bapswarrior

Michael Carr and Karen Bocock are analysts for the Portfolio Optimization Group. Carr and Bocock are discussing the firm’s mean variance optimization model for equity holdings and the pros and cons of using market model estimates or historical estimates as inputs to the model.

• Carr states, “One of the main concerns I have about the model is that whether we are using market model estimates or historical estimates, we are implicitly assuming that the historical relationship between the stock and the market is indicative of the future.”
• Bocock replies, “One of the main advantages to using the market model estimates is the fact that there are fewer parameters to estimate.”

With regard to their statements about methods for computing the inputs for a mean-optimization model:

A) both are incorrect.

B) only one is correct.

C) both are correct.

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Carr’s statement is correct. Using historical estimates and market model estimates both involve the implicit assumption that the historical relationship between a stock and the market is indicative of the future relationship. The historical estimate method uses direct historical means, variances, and correlations as inputs to the model. The market model method regresses historical returns against returns for the market and assumes that returns for each asset are correlated with returns to the market. Since both methods use some form of historical data, both assume that history is indicative of the future.
Bocock is also correct. The historical estimate method requires a large number of estimates, especially for computing the covariances between every stock in a portfolio. The market model estimate method simplifies the process significantly (resulting in fewer parameters) since all stock returns are assumed to be correlated with the market.

bapswarrior

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) +1.4%.

C) +1.6%.

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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 60.g)

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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.

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The assumption should be that there are no taxes and that there are no transactions costs. (Study Session 18, LOS 60.g)

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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.

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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 60.a)

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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%.

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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 60.a)

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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.

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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 60.b)

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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.

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This is the definition of the global minimum variance portfolio. (Study Session 18, LOS 60.b)

bapswarrior

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) market portfolio is the tangency portfolio.

C) expected value of firm-specific surprises is zero.

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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.

bapswarrior

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:

Point 1:	Using the historical estimate is far simpler and involves fewer computations than the market model method.
Point 2:	The use of market model estimates implicitly assumes that the market itself is mean-variance efficient.
Point 3:	Both the use of market model estimates and historical estimates rely on historical data to some degree.
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 2 and 3, but disagree with Point 1.

C) agree with Points 1 and 4, but disagree with Point 3.

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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.

bapswarrior

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 divided by the standard deviation of the market portfolio.

C) the beta of i times the beta of j times the variance of the market portfolio.

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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.

bapswarrior

Jim Williams, CFA, manages individual investors' portfolios for Clarence Farlow Associates. Clarence Farlow Jr., CEO of Clarence Farlow Associates, is looking for some new investment ideas. Farlow is obsessive about value, however, and never buys stocks that look expensive. He has assigned Williams to assess the investment merits of several securities. Specifically, Williams has collected the following data for three possible investments.

Stock	Price Today	Forecasted Price*	Dividend	Beta
Alpha	25	31	2	1.6
Omega	105	110	1	1.2
Lambda	10	10.80	0	0.5
*Forecast Price = expected price one year from today.

Williams plans to value the three securities using the security market line, and has assembled the following information for use in his valuation:

• Securities markets are in equilibrium.
• The prime interest rate is expected to rise by about 2% in the year ahead.
• Inflation is expected to be 1% over the upcoming year.
• The expected return on the market is 12% and the risk-free rate is 4%.
• The market portfolio's standard deviation is 40%.

Williams eventually decides to construct a portfolio consisting of 10 shares of Alpha, 2 shares of Omega, and 20 shares of Lambda.Based on valuation via the SML, which of the following statements is most accurate?

A) Williams should buy Alpha but not Omega.

B) Both Alpha and Omega are overpriced.

C) Neither Alpha nor Lambda is correctly priced.

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SML valuation hinges on the relationship between the forecasted return (FR) and expected return (ER).

FR = (ending price − beginning price + dividends) / beginning price.

ER = RFR + β (RMkt − RFR).

• For Alpha: FR = (31 − 25 + 2) / 25 = 32%, ER = 4 + 1.6(12 − 4) = 16.8%.
  Since FR > ER, stock is underpriced.
  

• For Omega: FR = (110 − 105 + 1) / 105 = 5.7%, ER = 4 + 1.2(12 − 4) = 13.6%.
  Since FR < ER, stock is overpriced.
  

• For Lambda: FR = (10.8 − 10 + 0) / 10 = 8%, ER = 4 + 0.5(12 − 4) = 8%.
  Since FR = ER, stock is correctly priced.

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The covariance of Omega with the market portfolio is closest to:

A) 0.576.

B) 0.480.

C) 0.192.

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Beta = covi,M / market portfolio variance, so covi,M = 1.2 × (0.4)2 = 0.192.

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Williams calculates the required return for Omega. According to the capital asset pricing model (CAPM) the required return is closest to:

A) 12.0%.

B) 13.6%.

C) 5.7%.

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The required return (RR) uses the equation of the SML: risk-free rate + Beta × (expected market rate − risk-free rate). For Omega, RR = 4 + 1.2(12 − 4) = 13.6%. The expected return of 5.7% need not be the same as the required return under CAPM.

bapswarrior

The capital market line:

A) helps determine asset allocation.

B) uses nondiversifiable risk.

C) has a slope equal to the market risk premium.

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The purpose of the CML is to determine the percentages allocated to the market portfolio and the risk-free asset. Both remaining answers reflect characteristics of the security market line.

bapswarrior

Which of the following statements about using the capital asset pricing model (CAPM) to value stocks is least accurate?

A) The CAPM reflects unsystematic risk using standard deviation.

B) If the CAPM expected return is too low, then the asset’s price is too high.

C) The model reflects how market forces restore investment prices to equilibrium levels.

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The capital asset pricing model assumes all investors hold the market portfolio, and as such unsystematic risk, or risk not related to the market, does not matter. Thus, the CAPM does not reflect unsystematic risk and does not rely on standard deviation as the measure of risk but instead uses beta as the measure of risk. The remaining statements are accurate.

bapswarrior

Glimmer Glass has a correlation of 0.67 with the market portfolio, a variance of 23%, and an expected return of 14%. The market portfolio has an expected return of 11% and a variance of 13%. Glimmer stock is approximately:

A) 11% less volatile than the average stock.

B) 4% more volatile than the average stock.

C) 19% more volatile than the average stock.

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Beta is equal to the covariance divided by the market portfolio variance, or the product of the correlation and the ratio of the stock standard deviation to the market standard deviation. To derive the standard deviation, we take the square root of the variance. So beta = 0.67 × 0.479583 / 0.360555 = 0.891183. Glimmer shares are about 11% less volatile than the average stock.

bapswarrior

Kaskin, Inc., stock has a beta of 1.2 and Quinn, Inc., stock has a beta of 0.6. Which of the following statements is most accurate?

A) The expected rate of return will be higher for the stock of Kaskin, Inc., than that of Quinn, Inc.

B) The stock of Kaskin, Inc., has more total risk than Quinn, Inc.

C) The stock of Quinn, Inc., has more systematic risk than that of Kaskin, Inc.

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Beta is a measure of systematic risk. Since only systematic risk is rewarded, it is safe to conclude that the expected return will be higher for Kaskin’s stock than for Quinn’s stock.