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LOS g: Explain the market model, and state and interpret the market model’s predictions with respect to asset returns, variances, and covariances. ffice ffice" />
Q1. The single-factor market model predicts that the covariance between two assets (asset i and asset j) is equal to:
A) the beta of i times the beta of j.
B) the beta of i times the beta of j times the variance of the market portfolio.
C) the beta of i times the beta of j divided by the standard deviation of the market portfolio.
Correct answer is B)
One of the predictions of the single-factor market model is that Cov(Ri,Rj) = bibjsM2. In other words, the covariance between two assets is related to the betas of the two assets and the variance of the market portfolio.
Q2. The single-factor market model predicts that the systematic portion of the variance of an asset’s return is equal to the:
A) square of the asset's beta times the variance of the market portfolio.
B) covariance between the asset's returns and the market returns.
C) asset's beta.
Correct answer is A)
One of the predictions of the single-factor market model is that Var(Ri) = bi2sM2 + sei2. In other words, there are two components to the variance of the returns on asset i: a systematic component related to the asset’s beta (bi2sM2) and an unsystematic component related to firm-specific surprises (sei2).
Q3. Joseph Capital Management is considering implementing a mean-variance optimization model as part of their portfolio management process, however, the firm’s investment committee is unsure whether the model should use historical estimates or market model estimates for the inputs to the model. Joseph’s Senior Portfolio Manager, Travis Palmer, puts together a memo to the committee contrasting the two methods of calculating inputs. The memo includes the following points:
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Point 1: |
Using the historical estimate is far simpler and involves fewer computations than the market model method. |
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Point 2: |
The use of market model estimates implicitly assumes that the market itself is mean-variance efficient. |
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Point 3: |
Both the use of market model estimates and historical estimates rely on historical data to some degree. |
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Point 4: |
One of the problems with using market model estimates for estimating returns is that the market model implicitly assumes the market index is representative of the entire market. |
After reviewing Palmer’s memo, Joseph’s investment committee would be CORRECT to:
A) agree with Point 3, but disagree with Points 2 and 4.
B) agree with Points 1 and 4, but disagree with Point 3.
C) agree with Points 2 and 3, but disagree with Point 1.
Correct answer is C)
The committee should disagree with Point 1. The use of historical estimates involves computing the covariance of between each stock in a portfolio with every other stock in the portfolio, while the use of the market model only relies on computing the covariance of each stock with the market index, resulting in fewer computations.
The committee should agree with Points 2, 3, and 4. The market model regresses historical returns of a stock/portfolio with the corresponding returns of a market index and implicitly assumes that historical relationships are reflective of future relationships. The market model also implicitly assumes that the market itself is mean-variance efficient and that the index used for market returns is representative of the entire market.
Q4. Which of the following is NOT an assumption necessary to derive the single-factor market model? The:
A) firm-specific surprises are uncorrelated across assets.
B) expected value of firm-specific surprises is zero.
C) market portfolio is the tangency portfolio.
Correct answer is C)
The result that the market portfolio is the tangency portfolio is a prediction of the CAPM model, not the market model. The market model assumes that there are two sources of risk, unanticipated macroeconomic events and firm-specific events. We use the return on the market portfolio as a proxy for the macroeconomic factor and assume all stocks have varying degrees of sensitivity to this macro factor. In addition, each stock’s returns are uniquely affected by firm-specific events uncorrelated across stocks and with the macro events. The remaining choices are the assumptions necessary to derive the single-factor market model.
Q5. Carl Dursham recently earned the CFA designation and has just been hired by Quad Cities Consultants, which is a money management firm for private, high net worth clients. Quad Cities Consultants has just assigned Dursham his first client. The client’s name is Sally Litner. Litner has just received a multi-million dollar inheritance consisting of certificates of deposit that are about to mature. She is only 30 years old and recognizes that she should probably invest in assets like stocks that have a higher risk and return. Litner is a high school mathematics teacher and has an aptitude for formulas and equations, but she has never applied it to investments. Litner feels that Dursham will probably do a good job for her, but she wants him to explain to her how he will approach creating her portfolio.
When Dursham and Litner first meet, Litner says that she has heard of a stock that has done very well and is expected to continue to experience dramatic increases in the future. The name of the stock is IntMarket Corporation, which is a company that facilitates commerce on the Internet, and its recent return and standard deviation are 24% and 60% respectively. She asks Dursham if he thinks she should invest 100% of her portfolio in IntMarket Corporation. Dursham looks up the beta of IntMarket and finds that it is 1.6. He says that IntMarket Corporation might be a good first position, and he says that a good second position might be Granite Bank. The return and standard deviation of the bank stock is 12% and 30% respectively. Its beta is 0.9. The covariance of the bank stock with IntMarket Corporation is 576.
Dursham explains how diversification can lower risk and computes the statistics for portfolios that have various weights in IntMarket and Granite Bank. Litner is intrigued by Dursham’s demonstration concerning the effects of diversification. She asks about the effect of adding a third asset to the portfolio. To help illustrate the benefits of diversification further, Dursham chooses Capital Commodities Mutual fund, which invests in assets related to the production of raw materials and other commodities. The recent return and standard deviation of Capital Commodities has been 8% and 18% respectfully. The correlation of Capital Commodities with the other two stocks is effectively zero. Dursham computes the return and standard deviation of a portfolio consisting of 50% IntMarket, 30% Granite Bank, and 20% Capital Commodities.
Dursham takes time to explain the principle and assumptions behind mean-variance analysis and why it is important. He says the four underlying principals are i) investors are risk averse, ii) necessary statistics of returns can be calculated, iii) the returns have a normal distribution, and iv) the tax rate is fixed at some positive rate like 28%. During the discussion, Litner says she thinks the three stocks IntMarket Corporation, Granite Bank, and Capital Commodities may be all she needs in her portfolio. She asks Dursham to choose the weights for those three stocks that will minimize the variance and let that be her portfolio. If they desire a higher return, she adds using terms she has just learned, they can just leverage up that portfolio.
If the recent return of the market was 14%, and the risk-free rate is 3%, using the market model what was the alpha of IntMarket Corporation?
A) +4.4%.
B) +1.6%.
C) +1.4%.
Correct answer is B)
When using the market model, alpha is the difference between the realized return and that predicted by the product of the beta and the market return. The risk-free rate is not a part of the computation. The recent return of IntMarket was 24%. The predicted return based upon a beta equal to 1.6 and a market return of 14% is the product of these values: 22.4%. Thus the alpha is 24% ? 22.4% = 1.6%. (Study Session 18, LOS 66.g)
Q6. Of Dursham’s list of the assumptions underlying mean-variance analysis, which of the following is the least likely to be one of the generally accepted assumptions?
A) Necessary statistics of returns can be calculated.
B) The tax rate is fixed at some positive rate like 28%.
C) The returns have a normal distribution.
Correct answer is B)
The assumption should be that there are no taxes and that there are no transactions costs. (Study Session 18, LOS 66.g)
Q7. A portfolio invested 50% in IntMarket and 50% in Granite Bank would have an expected return:
A) lower than that of Granite Bank and a higher standard deviation than that of Granite Bank.
B) greater than that of Granite Bank and a lower standard deviation than that of Granite Bank.
C) greater than that of Granite Bank and a higher standard deviation than that of Granite Bank.
Correct answer is C)
The average will obviously be higher than that of Granite Bank. The average is 18% = (0.5 × 24%) + (0.5 × 12%). The variance of the 50/50 portfolio is 1413 = (0.5 × 0.5 × 60 × 60) + (0.5 × 0.5 × 30 × 30) + (2 × 0.5 × 0.5 × 576); the standard deviation is about 37.6%, which is greater than the 30% standard deviation of Granite Bank. (Study Session 18, LOS 66.a)
Q8. The portfolio that Dursham recommends using the two stocks and the mutual fund would have a standard deviation that is closest in value to:
A) 36.0%.
B) 34.2%.
C) 36.7%.
Correct answer is B)
Since the return of Capital Commodities is uncorrelated with the returns of the two stocks, the variance of the portfolio is 1166.8 = (0.5 × 0.5 × 60 × 60) + (0.3 × 0.3 × 30 × 30) + (0.2 × 0.2 × 18 × 18) + (2 × 0.5 × 0.3 × 576) The standard deviation is √34.2%. (Study Session 18, LOS 66.a)
Q9. When compared to all other possible portfolios, the portfolio that has the smallest variance, which Litner requests, would have a Sharpe ratio that:
A) may or may not be the highest of all possible portfolios; there is no general rule.
B) is the highest of all possible portfolios.
C) could not be the highest of all possible portfolios.
Correct answer is C)
Minimizing the variance does not produce the portfolio with the highest Sharpe ratio. A point along the efficient frontier above the minimum variance portfolio will have both a higher return and standard deviation, but it will have a higher Sharpe ratio. (Study Session 18, LOS 66.b)
Q10. The portfolio that Litner requests, the one that has the smallest variance of all possible portfolios, would best be described as the:
A) market portfolio.
B) global minimum variance portfolio.
C) efficient variance portfolio.
Correct answer is B)
This is the definition of the global minimum variance portfolio. (Study Session 18, LOS 66.b)
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发表于 2009-4-2 12:55
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