12 3 Consider two assets—Lo and Hi—with the characteristics described in the table below:

Example 8.12 3 Consider two assets—Lo and Hi—with the characteristics described in the table below:

Expected

Risk (standard

Asset

return, deviation), r S

Clearly, asset Lo offers a lower return than Hi does, but Lo is also less risky than Hi. It is natural to think that a portfolio combining Lo and Hi would offer a return that is between 6% and 8% and that the portfolio’s risk would also fall between the risk of Lo and Hi (between 3% and 8%). That intuition is only partly correct.

The performance of a portfolio consisting of assets Lo and Hi depends not only on the expected return and standard deviation of each asset (given above), but also on how the returns on the two assets are correlated. We will illustrate the results of three specific scenarios: (1) returns on Lo and Hi are perfectly positively correlated, (2) returns on Lo and Hi are uncorrelated, and (3) returns on Lo and Hi are perfectly negatively correlated.

The results of the analysis appear in Figure 8.6. Whether the correlation between Lo and Hi is + 1 , 0, or - 1 , a portfolio of those two assets must have an expected return between 6% and 8%. That is why the line segments at left in Figure 8.6 all range between 6% and 8%. However, the standard deviation of a portfolio depends critically on the correlation between Lo and Hi. Only when Lo and Hi are perfectly positively correlated can it be said that the portfolio standard deviation must fall between 3% (Lo’s standard deviation) and 8% (Hi’s standard deviation). As the correlation between Lo and Hi becomes weaker (that is, as the correlation coefficient falls), investors may find that they can form portfolios of Lo and Hi with standard deviations that are even less than 3% (that is, portfolios that are less risky than holding asset Lo by itself). That is why the line segments at right in Figure 8.6 vary. In the special case when Lo and Hi are perfectly nega- tively correlated, it is possible to diversify away all of the risk and form a port- folio that is risk free.

CHAPTER 8

Risk and Return

FIGURE 8.6

Coefficient

Ranges of Return

Ranges of Risk

Possible Correlations

+1 (Perfect positive)

Range of portfolio return ( ) and risk ( r p s r p )

for combinations of assets

0 (Uncorrelated)

Lo and Hi for various correlation coefficients

–1 (Perfect negative)

Portfolio Return (%)

Portfolio Risk (%)

(r p )

(σ r p )

INTERNATIONAL DIVERSIFICATION One excellent practical example of portfolio diversification involves including

foreign assets in a portfolio. The inclusion of assets from countries with business cycles that are not highly correlated with the U.S. business cycle reduces the port- folio’s responsiveness to market movements. The ups and the downs of different markets around the world offset each other, at least to some extent, and the result is a portfolio that is less risky than one invested entirely in the U.S. market.

Returns from International Diversification Over long periods, internationally diversified portfolios tend to perform better

(meaning that they earn higher returns relative to the risks taken) than purely domestic portfolios. However, over shorter periods such as a year or two, interna- tionally diversified portfolios may perform better or worse than domestic portfolios. For example, consider what happens when the U.S. economy is performing rela- tively poorly and the dollar is depreciating in value against most foreign currencies. At such times, the dollar returns to U.S. investors on a portfolio of foreign assets can

be very attractive. However, international diversification can yield subpar returns, particularly when the dollar is appreciating in value relative to other currencies. When the U.S. currency appreciates, the dollar value of a foreign-currency- denominated portfolio of assets declines. Even if this portfolio yields a satisfactory return in foreign currency, the return to U.S. investors will be reduced when foreign profits are translated into dollars. Subpar local currency portfolio returns, coupled with an appreciating dollar, can yield truly dismal dollar returns to U.S. investors.

Overall, though, the logic of international portfolio diversification assumes that these fluctuations in currency values and relative performance will average out over long periods. Compared to similar, purely domestic portfolios, an inter-

political risk nationally diversified portfolio will tend to yield a comparable return at a lower

Risk that arises from the

level of risk.

possibility that a host government will take actions

harmful to foreign investors or Risks of International Diversification that political turmoil will

In addition to the risk induced by currency fluctuations, several other financial

PART 4

Risk and the Required Rate of Return

GLOBAL focus An International Flavor to Risk Reduction

in practice Earlier in this chapter Staunton calculated the historical returns diversified portfolio of 2.07, slightly (see Table 8.5 on

on a portfolio that included U.S. stocks lower than the 2.10 coefficient of page 318), we learned that from

variation reported for U.S. stocks in 1900 through 2009 the U.S. stock

as well as stocks from 18 other coun-

tries. This diversified portfolio produced Table 8.5.

market produced an average annual

returns that were not quite as high as

nominal return of 9.3 percent, but that

3 International mutual funds do return was associated with a relatively

the U.S. average, just 8.6 percent per

not include any domestic assets high standard deviation: 20.4 percent

year. However, the globally diversified

portfolio was also less volatile, with an whereas global mutual funds include per year. Could U.S. investors have

annual standard deviation of 17.8 per- both foreign and domestic assets. done better by diversifying globally?

How might this difference affect The answer is a qualified yes. Elroy

cent. Dividing the standard deviation

their correlation with U.S. equity Dimson, Paul Marsh, and Mike

by the annual return produces a coeffi-

cient of variation for the globally

mutual funds?

Source: Elroy Dimson, Paul Marsh, and Mike Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton University Press, 2002).

arises from the possibility that a host government will take actions harmful to foreign investors or that political turmoil will endanger investments. Political risks are particularly acute in developing countries, where unstable or ideologi- cally motivated governments may attempt to block return of profits by foreign investors or even seize (nationalize) their assets in the host country. For example, reflecting President Chavez’s desire to broaden the country’s socialist revolution, Venezuela issued a list of priority goods for import that excluded a large per- centage of the necessary inputs to the automobile production process. As a result, Toyota halted auto production in Venezuela, and three other auto manufacturers temporarily closed or deeply cut their production there. Chavez also has forced most foreign energy firms to reduce their stakes and give up control of oil projects in Venezuela.

For more discussion of reducing risk through international diversification, see the Global Focus box above.