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LECTURE 6 : INTERNATIONAL PORTFOLIO DIVERSIFICATION / PRACTICAL ISSUES

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LECTURE 6 :INTERNATIONAL PORTFOLIO DIVERSIFICATION / PRACTICAL ISSUES

(Asset Pricing and Portfolio Theory)

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

- Practical issues
- Portfolio weights and the standard error
- Rebalancing

- 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

US Stock

Market

53%

10%

International Investments

Risk (%)

Non Diversifiable Risk

domestic

international

Number of Stocks

- 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 Exchange Rate

Investment horizon : 1 year

rUS / ERUSD

Domestic Investment

(e.g. equity, bonds, etc.)

$

$

rEuro / EREuro

Euro

Euro

International Investment

(e.g. equity, bonds, etc.)

$

$

- 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 ($/£).

- 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)

Eun and Resnik (1988)

Practical Considerations

- 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.

- 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.

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

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

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

- 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.

(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.

True Optimal Portfolio

UK

Annual Returns(%)

Germany

US

Volatility (%)

Britton-Jones (1999) – Journal of Finance

- 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

- 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.

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

- 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.

END OF LECTURE