Question

Stock	A	B	C	D	E
Amount	$1,000,000	675,000	750,000	500,000	75,000
Beta	1.2	0.5	1.4	0.75	-1.3

Assume the portfolio manager has invested $3 million in the following common stocks, what is the beta of the portfolio?   

A. 0.96
	B. 1.02
	C. 0.51
	D. 1.03

answers C is incorrect. which one is correct and why?

Answer 1

Answer - Option (a) = 0.96

Calculation :-

Total Amount Invested = $3million or $3000000

Step 1 - Find out the weights of each stock :-

Weight of Stock A = $1000000 / $3000000 = 0.333333

Weight of Stock B = $675000 / $3000000 = 0.225

Weight of Stock C = $750000 / $3000000 = 0.25

Weight of Stock D = $500000 / $3000000 = 0.166667

Weight of Stock E = $75000 / $3000000 = 0.025

Step 2 - Calculate Weighted Average of Beta :-

Beta A = 0.333333 x 1.2 = 0.40

Beta B = 0.225 x 0.5 = 0.1125

Beta C = 0.25 x 1.4 = 0.35

Beta D = 0.166667 x 0.75 = 0.125

Beta E = 0.025 x -1.3 = (-)0.0325

Step 3 - Calculate Beta of the Portfolio by simply adding all the Beta's calculated in Step 2

Beta of the Portfolio = 0.40 + 0.1125 + 0.35 + 0.125 + (-)0.0325

Beta of the Portfolio = 0.955 or 0.96