The returns for each security, i, in the first market are generated by the relationship: where ϵ1iis the term that measures the surprises in the returns of stock iin market l. These surprises are normally distributed; their mean is zero. The returns on security jin the second market are generated by the relationship

where ε2jis the term that measures the surprises in the returns of stock jin market 2. These surprises are normally distributed; their mean is zero. The standard deviation of ε1iand ε2jfor any two stocks, iand 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? (Note: The correlation between ε1iand ε1jfor any iand jis zero, and the correlation between ε2iand ε2jfor any iand jis zero.) b.If the correlation between ε1iand ε1jin the first market is .9 and the correlation between ε2iand ε2jin the second market is zero, in which market would a risk-averse person prefer to invest? c.If the correlation between ε1iand ε1jin the first market is zero and the correlation between ε2iand ε2jin 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? 12.9 Assume that the following market model adequately describes the return-generating behaviour of risky assets: Here: Rit= The return on the ith asset at time t. RMt= The return on a portfolio containing all risky assets in some proportion at time t. RMtand εitare statistically independent.

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