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, come consideration is given to the risk involved with the stocks. A risk index on a scale of 1 to 10 (with 10 being the most risky) is assigned to each of the 2 stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in each stock.
The following table provides a summary of the return and risk:
|
Stock
|
Estimated Return
|
Risk index
|
|
Petrochemical
|
12%
|
9
|
|
Utility
|
6%
|
4
|
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.
1a. How much should be invested in each stock?
1b. What is the average risk for the investment?
1c. What is the estimated return for this investment?
Let x = the proportion of the investment in Petrochemical. Then 1 - x is the proportion of the investment in Utility. To maximize the return the investor should invest as much as possible in Petrochemical (higher return of 12%) while making sure that the average risk index does not exceed 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 should be invested in Petrochemical while 0.6 * $50,000 = $30,000 should be invested in Utility.
The average risk for the investment = 0.4 * 9 + 0.6 * 4 = 3.6 + 2.4 = 6.
The estimated return = 0.4 * 12% + 0.6 * 6% = 4.8% + 3.6% = 8.4%.
Referring to the information listed above, suppose the investor has changed his attitude about the investment and wishes to give greater emphasis to the risk of the investment. Now the investor wishes to minimize the risk of the investment as long as a return of at least 8% is generated.
1a. How much should be invested in each stock?
1b. What is the average risk for the investment?
1c. What is the estimated return for this investment?