Question

The management of a private investment club has a fund of $230,000 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 (x), medium risk (y), and low risk (z). Management estimates that high risk stocks will have a rate of return of 15%/year; medium risk stocks, 10%/year; and low risk stocks, 6%/year. The amount of money invested in low risk stocks is to be twice the sum of the amount invested in stocks of the other two categories. If the investment goal is to have a rate of return of 9% 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.) = 230,000 = z = 20,700

Answer 1

Solution:

Let total of amount invested in high risk and medium risk stock = X

Amount invested in low risk stock = 2X

Now

X + 2X = $230,000

X = 76,667

Amount invested in low risk stock = $76,666.66*2 = $153,333

Total required return = $230,000 * 9% = $20,700

Return on low risk stock = $153,333 * 6% = $9,200

Required return on high and medium risk stock = $20,700 - $9,200 = $11,500

Let weight of investment between high risk stock and medium risk stock = x and (1-X)

Now

($76,667 * X) * 15% + [$76,667 * (1-X)] * 10% = $11,500

$11,500 X + $7,667 - 7667X = $11,500

X = 1

Therefore amount to be invested in High risk stock = $76,667 *1 = $76,667

Amount to be invested in medium risk stock = 0

Amount to be invsted in low risk stock = $153,333