There are two stock markets, each driven by the same common force, F, with an expected value

Question:

There are two stock markets, each driven by the same common force, F, with an expected value of zero and standard deviation of 10 percent. There are many securities in each market; thus, you can invest in as many stocks as you wish. Due to restrictions, however, you can invest in only one of the two markets. The expected return on every security in both markets is 10 percent.

The returns for each security, i, in the first market are generated by the relationship:

R₁_i = .10 + 1.5 F + ε₁_i

where ε₁_i is the term that measures the surprises in the returns of Stock i in Market 1. These surprises are normally distributed; their mean is zero. The returns on Security j in the second market are generated by the relationship:

R₂_i = .10 + .5 F + ε₂_j

where ε₂_j is the term that measures the surprises in the returns of Stock j in Market 2. These surprises are normally distributed; their mean is zero. The standard deviation of ε₁_i and ε₂_i for any two stocks, i and j, is 20 percent.

a. If the correlation between the surprises in the returns of any two stocks in the first market is zero, and if the correlation between the surprises in the returns of any two stocks in the second market is zero, in which market would a risk-averse person prefer to invest?

b. If the correlation between ε₁_i and ε₁_j in the first market is .9 and the correlation between ε₂_i and ε₂_jin the second market is zero, in which market would a risk-averse person prefer to invest?

c. If the correlation between ε₁_i and ε₁_j in the first market is zero and the correlation between ε₂_i and ε₂_j in the second market is .5, in which market would a risk-averse person prefer to invest?

d. In general, what is the relationship between the correlations of the disturbances in the two markets that would make a risk-averse person equally willing to invest in either of the two markets?

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