Question

You have $30,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 7 percent. If your goal is to create a portfolio with an expected return of 11.1 percent,

A) How much money will you invest in Stock X?

A) $47,571

B) $16,692

C) $17,571

D) $18,450

E) $18,274

B) How much money will you invest in Stock Y?

A) $11,932

B) $13,050

C) $12,429

D) $12,926

E) $11,808

Answer 1

Answer to question A: Option C is correct.
Answer to question B: Option C is correct.

Explanation:

(Percentage of amount invested in stock X)*(Expected return of stock X)+(Percentage of amount invested in stock Y)*(Expected return of stock Y)=Expected portfolio return

Suppose we invest $x in stock X and $30000-$x in stock Y
Percentage of amount we need to invest in stock X=x/30000
Percentage of amount we need to invest in stock Y=(30000-x)/30000
Expected return of stock X=14%
Expected return of stock Y=7%
Expected portfolio return=11.1%
So, (x/30000)*14%+[(30000-x)/30000]*7%=11.1%
=>x*14%+(30000-x)*7%=11.1%*30000
=>0.14x+30000*7%-x*7%=3330
=>0.14x+2100-x*0.07=3330
=>0.14x-0.07x=3330-2100
=>(0.14-0.07)*x=1230
=>0.07*x=1230
=>x=1230/0.07
=>x=17571.42857
And 30000-x=30000-17571.42857=12428.57143

Amount to be invested in stock X=$17571.42857 or $17571 (Rounded to two decimal places)
Amount to be invested in stock Y=$12428.57143 or $12429 (Rounded to two decimal places)