You would like to invest $20,000 and have a portfolio expected return of 12 percent. You...

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You would like to invest $20,000 and have a portfolio expectedreturn of 12 percent. You are considering two securities, X and Y.X has an expected return of 20 percent and Y has an expected returnof 10 percent. How much should you invest in stock X if you investthe balance in stock Y to achieve the 12 percent portfolioreturn?
a) $5,500
b)
$4,000
c)
$7,000
d)
$6,250

Answer & Explanation Solved by verified expert

4.3 Ratings (871 Votes)

$4,000

Working:

Step-1:Calculation of weight of each investment

Suppose weight of investment in X is "w" and weight of investment in Y is "1-w".

Portfolio return	=	sum of weighted return
0.12	=	(w0.20)+((1-w)0.10)
0.12	=	0.20w+0.10-0.10w
0.12	=	0.10w+0.10
0.02	=	0.10w
w	=	0.20
1-w	=	0.80

Step-2:Calculation of investment in Stock X

Investment in X	=	Total investment	*	Weight of X
	=	$ 20,000	*	0.20
	=	$ 4,000

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Transcribed Image Text

You would like to invest $20,000 and have a portfolio expectedreturn of 12 percent. You are considering two securities, X and Y.X has an expected return of 20 percent and Y has an expected returnof 10 percent. How much should you invest in stock X if you investthe balance in stock Y to achieve the 12 percent portfolioreturn?a) $5,500b)$4,000c)$7,000d)$6,250