Assume the Capital Asset Pricing Model (CAPM) holds, and the market consists of two risky assets, Stocks A and B, and a risk-free asset.

Stock A: 10 shares outstanding, currently priced at $10 per share.

Stock B: 5 shares outstanding, currently priced at $4 per share.

You expect that one period from today:

Stock A will be priced at $11 per share.

Stock B will be priced at $5 per share.

The risk-free rate over the period is 4%.

What is the beta of Stock B?

Enter your final answer as a number rounded to two decimal places. For example, enter 1.23 if your answer is 1.234, and -1.23 if your answer is -1.234.

Question

Assume the Capital Asset Pricing Model (CAPM) holds, and the market consists of two risky assets, Stocks A and B, and a risk-free asset.

Stock A: 10 shares outstanding, currently priced at $10 per share.

Stock B: 5 shares outstanding, currently priced at $4 per share.

You expect that one period from today:

Stock A will be priced at $11 per share.

Stock B will be priced at $5 per share.

The risk-free rate over the period is 4%.

What is the beta of Stock B?

Enter your final answer as a number rounded to two decimal places. For example, enter 1.23 if your answer is 1.234, and -1.23 if your answer is -1.234.

BlackTom AI · Accepted Answer

The question asks us to determine Stock B's beta under CAPM, given a simple market with two risky assets (A and B) and a risk-free asset. No answer choices are provided, so I will lay out the full reasoning and calculation steps you would typically use to arrive at beta.

First, identify the market portfolio. Under CAPM, the market is usually taken as the value-weighted portfolio of all risky assets available to invest. Here, the two stocks A and B form the market (along with the risk-free asset). Compute their current market values to get weights:
- Stock A: 10 shares × $10 = $100
- Stock B: 5 shares × $4 = $20
- Total market value = $100 + $20 = $120
- Weight of A in the market, w_A = $100/$120 = 5/6 ≈ 0.8333
- Weight of B in the market, w_B = $20/$120 = 1/6 ≈ 0.1667

Second, determine the expected (or one-period) returns for the two stocks and for the market portfolio, based on the information given (no dividends are mentioned, so I assume capital gain only):
- Stock A price today = $10; expected price next period = $11; return R_A = (11 - 10) / 10 = 0.10 = 10%
- Stock B price today = $4; expected price next period = $5; return R_B = (5 - 4) / 4 = 0.25 = 25%
- Market return R_M is the value-weighted average of the two stock returns: R_M = w_A × R_A + w_B × R_B = 0.8333 × 0.10 + 0.1667 × 0.25
  = 0.08333 + 0.04167 ≈ 0.125 = 12.5%

Third, apply the CAPM relationship to solve for beta. Under CAPM, the expected return on an asset i satisfies:
R_i = R_f + β_i × (R_M − R_f)
where R_f is the risk-free rate. Solve for beta for Stock B:
- R_f = 4% = 0.04
- R_M = 12.5% = 0.125
- R_B = 25% = 0.25
Then β_B = (R_B − R_f) / (R_M − R_f) = (0.25 − 0.04) / (0.125 − 0.04) = 0.21 / 0.085 ≈ 2.4706
Rounding to two decimals gives β_B ≈ 2.47.

Notes and potential caveats:
- This calculation assumes no dividends and that one-period returns are the relevant inputs.
- It also assumes the market portfolio is the value-weighted combination of A and B with weights computed from current market values, which is standard when only those assets are considered.
- If different phrasing of the market (e.g., including a broader set of assets or different pricing) were used, the beta could differ.

In summary, using CAPM with the described setup, Stock B’s beta comes out to approximately 2.47. If you were comparing alternatives or checking consistency, you would perform the same steps with any other candidate beta values and see which one aligns with the CAPM equation given the calculated market return.

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