STOCK INVESTMENTS. Idaho investments is a small, newly formed investment group that will invest exclusively in local stocks. The group is planning its initial investment of $1 0 0 ,0 0 0 , which it will allocate between two stocks—Tater, Inc. and Lakeside Resorts. If the group is successful with these investments, it plans to expand its portfolio further into other Idaho-based stocks. For each of the stocks, the group has estimated three numbers:
• The projected annual return per share with reinvested dividends
• A “potential” index—a number between 0 and 1 that measures the likelihood of high returns in a one-year period
• A “risk” index—a number between 0 and 1 that measures the likelihood of a substantial loss in a one- year period
The portfolio potential factor is obtained by summing the products of the potential factor for an investment times the fraction of the total investment dollars in that investment. For example, if X, is the amount invested in Later and X2 is the amount invested in Lakeside Resorts, the portfolio potential would be:
(X]/100000)(potential index for Tater) +
(X2/100000)(potential index for Lakeside)
The portfolio risk factor is obtained in a similar manner. The current share price and the group estimates for these factors are summarized in the following table.
Formulate and solve for the optimal investment strategy in order to maximize overall expected annual return for Idaho investments if it wishes to:
• Invest all $100,000.
• Keep the portfolio potential at .25 or higher.
• Restrict the portfolio risk to .5 or lower.