Questions: Rick Kish has a 100,000 stock portfolio. Thirty-two thousand dollars is invested in a stock with a beta of 0.75 and the remainder is invested in a stock with a beta of 1.38. These are the only two investments in his portfolio. What is his portfolio's beta? a. 1.30 b. 1.36 c. 1.24 d. 1.18

Rick Kish has a 100,000 stock portfolio. Thirty-two thousand dollars is invested in a stock with a beta of 0.75 and the remainder is invested in a stock with a beta of 1.38. These are the only two investments in his portfolio. What is his portfolio's beta? a. 1.30 b. 1.36 c. 1.24 d. 1.18
Transcript text: Rick Kish has a $\$ 100,000$ stock portfolio. Thirty-two thousand dollars is invested in a stock with a beta of 0.75 and the remainder is invested in a stock with a beta of 1.38 . These are the only two investments in his portfolio. What is his portfolio's beta? a. 1.30 b. 1.36 C. 1.24 d. 1.18
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Solution

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Solution Steps

To find the portfolio's beta, we need to calculate the weighted average of the betas of the individual stocks. The weights are determined by the proportion of the total investment in each stock. Specifically, we multiply the beta of each stock by its respective weight in the portfolio and sum these products to get the portfolio's beta.

Step 1: Determine the Weights of Each Stock in the Portfolio

The total investment is \(\$100,000\). The investment in the first stock is \(\$32,000\). Therefore, the weight of the first stock in the portfolio is: \[ \text{Weight of Stock 1} = \frac{32,000}{100,000} = 0.32 \] The remainder of the investment, \(\$68,000\), is in the second stock. Thus, the weight of the second stock is: \[ \text{Weight of Stock 2} = \frac{68,000}{100,000} = 0.68 \]

Step 2: Calculate the Portfolio's Beta

The beta of the portfolio is the weighted average of the betas of the individual stocks. The beta of the first stock is \(0.75\) and the beta of the second stock is \(1.38\). Therefore, the portfolio's beta is calculated as follows: \[ \text{Portfolio Beta} = (0.32 \times 0.75) + (0.68 \times 1.38) \] \[ = 0.24 + 0.9384 = 1.1784 \]

Final Answer

The portfolio's beta is \(\boxed{1.18}\).

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