Question 11 (8 points) Typically, for portfolio optimization problem, we minimize portfolio risk given a expected return target with multiple assets. However, it will take too much time to deal with even a three-asset portfolio optimization problem during an less than two-hour exam. Therefore, we will use a two-asset example. With only two assets, we can't minimize portfolio risk given a expected return target, since there is only one combination of the two assets that gives the target risk. Bases on this, we will maximize the portfolio expected return given a portfolio risk target in this two-asset portfolio optimization problem. Below you can find the statistics for Stock A and Stock B. Stock A Stock B 10% 2% Expected Returns Variance of Return Covariance 0.0400 0.0036 0.008 You want to construct a portfolio with stock A and B. Your target portfolio variance is 0.0087. (a) (3 points) Set up the question by writing the maximum function and the constraint. (b) (2 points) Set up the Lagrange Function. (c) (3 points) Take first-order (partial) derivative of the Lagrange function with respect to each variable including the Lagrange multiplier and set them to 0. Question 11 (8 points) Typically, for portfolio optimization problem, we minimize portfolio risk given a expected return target with multiple assets. However, it will take too much time to deal with even a three-asset portfolio optimization problem during an less than two-hour exam. Therefore, we will use a two-asset example. With only two assets, we can't minimize portfolio risk given a expected return target, since there is only one combination of the two assets that gives the target risk. Bases on this, we will maximize the portfolio expected return given a portfolio risk target in this two-asset portfolio optimization problem. Below you can find the statistics for Stock A and Stock B. Stock A Stock B 10% 2% Expected Returns Variance of Return Covariance 0.0400 0.0036 0.008 You want to construct a portfolio with stock A and B. Your target portfolio variance is 0.0087. (a) (3 points) Set up the question by writing the maximum function and the constraint. (b) (2 points) Set up the Lagrange Function. (c) (3 points) Take first-order (partial) derivative of the Lagrange function with respect to each variable including the Lagrange multiplier and set them to 0