whether this systematic risk can be reduced by widening the choice of stocks in the portfolio to include foreign stock (or assets)?

5. 2) The efficient frontier gives the risk return trade-off. If we can widen the set of asset (include foreign as well as domestic assets), then it may be possible to substantially move the efficient frontier ‘to the left’. Whether the historic low correlations will persist in the future and whether the volatilities and the average returns are constant over time?

6. 3) If we include foreign assets in the portfolio, then the investor will usually be interested in the return (and risk) measured in terms of her ‘home currency’ If the investor hedges the risk, then exchange rate risk can be ignored 4) Determine the optimal portfolio weights – depend on our estimates of the future values of the expected returns, variances and covariances between the assets.

7. Relative Size of World Stock Markets (31st Dec. 2008) US Stock Market 48.38% 10.2%

8. International Investments

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

10. 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

11. The Exchange Rate

12. 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.) $ $

13. 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($/£), depreciate to 2.20 ($/£).

14. Example : Currency Risk (Cont.)

15. 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)

16. Variance of USD Returns Eun and Resnik (1988)

17. Practical Considerations

18. 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.

19. 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.

20. No Short Sales Allowed (i.e. wi > 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

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

22. Jorion (1992) - The Paper Bond markets (US investor’s 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

23. 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.

24. 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.

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

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

27. 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 : 1977–1986, 1986–1996) • Methodology used : • Regression analysis • Non-negative restrictions on weights not used

28. Britten-Jones (1999) : Optimum Weights

29. 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.

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

31. 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.