Question

1. You own a stock portfolio invested 25 percent in Stock Q, 20 percent in Stock R, 15 percent in Stock S, and 40 percent in Stock T. The betas for these four stocks are .9, 1.4, 1.1 and 1.8, respectively. What is the portfolio beta?

1. You want to create a portfolio equally as risky as the market (i.e, a portfolio with beta equal to 1), and you have $1,000,000 to invest. Given this information, fill in the rest of the following table:

Asset	Investment	Beta
Stock A	$200,000	.70
Stock B	$250,000	1.10
Stock C		1.60
Risk-free asset

Answer 1

1)
Portfolio beta is the sum of weighted beta of portfolio.
	Stock		Weight	Beta
			a	b	a*b
	Q		25%	0.9	0.2
	R		20%	1.4	0.3
	S		15%	1.1	0.2
	T		40%	1.8	0.7
	Portfolio beta				1.4
2)			Investment	Beta
	Stock C		$          3,65,600
	Risk-free asset		$          1,84,375	0
Working:
Risk free asset has beta of 0.
Weight of :
Stock A	$       2,00,000	/	$       10,00,000	=	0.20
Stock B	$       2,50,000	/	$       10,00,000	=	0.25
Suppose weight of Risk free asset is "w".Portfolio beta is 1.So, weight of Stock C is (1-0.20-0.25-w) or (0.55-w).
Now, as per question,
Portfolio beta		=	Sum of weighted beta
1		=	(0.20*0.70)	+	(0.25*1.10)	+	((0.55-w)*1.60)	+	(w*0)
1		=	0.14	+	0.275	+	((0.55-w)*1.60)	+	0
1		=	0.415	+	((0.55-w)*1.60)
0.585		=	(0.55-w)*1.60
0.365625		=	0.55-w
w		=	0.1844
So, weight of :
Risk free asset			0.1844
Stock C	0.55-0.1844	=	0.3656
Stock A			0.2000
Stock B			0.2500
Total			1.0000
Investment in :
Stock C		=	$       10,00,000	*	0.3656	=	$       3,65,600
Risk free asset		=	$       10,00,000	*	0.1844	=	$       1,84,375