Copyright © 2009 Pearson Prentice Hall. All rights reserved. Chapter 9 The Case for International...

Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Chapter 9

The Case for International Diversification

Copyright © 2009 Pearson Prentice Hall. All rights reserved. 9 - 2

International Investing

Foreign investment allows investors to reduce the total risk of the portfolio while offering additional return potential.

By expanding the investment opportunity set, international diversification helps to improve the risk-adjusted performance of a portfolio.


Traditional Case for International Diversification A low international correlation allows for

reduction of volatility of a global portfolio. A low international correlation provides profit

opportunities for an active investor. Otherwise, the lower the correlation, the bigger

the risk reduction. Covd,f = ρd,fσdσf


The expected return on the portfolio is simply equal to the average expected return on the two asset classes:

E(Rp) = wdE(Rd) + wfE(Rf)

The standard deviation of the portfolio is equal to:

p = (wd2d

2 + wf2f

2 + 2wdwfdfdf)1/2

The portfolio’s total risk (σp) will always be less than the average of the two standard deviations (wdσd + wfσf).

The only case in which it will be equal is when ρd,f = +1.

Traditional Case for International Diversification (conti.)


Example 9.1

Assume that the domestic and foreign assets have standard deviations of σd = 15% and σf = 17% respectively, with a correlation of ρd,f = 0.4

1. What is the standard deviation of a portfolio equally invested in domestic and foreign assets?

2. What is the standard deviation of a portfolio with a 40% investment in the foreign asset?

3. What is the standard deviation of a portfolio equally invested in domestic and foreign assets if the correlation is 0.5? What if the correlation is 0.8?


Example 9.1(Answer)

1. p = ((0.5)2 (0.15)2 + (0.5)2(0.17)2 +

2(0.5)(0.5)(0.4)(0.15)(0.17))1/2 = 13.4%

2. p = ((0.6)2 (0.15)2 + (0.4)2(0.17)2 +

2(0.6)(0.4)(0.4)(0.15)(0.17))1/2 = 13.27%

3. p = ((0.5)2 (0.15)2 + (0.5)2(0.17)2 +

2(0.5)(0.5)(0.5)(0.15)(0.17))1/2 = 13.87%

p = ((0.5)2 (0.15)2 + (0.5)2(0.17)2 +

2(0.5)(0.5)(0.8)(0.15)(0.17))1/2 = 15.18%


Currency Considerations

The dollar value of an asset is equal to its local currency value (V) multiplied by the exchange rate (S) (number of dollars/local currency):

V$ = V S The rate of return over the period is:

r$ = r + s + (r s)

where r = return in local currency

s = percentage exchange rate movement


Example 9.2 – Currency Risk

Suppose that we have a foreign investment with the following characteristics:

σ = 15.5%, σs = 7% and ρ = 0

What is the risk in domestic currency and the contribution of currency risk?


Example 9.2 (Answer)

The risk in domestic currency

σf = ((15.5%)2 +(7%)2 +2(0)(15.5%)(7%))1/2

=17%

Contribution of currency risk:

σf – σ = 17% - 15.5% = 1.5%


Exhibit 9.2: Risk-Return Trade-off of Internationally Diversified Portfolios


Exhibit 9.3 Risk-Return Trade-Off of Internationally Diversified versus Domestic-Only Portfolios


Exhibit 9.3 (conti.)

The global efficient frontier is to the left of the domestic efficient frontier, showing the increased return opportunities and risk diversification benefits brought by the enlarged investment universe.

A prerequisite for this argument is that the various capital markets of the world have somewhat independent price behaviors.


Exhibit 9.4: Correlation of Stock Markets, 1997-2007 Monthly returns in U.S. dollars (bottom left) and currency hedged (top right)



In general, the low correlation across countries offers risk-diversification and return opportunities.

Emerging markets present a positive but rather low correlation with developed marlets.

The correlation coefficients in the top right part of the matrix are very similar to the U.S. dollar correlations.


Exhibit 9.5: Correlation of Bond Markets, January 1992-2002 Monthly Returns in U.S. Dollar (bottom right) and Currency Hedged (top right)



In general, bond return variations are not highly correlated across countries.

The correlation of foreign bonds with the U.S. stock market is quite small. So foreign bonds offer excellent diversification benefits to a U.S. stock portfolio manager.



Regional blocs do appear. Eurozone bond markets now exhibit a correlation

close to 1.0 for government bonds. The correlation coefficients in the top right part of

the matrix are somewhat different from the U.S. dollar correlations. This is because there exists a correlation between currency movements and bond yield movements.


Portfolio Return Performance

A common way to evaluate a portfolio’s risk-adjusted performance is to evaluate its Sharpe Ratio.

The Sharpe Ratio is the ratio of return on a portfolio, in excess of the risk-free rate, divided by its standard deviation.

p

fp rREratioSharpe

)(


Sharpe Ratio

In other words, the Sharpe ratio measures the excess return per unit of risk.

Money managers attempt to maximize the Sharpe ratio.

Investing in foreign assets allows a reduction in portfolio risk and possibly an increased return.


Example 9.4 – Sharpe Ratio

You are given the following information:

σf = 17%, σd = 15%, ρdf = 0.4, E(Rf)=E(Rd) =10%, rfd = rff = 4%

1. Calculate the Sharpe ratios for the domestic asset, the foreign asset and an internationally diversified portfolio equally invested in the domestic and foreign assets.

2. E(Rf) = 12%, E(Rd) =10%


Example 9.4 (Answer)

1.

2.

353.0%17

%4%10

4.0%15

%4%10

f

d

ratioSharpe

ratioSharpe

E(Rp) = 0.5(10%) + 0.5(10%) = 10%p = ((0.5)2 (0.15)2 +(0.5)2(0.17)2

+2(0.5)(0.5)(0.4)(0.15)(0.17))1/2 = 13.4%

448.0%4.13

%4%10

pratioSharpe

522.0%4.13

%4%11

pratioSharpe


Exhibit 9.7: Efficient Frontier for Stocks (U.S. dollar,1980-1990)



Any domestic U.S. stock/bond strategy is strongly dominated by a global stock/bond strategy.

A domestic portfolio of U.S. stocks and bonds tends to have half the return of that on a global efficient allocation with the same risk level.


Exhibit 9.8: Global Efficient Frontier for Stocks and Bonds (U.S. dollar, 1980-1990)


Exhibit 9.9a: Global Efficient Frontiers for Non-U.S. Investors Japanese yen (1980-1990)


Exhibit 9.9b: Global Efficient Frontiers for Non-U.S. Investors British Pound (1980-1990)


Exhibit 9.9c: Global Efficient Frontiers for Non-U.S. Investors Deutsche Mark (1980-1990)


Exhibit 9.10: Mean Return and Correlation of Selected Markets with the U.S. Equity Market Five Year Period from 1971 to 2000, in U.S. Dollars


Case Against International Diversification

International correlations have trended upward over the past decade.

It has also been observed that international correlation increases in periods of high market volatility. The increases in correlations have been due to such factors as deregulation, capital mobility, free trade, and the globalization of corporations.

Markets that used to be segmented are moving towards global integration.


Exhibit 9.12: Value of Cross-Border M&As, 1987-2005


Barriers to International Investment

Familiarity with Foreign Markets Political Risk Market Efficiency (liquidity) Regulations Transaction Costs Taxes Currency Risk

can be hedged with derivative is smaller than the risk of the corresponding stock or

bond market


Exhibit 9.14: Average Correlation of Countries and of Industries



Numerous studies show that industry factors have a growing influence on stock returns relative to country-specific factors.

Although the industry factors have become prominent, the regional factors are still present.


The Case for Emerging Markets

Expected profit is potentially large. The local risks (volatility, liquidity and

political risks) are higher. Emerging markets also present a positive

but moderate correlation with developed markets.

The correlation with the world index of developed markets from 1987 to 2007 was 0.64.


The Case for Emerging Markets (conti.)

The volatility of emerging markets is much larger than that of developed markets.

Investment risk in emerging economies often comes from the possibility of a financial crisis. e.g. Mexican peso crisis (1994) Asian financial crisis (1997)


Exhibit 9.15 Performance of World Developed Markets and Emerging Markets


Investability in Emerging Markets

Restrictions can take the form of:Foreign ownershipFree floatRepatriation of income or capitalDiscriminatory taxesForeign currency restrictions Authorized investors

Copyright © 2009 Pearson Prentice Hall. All rights reserved. Chapter 9 The Case for International...

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