微信客服：xiaoxionga100
微信客服：ITCS521
FINS5513-无代写
时间：2023-03-14
HD EDU
1
HD
EDU
FINS5513
教科书后练习题总结二
HD EDU
2
HD EDU
3
FINS5513 Investments & Portfolio Selection
Selected Practice Questions from BKM
答案和解题注释在最后几页 Q1. The individual investor's optimal portfolio is designated by A. the point of tangency with the indifference curve and the capital allocation line. B. the point of highest reward to variability ratio in the opportunity set. C. the point of tangency with the opportunity set and the capital allocation line. D. the point of the highest reward to variability ratio in the indifference curve. E. None of the options are correct. Q2. The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is A. 0.0. B. 1.0. C. 0.5. D. –1.0. E. any negative number. Q3. If a firm's beta was calculated as 1.3 in a regression equation, a commonly-used adjustment technique would provide an adjusted beta of A. less than 1.0 but greater than zero. B. between 0.3 and 0.9. C. between 1.0 and 1.3. D. greater than 1.3. E. zero or less. Q4. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 150 stocks in order to construct a mean-variance efficient portfolio constrained by 150 investments. They will need to calculate ____________ covariances. A. 12 B. 150 C. 22,500 D. 11,175
HD EDU
4
Q5. Assume that stock market returns do follow a single-index structure. An investment fund analyzes 200 stocks in order to construct a mean-variance efficient portfolio constrained by 200 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor. A. 200; 19,900 B. 200; 200 C. 19,900; 200 D. 19,900; 19.900 Q6. Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 16%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 11%, and there are no firm-specific events affecting the stock performance. The β of the stock is A. 0.67. B. 0.75. C. 1.0. D. 1.33. E. 1.50. Q7. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.20 and σM was 0.16, the β of the portfolio would be approximately A. 0.64. B. 0.80. C. 1.25. D. 1.56. Q8. The index model for stock A has been estimated with the following result: RA = 0.01 + 0.9RM + eA. If σM = 0.25 and R2A = 0.25, the standard deviation of return of stock A is A. 0.2025. B. 0.2500. C. 0.4500. D. 0.8100.
HD EDU
5
Q9. The index model has been estimated for stocks A and B with the following results: RA = 0.01 + 0.5RM + eA. RB = 0.02 + 1.3RM + eB. σM = 0.25; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A. 0.0384. B. 0.0406. C. 0.1920. D. 0.0050. E. 0.4000. Q10. The security characteristic line (SCL) associated with the single-index model is a plot of A. the security's returns on the vertical axis and the market index's returns on the horizontal axis. B. the market index's returns on the vertical axis and the security's returns on the horizontal axis. C. the security's excess returns on the vertical axis and the market index's excess returns on the horizontal axis. D. the market index's excess returns on the vertical axis and the security's excess returns on the horizontal axis. E. the security's returns on the vertical axis and Beta on the horizontal axis. Q11. The market portfolio has a beta of A. 0. B. 1. C. –1. D. 0.5. Q12. The risk-free rate and the expected market rate of return are 0.06 and 0.12, respectively. According to the capital asset pricing model (CAPM), the expected rate of return on security X with a beta of 1.2 is equal to A. 0.06. B. 0.144. C. 0.12. D. 0.132. E. 0.18.
HD EDU
6
Q13. The market risk, beta, of a security is equal to A. the covariance between the security's return and the market return divided by the variance of the market's returns. B. the covariance between the security and market returns divided by the standard deviation of the market's returns. C. the variance of the security's returns divided by the covariance between the security and market returns. D. the variance of the security's returns divided by the variance of the market's returns. Q14. According to the Capital Asset Pricing Model (CAPM), underpriced securities have A. positive betas. B. zero alphas. C. negative betas. D. positive alphas. E. None of the options are correct. Q15. Your opinion is that CSCO has an expected rate of return of 0.13. It has a beta of 1.3. The risk-free rate is 0.04 and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security is A. underpriced. B. overpriced. C. fairly priced. D. Cannot be determined from data provided. Q16. Your opinion is that CSCO has an expected rate of return of 0.15. It has a beta of 1.3. The risk-free rate is 0.04 and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security is A. underpriced. B. overpriced. C. fairly priced. D. Cannot be determined from data provided. E. None of the options are correct.
HD EDU
7
Q17. The risk-free rate is 4%. The expected market rate of return is 11%. If you expect CAT with a beta of 1.0 to offer a rate of return of 10%, you should A. buy CAT because it is overpriced. B. sell short CAT because it is overpriced. C. sell short CAT because it is underpriced. D. buy CAT because it is underpriced. E. None of the options, as CAT is fairly priced. Q18. What is the expected return of a zero-beta security? A. The market rate of return B. Zero rate of return C. A negative rate of return D. The risk-free rate Q19. An overpriced security will plot A. on the security market line. B. below the security market line. C. above the security market line. D. either above or below the security market line depending on its covariance with the market. E. either above or below the security-market line depending on its standard deviation. Q20. The capital asset pricing model assumes A. all investors are price takers. B. all investors have the same holding period. C. investors pay taxes on capital gains. D. all investors are price takers and have the same holding period. E. all investors are price takers, have the same holding period, and pay taxes on capital gains. Q21. If investors do not know their investment horizons for certain, A. the CAPM is no longer valid. B. the CAPM underlying assumptions are not violated. C. the implications of the CAPM are not violated as long as investors' liquidity needs are not priced. D. the implications of the CAPM are no longer useful.
HD EDU
8
Q22. One of the assumptions of the CAPM is that investors exhibit myopic behavior. What does this mean? A. They plan for one identical holding period. B. They are price takers who can't affect market prices through their trades. C. They are mean-variance optimizers. D. They have the same economic view of the world. E. They pay no taxes or transactions costs. Q23. The amount that an investor allocates to the market portfolio is negatively related to I) the expected return on the market portfolio. II) the investor's risk aversion coefficient. III) the risk-free rate of return. IV) the variance of the market portfolio. A. I and II. B. II and III. C. II and IV. D. II, III, and IV. E. I, III, and IV. Q24. An investor will take as large a position as possible when an equilibrium-price relationship is violated. This is an example of A. a dominance argument. B. the mean-variance efficiency frontier. C. a risk-free arbitrage. D. the capital asset pricing model. Q25. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 18%. The standard deviation on the factor portfolio is 16%. The beta of the well-diversified portfolio is approximately A. 0.80. B. 1.13. C. 1.25. D. 1.56.
HD EDU
9
Q26. Consider the single-factor APT. Stocks A and B have expected returns of 15% and 18%, respectively. The risk-free rate of return is 6%. Stock B has a beta of 1.0. If arbitrage opportunities are ruled out, stock A has a beta of A. 0.67. B. 1.00. C. 1.30. D. 1.69. E. 0.75. Q27. Consider the multifactor APT with two factors. The risk premiums on the factor 1 and factor 2 portfolios are 5% and 6%, respectively. Stock A has a beta of 1.2 on factor-1, and a beta of 0.7 on factor-2. The expected return on stock A is 17%. If no arbitrage opportunities exist, the risk-free rate of return is A. 6.0%. B. 6.5%. C. 6.8%. D. 7.4%. Q28. Consider the multifactor APT. There are two independent economic factors, F1 and F2. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios: Portfolio Beta on F1 Beta on F2 Expected Return A 1 2 19% B 2 0 12% Assuming no arbitrage opportunities exist, the risk premium on the factor F1 portfolio should be A. 3%. B. 4%. C. 5%. D. 6%. Q29. A well-diversified portfolio is defined as A.one that is diversified over a large enough number of securities that the nonsystematic variance is essentially zero. B. one that contains securities from at least three different industry sectors. C. a portfolio whose factor beta equals 1.0. D. a portfolio that is equally weighted.
HD EDU
10
Q30. Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 6%, the risk premium on the first factor portfolio is 4%, and the risk premium on the second factor portfolio is 3%. If portfolio A has a beta of 1.2 on the first factor and .8 on the second factor, what is its expected return? A. 7.0% B. 8.0% C. 9.2% D. 13.0% E. 13.2% Q31. As diversification increases, the total variance of a portfolio approaches A. 0. B. 1. C. the variance of the market portfolio. D. infinity. E. None of the options are correct. Q32. Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A. the α of the asset. B. the β of the asset. C. the σ of the asset. D. the δ of the asset.
HD EDU
11
答案 Q1 A Q2 D Q3 C = !" + #" Q4 D 题干说 do not resemble a single-index structure, 即使用 Markowitz 模型时需要用到的
参数数量为： 1 个 risk-free rate n 个 sample means n 个 sample variances (%!&%)! 个 sample covariances Q5 B 题干说 resemble a single-index structure, 即使用 SIM 模型时需要用到的参数数量为： ( , ()), )! 各一个 n 个 sample means n 个 sample variances n 个 Beta Q6 C 第一步：正确列出 SIM 公式 = + ) + * 注意 表示的是 Excess Return，即 需要扣掉 risk-free rate * 代表着 error term，如果题目没有明说，一般可以默认为 0 第二步：正确代入 SIM公式，求解 0.11 = 0 + × (0.16 − 0.05) + 0 解出β = 1 Q7 C 第一步：从五个和 beta相关的公式中，找出正确的公式 ! = !+! + ,! 由于题目说 well-diversified portfolio，因此 ,! = 0 (因为 unsystematic risk 都被分散掉了，木得了) 第二步：正确代入公式，求解 0.2! = ! × 0.16! + 0 得出 = 1.25 Q8 C 第一步：从五个和 beta相关的公式中，找出正确的公式 ! = !+!!
HD EDU
12
第二步：从题干中找到正确数据
注意，题干中的 R2A 其实指的是 r-squared，并不是指 return，如果你把这个数据当做return 使用，这道题就解不出来了。所以这道题是个很坑的题型，条件给的不明不白
的。
另外还有一个坑点，就是题目给你的!是已经平方了的，不需要再平方一次 ! = 0.25 ) = 0.25
那么，公式中所需要的 beta 哪里来？ Beta 在题干中的 Single Index Model 公式中暗暗的告诉你了，它是等式的斜率 = 0.9
第三步：正确代入公式，求解 0.25 = 0.9! × 0.25!!
解出 = 0.45
注意，如果你算出的答案是 0.2025，这个是 variance，而不是 standard deviation Q9 B 第一步：从五个和 beta相关的公式中，找出正确的公式 F* , -G = *-)!
第二步：从题干中找到正确数据 . = 0.5 / = 1.3 ) = 0.25
第三步：正确代入公式，求解(, ) (., /) = 0.5 × 1.3 × 0.25! = 0.040625 Q10 C Q11 B Q12 D Q13 A Q14 D Q15 B 第一步：用 CAPM公式算出 equilibrium 状态下的 () :() = ( + F+ − (G = 0.04 + 1.3 × (0.115 − 0.04) = 0.1375 第二步：那 CAPM算出的 () 和题目告诉你的 your opinion 比较 () = 0.1375 > 0.13 你可以计算通过 alpha，来判断它是高估了还是低估了
HD EDU
13
= 0.13 − 0.1375 = −0.0075 < 0 → 如果弄不清楚这个逻辑，可以直接代入 Excel 计算器，专门有一页是给这个题的 Q16 A 原理同 15 题 Q17 B 原理同 15 题，建议使用 Excel 计算器的模板 Overpriced 和 sell 是绑定的，所以他们必须出现在一个选项中 Under-priced 和 buy 是绑定的 Q18 D 把 = 0 代入 CAPM 的公式，就能得出回报率等于( Q19 B Security Market Line 是 CAPM 等式的那条直线 Overpriced 代表着 negative alpha，回报率低于 CAPM，因此在 SML 下方 Underpriced 代表着 positive alpha，回报率高于 CAPM，因此在 SML 上方 你看，很绕吧 Q20 D CAPM 的一大假设就是没有 tax，所以 C 和 E 不能选 不要一看到这种题就选最长的那个选项，可能有坑 Q21 C 这题的 C 选项就是 CAPM 的一个假设，不需要真的理解，记忆一下即可 一般而言，CAPM 假设所有投资人都有一个 certain investment horizon 但是这不是必须的，只要投资人的 liquidity needs are not priced，CAPM 仍然成立 Q22 A CAPM 假设，所有投资人都只关注一个投资期限内的事情，所以他们都有 the same holding period Q23 D 这道题考察的是这个公式（一般不需要计算） = ()) − ()! 这个公式是计算 y，即分配多少比例的资金到 risky assets 1-y 为分配到 risk-free assets 的资金比例 通过观察公式，你会发现：
§ y 和 ()) 成正比
§ y 和 , )! , ( 成反比 Q24 C 这题是不太常见的概念题，万一考到了，失分率很高 什么是 equilibrium-price relationship is violated?
即，CAPM 估计出来的 return，和实际上的 return 不付了，会有 overpriced 和 underpriced 情况。这时，有些人就可以采取 risk-free arbitrage（无风险套利）的方式，
从差价中获利
HD EDU
14
Q25 B one-factor APT 就是 Single Index Model
大家看到 APT (Arbitrage Pricing Theory) 这个术语不要害怕，它在我们的题目中，基本
就是只是一个装饰作用，没有啥实际意义，我们该用什么公式还是用什么公式
找出正确的公式 ! = !+! + ,!
和这份练习题中第七题的做法一样 Q26 E 第一步：找到 single-factor APT 公式 = + ## 第二步：分别列出 stock A 和 stock B 的等式 : 15%− 6% = 0 + . × # : 18%− 6% = 0 + 1 × # 第三步：解方程得出结果 # = 12% . = 0.75 Q27 C 第一步：我们先找到multifactor APT 的公式 = + ## + !! +⋯+ %% 遇到这种题，题目给我们什么，我们就代入什么 第二步：整理条件 # = 1.2, # = 5% ! = 0.7, ! = 6% 由于 no arbitrage opportunities exist, = 0 第三步：代入公式 = 0 + 1.2 × 5%+ 0.7 × 6% 得出 = 10.2%
第四步：不要忘记第三步得出来的 R 是 Excess Return，为了求出 risk-free rate，你
要加回 stock expected return = () − ( 10.2% = 17%− (
得出( = 6.8% Q28 A 第一步：我们先找到multifactor APT 的公式 = + ## + !! +⋯+ %% 第二步：代入公式（这题因为有两个 portfolio A 和 B，所以我们要代入两次） : 19% − 6% = 0 + 1 × # + 2 × !
HD EDU
15
: 12% − 6% = 0 + 2 × # + 0 × !
第三步：解方程 # = 3% Q29 A Q30 E 第一步：我们先找到multifactor APT 的公式 = + ## + !! +⋯+ %% 第二步：代入公式 = 0 + 1.2 × 4%+ 0.8 × 3% = 7.2%
第三步：千万不要忘记，公式求出来的是 Excess Return，你需要加回 () = + ( = 7.2% + 6% = 13.2% Q31 C Q32 B 题干中说的 Regression line 即 Security Characteristic Line (SCL)，也是 SIM Model 的回
归直线，它的斜率为 beta ，截距为 alpha = + ## =实际回报率− CAPM 回报率
1
HD
EDU
FINS5513
教科书后练习题总结二
HD EDU
2
HD EDU
3
FINS5513 Investments & Portfolio Selection
Selected Practice Questions from BKM
答案和解题注释在最后几页 Q1. The individual investor's optimal portfolio is designated by A. the point of tangency with the indifference curve and the capital allocation line. B. the point of highest reward to variability ratio in the opportunity set. C. the point of tangency with the opportunity set and the capital allocation line. D. the point of the highest reward to variability ratio in the indifference curve. E. None of the options are correct. Q2. The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is A. 0.0. B. 1.0. C. 0.5. D. –1.0. E. any negative number. Q3. If a firm's beta was calculated as 1.3 in a regression equation, a commonly-used adjustment technique would provide an adjusted beta of A. less than 1.0 but greater than zero. B. between 0.3 and 0.9. C. between 1.0 and 1.3. D. greater than 1.3. E. zero or less. Q4. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 150 stocks in order to construct a mean-variance efficient portfolio constrained by 150 investments. They will need to calculate ____________ covariances. A. 12 B. 150 C. 22,500 D. 11,175
HD EDU
4
Q5. Assume that stock market returns do follow a single-index structure. An investment fund analyzes 200 stocks in order to construct a mean-variance efficient portfolio constrained by 200 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor. A. 200; 19,900 B. 200; 200 C. 19,900; 200 D. 19,900; 19.900 Q6. Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 16%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 11%, and there are no firm-specific events affecting the stock performance. The β of the stock is A. 0.67. B. 0.75. C. 1.0. D. 1.33. E. 1.50. Q7. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.20 and σM was 0.16, the β of the portfolio would be approximately A. 0.64. B. 0.80. C. 1.25. D. 1.56. Q8. The index model for stock A has been estimated with the following result: RA = 0.01 + 0.9RM + eA. If σM = 0.25 and R2A = 0.25, the standard deviation of return of stock A is A. 0.2025. B. 0.2500. C. 0.4500. D. 0.8100.
HD EDU
5
Q9. The index model has been estimated for stocks A and B with the following results: RA = 0.01 + 0.5RM + eA. RB = 0.02 + 1.3RM + eB. σM = 0.25; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A. 0.0384. B. 0.0406. C. 0.1920. D. 0.0050. E. 0.4000. Q10. The security characteristic line (SCL) associated with the single-index model is a plot of A. the security's returns on the vertical axis and the market index's returns on the horizontal axis. B. the market index's returns on the vertical axis and the security's returns on the horizontal axis. C. the security's excess returns on the vertical axis and the market index's excess returns on the horizontal axis. D. the market index's excess returns on the vertical axis and the security's excess returns on the horizontal axis. E. the security's returns on the vertical axis and Beta on the horizontal axis. Q11. The market portfolio has a beta of A. 0. B. 1. C. –1. D. 0.5. Q12. The risk-free rate and the expected market rate of return are 0.06 and 0.12, respectively. According to the capital asset pricing model (CAPM), the expected rate of return on security X with a beta of 1.2 is equal to A. 0.06. B. 0.144. C. 0.12. D. 0.132. E. 0.18.
HD EDU
6
Q13. The market risk, beta, of a security is equal to A. the covariance between the security's return and the market return divided by the variance of the market's returns. B. the covariance between the security and market returns divided by the standard deviation of the market's returns. C. the variance of the security's returns divided by the covariance between the security and market returns. D. the variance of the security's returns divided by the variance of the market's returns. Q14. According to the Capital Asset Pricing Model (CAPM), underpriced securities have A. positive betas. B. zero alphas. C. negative betas. D. positive alphas. E. None of the options are correct. Q15. Your opinion is that CSCO has an expected rate of return of 0.13. It has a beta of 1.3. The risk-free rate is 0.04 and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security is A. underpriced. B. overpriced. C. fairly priced. D. Cannot be determined from data provided. Q16. Your opinion is that CSCO has an expected rate of return of 0.15. It has a beta of 1.3. The risk-free rate is 0.04 and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security is A. underpriced. B. overpriced. C. fairly priced. D. Cannot be determined from data provided. E. None of the options are correct.
HD EDU
7
Q17. The risk-free rate is 4%. The expected market rate of return is 11%. If you expect CAT with a beta of 1.0 to offer a rate of return of 10%, you should A. buy CAT because it is overpriced. B. sell short CAT because it is overpriced. C. sell short CAT because it is underpriced. D. buy CAT because it is underpriced. E. None of the options, as CAT is fairly priced. Q18. What is the expected return of a zero-beta security? A. The market rate of return B. Zero rate of return C. A negative rate of return D. The risk-free rate Q19. An overpriced security will plot A. on the security market line. B. below the security market line. C. above the security market line. D. either above or below the security market line depending on its covariance with the market. E. either above or below the security-market line depending on its standard deviation. Q20. The capital asset pricing model assumes A. all investors are price takers. B. all investors have the same holding period. C. investors pay taxes on capital gains. D. all investors are price takers and have the same holding period. E. all investors are price takers, have the same holding period, and pay taxes on capital gains. Q21. If investors do not know their investment horizons for certain, A. the CAPM is no longer valid. B. the CAPM underlying assumptions are not violated. C. the implications of the CAPM are not violated as long as investors' liquidity needs are not priced. D. the implications of the CAPM are no longer useful.
HD EDU
8
Q22. One of the assumptions of the CAPM is that investors exhibit myopic behavior. What does this mean? A. They plan for one identical holding period. B. They are price takers who can't affect market prices through their trades. C. They are mean-variance optimizers. D. They have the same economic view of the world. E. They pay no taxes or transactions costs. Q23. The amount that an investor allocates to the market portfolio is negatively related to I) the expected return on the market portfolio. II) the investor's risk aversion coefficient. III) the risk-free rate of return. IV) the variance of the market portfolio. A. I and II. B. II and III. C. II and IV. D. II, III, and IV. E. I, III, and IV. Q24. An investor will take as large a position as possible when an equilibrium-price relationship is violated. This is an example of A. a dominance argument. B. the mean-variance efficiency frontier. C. a risk-free arbitrage. D. the capital asset pricing model. Q25. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 18%. The standard deviation on the factor portfolio is 16%. The beta of the well-diversified portfolio is approximately A. 0.80. B. 1.13. C. 1.25. D. 1.56.
HD EDU
9
Q26. Consider the single-factor APT. Stocks A and B have expected returns of 15% and 18%, respectively. The risk-free rate of return is 6%. Stock B has a beta of 1.0. If arbitrage opportunities are ruled out, stock A has a beta of A. 0.67. B. 1.00. C. 1.30. D. 1.69. E. 0.75. Q27. Consider the multifactor APT with two factors. The risk premiums on the factor 1 and factor 2 portfolios are 5% and 6%, respectively. Stock A has a beta of 1.2 on factor-1, and a beta of 0.7 on factor-2. The expected return on stock A is 17%. If no arbitrage opportunities exist, the risk-free rate of return is A. 6.0%. B. 6.5%. C. 6.8%. D. 7.4%. Q28. Consider the multifactor APT. There are two independent economic factors, F1 and F2. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios: Portfolio Beta on F1 Beta on F2 Expected Return A 1 2 19% B 2 0 12% Assuming no arbitrage opportunities exist, the risk premium on the factor F1 portfolio should be A. 3%. B. 4%. C. 5%. D. 6%. Q29. A well-diversified portfolio is defined as A.one that is diversified over a large enough number of securities that the nonsystematic variance is essentially zero. B. one that contains securities from at least three different industry sectors. C. a portfolio whose factor beta equals 1.0. D. a portfolio that is equally weighted.
HD EDU
10
Q30. Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 6%, the risk premium on the first factor portfolio is 4%, and the risk premium on the second factor portfolio is 3%. If portfolio A has a beta of 1.2 on the first factor and .8 on the second factor, what is its expected return? A. 7.0% B. 8.0% C. 9.2% D. 13.0% E. 13.2% Q31. As diversification increases, the total variance of a portfolio approaches A. 0. B. 1. C. the variance of the market portfolio. D. infinity. E. None of the options are correct. Q32. Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A. the α of the asset. B. the β of the asset. C. the σ of the asset. D. the δ of the asset.
HD EDU
11
答案 Q1 A Q2 D Q3 C = !" + #" Q4 D 题干说 do not resemble a single-index structure, 即使用 Markowitz 模型时需要用到的
参数数量为： 1 个 risk-free rate n 个 sample means n 个 sample variances (%!&%)! 个 sample covariances Q5 B 题干说 resemble a single-index structure, 即使用 SIM 模型时需要用到的参数数量为： ( , ()), )! 各一个 n 个 sample means n 个 sample variances n 个 Beta Q6 C 第一步：正确列出 SIM 公式 = + ) + * 注意 表示的是 Excess Return，即 需要扣掉 risk-free rate * 代表着 error term，如果题目没有明说，一般可以默认为 0 第二步：正确代入 SIM公式，求解 0.11 = 0 + × (0.16 − 0.05) + 0 解出β = 1 Q7 C 第一步：从五个和 beta相关的公式中，找出正确的公式 ! = !+! + ,! 由于题目说 well-diversified portfolio，因此 ,! = 0 (因为 unsystematic risk 都被分散掉了，木得了) 第二步：正确代入公式，求解 0.2! = ! × 0.16! + 0 得出 = 1.25 Q8 C 第一步：从五个和 beta相关的公式中，找出正确的公式 ! = !+!!
HD EDU
12
第二步：从题干中找到正确数据
注意，题干中的 R2A 其实指的是 r-squared，并不是指 return，如果你把这个数据当做return 使用，这道题就解不出来了。所以这道题是个很坑的题型，条件给的不明不白
的。
另外还有一个坑点，就是题目给你的!是已经平方了的，不需要再平方一次 ! = 0.25 ) = 0.25
那么，公式中所需要的 beta 哪里来？ Beta 在题干中的 Single Index Model 公式中暗暗的告诉你了，它是等式的斜率 = 0.9
第三步：正确代入公式，求解 0.25 = 0.9! × 0.25!!
解出 = 0.45
注意，如果你算出的答案是 0.2025，这个是 variance，而不是 standard deviation Q9 B 第一步：从五个和 beta相关的公式中，找出正确的公式 F* , -G = *-)!
第二步：从题干中找到正确数据 . = 0.5 / = 1.3 ) = 0.25
第三步：正确代入公式，求解(, ) (., /) = 0.5 × 1.3 × 0.25! = 0.040625 Q10 C Q11 B Q12 D Q13 A Q14 D Q15 B 第一步：用 CAPM公式算出 equilibrium 状态下的 () :() = ( + F+ − (G = 0.04 + 1.3 × (0.115 − 0.04) = 0.1375 第二步：那 CAPM算出的 () 和题目告诉你的 your opinion 比较 () = 0.1375 > 0.13 你可以计算通过 alpha，来判断它是高估了还是低估了
HD EDU
13
= 0.13 − 0.1375 = −0.0075 < 0 → 如果弄不清楚这个逻辑，可以直接代入 Excel 计算器，专门有一页是给这个题的 Q16 A 原理同 15 题 Q17 B 原理同 15 题，建议使用 Excel 计算器的模板 Overpriced 和 sell 是绑定的，所以他们必须出现在一个选项中 Under-priced 和 buy 是绑定的 Q18 D 把 = 0 代入 CAPM 的公式，就能得出回报率等于( Q19 B Security Market Line 是 CAPM 等式的那条直线 Overpriced 代表着 negative alpha，回报率低于 CAPM，因此在 SML 下方 Underpriced 代表着 positive alpha，回报率高于 CAPM，因此在 SML 上方 你看，很绕吧 Q20 D CAPM 的一大假设就是没有 tax，所以 C 和 E 不能选 不要一看到这种题就选最长的那个选项，可能有坑 Q21 C 这题的 C 选项就是 CAPM 的一个假设，不需要真的理解，记忆一下即可 一般而言，CAPM 假设所有投资人都有一个 certain investment horizon 但是这不是必须的，只要投资人的 liquidity needs are not priced，CAPM 仍然成立 Q22 A CAPM 假设，所有投资人都只关注一个投资期限内的事情，所以他们都有 the same holding period Q23 D 这道题考察的是这个公式（一般不需要计算） = ()) − ()! 这个公式是计算 y，即分配多少比例的资金到 risky assets 1-y 为分配到 risk-free assets 的资金比例 通过观察公式，你会发现：
§ y 和 ()) 成正比
§ y 和 , )! , ( 成反比 Q24 C 这题是不太常见的概念题，万一考到了，失分率很高 什么是 equilibrium-price relationship is violated?
即，CAPM 估计出来的 return，和实际上的 return 不付了，会有 overpriced 和 underpriced 情况。这时，有些人就可以采取 risk-free arbitrage（无风险套利）的方式，
从差价中获利
HD EDU
14
Q25 B one-factor APT 就是 Single Index Model
大家看到 APT (Arbitrage Pricing Theory) 这个术语不要害怕，它在我们的题目中，基本
就是只是一个装饰作用，没有啥实际意义，我们该用什么公式还是用什么公式
找出正确的公式 ! = !+! + ,!
和这份练习题中第七题的做法一样 Q26 E 第一步：找到 single-factor APT 公式 = + ## 第二步：分别列出 stock A 和 stock B 的等式 : 15%− 6% = 0 + . × # : 18%− 6% = 0 + 1 × # 第三步：解方程得出结果 # = 12% . = 0.75 Q27 C 第一步：我们先找到multifactor APT 的公式 = + ## + !! +⋯+ %% 遇到这种题，题目给我们什么，我们就代入什么 第二步：整理条件 # = 1.2, # = 5% ! = 0.7, ! = 6% 由于 no arbitrage opportunities exist, = 0 第三步：代入公式 = 0 + 1.2 × 5%+ 0.7 × 6% 得出 = 10.2%
第四步：不要忘记第三步得出来的 R 是 Excess Return，为了求出 risk-free rate，你
要加回 stock expected return = () − ( 10.2% = 17%− (
得出( = 6.8% Q28 A 第一步：我们先找到multifactor APT 的公式 = + ## + !! +⋯+ %% 第二步：代入公式（这题因为有两个 portfolio A 和 B，所以我们要代入两次） : 19% − 6% = 0 + 1 × # + 2 × !
HD EDU
15
: 12% − 6% = 0 + 2 × # + 0 × !
第三步：解方程 # = 3% Q29 A Q30 E 第一步：我们先找到multifactor APT 的公式 = + ## + !! +⋯+ %% 第二步：代入公式 = 0 + 1.2 × 4%+ 0.8 × 3% = 7.2%
第三步：千万不要忘记，公式求出来的是 Excess Return，你需要加回 () = + ( = 7.2% + 6% = 13.2% Q31 C Q32 B 题干中说的 Regression line 即 Security Characteristic Line (SCL)，也是 SIM Model 的回
归直线，它的斜率为 beta ，截距为 alpha = + ## =实际回报率− CAPM 回报率
