Investing Case all possibilities 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 a 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. Lydia also reads the investment advice columns of the financial magazines, and she has noticed that on average, the advice of the investment advisers turns out to be very good. Therefore, she decides to follow the advice given in the latest issue of one of the magazines. In his monthly column the editor Jonathan Taylor recommends three stocks that he believes will rise far above market average. In addition, the well-known mutual fund guru Donna Carter advocates the purchase of three more stocks that she thinks will outperform the market over the next year. BIGBELL (ticker symbol on the stock exchange: BB), one of the nations largest telecommunications companies, trades at a price-earnings ratio well below market average. Huge investments over the last eight months have depressed earnings considerably. However, with their new cutting-edge technology, the company is expected to significantly raise their profit margins. Taylor predicts that the stock will rise from its current price of $60 per share to $72 per share within the next year. LOTSOFPLACE (LOP) is one of the leading hard drive manufacturers in the world. The industry recently underwent major consolidation, as fierce price wars over the last few years were followed by many competitors going bankrupt or being bought by LOTSOFPLACE and its competitors. Due to reduced competition in the hard drive market, revenues and earnings are expected to rise considerably over the next year. Taylor predicts a one-year increase of 42 percent in the stock of LOTSOFPLACE from the current price of $127 per share. INTERNETLIFE (ILI) has survived the many ups and downs of Internet companies. With the next Internet frenzy just around the corner, Taylor expects a doubling of this companys stock price from $4 to $8 within a year. HEALTHTOMORROW (HEAL) is a leading biotechnology company that is about to get approval for several new drugs from the Food and Drug Administration, which will help earnings to grow 20 percent over the next few years. In particular a new drug to significantly reduce the risk of heart attacks is supposed to reap huge profits. Also, due to several new greattasting medications for children, the company has been able to build an excellent image in the media. This public relations coup will surely have positive effects for the sale of its over-thecounter medications. Carter is convinced that the stock will rise from $50 to $75 per share within a year. QUICKY (QUI) is a fast-food chain which has been vastly expanding its network of restaurants all over the United States. Carter has followed this company closely since it went public some 15 years ago when it had only a few dozen restaurants on the west coast of the United States. Since then the company has expanded, and it now has restaurants in every state. Due to its emphasis on healthy foods, it is capturing a growing market share. Carter believes that the stock will continue to perform well above market average for an increase of 46 percent in one year from its current stock price of $150. AUTOMOBILE ALLIANCE (AUA) is a leading car manufacturer from the Detroit area that just recently introduced two new models. These models show very strong initial sales, and therefore the companys stock is predicted to rise from $20 to $26 over the next year. On the World Wide Web Lydia found data about the risk involved in the stocks of these companies. The historical variances of return of the six stocks and their covariances are shown below:

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 doesnt 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 Lydias approach to her investment strategy?

Company LOP ILI HEAL QUI AUA Variance 0.032 0.333 0.125 0.065 0.08 ILI 0.03 0.085 QUI 0.027 0.05 0.02 0.05 Covariances LOP HEAL 0.031 0.07 0.11 AUA 0.01 0.02 0.042 0.06 0.02 0.005 LOP ILI HEAL QUI