Your friend\'s portfolio manager has suggested two high-yielding stocks: Consoli

Question

Your friend's portfolio manager has suggested two high-yielding stocks: Consolidated Edison (ED) and Royal Bank of Scotland (RBS-K). ED shares cost $40, yield 5.5% in dividends, and have a risk index of 1.2 per share. RBS-K shares cost $25, yield 7.5% in dividends, and have a risk index of 1.4 per share. You have up to $28000 to invest and would like to earn at least $1540 in dividends. How many shares (to the nearest tenth of a unit) of each stock should you purchase in order to meet your requirements and minimize the total risk index for your portfolio?
Buy _______ shares of ED and ______ shares of RBS-K. The minimum total risk index is c = _______ .

Explanation / Answer

Let

x = No of shares ED
y = No of shares RBS

Minimize C = 1.2x + 1.4y

subject to

40x + 25y <= 28,000

0.055*40x + .075*25y >= 1540
x >= 0 , y >= 0

Solving Above equation using simulatneous Equation

40x + 25y = 28,000 ......................................in equation 1

0.055*40x + .075*25y = 1540 ....................in equation 2

We use to multiply 0.075 in equation 1 We get

0.075*40x + .075*25y = 28000 *0.075

0.055*40x + .075*25y = 1540

After subtraction of both we get

0.02*40X = 560

X = 560/0.8

X = 700 Share

Y =(28000 - 40*700)/25

Y = 0 Share

Minimum total risk index is c =  1.2x + 1.4y

Minimum total risk index is c = 1.2*700 + 1.4*0

Minimum total risk index is c = $ 840

Answer

Buy 700  shares of ED and _0 shares of RBS-K. The minimum total risk index is c = __$ 840    .

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