LECTURE 6 :LECTURE 6 :

INTERNATIONAL INTERNATIONAL PORTFOLIO PORTFOLIO DIVERSIFICATION / DIVERSIFICATION / PRACTICAL ISSUESPRACTICAL ISSUES

(Asset Pricing and Portfolio (Asset Pricing and Portfolio Theory)Theory)

ContentsContents

International Investment International Investment – Is there a case ? Is there a case ? – Importance of exchange rate Importance of exchange rate – Hedging exchange rate risk ? Hedging exchange rate risk ?

Practical issues Practical issues Portfolio weights and the standard Portfolio weights and the standard

error error RebalancingRebalancing

IntroductionIntroduction

The market portfolioThe market portfolio International investments : International investments :

– Can you enhance your risk return profile ? Can you enhance your risk return profile ? – Some facts 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 biasHome country bias International diversification is easy (and International diversification is easy (and

‘cheap’)‘cheap’)– Improvements in technology (the internet)Improvements in technology (the internet)– ‘‘Customer friendly’ products : Mutual funds, Customer friendly’ products : Mutual funds,

investment trusts, index fundsinvestment trusts, index funds

Relative Size of World Relative Size of World Stock Markets (31Stock Markets (31stst Dec. Dec. 2003)2003)

US

UK

Japan

France

Germany

Switzerland

Canada

Australia

Holland

Italy

Spain

next 5 largest

others

US Stock Market53%

10%

International International InvestmentsInvestments

Risk (%)

Number of Stocks

Non Diversifiable Risk

domestic

international

Benefits of Benefits of International International DiversificationDiversification

Benefits and Costs of Benefits and Costs of International International Investments Investments Benefits : Benefits :

– Interdependence of domestic and Interdependence of domestic and international stock markets international stock markets

– Interdependence between the foreign Interdependence between the foreign stock returns and exchange ratestock returns and exchange rate

Costs : Costs : – Equity risk : could be more (or less than Equity risk : could be more (or less than

domestic market)domestic market)– Exchange rate risk Exchange rate risk – Political risk Political risk – Information riskInformation risk

The Exchange RateThe Exchange 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 International InvestmentInvestment

Example : Currency Example : Currency RiskRisk A US investor wants to invest in a British firm A US investor wants to invest in a British firm

currently selling for £40. With $10,000 to currently selling for £40. With $10,000 to invest and an exchange rate of $2 = £1invest and an exchange rate of $2 = £1

Question : Question : – How many shares can the investor buy ? – A : 125How many shares can the investor buy ? – A : 125– What is the return under different scenarios ? What is the return under different scenarios ?

(uncertainty : what happens over the next year ?)(uncertainty : what happens over the next year ?) Different returns on investment (share price falls to £ Different returns on investment (share price falls to £

35, stays at £40 or increases to £45)35, stays at £40 or increases to £45) Exchange rate (dollar) stays at 2($/£), appreciate to Exchange rate (dollar) stays at 2($/£), appreciate to

1.80($/£), depreciate to 2.20 ($/£). 1.80($/£), depreciate to 2.20 ($/£).

Example : Currency Example : Currency Risk (Cont.)Risk (Cont.)Share Share

Price (£)Price (£)£-Return £-Return $-Return $-Return

S=1.80($/S=1.80($/£)£)

$-Return$-ReturnS=2.00($/S=2.00($/

£)£)

$-Return$-ReturnS=2.20($/S=2.20($/

£)£)

£ 35£ 35 -12.5%-12.5% -21.25%-21.25% -12.5%-12.5% 3.75%3.75%

£ 40£ 40 0%0% -10%-10% 0%0% 10%10%

£ 45£ 45 +12.5%+12.5% 1.25%1.25% 12. 5%12. 5% 23.75%23.75%

How Risky is the How Risky is the Exchange Rate ? Exchange Rate ? Exchange rate provides additional dimension Exchange rate provides additional dimension

for diversification if exchange rate and for diversification if exchange rate and foreign returns are not perfectly correlatedforeign returns are not perfectly correlated

Expected return in domestic currency (say Expected return in domestic currency (say £) on foreign investment (say US) £) on foreign investment (say US) – Expected appreciation of foreign currency ($/£)Expected appreciation of foreign currency ($/£)– Expected return on foreign investment in foreign Expected return on foreign investment in foreign

currency (here US Dollar)currency (here US Dollar)Return : E(RReturn : E(Rdomdom) = E(S) = E(SAppApp) + E(R) + E(Rforfor))

Risk : Risk : Var(R Var(Rdomdom) = var(S) = var(SAppApp) + Var(R) + Var(Rforfor) + 2Cov(S) + 2Cov(SAppApp, , RRforfor))

Variance of USD Variance of USD ReturnsReturns

CountryCountry Ex. RateEx. Rate Local Local Ret.Ret.

2 Cov2 Cov

CanadaCanada 4.264.26 84.9184.91 10.8310.83

France France 29.6629.66 61.7961.79 8.558.55

GermanyGermany 38.9238.92 41.5141.51 19.5719.57

JapanJapan 31.8531.85 47.6547.65 20.5020.50

Switzerl.Switzerl. 55.1755.17 30.0130.01 14.8114.81

UKUK 32.3532.35 51.2351.23 16.5216.52

Eun and Resnik (1988)

Practical Practical ConsiderationsConsiderations

Portfolio Theory : Portfolio Theory : Practical Issues Practical Issues (General)(General) All investors do not have the same views about All investors do not have the same views about

expected returns and covariances. However, we can expected returns and covariances. However, we can still use this methodology to work out optimal still use this methodology to work out optimal proportions / weights for each individual investor. proportions / weights for each individual investor.

The optimal weights will change as forecasts of The optimal weights will change as forecasts of returns and correlations changereturns and correlations change

Lots of weights might be negative which implies short Lots of weights might be negative which implies short selling, possibly on a large scale (if this is impractical selling, possibly on a large scale (if this is impractical you can calculate weights where all the weights are you can calculate weights where all the weights are forced to be positive). forced to be positive).

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

Portfolio Theory : Portfolio Theory : Practical Issues Practical Issues (General)(General)

To overcome the sensitivity problem : To overcome the sensitivity problem : … … choose the weights to minimise portfolio variance choose the weights to minimise portfolio variance

(weights are independent of ‘badly measured’ (weights are independent of ‘badly measured’ expected returns).expected returns).

… … choose ‘new weights’ which do not deviate from choose ‘new weights’ which do not deviate from existing weights by more than x% (say 2%)existing weights by more than x% (say 2%)

… … choose ‘new weights’ which do not deviate from choose ‘new weights’ which do not deviate from ‘index tracking weights’ by more than x% (say 2%)‘index tracking weights’ by more than x% (say 2%)

… … do not allow any short sales of risky assets (only do not allow any short sales of risky assets (only positive weights). positive weights).

… … limit the analysis to only a number (say 10) countries. limit the analysis to only a number (say 10) countries.

No Short Sales No Short Sales Allowed (i.e. wAllowed (i.e. wii > 0) > 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

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

Jorion (1992) - The Jorion (1992) - The Paper Paper Bond markets (US investor’s point of view)Bond markets (US investor’s point of view)

Sample period : Sample period : Jan. 1978-Dec. 1988Jan. 1978-Dec. 1988 Countries : Countries :

USA, Canada, Germany, Japan, UK, Holland, FranceUSA, Canada, Germany, Japan, UK, Holland, France Methodology applied : Methodology applied :

MCS, optimum portfolio risk and return calculations MCS, optimum portfolio risk and return calculations Results : Results :

– Huge variation in risk and return Huge variation in risk and return – Zero weights : Zero weights :

US 12% of MCS US 12% of MCS Japan 9% of MCS Japan 9% of MCS other countries at least 50% of the MCSother countries at least 50% of the MCS

Monte Carlo Monte Carlo Simulation and Simulation and Portfolio TheoryPortfolio Theory Suppose k assets (say k = 3)Suppose k assets (say k = 3)

(1.) Calculate the expected returns, variances and (1.) Calculate the expected returns, variances and covariances for all k assets (here 3), using n-observations covariances for all k assets (here 3), using n-observations of ‘real data’. of ‘real data’.

(2.) Assume a model which forecasts stock returns : (2.) Assume a model which forecasts stock returns :

RRtt = = + + tt

(3.) Generate (nxk) multivariate normally distributed (3.) Generate (nxk) multivariate normally distributed random numbers with the characteristics of the ‘real data’ random numbers with the characteristics of the ‘real data’ (e.g. mean = 0, and variance covariances). (e.g. mean = 0, and variance covariances).

(4.) Generate for each asset n-‘simulated returns’ using (4.) Generate for each asset n-‘simulated returns’ using the model above. the model above.

Monte Carlo Simulation Monte Carlo Simulation and Portfolio Theory and Portfolio Theory (Cont.)(Cont.)

(5.) Calculate the portfolio SD and return of the (5.) Calculate the portfolio SD and return of the optimum portfolio using the ‘simulated returns optimum portfolio using the ‘simulated returns data’. data’.

(6.) Repeat steps (3.), (4.) and (5.) 1,000 times(6.) Repeat steps (3.), (4.) and (5.) 1,000 times

(7.) Plot an xy scatter diagram of all 1,000 pairs (7.) Plot an xy scatter diagram of all 1,000 pairs of SD and returns. of SD and returns.

Jorion (1992) - Monte Jorion (1992) - Monte Carlo ResultsCarlo Results

An

nu

al R

etu

rns(

%)

Volatility (%)

UK

GermanyUS

True Optimal Portfolio

Britton-Jones (1999) – Britton-Jones (1999) – Journal of FinanceJournal of Finance

Britton-Jones (1999) – Britton-Jones (1999) – The Paper The Paper International diversification : Are the optimal International diversification : Are the optimal

portfolio weights statistically significantly portfolio weights statistically significantly different from ZERO ? different from ZERO ?

Returns are measured in US Dollars and fully Returns are measured in US Dollars and fully hedgedhedged

11 countries : US, UK, Japan, Germany, … 11 countries : US, UK, Japan, Germany, … Data : monthly data 1977 – 1996 (two Data : monthly data 1977 – 1996 (two

subperiods : 1977–1986, 1986–1996)subperiods : 1977–1986, 1986–1996) Methodology used : Methodology used :

– Regression analysis Regression analysis – Non-negative restrictions on weights not usedNon-negative restrictions on weights not used

Britten-Jones (1999) : Britten-Jones (1999) : Optimum WeightsOptimum Weights

1977-19961977-1996 1977-19861977-1986 1987-19961987-1996

weightweightss

t-statst-stats weightweightss

t-statst-stats weightweightss

t-statst-stats

AustraliAustraliaa

12.812.8 0.540.54 6.86.8 0.200.20 21.621.6 0.660.66

AustriaAustria 3.03.0 0.120.12 -9.7-9.7 -0.22-0.22 22.522.5 0.740.74

BelgiumBelgium 29.029.0 0.830.83 7.17.1 0.150.15 6666 1.211.21

CanadaCanada -45.2-45.2 -1.16-1.16 -32.7-32.7 -0.64-0.64 -68.9-68.9 -1.10-1.10

DenmarDenmarkk

14.214.2 0.470.47 -29.6-29.6 -0.65-0.65 68.868.8 1.781.78

France France 1.21.2 0.040.04 -0.7-0.7 -0.02-0.02 -22.8-22.8 -0.48-0.48

GermanGermanyy

-18.2-18.2 -0.51-0.51 9.49.4 0.190.19 -58.6-58.6 -1.13-1.13

ItalyItaly 5.95.9 0.290.29 22.222.2 0.790.79 -15.3-15.3 -0.52-0.52

JapanJapan 5.65.6 0.240.24 57.757.7 1.431.43 -24.5-24.5 -0.87-0.87

UKUK 32.532.5 1.011.01 42.542.5 0.990.99 3.53.5 0.070.07

USUS 59.359.3 1.261.26 27.027.0 0.410.41 107.9107.9 1.531.53

SummarySummary

A case for International A case for International diversification ? diversification ? – Empirical (academic) evidence : YesEmpirical (academic) evidence : Yes– Need to consider the exchange rate Need to consider the exchange rate

Portfolio weights Portfolio weights – Very sensitive to parameter inputsVery sensitive to parameter inputs– Seem to have large standard errors Seem to have large standard errors

Suggestions to make portfolio theory Suggestions to make portfolio theory workable in practice. workable in practice.

References References

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

ReferencesReferences

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

Britton-Jones, M. (1999) ‘The Sampling Britton-Jones, M. (1999) ‘The Sampling Error in Estimates of Mean-Variance Error in Estimates of Mean-Variance Efficient Portfolio Weights’, Efficient Portfolio Weights’, Journal of Journal of FinanceFinance, Vol. 52, No. 2, pp. 637-659, Vol. 52, No. 2, pp. 637-659

Eun, C.S. and Resnik, B.G. (1988) Eun, C.S. and Resnik, B.G. (1988) ‘Exchange Rate Uncertainty, Forward ‘Exchange Rate Uncertainty, Forward Contracts and International Portfolio Contracts and International Portfolio Selection’, Selection’, Journal of FinanceJournal of Finance, Vol XLII, , Vol XLII, No. 1, pp. 197-215. No. 1, pp. 197-215.

END OF LECTUREEND OF LECTURE