Suppose that the US stock market will have a return of 20% with probability two-thirds or a return of -17.5% with probability one-third during the upcoming year. The treasury bill rate is 2% per year and we assume this asset is riskless.

a) You manage the portfolio of a mean-variance investor whose relative risk aversion is equal to 4. If the portfolio can only be invested in the aggregate US stock market and in Treasury bills, what fraction should be in the US stock market?

b) Assume you are able to buy foreign stocks as well as domestic stocks. A large number of foreign markets are available, each with the same expected return and standard deviation as the US market and with a correlation of 0.5 with each other and with the US market. Since all the markets have the same standard deviation and correlations, an equally-weighted portfolio containing each of the national stock markets has the lowest possible standard deviation (and variance). Calculate the standard deviation of this portfolio as the number of foreign markets goes to infinity.

c) You still manage the portfolio for a mean-variance investor whose relative risk aversion is equal to 4. Calculate the fraction of the investor's portfolio that should be invested in the global equity portfolio as the number of foreign markets goes to infinity from part b).

d) How would an increase in the correlation between national stock markets from 0.5 to 1 affect the benefits of international diversification in part b) and part c)?

e) A newspaper columnist writes " The events of the last six months have shown the stupidity of the case for international investing. Foreign markets have done poorly while the US market has pulled ahead. Ignore the recommendation to diversify internationally and keep your money safe in the US stock market." Do you agree with the column? Why or why not?