See the attached spreadsheet for a table of various monthly returns
Download attached spreadsheet for a table of various monthly returns
over the past five years. Create a portfolio of the three stocks that consists of 10% Stock A, 70% Stock B, and 20% Stock C. What is the beta of the portfolio?

Question

See the attached spreadsheet for a table of various monthly returns 
Download attached spreadsheet for a table of various monthly returns
over the past five years. Create a portfolio of the three stocks that consists of 10% Stock A, 70% Stock B, and 20% Stock C. What is the beta of the portfolio?

BlackTom AI · Accepted Answer

Question restatement: The task describes creating a portfolio with 10% in Stock A, 70% in Stock B, and 20% in Stock C, and asks for the portfolio beta.

Option availability note: The provided data indicates an answer of 1.12, but there are no answer choices listed in answer_options. Without explicit options to evaluate, we cannot compare candidate results. The primary calculation still requires identifying the betas of the individual stocks or enough information to derive them.

Key concept: The beta of a portfolio is the weighted sum of the betas of its components, assuming a common market benchmark. The formula is: Beta_portfolio = w_A * Beta_A + w_B * Beta_B + w_C * Beta_C, where w_i are the portfolio weights.

What we need to compute: To determine Beta_portfolio, we must know Beta_A, Beta_B, and Beta_C (each stock's beta with respect to the same market index, e.g., the S&P 500). These betas are typically provided in a data table or can be estimated from historical returns against the market.

Why the data given is insufficient on its own: Although the weights are specified (0.10, 0.70, 0.20), the betas of Stock A, Stock B, and Stock C are not provided in the prompt or attached spreadsheet excerpt. Without Beta_A, Beta_B, and Beta_C, the portfolio beta cannot be computed.

What would be needed if we had betas: If you supply Beta_A, Beta_B, and Beta_C, we would multiply each by its weight and sum them:
- Contribution from A: 0.10 * Beta_A
- Contribution from B: 0.70 * Beta_B
- Contribution from C: 0.20 * Beta_C
Then Beta_portfolio = (0.10 * Beta_A) + (0.70 * Beta_B) + (0.20 * Beta_C).

If the spreadsheet or dataset includes annualized or historical betas for each stock, we can perform the calculation directly. Alternatively, if you only have stock returns and the market returns, we could estimate Betas via regression of each stock’s returns on market returns, and then apply the weights above.

Edge considerations: If any of the betas are provided as ranges or with uncertainty, the resulting portfolio beta will inherit that uncertainty. If the stocks are perfectly uncorrelated with the market in the dataset (beta near zero), the portfolio beta would be largely driven by Stock B given its 70% allocation, though it would still be a weighted sum of all three.

Summary guidance: To determine the exact portfolio beta of 10% A, 70% B, 20% C, you need Beta_A, Beta_B, and Beta_C. With those, compute Beta_portfolio = 0.10*Beta_A + 0.70*Beta_B + 0.20*Beta_C. Since answer options are not provided and the betas are not listed, we cannot verify whether 1.12 is correct from the given information.

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