Stock A has an expected return of 8% and the standard deviation of the return is 15%. Stock B has an expected return of 6%, standard deviation of 15%.(a) If the returns on the two stocks have zero correlation, and the risk-free rate is 2%, is there
an arbitrage opportunity here? If so, how would you exploit it? Is it rational to hold stock
B even if it has the same variability but lower mean return than stock A?(b) Suppose the same investor has mean-variance preferences and she can invest in the risk-free
asset, in addition to stocks A and B. Recall that the risk-free rate is 2%. Assume the
correlation of the two stock returns is 0.5 and RRA is 4. What percentage of her wealth
does she invest in the risk-free asset?(c) Assume now that the investor can only invest in the risky assets (i.e., no risk-free asset),
what percentage of her wealth will she invest in each asset? (We did not do this formula in
class so you will have to derive it for a fully correct numerical answer). Show the optimal
solution in a diagram. You will get a large percentage of the credit by showing a correct
diagram.
Compare in a diagram the solution to parts b) and c). [note: specifically really need the formula and diagram](d) How do your answers to parts (b) and (c) change if the RRA increased? Be specific about
which assets will have higher weights and which assets will have lower weights. Explain in
each case.
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