PLEASE SOLVE WITH EXCEL QM

(Portfolio selection problem) Daniel Grady is the

financial advisor for a number of professional athletes.

An analysis of the long-term goals for many of these

athletes has resulted in a recommendation to purchase

stocks with some of the income that they have set aside

for investments. Five stocks have been identified as hav-

ing very favorable expectations for future performance.

Although the expected return is important in these

investments, the risk, as measured by the beta of the

stock, is also important. (A high value of beta indicates

that the stock has a relatively high risk.) The expected

return and the beta for five stocks are as follows:

Daniel would like to minimize the beta of the stock

portfolio (calculated using a weighted average of

the amounts put into the different stocks) while

maintaining an expected return of at least 11%.

Since future conditions may change, Daniel has

decided that no more than 35% of the portfolio

should be invested in any one stock.

(a) Formulate this as a linear program. (Hint: Define

each variables as the proportion of the total

investment that would be put in that stock. Include

a constraint that restricts the sum of these vari-

ables to be 1.)

(b) Solve this problem. What are the expected return

and beta for this portfolio?

2 3 4 5 STOCK 1 Expected return (%) 11.0 Beta 1.20 15.0 9.0 0.85 6.5 0.55 13.0 1.25 1.40