In August 2011, Bank of Hawaii (BOH) stock cost $45 per share, yielded 4% per year in dividends, and had a risk index of 3.0 per share, while JPMorgan Chase (JPM) stock cost $40 per share, yielded 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?

Question
Asked Mar 27, 2019
44 views

In August 2011, Bank of Hawaii (BOH) stock cost $45 per share, yielded 4% per year in dividends, and had a risk index of 3.0 per share, while JPMorgan Chase (JPM) stock cost $40 per share, yielded 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?

check_circle

Expert Answer

Step 1

Let the number of shares of BOH in protfolio be x

the number of shares of JPM in portfolio be y

BOH Stock cost per share = $45

JPM stock cost per share = $40

The total amount can be invested is up to 25000. So we say

45x+40y ≤ 25000

Yield on BOH shares  is 4% per year and yield on JPM shares is 2.5% and we need at least the dividend to be $796 per year.

Dividends on BOH shares = 45x*4.0% = 45*0.04*x=1.8x

Dividends on JPM shares = 40y*2.5% = 40*0.025*y = y

Total dividends = 1.8x+y and we know at least dividends should be $796 . So

1.8x + y ≥ 796

We need to minimise the Total Risk index. Risk index of BOH is 3 per share and risk index of JPM is 2 per share. 

Total risk Index R = 3x+2y

 

Step 2

Here we need to minimise the Total risk index keeping the constraints in mind. We need to invest enough amount in BOH shares and remaining in JPM shares, such that we get dividends of 796 per year.

We know we can invest upto 25000 and So we invest just enoug money in BOH ...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Algebra

Applications of Mathematics

Related Algebra Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Condense the expression to the logarithm of a single quantity (c) 4 [lnz +ln(z +5)] −2ln(z −5)

A: Consider the provided expression.

question_answer

Q: Hello, I am not confident in this Linear Algebra question:   Suppose that a nonhomogeneous system wi...

A: The system is equivalent to Ax=b.We have 10 linear equations in 8 unknowns. So dimension of A= 10x8.

question_answer

Q: In the following exercise, find the coordinates of the vertex for the parabola defined by the given ...

A: We are given equation of parabola as 

question_answer

Q: 6. For the given functions f and g, algebraically find (f-g)(x) f(x) = -5x3- 7x2 - 8x g(x) = 12x3- 6...

A: Given, 

question_answer

Q: A car rental company charges an initial fee plus an additional fee for each mile driven. The charge ...

A: The charge to rent economy car is given by the function,

question_answer

Q: graph g(x)=4log1/2x plot at least two points on the graph, draw all asymptotes,

A: Given information:The given gunction is g(x)=4log1/2x.

question_answer

Q: This Question: 1 pt th 25 of 30 (4 complete) Find f(g(x)) and g(fx)) and determine whether the pair ...

A:          Given,

question_answer

Q: Solve the rational inequality and graph the solution set on a real number line. Express the solution...

A:         Given,

question_answer

Q: O LINES AND FUNCTIONS OD Paul Combining functions to write a new function that models a re... Españo...

A: Given information:The standard charge S (in dollars) is given by the function S=18.95+0.50M, where M...