Part 1Suppose the market portfolio has an expected return of 10 %10% and a volatility of 20 %20%, while Microsoft's stock has a volatility of 30 %30%.a. Given its higher volatility, should we expect Microsoft to have an equity cost of capital that is higher than 10 %10%?b. What would have to be true for Microsoft's equity cost of capital to be equal to 10 %10%? Part 1a. Given its higher volatility, should we expect Microsoft to have an equity cost of capital that is higher than 10 %10%? (Select the best choice below.) A. No, volatility includes diversifiable risk, and so cannot be used to assess the equity cost of capital. Your answer is correct.B. Yes, higher volatility implies higher risk, so Microsoft is riskier than the market and should therefore have a higher return. C. Yes, although some of Microsoft's risk is diversifiable, enough is systematic so that it should have a higher return than the market. D. There is not enough information in this problem to answer this question definitively. Part 2b. What would have to be true for Microsoft's equity cost of capital to be equal to 10 %10%? (Select from the drop-down menus.)Microsoft stock would need to have a [input] ▼ empty selection that is [input] ▼ empty selection [input]enter your response here . (Round to two decimal places.)

Question

Part 1Suppose the market portfolio has an expected return of 10 %10% and a volatility of 20 %20%​, while Microsoft​'s stock has a volatility of 30 %30%.a. Given its higher​ volatility, should we expect Microsoft to have an equity cost of capital that is higher than 10 %10%​?b. What would have to be true for Microsoft​'s equity cost of capital to be equal to 10 %10%​? Part 1a. Given its higher​ volatility, should we expect Microsoft to have an equity cost of capital that is higher than 10 %10%​? ​(Select the best choice​ below.) A. ​No, volatility includes diversifiable​ risk, and so cannot be used to assess the equity cost of capital. Your answer is correct.B. ​Yes, higher volatility implies higher​ risk, so Microsoft is riskier than the market and should therefore have a higher return. C. ​Yes, although some of Microsoft​'s risk is​ diversifiable, enough is systematic so that it should have a higher return than the market. D. There is not enough information in this problem to answer this question definitively. Part 2b. What would have to be true for Microsoft​'s equity cost of capital to be equal to 10 %10%​? ​(Select from the​ drop-down menus.)Microsoft stock would need to have a  [input] ▼  empty selection that is [input] ▼  empty selection [input]enter your response here . ​ (Round to two decimal​ places.)

BlackTom AI · Accepted Answer

Systematic risk (beta), not total volatility, determines expected return under the CAPM. The CAPM formula is E[R_i] = R_f + β_i (E[R_m] − R_f); thus two stocks with different total volatilities can have the same expected return if their betas are the same.

Step-by-step reasoning and calculations:
1. Relevant concepts:
- Total volatility (standard deviation) measures total risk (systematic + idiosyncratic).
- Beta measures systematic risk: β_i = Cov(R_i, R_m) / Var(R_m).
- Under CAPM, expected return depends only on beta, not total volatility.

2. Answer to part (a):
- Option A is correct: No, higher volatility alone does not imply a higher equity cost of capital because volatility includes diversifiable (idiosyncratic) risk which does not command a risk premium. Options B and C are incorrect because they assume total volatility maps to higher required return; only systematic (non-diversifiable) risk matters. Option D is incorrect because CAPM provides the framework to determine whether the expected return should differ—if beta is known, we can decide.

3. What must be true for Microsoft’s cost of equity to equal 10% (part b)?
- For Microsoft’s expected return to equal the market’s 10%, Microsoft’s beta must equal 1. Under CAPM, if β = 1 then E[R_i] = R_f + 1·(E[R_m] − R_f) = E[R_m] = 10%.

4. Intermediate calculations illustrating the beta relation:
- Market volatility σ_m = 20% → Var(R_m) = σ_m^2 = 0.20^2 = 0.04.
- If β = 1, then Cov(R_MSFT, R_m) = β · Var(R_m) = 1 · 0.04 = 0.04.
- Given Microsoft’s σ_MSFT = 30% = 0.30, the correlation required would be:
  Corr = Cov / (σ_MSFT · σ_m) = 0.04 / (0.30 · 0.20) = 0.04 / 0.06 = 0.6667 ≈ 0.67.
  (This shows how Microsoft could have higher total volatility yet still have β = 1.)

5. Why the correct answer is correct:
- CAPM ties expected return to beta, so higher total volatility alone is not sufficient to claim a higher cost of equity. For equality with the market return, Microsoft’s systematic exposure (beta) must be equal to the market’s (β = 1).

6. Why other choices for (a) are wrong:
- B and C incorrectly equate higher total volatility with higher required return without separating diversifiable risk.
- D is wrong because CAPM gives sufficient conceptual information to state the condition (β = 1).

Conclusion: Microsoft would need to have a beta that is equal to 1 for its equity cost of capital to be 10%. This confirms the provided answer: "beta" and "equal to" (i.e., beta = 1).

类似问题

Question1.11 According to the Capital Asset Pricing Model (CAPM), in a disequilibrium, overpriced securities have ______ None of the options is correct. negative betas. zero alphas. positive alphas. positive betas. ResetMaximum marks: 2.5 Flag question undefined

Question1.9 According to the Capital Asset Pricing Model (CAPM), in a disequilibrium, overpriced securities have ______ positive alphas. zero alphas. negative betas. None of the options is correct. positive betas. ResetMaximum marks: 2.5 Flag question undefined

Part 1Suppose PepsiCo's stock has a beta of 1.071.07. If the risk-free rate is 3 %3% and the expected return of the market portfolio is 8 %8%, what is PepsiCo's equity cost of capital? Part 1PepsiCo's equity cost of capital is [input]enter your response here %. (Round to two decimal places.)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单