Jim Long was in the process of analyzing the portfolio of Carol Jones. Mrs$.$ Jones an elderly widow had come to him with unusual request. She owned a substantial number of shares of common stocks of Exxon, General Mills, Minnesota Mining and Manufacturing $(3$M$),$ and Sears, Roebuck & company, and she wanted him to manage her portfolio. Her single requirement was that the portfolio should contain one or more of these four stocks and no others. During their thirty years of marriage, Jones and her husband had held some of or all these four securities in their portfolio. She was adamant that her portfolio comprises some or all these stocks. Initially, Long had tried to convince Mrs$.$ Jones of the benefits of adding additional securities$,$ fixed income and equity to her portfolio. When she refused, he asked her why she needed professional help in managing her portfolio. She responded that she is asking for a specific help in comparing the following investment strategies: Portfolio Allocations

Portfolio Exxon G$-$Mills $3$M Sears TOTAL

A $50\mathrm{.}00\%0\mathrm{.}00\%0\mathrm{.}00\%50\mathrm{.}00\%100\mathrm{.}00\%$

B $0\mathrm{.}00\%50\mathrm{.}00\%0\mathrm{.}00\%50\mathrm{.}00\%100\mathrm{.}00\%$

C $0\mathrm{.}00\%50\mathrm{.}00\%50\mathrm{.}00\%0\mathrm{.}00\%100\mathrm{.}00\%$

D $33\mathrm{.}33\%0\mathrm{.}00\%33\mathrm{.}33\%33\mathrm{.}33\%100\mathrm{.}00\%$

E $33\mathrm{.}33\%33\mathrm{.}33\%33\mathrm{.}33\%0\mathrm{.}00\%100\mathrm{.}00\%$

F $25\mathrm{.}00\%25\mathrm{.}00\%25\mathrm{.}00\%25\mathrm{.}00\%100\mathrm{.}00\%$ In addition, Mrs$.$ Jones is open for any asset$-$allocation recommendations.

Mr$.$ Long, vice president of a highly successful investment$-$counseling firm in the Southeast, generally managed accounts containing a large number of securities$.$ For this reason, his initial reaction had been to reject Jones$$s business. But upon further consideration, he realized that the special nature of her request would allow him to try an approach that was unmanageable with his other clients.

While in graduate school, Mr$.$ Long had been exposed to the concept of portfolio analysis using Markowitz Diversification. As initial step, he gathered quarterly returns on the four stocks. These returns are givenin the appendix. $($See StockData tab$)$