There are two stock markets, each driven by the same common force,F, with an expected value of zero and standard deviation of 8 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 8 percent.

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

R_1i= .08 + 2.5F+ _1i

where _1iis the term that measures the surprises in the returns of Stockiin Market 1. These surprises are normally distributed; their mean is zero. The returns on Securityjin the second market are generated by the relationship:

R_2j= .08 + 1.5F+ _2j

where _2jis the term that measures the surprises in the returns of Stockjin Market 2. These surprises are normally distributed; their mean is zero. The standard deviation of _1iand _2ifor any two stocks,iandj, is 20 percent.

Assume thecorrelation between the surprises in the returns of any two stocks in the first market is zero, and the correlation between the surprises in the returns of any two stocks in the second market is zero.

a.What are thevariances for the first and second market?(Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

b. Assume thecorrelation between _1iand _1jin the first market is .8 and the correlation between _2iand _2jin the second market is zero. What are thevariancesfor the first and second market?(Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)