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 1.0 per share. RBS-K shares cost $25, yield 7.5% in dividends, and have a risk index of 1.5 per share. You have up to $24,000 to invest and would like to earn at least $1,320 in dividends. How many shares (to the nearest whole number) of each stock should you purchase in order to meet your requirements and minimize the total risk index for your portfolio

Answer 1

Answer:

Purchase 600 shares of ED and 0 shares of RBS-K. The minimum risk index is 600

Explanation:

Let’s assume shares to be purchased in ED is x and purchased in RBS-K is y. You have maximum amount to invest is $24000.So we can say that 40x+25y 24,000.

Al least you should earn 0.055(40x) + 0.075(25y) 1320 where x and y 0.

Minimize C =1.0x+1.5y, Subject to 40x+25y 24,000 and 0.055(40x) +0.075(25y) 1320

Graph, Corner points

1 Suppose Point A (500,700) 500 shares of x and 700 shares of y

40x+25y= 24,000

40(500) +25(700)

37500 > 24,000 and

C =1.0x+1.5y = 1.0(500) +1.5(700) = 1550

2) point B (0,625)

Investment=$15,625 an C=938

3) point C (0,500). Investment=$12,500 C=750

4) Point D (600,0) investment=$24,000 and Risk is 600, Return is. 0.055(40x) +0.075(25y) = $1320

Answer 2

Answer:

600 shares of ED will fullfill the requirements.

Explanation:

We have to look which share does a bnetter yield considering the risk

$\left[\begin{array}{ccc}&ED&RBS-K\\Share Price&40&25\\Yield&0.055&0.075\\Dividend&2.2&1.875\\Dividend / Risk&2.2&1.25&\\\end{array}\right]$

as the ED is superior the thus we use all our budget on it and will only replace it if we do not meet the minimum requirement:

24,000 / 40 shares = 600 shares

return of ED at 600 shares

600 x 40 each x 0.055 = 1,320

As this amount is exactly our bare minimum we can only purchase ED shares.