Question 3 [30 points] An investor is considering allocating fractions of her investment dollars in common stock in four different companies for the next year: IBM, AT&T, General Motors (GM), and General Electric (GE). Based on statistical analysis of the market data, she has estimated the expected annual returns, as well as standard deviations and correlations of these annual returns: Company Expected Annual Return (%) Standard Deviation of Annual Return (%) IBM 17.85 30.53 AT&T 12.70 19.47 GM 19.33 27.07 GE 22.99 15.00 Correlations IBM AT&T GM GE IBM 1 AT&T 0.158 T GM 0.078 0.241 GE 0.579 0.302 0.282 a) [10 points] Suppose that the target expected return of the portfolio is 20%. What is the minimum standard deviation of the investor's portfolio? What is the optimal asset allocation? (hint: solve in Excel) b) [5 points] If the returns of each asset are normally distributed with the means, standard deviations, and correlations given in the above tables, what is the distribution of the portfolio return from part a? c) [5 points] If the returns of each asset are normally distributed with the means, standard deviations, and correlations given in the above tables, what is the probability that the portfolio from part a) loses money? d) [10 points] Suppose that the target standard deviation of the portfolio is 13% What is the maximum expected return on the investor's portfolio? What is the optimal asset allocation? (hint: solve in Excel)