International-Financial-Management---Bekaert-2e---Solutions---Ch13.doc

1、9Chapter 13: International Capital Market EquilibriumChapter 13International Capital Market EquilibriumQUESTIONS1. Is the volatility of the dollar return to an investment in the Japanese equity market the sum of the volatility of the Japanese equity market return in yen plus the volatility of yen/do

2、llar exchange rate changes? Why or why not?Answer: It is not. Even though the dollar return on investing in Japanese equity is approximately the yen return on the Japanese equity market plus the rate of change in the dollar/yen exchange rate, the volatility of this sum is not the sum of the volatili

3、ties. Intuitively, because the equity risk and currency risk are not highly correlated, part of the volatility of the individual components is diversified away. Technically, the variance of the dollar returns can be written as follows:Varr(t + 1,) + s(t + 1) = Varr(t + 1,) + Vars(t + 1) +2Volr(t + 1

4、, )Vol s(t + 1)where r(t + 1,) is the yen-denominated equity return, s(t+1) is the rate of change in the dollar/yen exchange rate, and is the correlation between the yen equity return and dollar/yen exchange rate changes. Because volatility, Vol, is the square root of the variance, we know that the

5、volatility of the dollar return on a Japanese equity investment isVolr(t + 1,) + s(t + 1) = Volr(t + 1,)2 + Vols(t + 1) 2 +2Volr(t + 1, )Vol s(t + 1)0.5Clearly, only when the correlation is exactly 1 will the right-hand side have the form (A2 + 2AB + B2)0.5 = (A + B)20.5 = (A + B)Hence, only then wi

6、ll the volatility of the sum be the sum of the volatilities. When there is perfect correlation, there is no natural diversification advantage to having exposure to two sources of risk. However, as long as 1, the total volatility of the dollar return to investing in the Japanese equity market will be

7、 less than the sum of the two volatilities.2. Why is the variance of a portfolio of internationally diversified stocks likely to be lower than the variance of a portfolio of U.S. stocks?Answer: With international stocks, the investor can diversify away U.S.-specific sources of volatility (e.g. U.S.s

8、pecific business cycle movements, changes in U.S. monetary policy, changes in U.S. interest rates, etc.). Technically, the variance of an equally weighted portfolio converges to the average covariance between these stocks when the number of stocks gets very large. The average covariance among U.S. s

9、tocks is higher than the average covariance among a set of U.S. and international stocks.3. How can you increase the Sharpe ratio of a portfolio? What type of stocks would you have to add to it in order to do so?Answer: To increase the Sharpe ratio on your portfolio, you must add stocks that increas

10、e the expected return on your portfolio and/or reduce the volatility of the portfolio (for instance, because the stocks exhibit low correlation with the portfolio you already have). One way to think of the problem is to compute the following hurdle rate, Hurdle rate = In this equation rf is the risk

11、 free rate, is the correlation between the portfolio you have and the stock you want to add to the portfolio, Er and Volr are the expected return and volatility of the portfolio you are holding, and Volr* is the volatility of the stock you want to add. The hurdle rate is higher when the existing por

12、tfolio has a high Sharpe ratio, the stock you are adding is more volatile, or there is high correlation between the return on the portfolio and the return on the stock you are adding to the portfolio. 4. Why is the hurdle rate in Section 13.2 lower for Japan than for Canada? Should U.S. investors st

13、ill invest in Canada?Answer: From the formula in the answer to Question 3, we see that the two main drivers of the hurdle rates are the correlations between Canadian and U.S. returns and between Japanese and U.S. returns (reported in Exhibit 13.6), and the volatilities of Canadian and Japanese retur

14、ns (reported in Exhibit 13.1). The most important number is the correlation. Of the G7 countries, the Canadian returns have the highest correlation with U.S. returns, whereas the Japanese returns have the lowest correlation. It is this difference that makes Japan have the lowest hurdle rate and Cana

15、da the highest. Whether U.S. investors should still invest in Canada depends on their opportunity set. The hurdle rate for Canada, reported in Exhibit 13.7, suggests that even if the expected return on Canadian stock is only a bit lower than that of the U.S., it is still a valuable investment that i

16、ncreases the Sharpe ratio. However, if the U.S. investor can invest in Japanese securities first, the Canadian hurdle rate will increase considerably, because the U.S.-Japan diversified portfolio has a high Sharpe ratio. In that case, it may not be optimal to go long Canadian securities unless you really believe the Canadian stock market will have an expected return h