of the optimal portfolio? 4. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. 5. What is the reward-to-variability ratio of the best feasible CAL? 6. You require that your portfolio yield an expected return of 14%, and that it be efficient on the best feasible CAL. a. What is the standard deviation of your portfolio? b. What is the proportion invested in the T-bill fund and each of the two risky funds? 7. If you were to use only the two risky funds, and still require an expected return of 14%, what must be the investment proportions of your portfolio? Compare its standard devi- ation to that of the optimized portfolio in problem 6. What do you conclude? 8. Suppose that you face the same opportunity set, but you cannot borrow. You wish to construct a portfolio of only stocks and bonds with an expected return of 24%. What II. Portfolio Theory 8. Optimal Risky Portfolio The McGraw−Hill Companies, 2001           242 PART II Portfolio Theory     are the appropriate portfolio proportions and the resulting standard deviations? What reduction in standard deviation could you attain if you were allowed to borrow at the risk-free rate? 9. Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%. a. In light of the apparent inferiority of gold with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so. b. Given the data above, reanswer (a) with the additional assumption that the correla- tion coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in ones portfolio. Could this set of assumptions for expected returns, standard deviations, and correlation represent an equilibrium for the security market? 10. Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows:   Stock Expected Return Standard Deviation   A 10% 5% B 15 10 Correlation 1