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...

 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 - 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