Formulate but do not solve the problem. The management of a private investment c

Question

Formulate but do not solve the problem. The management of a private investment club has a fund of $200,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of 17%/year; medium-risk stocks, 11%/year; and low-risk stocks, 6%/year. The investment in low-risk stocks is to be twice the sum of the investments in stocks of the other two categories. If the investment goal is to have an average rate of return of 9%/year on the total investment, determine how much the club should invest in each type of stock. (Assume that all the money available for investment is invested. Let x, y, and z denote the amount, in dollars, invested in high-, medium-, and low-risk stocks, respectively.) = 200,000 .09(200,000)

Explanation / Answer

Total fund available for investment in stocks = 200,000 (in dollars)

x = amount invested in high - risk stocks ; return = 17%/year

y = amount invested in meduim - risk stocks ; return = 11%/year

z = amount invested in low - risk stocks ; return = 6%/year

Also, Given that : z= 2*(x+ y) = 2x + 2y

Total return = investment in particular stocks * stocks respective rate of return

Average return = 9%/year

or, using the relationship between x,y and z

200,000*(0.09) = x * (0.17) + y * (0.11) + (2x+2y)* (0.06)

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