Consider an economy where CAPM holds, the risk free rate is Rf = 2% and the return of the market portfolio has expectation ERm = 10% and standard deviation 40%.
(a) Draw the capital market line. What is the optimal portfolio of a mean-variance in-vestor with risk aversion A = 2? What is the mean and standard deviation of this portfolio? Show this portfolio in the .gure. What is the value of this investor’s mean-variance utility function if he invests in this optimal portfolio (i.e., what is ERp-(A/2) Var (Rp))?
(b) What is the optimal portfolio of an investor with risk aversion A = 4? What is its mean and standard deviation? Show this portfolio in argue too. What is the value of this investor’s mean-variance utility function when investing optimally?
(c) Now presume that due to a reduction in uncertainty, the standard deviation of the market return falls to 20 percent, while other parameters are unchanged. Draw the new capital market line. What are the new optimal portfolios of the two investors? What are these portfolios means and standard deviations? Show them in the figure. Which investor's portfolio share of risky assets changes by more relative to earlier? Why?
(d) What are the values of the two investors’ utility functions now, given their new optimal investments? Which investor’s utility increases by more relative to before? Why?
Comment on this statement: .Reductions in risk is most beneficial to conservative investors who are highly sensitive to actuations in their wealth.