Deck 9: The Case for International Diversification  

Question 1

The currencies of several emerging countries depreciate at a rapid pace. Does it imply that you should not invest in their stock markets? For example, the Polish zloty went from 15,767 to 21,444 zlotys per U.S. dollar in 1993. The Polish stock market went from 1,040 to 12,439 during the same period. Guess why the zloty depreciated.

Answer 1

No. A rapid depreciation of a currency is generally caused by a rampant inflation. Stocks are claims on real assets and their prices tend to go up with inflation. The question is whether they go up faster or slower than the inflation rate?
During 1993, the Polish inflation rate was around 40%, explaining the zloty's depreciation. The Polish stock market appreciation was extremely high. The privatization program drew enormous interest in 1992 and 1993. The rise in stock prices was either based on expectations of very high future economic growth or was somewhat irrational. The 1994 performance of the stock market was very bad.

Question 2

The annualized performance, in U.S. dollars, of the U.S. and European stock indices are:
Return_US = 10% $\sigma$ _US = 16%
Return_europe=11% $\sigma$ _europe =18%
Correlation = 0.60
a. What would be the return and risk of a portfolio invested half in the U.S. market and half in the European index?
b. What if the correlation increases to 0.8?

Answer 2

a. Return_portfolio = 50% Return_US+ 50% Return_europe = 10.5%. $\sigma$ ²_portfolio =
$$\left( 0.5 \times \sigma _ { \mathrm { LE } } \right) ^ { 2 } + \left( 0.5 \times \sigma _ { \text {euope } } \right) ^ { 2 } + 2 \times 0.6 \times 0.5 \times 0.5 \times \sigma _ { \mathrm { LE } } \times \sigma _ { \text {euope } } = 231.4$$
$\sigma$ _{portfolio = 15.21%.}
b. The return of the portfolio remains unchanged at 10.5%. The risk is higher at:
$\sigma$ ²_{portfolio =}
$$\left( 0.5 \times \sigma _ { \mathrm { LE } } \right) ^ { 2 } + \left( 0.5 \times \sigma _ { \text {euope } } \right) ^ { 2 } + 2 \times 0.8 \times 0.5 \times 0.5 \times \sigma _ { \mathrm { LE } } \times \sigma _ { \text {euppe } } = 260.2$$
$\sigma$ _portfolio =16.13%.

Question 3

In 1994, the United States was experiencing a fairly strong economic recovery, ahead of other nations. Fears of an overheating economy led to sudden inflationary fears for the next few years.
a. Would you expect U.S. interest rates to rise or drop?
b. Would you expect the dollar to depreciate or appreciate?
c. Would you expect a foreign bond portfolio to be a good investment compared to a U.S. dollar portfolio under this scenario?

Answer 3

a. Inflationary fears will cause interest rates to rise, even if the real interest rate remains constant. Economic growth could also lead to higher real interest rates.
b. The dollar is likely to depreciate because of higher expected inflation. This could be offset by higher real interest rates, which could attract foreign capital flows.
c. The rise of U.S. interest rates will cause the market price of U.S. bonds to fall. It is, therefore, appropriate to invest in foreign bonds rather than U.S. bonds. The likely depreciation of the dollar makes such an investment even more interesting (the foreign currency in which the bonds are denominated will appreciate against the dollar during the investment period and the investor will make a foreign exchange profit when reselling his bonds).

Question 4

The Japanese stock market has a sigma of 18%, when computed in yen. The U.S. stock market has a sigma of 17% in US$ and the US$/¥ exchange rate has a sigma of 6%. The correlation between the Japanese stock market and $/¥ currency movements is -0.1; in other words, the Japanese stock market tends to go up when the yen goes down. The correlation between the Japanese and U.S.
stock markets is equal to 0.4, measured either in local currency of in dollars.
a. What is the sigma of the Japanese market when expressed in dollars?
b. Using this number, calculate the sigma, in dollars, of a portfolio made up of 50% of Japanese stocks and 50% of U.S. stocks.

Question 5

Assume that the domestic volatility (standard deviation in yen) of the Japanese stock market is 18%. The volatility of the yen against the U.S. dollar is 6%.
a. What would the dollar volatility of the Japanese stock market be for a U.S. investor if the correlation between the Japanese stock market returns and exchange rate movements were zero?
b. Suppose the dollar volatility of the Japanese stock market is 18.4%, what can you conclude about the correlation between the Japanese stock market movements and exchange rate movements?

Question 6

The French stock market has a sigma of 20%, when computed in euros. The U.S. stock market has a sigma of 16% in US$ and the €/US$ exchange rate has a sigma of 6%.
a. Assuming that the correlation between stock market and currency movements is zero, what is the sigma of the U.S. stock market when expressed in €.
b. Using this number, calculate the sigma, in €, of a portfolio made up of 50% of French stocks and 50% of U.S. stocks (zero-correlation between the two markets).

Question 7

You consider investing in four very volatile emerging markets. These are small countries just opening up to foreign investment. You spread your money equally across them. After a year, the following observations are made on the performance of each market:
$$\begin{array} { c c c c } \text { Cauntry } & \begin{array} { c } \text { Return in } \\\text { Lactal Currency }\end{array} & \begin{array} { c } \text { Currency } \\\text { Depreciation }\end{array} & \text { Comument } \\\hline \text { A } & 400 \% & 20 \% & \text { High inflation, high } \text { growth } \\\text { B } & 60 \% & 10 \% & \\\text { C } &0 & 40 \% & \text { High inflation, low growth } \\\text { D } & - 100 \% & 80 \% & \text { Foreigners } \text { got exprapriated }\end{array}$$ a. Calculate the return, in dollars, on each market. The currency depreciation is equal to the drop in the dollar value of one unit of local currency. For example, if the peso moves from 1 dollar per peso to 0.8 dollar per peso, the depreciation of the peso is measured as 20%.
b. What is the return on a portfolio equally invested in each market?

Question 8

Try to find some reasons why:
a. Stock and bond markets should be strongly correlated and,
b. Stock and bond markets should be weakly correlated.

Question 9

You consider investing in some emerging country. Its recent economic growth rate is around 7%, well above the average growth rate of developed countries estimated at 2% by the OECD. Its annual inflation rate is around 10%, well above the average inflation rate of developed countries estimated at 2% by the OECD. The currency of the emerging country has been depreciating at an annual rate of around 8% against major currencies. While the volatility of the World stock index (standard deviation of dollar returns) is around 15%, the stock market of this emerging country has a volatility of 25%. The correlation of this emerging stock market with the World index is only 0.2.
a. Are the high inflation rate and weak currency sufficient reasons to avoid investing in this emerging country?
b. Is the high volatility of the local market a sufficient reason to avoid investing in this emerging country?
c. Suggest why you would consider investing in this emerging country.

Question 10

You consider investing in an emerging market. Its stock market volatility (standard deviation of returns measured in U.S. dollars) is 25%. The volatility of the World index of developed markets is 15%. The correlation between the emerging market and the World index is 0.2.
a. What would be the volatility of a portfolio invested 95% in the World index and 5% in this emerging market?
b. Compare the result found in the previous question with the volatility of the World index and give an intuitive explanation.

Question 11

Assume that the domestic volatility (standard deviation in yen) of the Japanese bond market is 8%. The volatility of the yen against the U.S. dollar is 6%.
a. What would the dollar volatility of the Japanese bond market be for a U.S. investor if the correlation between the Japanese stock market returns and exchange rate movements were zero?
b. Suppose the dollar volatility of the Japanese stock market is 11.35%, what can you conclude about the correlation between the Japanese bond market movements and exchange rate movements?

Question 12

Here are the expected returns and risks of two assets:
E(R₁) = 10% $\sigma$ ₁ == 16%
E(R₂)= 14% $\sigma$ ₂ = 16%
a. Assume a correlation of 0.5 and draw all the portfolios made up of the two assets in an Expected Return/Risk graph.
b. Same question assuming successively a correlation of -1, 0, and +1.
c. Looking at the four graphs, what do you conclude about the importance of correlation in
risk-reduction?

Question 13

You have collected some risk and return estimates for various market indexes. These indexes are the World stock market index of developed markets, the Morgan Stanley Capital International (MSCI) Europe, Australasia and Far East (EAFE) index, and the International Finance Corporation (IFC) Composite index of emerging markets. Here are some risk and return estimates for the future:
All return and risk measures are calculated in U.S. dollars and are expressed in % per year. The correlation matrix is given below:
a. Calculate the return and risk of a portfolio invested in the following proportions:
b. Try to derive some estimate of the efficient frontier obtained by using these three indexes
(no short sales are allowed).

Question 14

Suppose that you overheard the following statements at a conference for institutional investors:
(A German national): "My money manager knows the German firms very well; why should I bother to invest in French and American shares? I am not familiar with their names or their operations, and I will have to pay much higher costs to buy them."
(A French national): "Why should I buy German and American shares? The foreign brokers will give preferential treatment to their domestic clients, and I am going to get a lousy deal in terms of prices and costs. Furthermore, I can't read the financial statements of these companies, as they are written in German or English, and with different accounting methods."
(An American national): "I can't even pronounce the names of these foreign companies; how could I defend investing abroad in front of my board of trustees? By the way, what is the capital of Switzerland: Geneva or Zurich?"
How would you try to convince these people to diversify their portfolios if you were the marketing representative of a big international money manager?

Question 15

Assume that the domestic and foreign assets have standard deviations of $\sigma$ _d =16% and $\sigma$ _f = 19%, respectively, with a correlation of $\rho$ _df = 0.6. The risk-free rate is equal to 5% in both countries.
a. The expected returns of the domestic and foreign assets are both equal to 10%, E(R_d) =E(R_f) = 10%. Calculate the Sharpe ratios for the domestic asset, the foreign asset, and an internationally- diversified portfolio equally invested in the domestic and foreign assets. What do you conclude?
b. Assume now that the expected return on the foreign asset is higher than on the domestic asset, E(R_d) = 10% but E(R_f) =12%. Calculate the Sharpe ratio for an internationally diversified portfolio equally invested in the domestic and foreign assets, and compare your findings to those in Question (a).