Question

Your portfolio manager has suggested two high-yielding stocks: The Altria Group (MO) and Reynolds America (RAI). MO shares cost $50, yield 4.5% in dividends, and have a risk index of 2.0 per share. RAI shares cost $55, yield 5% in dividends, and have a risk index of 3.0 per share. You have up to $7,200 to invest and would like to earn at least $335 in dividends. How many shares (to the nearest whole number) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio? What is the minimum total risk index?

Answer 1

Let Assume that investmet in MO is x and RAI is y

x+y = $7200..........(1)

x(4.5%)+y(5%)= $335......(2)

x= $7200-y

Substitute x in equation (2)

$7200-y(4.5%)+y(5%) = 335

324- .045y + .05y = 335

.005y = 11

y= $2200

So, x= $7200 - $2200 = $5000

Investment in MO = $5000

Investment in RAI = $2200

Number of shares of MO =(5000÷50) = 100 shares

Number of shares of RAI = ($2200÷55) = 40 shares

Total risk index of portfolio

(5000/7200)*2 + (2200/7200)*3

1.389+ .916 = 2.305

Minimum total risk index = 2.305