Calculate the beta of a portfolio with the following stocks: 25% of a stock with a beta of 1.1, 35% of a stock with a beta of 1.6, and the balance of a stock with beta of 0.9

Question

BlackTom AI · Accepted Answer

We start by identifying the portfolio weights and the betas of each stock. The first stock has a weight of 25% (0.25) and beta 1.1. The second stock has a weight of 35% (0.35) and beta 1.6. The remaining weight is 1 - 0.25 - 0.35 = 0.40, which corresponds to the third stock with beta 0.9.

To find the portfolio beta, multiply each stock's beta by its weight and sum the results:
- Contribution of stock 1: 0.25 × 1.1 = 0.275
- Contribution of stock 2: 0.35 × 1.6 = 0.56
- Contribution of stock 3: 0.40 × 0.9 = 0.36

Add these contributions together to get the portfolio beta: 0.275 + 0.56 + 0.36 = 1.195.

If you round to two decimal places, you get 1.20. Different rounding practices (e.g., rounding at intermediate steps vs. only at the end) can slightly change the final displayed value, but the underlying calculation remains the same. The methodology here relies on the weighted-average formula for portfolio beta, which assumes beta is additive with respect to the weights and that the betas of individual assets are given.

Key subtlety to avoid missteps: ensure that the weights sum to 1 and that you apply each weight to the corresponding asset beta before summing. Misallocating weights or mixing up beta values would lead to an incorrect result. Also, be mindful of whether you’re asked to report the answer to two decimals or more; the exact unrounded result is 1.195.

Calculate the beta of a portfolio with the following stocks: 25% of a stock with a beta of 1.1, 35% of a stock with a beta of 1.6, and the balance of a stock with beta of 0.9Numerical

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