A winner of the Texas Lotto has decided to invest $50,000 per year in the stock

Question

A winner of the Texas Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1–10 (with 10 being the most risky) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The attached table provides a summary of the return and risk. The investor would like to maximize the return on the investment, but the average risk index of the investment should not be higher than 6.

Question 6

The optimal dollar amount invested in Petrochemical stock is _________ dollars, and the optimal dollar amount invested in Utility stock is ___________ dollars. (Please only enter an integer and include no units. Hint: The total risk on each stock is the risk index times the investment in dollars. When you use Excel QM, you need to end the total risk in the right hand side of the constraint not simply the risk index.)

A.20,000, 30,000

B.30,000, 20,000

C.10,000, 15,000

D.15,000, 10,000

Question 7

The average risk index (not in dollar amount) for the optimal investment is , and the estimated best/maximum return for this investment is . (Please only enter an integer and include no units.)

A winner of the Texas Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1–10 (with 10 being the most risky) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The attached table provides a summary of the return and risk. The investor would like to maximize the return on the investment, but the average risk index of the investment should not be higher than 6.

Question 6

The optimal dollar amount invested in Petrochemical stock is _________ dollars, and the optimal dollar amount invested in Utility stock is ___________ dollars. (Please only enter an integer and include no units. Hint: The total risk on each stock is the risk index times the investment in dollars. When you use Excel QM, you need to end the total risk in the right hand side of the constraint not simply the risk index.)

A.20,000, 30,000

B.30,000, 20,000

C.10,000, 15,000

D.15,000, 10,000

Question 7

The average risk index (not in dollar amount) for the optimal investment is , and the estimated best/maximum return for this investment is . (Please only enter an integer and include no units.)

Explanation / Answer

Let x be the proportion of the investment in Petrochemical  

Then 1 - x will be the proportion of the investment in Utility

In order to maximize return the investor will try to invest as much as possible in Petrochemical as it gives higher rate of return of 12% keeping in mind that the average risk is not greater than 6.

Thus: 9 * x + 4 * (1 - x) = 6 --> 9 * x + 4 - 4 * x = 6 --> 5 * x = 2 --> x = 0.4.

0.4 * $50,000 = $20,000 be invested in Petrochemical

0.6 * $50,000 = $30,000 be invested in Utility.


The average risk for the investment = 0.4 * 9 + 0.6 * 4 = 3.6 + 2.4 = 6.

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