1. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 16% and a standard deviation of return of 20.0%. Stock B has an expected return of 12% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is 0.50. The risk-free rate of return is 8%. The proportion of the optimal risky portfolio that should be invested in stock A is _________.
2. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 31%. Stock B has an expected return of 13% and a standard deviation of return of 16%. The correlation coefficient between the returns of A and B is .5. The risk-free rate of return is 6%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately _________.
3. The expected return of a portfolio is 9.9%, and the risk-free rate is 5%. If the portfolio standard deviation is 13%, what is the reward-to-variability ratio of the portfolio?