Question

A portfolio is comprised of the following stocks. What is the portfolio beta? Stock Market Value of Shares Beta

A $ 14,000 1.79 B $ 17,500 .98 C $ 8,600 1.16 1.18 1.45 1.30 1.37

You own a $25,000 portfolio that is invested in a risk-free security and Stock A. The beta of Stock A is 1.70 and the portfolio beta is .95. What is the amount of the investment in Stock A?

$14,791

$11,331

$13,971

$16,531

Answer 1

Solution:
1.	Answer is 3rd option 1.30
Working Notes:
	Beta of a Portfolio = Weighted average beta of individual assets.
	Stock A with a beta BA= 1.79
	WA = investment A/ total investment
	= $14,000/($14,000 + $17,500 + $8,600)
	= 0.349127
	Stock B with a beta BB= 0.98
	WB = investment in B/ total investment
	= 17,500/($14,000 + $17,500 + $8,600)
	= 0.43640897755
	Stock C with a beta BC= 1.16
	WC = investment in B/ total investment
	= 8,600/($14,000 + $17,500 + $8,600)
	= 0.21446384
	Beta of a Portfolio = Weighted average beta of individual assets.
	= BA x WA + BB x WB + BC x WC
	=1.79 x 0.349127 + 0.98 x 0.43640897755 + 1.16 x 0.21446384
	= 1.301396182
	=1.30
2.	Answer is 3rd option $13,971
Working Notes:
	Beta of a Portfolio = Weighted average beta of individual assets.
	Beta of a Portfolio = 0.95
	Stock A with a beta BA= 1.70
	WA = investment A/ total investment
	= Investment in A / $25,000
	Risk free security with a beta Brf= 0	[Risk free security have beta Zero ]
	W Risk free = investment in Risk free security/ total investment
	= investment in Risk free security/$25,000
	Beta of a Portfolio = Weighted average beta of individual assets.
	0.95= BA x WA + Brf x Wrf
	0.95= 1.70 x (investment in A/$25,000) + 0 x (investment in rf /$25,000)
	0.95= 1.70 x (investment in A/$25,000) + 0
	0.95= 1.70 x (investment in A/$25,000)
	Investment in A = 0.95 x 25,000 /1.70
	Investment in A = $13,970.58824
	Investment in A = $13,971
Please feel free to ask if anything about above solution in comment section of the question.