Suppose the beta of a four-asset portfolio is 1.8.The portfolio is composed of $1,500 invested in Stock W, $2,000 in Stock X, $2,500 in Stock Y, and $3,000 in Stock Z.What is the beta of Stock Z if the betas of Stock W, X, and Y are 0.7, 1.3, and 2.5, respectively?
A)0.7
B)1.1
C)1.6
D)2.1

Question

Quizplus · Accepted Answer

The beta of the portfolio is calculated as the weighted average of the betas of the individual stocks, with the weights being the proportion of the total investment in each stock. The total investment in the portfolio is $1,500 + $2,000 + $2,500 + $3,000 = $9,000. The weighted beta of the portfolio is calculated as follows:$$ \text{Portfolio Beta} = \left(\frac{1500}{9000} \times 0.7\right) + \left(\frac{2000}{9000} \times 1.3\right) + \left(\frac{2500}{9000} \times 2.5\right) + \left(\frac{3000}{9000} \times \text{Beta of Z}\right) = 1.8 $$Solving for the beta of Z:$$ \left(\frac{1500}{9000} \times 0.7\right) + \left(\frac{2000}{9000} \times 1.3\right) + \left(\frac{2500}{9000} \times 2.5\right) + \left(\frac{3000}{9000} \times \text{Beta of Z}\right) = 1.8 $$$$ 0.1167 + 0.2889 + 0.6944 + \left(\frac{3000}{9000} \times \text{Beta of Z}\right) = 1.8 $$$$ 1.1 + \left(\frac{1}{3} \times \text{Beta of Z}\right) = 1.8 $$$$ \frac{1}{3} \times \text{Beta of Z} = 0.7 $$$$ \text{Beta of Z} = 2.1 $$

Suppose the Beta of a Four-Asset Portfolio Is 1