Part 1Suppose Autodesk stock has a beta of 2.522.52, whereas Costco stock has a beta of 0.650.65. If the risk-free interest rate is 4.08 %4.08% and the expected return of the market portfolio is 11.35 %11.35%, what is the expected return of a portfolio that consists of 45 %45% Autodesk stock and 55 %55% Costco stock, according to the CAPM? Part 1The beta of the portfolio is [input]enter your response here . (Round to two decimal places.)

Question

Part 1Suppose Autodesk stock has a beta of 2.522.52​, whereas Costco stock has a beta of 0.650.65. If the​ risk-free interest rate is 4.08 %4.08% and the expected return of the market portfolio is 11.35 %11.35%​, what is the expected return of a portfolio that consists of 45 %45% Autodesk stock and 55 %55% Costco ​stock, according to the​ CAPM? Part 1The beta of the portfolio is [input]enter your response here . ​ (Round to two decimal​ places.)

BlackTom AI · Accepted Answer

Portfolio beta equals the weighted average of the individual asset betas, so use the portfolio weights to combine the betas.

1. Relevant knowledge points and concepts
- Beta measures a stock’s sensitivity to market movements. 
- The beta of a portfolio is the weighted average of the betas of the individual holdings: βp = Σ (wi * βi), where wi are portfolio weights (in decimals).
- CAPM uses that portfolio beta to compute expected return: E[Rp] = Rf + βp (E[Rm] − Rf). (This step is not required for the requested blank but is shown for completeness.)

2. Complete reasoning process (step by step)
- Convert percentage weights to decimals: Autodesk weight wA = 45% = 0.45; Costco weight wC = 55% = 0.55.
- Use given betas: βA = 2.52, βC = 0.65.
- Compute weighted contributions and sum them to get portfolio beta.

3. Calculations with intermediate steps
- Contribution from Autodesk: 0.45 × 2.52 = 1.1340
- Contribution from Costco: 0.55 × 0.65 = 0.3575
- Sum: βp = 1.1340 + 0.3575 = 1.4915
- Round to two decimal places: βp ≈ 1.49

4. Why the correct answer is correct
- The portfolio beta formula directly produces 1.4915 when applying the precise weights and betas. Rounding to two decimals gives 1.49, so this is the correct portfolio beta.

5. Why other answers would be incorrect
- Using a simple (unweighted) average would yield (2.52 + 0.65)/2 = 1.585, which ignores portfolio weights and is incorrect.
- Forgetting to convert percentages to decimals or swapping weights would produce incorrect products.
- Rounding too early (e.g., rounding intermediate contributions before summing) could produce slight differences; always sum full precision then round final result.

6. Conclusion
The portfolio beta computed by the weighted-average formula is 1.4915, which rounds to 1.49. This confirms the provided answer of 1.49.

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