Question

During the first quarter of 2015, Toronto Dominion Bank (TD) stock cost $45 per share, was expected to yield 4% per year in dividends, and had a risk index of 3.0 per share, while CNA Financial Corp. (CNA) stock cost $40 per share, was expected to yield 2.5% per year in dividends, and had a risk index of 2.0 per share.† You have up to $25,000 to invest in these stocks, and would like to earn at least $796 in dividends over the course of a year. (Assume the dividends to be unchanged for the year.) How many shares (to the nearest tenth of a unit) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio?

Toronto Dominion Bank sharesCNA Financial Corp. shares

What is the minimum total risk index? (Round your answer to two decimal places.)

Answer 1

Answer:

Given,

TD : dividend per stock = 4%*45

= 0.04*45

= 1.8

Return/risk = 1.8/3

= 0.6

CNA : dividend per stock = 2.5%*45

= 0.25*45

= 1.125

Return/risk = 1.125/3 = 0.375

Here we observe that, return/risk for TD is more than CNA , so we prefer TD.

Dividend:

Share of TD = 796/1.8 = 442.22

Investment :

No. of shares of TD = 25000/45

= 555.56

Here we observe that, 555.56 > 442.22, i.e., the excess amount will increase risk.

Total risk index = 3*442.22

= 1326.66