# Question

Ever since the day she took her first economics class in high school, Lydia wondered about the financial practices of her parents. They worked very hard to earn enough money to live a comfortable middle-class life, but they never made their money work for them. They simply deposited their hard-earned paychecks in savings accounts earning nominal amount of interest. (Fortunately, there always was enough money when it came time to pay her college bills.) She promised herself that when she became an adult, she would not follow the same financially conservative practices as her parents.

And Lydia kept this promise. Every morning while getting ready for work, she watches the CNN financial reports. She plays investment games on the World Wide Web, finding portfolios that maximize her return while minimizing her risk. She reads The Wall Street Journal and Financial Times with a thirst she cannot quench.

(a) At first, Lydia wants to ignore the risk of all the investments. Given this strategy, what is her optimal investment portfolio; that is, what fraction of her money should she invest in each of the six different stocks? What is the total risk of her portfolio?

(b) Lydia decides that she doesn’t want to invest more than 40 percent in any individual stock. While still ignoring risk, what is her new optimal investment portfolio? What is the total risk of her new portfolio?

(c) Now Lydia wants to take into account the risk of her investment opportunities. For use in the following parts, formulate a quadratic programming model that will minimize her risk (measured by the variance of the return from her portfolio), while ensuring that her expected return is at least as large as her choice of a minimum acceptable value.

(d) Lydia wants to ensure that she receives an expected return of at least 35 percent. She wants to reach this goal at minimum risk. What investment portfolio allows her to do that?

(e) What is the minimum risk Lydia can achieve if she wants an expected return of at least 25 percent? Of at least 40 percent?

(f) Do you see any problems or disadvantages with Lydia’s approach to her investment strategy?

And Lydia kept this promise. Every morning while getting ready for work, she watches the CNN financial reports. She plays investment games on the World Wide Web, finding portfolios that maximize her return while minimizing her risk. She reads The Wall Street Journal and Financial Times with a thirst she cannot quench.

(a) At first, Lydia wants to ignore the risk of all the investments. Given this strategy, what is her optimal investment portfolio; that is, what fraction of her money should she invest in each of the six different stocks? What is the total risk of her portfolio?

(b) Lydia decides that she doesn’t want to invest more than 40 percent in any individual stock. While still ignoring risk, what is her new optimal investment portfolio? What is the total risk of her new portfolio?

(c) Now Lydia wants to take into account the risk of her investment opportunities. For use in the following parts, formulate a quadratic programming model that will minimize her risk (measured by the variance of the return from her portfolio), while ensuring that her expected return is at least as large as her choice of a minimum acceptable value.

(d) Lydia wants to ensure that she receives an expected return of at least 35 percent. She wants to reach this goal at minimum risk. What investment portfolio allows her to do that?

(e) What is the minimum risk Lydia can achieve if she wants an expected return of at least 25 percent? Of at least 40 percent?

(f) Do you see any problems or disadvantages with Lydia’s approach to her investment strategy?

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