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Corporate Finance, 3e (Berk/DeMarzo) Chapter 11 Optimal Portfolio Choice and the Capital Asset Pricing Model 11.1 The Expected Return of a Portfolio 1) Which of the following statements i... s FALSE? A) Without trading, the portfolio weights will decrease for the stocks in the portfolio whose returns are above the overall portfolio return. B) The expected return of a portfolio is simply the weighted average of the expected returns of the investments within the portfolio. C) Portfolio weights add up to 1 so that they represent the way we have divided our money between the different individual investments in the portfolio. D) A portfolio weight is the fraction of the total investment in the portfolio held in an individual investment in the portfolio. Explanation: A) Without trading, the portfolio weights will increase for the stocks in the portfolio whose returns are above the overall portfolio return. Section: 11.1 The Expected Return of a Portfolio Skill: Conceptual 2) Which of the following equations is INCORRECT? A) xi = B) Rp = Σi xiRi C) Rp = x1R1 + x2R2 + ... + xnRn D) E[Rp] = E[Σi xiRi] Explanation: A) xi = Section: 11.1 The Expected Return of a Portfolio Skill: Conceptual Use the information for the question(s) below. Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $50 per share, 200 shares of Lowes (LOW) at $30 per share, and 100 shares of Ball Corporation (BLL) at $40 per share. 3) The weight on Abbott Labs in your portfolio is: A) 50% B) 40% C) 30% D) 20% Explanation: A) Value of portfolio = 200 × $50 + 200 × $30 + 100 × $40 = $20,000 xi = value of security/value of portfolio = (200 × $50)/$20000 = .50 or 50% Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 4) The weight on Lowes in your portfolio is: A) 40% B) 20% C) 50% D) 30% Explanation: D) Value of portfolio = 200 × $50 + 200 × $30 + 100 × $40 = $20,000 xi = value of security/value of portfolio = (200 × $30)/$20000 = .30 or 30% Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 5) The weight on Ball Corporation in your portfolio is: A) 50% B) 40% C) 20% D) 30% Explanation: C) Value of portfolio = 200 × $50 + 200 × $30 + 100 × $40 = $20,000 xi = value of security/value of portfolio = (100 × $40)/$20000 = .20 or 20% Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 6) Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs has a return of -10%. The return on your portfolio over the year is: A) 0% B) 7.5% C) 3.5% D) 5.0% Explanation: C) | Stock | Weight | Return | W × R | ABT | 0.5 | -0.1 | -0.05 | LOW | 0.3 | 0.2 | 0.06 | BLL | 0.2 | 0.125 | 0.025 | | | Rp = | 0.035 Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 7) Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs has a return of -10%. The value of your portfolio over the year is: A) $21,000 B) $20,000 C) $20,700 D) $21,500 Explanation: C) | Stock | Weight | Return | W × R | ABT | 0.5 | -0.1 | -0.05 | LOW | 0.3 | 0.2 | 0.06 | BLL | 0.2 | 0.125 | 0.025 | | | Rp = | 0.035 Value of portfolio = 20000(1 + .035) = 20700 Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 8) Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs has a return of -10%. The weight on Ball Corporation in your portfolio after one year is closest to: A) 20.0% B) 12.5% C) 20.7% D) 21.7% Explanation: D) | Stock | Weight | Return | W × R | ABT | 0.5 | -0.1 | -0.05 | LOW | 0.3 | 0.2 | 0.06 | BLL | 0.2 | 0.125 | 0.025 | | | Rp = | 0.035 Value of portfolio = 20000(1 + .035) = 20700 Value of BLL = $4000(1 + .125) = $4500 Weight for BLL = 4500/20700 = 0.217391 Diff: 3 Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 9) Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs has a return of -10%. The weight on Abbott Labs in your portfolio after one year is closest to: A) -10.0% B) 43.5% C) 45.0% D) 50.0% Explanation: B) | Stock | Weight | Return | W × R | ABT | 0.5 | -0.1 | -0.05 | LOW | 0.3 | 0.2 | 0.06 | BLL | 0.2 | 0.125 | 0.025 | | | Rp = | 0.035 Value of portfolio = 20000(1 + .035) = 20700 Value of ABT = $10000(1 + -.10) = $9000 Weight for ABT = 9000/20700 = 0.434783 Diff: 3 Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 10) Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs has a return of -10%. The weight on Lowes in your portfolio after one year is closest to: A) 20.0% B) 34.8% C) 30.0% D) 36.0% Explanation: B) | Stock | Weight | Return | W × R | ABT | 0.5 | -0.1 | -0.05 | LOW | 0.3 | 0.2 | 0.06 | BLL | 0.2 | 0.125 | 0.025 | | | Rp = | 0.035 Value of portfolio = 20000(1 + .035) = 20700 Value of LOW = $6000(1 + .20) = $7200 Weight for LOW = 7200/20700 = 0.347826 Diff: 3 Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 11) Suppose you invest $15,000 in Merck stock and $25,000 in Home Depot stock. You expect a return of 16% for Merck and 12% for Home Depot. What is the expected return on your portfolio? A) 13.50% B) 14.00% C) 13.75% D) 14.50% Explanation: A) = (15,000/40,000)(.16) + (25,000/40,000)(.12) = .135 Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 12) Suppose you invest $15,000 in Merck stock and $25,000 in Home Depot stock. You receive an actual return of -8% for Merck and 12% for Home Depot. What is the actual return on your portfolio? A) 4.50% B) 4.00% C) 10.00% D) 2.00% Explanation: A) = (15,000/40,000)(-0.08) + (25,000/40,000)(.12) = .045 Section: 11.1 The Expected Return of a Portfolio Skill: Analytical 11.2 The Volatility of a Two-Stock Portfolio 1) Which of the following statements is FALSE? A) The covariance and correlation allow us to measure the co-movement of returns. B) Correlation is the expected product of the deviations of two returns. C) Because the prices of the stocks do not move identically, some of the risk is averaged out in a portfolio. D) The amount of risk that is eliminated in a portfolio depends on the degree to which the stocks face common risks and their prices move together. Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Conceptual 2) Which of the following statements is FALSE? A) While the sign of the correlation is easy to interpret, its magnitude is not. B) Independent risks are uncorrelated. C) When the covariance equals 0, the returns are uncorrelated. D) To find the risk of a portfolio, we need to know more than the risk and return of the component stocks; we need to know the degree to which the stocks' returns move together. Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Conceptual 3) Which of the following statements is FALSE? A) Dividing the covariance by the volatilities ensures that correlation is always between -1 and +1. B) Volatility is the square root of variance. C) The closer the correlation is to 0, the more the returns tend to move together as a result of common risk. D) If two stocks move together, their returns will tend to be above or below average at the same time, and the covariance will be positive. Explanation: C) The closer the correlation is to 1, the more the returns tend to move together as a result of common risk. Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Conceptual 4) Which of the following statements is FALSE? A) Stock returns will tend to move together if they are affect similarly by economic events. B) Stocks in the same industry tend to have more highly correlated returns than stocks in different industries. C) Almost all of the correlations between stocks are negative, illustrating the general tendency of stocks to move together. D) With a positive amount invest in each stock, the more the stocks move together and the higher their covariance or correlation, the more variable the portfolio will be. Explanation: C) Almost all of the correlations between stocks are positive, illustrating the general tendency of stocks to move together. Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Conceptual 5) Which of the following statements is FALSE? A) A stock's return is perfectly positively correlated with itself. B) When the covariance equals 0, the stocks have no tendency to move either together or in opposition of one another. C) The closer the correlation is to -1, the more the returns tend to move in opposite directions. D) The variance of a portfolio depends only on the variance of the individual stocks. Explanation: D) The variance of a portfolio depends on the variance and correlations of the individual stocks. Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Conceptual 6) Which of the following statements is FALSE? A) If two stocks move in opposite directions, one will tend to be above average when to other is below average, and the covariance will be negative. B) The correlation between two stocks has the same sign as their covariance, so it has a similar interpretation. C) The covariance of a stock with itself is simply its variance. D) The covariance allows us to gauge the strength of the relationship between stocks. Explanation: D) The correlation allows us to gauge the strength of the relationship between stocks. Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Conceptual 7) Which of the following equations is INCORRECT? A) Cov(Ri,Rj) = Σ(Ri - Ri)(Rj - Rj) B) Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) C) Corr(Ri,Rj) = D) Cov(Ri,Rj) = E[(Ri - E[Ri])(Rj - E[Rj])] Explanation: C) Corr(Ri,Rj) = Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical Use the table for the question(s) below. Consider the following returns: | Year End | Stock X Realized Return | Stock Y Realized Return | Stock Z Realized Return | 2004 | 20.1% | -14.6% | 0.2% | 2005 | 72.7% | 4.3% | -3.2% | 2006 | -25.7% | -58.1% | -27.0% | 2007 | 56.9% | 71.1% | 27.9% | 2008 | 6.7% | 17.3% | -5.1% | 2009 | 17.9% | 0.9% | -11.3% 8) The covariance between Stock X's and Stock Y's returns is closest to: A) 0.10 B) 0.29 C) 0.12 D) 0.69 Explanation: A) | Year End | Stock X Realized Return | Stock Y Realized Return | Stock X Deviation (RL - RL) | Stock Y Deviation (RH - RH) | (RL - RL) × (RH - RH) | 2004 | 20.1% | -14.6% | -4.7% | -18.1% | 0.00843889 | 2005 | 72.7% | 4.3% | 47.9% | 0.8% | 0.00391456 | 2006 | -25.7% | -58.1% | -50.5% | -61.6% | 0.31079056 | 2007 | 56.9% | 71.1% | 32.1% | 67.6% | 0.21727489 | 2008 | 6.7% | 17.3% | -18.1% | 13.8% | -0.02496211 | 2009 | 17.9% | 0.9% | -6.9% | -2.6% | 0.00177389 | average = | 24.8% | 3.5% | | | | | | | | | | | | Variance = | 0.125447467 | 0.177795367 | | | | Stdev = | 0.354185639 | 0.421657879 | | | | | | | | | | | | Covariance = | 0.103446133 | | | | | Correlation = | 0.692664763 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 9) The Volatility on Stock X's returns is closest to: A) 35% B) 10% C) 13% D) 42% Explanation: A) | Year End | Stock X Realized Return | Stock Y Realized Return | Stock X Deviation (RL - RL) | Stock Y Deviation (RH - RH) | (RL - RL) × (RH - RH) | 2004 | 20.1% | -14.6% | -4.7% | -18.1% | 0.00843889 | 2005 | 72.7% | 4.3% | 47.9% | 0.8% | 0.00391456 | 2006 | -25.7% | -58.1% | -50.5% | -61.6% | 0.31079056 | 2007 | 56.9% | 71.1% | 32.1% | 67.6% | 0.21727489 | 2008 | 6.7% | 17.3% | -18.1% | 13.8% | -0.02496211 | 2009 | 17.9% | 0.9% | -6.9% | -2.6% | 0.00177389 | average = | 24.8% | 3.5% | | | | | | | | | | | | Variance = | 0.125447467 | 0.177795367 | | | | Stdev = | 0.354185639 | 0.421657879 | | | | | | | | | | | | Covariance = | 0.103446133 | | | | | Correlation = | 0.692664763 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 10) The Volatility on Stock Y's returns is closest to: A) 35% B) 31% C) 42% D) 18% Explanation: C) | Year End | Stock X Realized Return | Stock Y Realized Return | Stock X Deviation (RL - RL) | Stock Y Deviation (RH - RH) | (RL - RL) × (RH - RH) | 2004 | 20.1% | -14.6% | -4.7% | -18.1% | 0.00843889 | 2005 | 72.7% | 4.3% | 47.9% | 0.8% | 0.00391456 | 2006 | -25.7% | -58.1% | -50.5% | -61.6% | 0.31079056 | 2007 | 56.9% | 71.1% | 32.1% | 67.6% | 0.21727489 | 2008 | 6.7% | 17.3% | -18.1% | 13.8% | -0.02496211 | 2009 | 17.9% | 0.9% | -6.9% | -2.6% | 0.00177389 | average = | 24.8% | 3.5% | | | | | | | | | | | | Variance = | 0.125447467 | 0.177795367 | | | | Stdev = | 0.354185639 | 0.421657879 | | | | | | | | | | | | Covariance = | 0.103446133 | | | | | Correlation = | 0.692664763 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 11) The Correlation between Stock X's and Stock Y's returns is closest to: A) 0.58 B) 0.29 C) 0.69 D) 0.10 Explanation: C) | Year End | Stock X Realized Return | Stock Y Realized Return | Stock X Deviation (RL - RL) | Stock Y Deviation (RH - RH) | (RL - RL) × (RH - RH) | 2004 | 20.1% | -14.6% | -4.7% | -18.1% | 0.00843889 | 2005 | 72.7% | 4.3% | 47.9% | 0.8% | 0.00391456 | 2006 | -25.7% | -58.1% | -50.5% | -61.6% | 0.31079056 | 2007 | 56.9% | 71.1% | 32.1% | 67.6% | 0.21727489 | 2008 | 6.7% | 17.3% | -18.1% | 13.8% | -0.02496211 | 2009 | 17.9% | 0.9% | -6.9% | -2.6% | 0.00177389 | average = | 24.8% | 3.5% | | | | | | | | | | | | Variance = | 0.125447467 | 0.177795367 | | | | Stdev = | 0.354185639 | 0.421657879 | | | | | | | | | | | | Covariance = | 0.103446133 | | | | | Correlation = | 0.692664763 Diff: 3 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 12) The variance on a portfolio that is made up of equal investments in Stock X and Stock Y stock is closest to: A) 0.12 B) 0.10 C) 0.69 D) 0.29 Explanation: A) | Year End | Stock X Realized Return | Stock Y Realized Return | Stock X Deviation (RL - RL) | Stock Y Deviation (RH - RH) | (RL - RL) × (RH - RH) | 2004 | 20.1% | -14.6% | -4.7% | -18.1% | 0.00843889 | 2005 | 72.7% | 4.3% | 47.9% | 0.8% | 0.00391456 | 2006 | -25.7% | -58.1% | -50.5% | -61.6% | 0.31079056 | 2007 | 56.9% | 71.1% | 32.1% | 67.6% | 0.21727489 | 2008 | 6.7% | 17.3% | -18.1% | 13.8% | -0.02496211 | 2009 | 17.9% | 0.9% | -6.9% | -2.6% | 0.00177389 | average = | 24.8% | 3.5% | | | | | | | | | | | | Variance = | 0.125447467 | 0.177795367 | | | | Stdev = | 0.354185639 | 0.421657879 | | | | | | | | | | | | Covariance = | 0.103446133 | | | | | Correlation = | 0.692664763 Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) = (.50)2(0.125447467) + (.50)2(0.177795367) + 2(.5)(.5)(0.103446133) = 0.118913264 Diff: 3 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 13) The covariance between Stock X's and Stock Z's returns is closest to: A) 0.05 B) 0.06 C) 0.10 D) 0.71 Explanation: A) | Year End | Stock X Realized Return | Stock Z Realized Return | Stock X Deviation (RL - RL) | Stock Z Deviation (RI - RI) | (RL - RL) × (RI - RI) | 2004 | 20.1% | 0.2% | -4.7% | 3.3% | -0.00155542 | 2005 | 72.7% | -3.2% | 47.9% | -0.1% | -0.00048871 | 2006 | -25.7% | -27.0% | -50.5% | -23.9% | 0.12061406 | 2007 | 56.9% | 27.9% | 32.1% | 30.9% | 0.09943858 | 2008 | 6.7% | -5.1% | -18.1% | -2.0% | 0.00367960 | 2009 | 17.9% | -11.3% | -6.9% | -8.2% | 0.00565832 | average = | 24.8% | -3.1% | | | | | | | | | | | | Variance = | 0.125447467 | 0.032239975 | | | | Stdev = | 0.354185639 | 0.179554936 | | | | | | | | | | | | Covariance = | 0.045469287 | | | | | Correlation = | 0.714973344 | | | | | | | | | | | Var(Port) = | 0.062156504 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 14) The Correlation between Stock X's and Stock Z's returns is closest to: A) 0.71 B) 0.60 C) 0.62 D) 0.05 Explanation: A) | Year End | Stock X Realized Return | Stock Z Realized Return | Stock X Deviation (RL - RL) | Stock Z Deviation (RI - RI) | (RL - RL) × (RI - RI) | 2004 | 20.1% | 0.2% | -4.7% | 3.3% | -0.00155542 | 2005 | 72.7% | -3.2% | 47.9% | -0.1% | -0.00048871 | 2006 | -25.7% | -27.0% | -50.5% | -23.9% | 0.12061406 | 2007 | 56.9% | 27.9% | 32.1% | 30.9% | 0.09943858 | 2008 | 6.7% | -5.1% | -18.1% | -2.0% | 0.00367960 | 2009 | 17.9% | -11.3% | -6.9% | -8.2% | 0.00565832 | average = | 24.8% | -3.1% | | | | | | | | | | | | Variance = | 0.125447467 | 0.032239975 | | | | Stdev = | 0.354185639 | 0.179554936 | | | | | | | | | | | | Covariance = | 0.045469287 | | | | | Correlation = | 0.714973344 | | | | | | | | | | | Var(Port) = | 0.062156504 Diff: 3 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 15) The variance on a portfolio that is made up of equal investments in Stock X and Stock Z stock is closest to: A) 0.62 B) 0.05 C) 0.12 D) 0.06 Explanation: D) | Year End | Stock X Realized Return | Stock Z Realized Return | Stock X Deviation (RL - RL) | Stock Z Deviation (RI - RI) | (RL - RL) × (RI - RI) | 2004 | 20.1% | 0.2% | -4.7% | 3.3% | -0.00155542 | 2005 | 72.7% | -3.2% | 47.9% | -0.1% | -0.00048871 | 2006 | -25.7% | -27.0% | -50.5% | -23.9% | 0.12061406 | 2007 | 56.9% | 27.9% | 32.1% | 30.9% | 0.09943858 | 2008 | 6.7% | -5.1% | -18.1% | -2.0% | 0.00367960 | 2009 | 17.9% | -11.3% | -6.9% | -8.2% | 0.00565832 | average = | 24.8% | -3.1% | | | | | | | | | | | | Variance = | 0.125447467 | 0.032239975 | | | | Stdev = | 0.354185639 | 0.179554936 | | | | | | | | | | | | Covariance = | 0.045469287 | | | | | Correlation = | 0.714973344 | | | | | | | | | | | Var(Port) = | 0.062156504 Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) = (.50)2(0.125447467) + (.50)2(0.032239975 + 2(.5)(.5)(0.045469287) = 0.062156504 Diff: 3 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 16) The Volatility on Stock Z's returns is closest to: A) 3% B) 13% C) 16% D) 18% Explanation: D) | Year End | Stock X Realized Return | Stock Z Realized Return | Stock X Deviation (RL - RL) | Stock Z Deviation (RI - RI) | (RL - RL) × (RI - RI) | 2004 | 20.1% | 0.2% | -4.7% | 3.3% | -0.00155542 | 2005 | 72.7% | -3.2% | 47.9% | -0.1% | -0.00048871 | 2006 | -25.7% | -27.0% | -50.5% | -23.9% | 0.12061406 | 2007 | 56.9% | 27.9% | 32.1% | 30.9% | 0.09943858 | 2008 | 6.7% | -5.1% | -18.1% | -2.0% | 0.00367960 | 2009 | 17.9% | -11.3% | -6.9% | -8.2% | 0.00565832 | average= | 24.8% | -3.1% | | | | | | | | | | | | Variance = | 0.125447467 | 0.032239975 | | | | Stdev = | 0.354185639 | 0.179554936 | | | | | | | | | | | | Covariance = | 0.045469287 | | | | | Correlation = | 0.714973344 | | | | | | | | | | | Var(Port) = | 0.062156504 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical Use the table for the question(s) below. Consider the following covariances between securities: | | Duke | Microsoft | Wal-Mart | Duke | 0.0568 | -0.0193 | 0.0037 | Microsoft | -0.0193 | 0.2420 | 0.1277 | Wal-Mart | 0.0037 | 0.1277 | 0.1413 17) The variance on a portfolio that is made up of equal investments in Duke Energy and Microsoft stock is closest to: A) .065 B) 0.090 C) .149 D) -0.020 Explanation: A) Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) = (.50)2(0.0568) + (.50)2(0.2420) + 2(.5)(.5)(-0.0193) = 0.0651 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 18) The variance on a portfolio that is made up of a $6000 investments in Duke Energy and a $4000 investment in Wal-Mart stock is closest to: A) .050 B) .045 C) .051 D) -0.020 Explanation: B) Total invested = $6000 + $4000 = $10,000 XDuke = = .60 XWal-Mart = = .40 Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) = (.60)2(0.0568) + (.40)2(0.1413) + 2(.6)(.4)(0.0037) = 0.0449 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical Use the table for the question(s) below. Consider the following returns: | Year End | Stock X Realized Return | Stock Y Realized Return | Stock Z Realized Return | 2004 | 20.1% | -14.6% | 0.2% | 2005 | 72.7% | 4.3% | -3.2% | 2006 | -25.7% | -58.1% | -27.0% | 2007 | 56.9% | 71.1% | 27.9% | 2008 | 6.7% | 17.3% | -5.1% | 2009 | 17.9% | 0.9% | -11.3% 19) Calculate the covariance between Stock Y's and Stock Z's returns . Answer: | Year End | Stock Y Realized Return | Stock Z Realized Return | Stock Y Deviation (RH - RH) | Stock Z Deviation (RI - RI) | (RL - RL) × (RH - RI) | 2004 | -14.6% | 0.2% | -18.1% | 3.3% | -0.00602724 | 2005 | 4.3% | -3.2% | 0.8% | -0.1% | -0.00000833 | 2006 | -58.1% | -27.0% | -61.6% | -23.9% | 0.14718262 | 2007 | 71.1% | 27.9% | 67.6% | 30.9% | 0.20924394 | 2008 | 17.3% | -5.1% | 13.8% | -2.0% | -0.00281401 | 2009 | 0.9% | -11.3% | -2.6% | -8.2% | 0.00212874 | average = | 3.5% | -3.1% | | | | | | | | | | | | Variance = | 0.177795367 | 0.032239975 | | | | Stdev = | 0.421657879 | 0.179554936 | | | | | | | | | | | | Covariance = | 0.069941142 | | | | | Correlation = | 0.923794031 | | | | | | | | | | | Var(Port) = | 0.087479407 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 20) Calculate the correlation between Stock Y's and Stock Z's returns . Answer: | Year End | Stock Y Realized Return | Stock Z Realized Return | Stock Y Deviation (RH - RH) | Stock Z Deviation (RI - RI) | (RL - RL) × (RH - RI) | 2004 | -14.6% | 0.2% | -18.1% | 3.3% | -0.00602724 | 2005 | 4.3% | -3.2% | 0.8% | -0.1% | -0.00000833 | 2006 | -58.1% | -27.0% | -61.6% | -23.9% | 0.14718262 | 2007 | 71.1% | 27.9% | 67.6% | 30.9% | 0.20924394 | 2008 | 17.3% | -5.1% | 13.8% | -2.0% | -0.00281401 | 2009 | 0.9% | -11.3% | -2.6% | -8.2% | 0.00212874 | average = | 3.5% | -3.1% | | | | | | | | | | | | Variance = | 0.177795367 | 0.032239975 | | | | Stdev = | 0.421657879 | 0.179554936 | | | | | | | | | | | | Covariance = | 0.069941142 | | | | | Correlation = | 0.923794031 | | | | | | | | | | | Var(Port) = | 0.087479407 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 21) Calculate the variance on a portfolio that is made up of equal investments in Stock Y and Stock Z stock . Answer: | Year End | Stock Y Realized Return | Stock Z Realized Return | Stock Y Deviation (RH - RH) | Stock Z Deviation (RI - RI) | (RL - RL) × (RH - RI) | 2004 | -14.6% | 0.2% | -18.1% | 3.3% | -0.00602724 | 2005 | 4.3% | -3.2% | 0.8% | -0.1% | -0.00000833 | 2006 | -58.1% | -27.0% | -61.6% | -23.9% | 0.14718262 | 2007 | 71.1% | 27.9% | 67.6% | 30.9% | 0.20924394 | 2008 | 17.3% | -5.1% | 13.8% | -2.0% | -0.00281401 | 2009 | 0.9% | -11.3% | -2.6% | -8.2% | 0.00212874 | average = | 3.5% | -3.1% | | | | | | | | | | | | Variance = | 0.177795367 | 0.032239975 | | | | Stdev = | 0.421657879 | 0.179554936 | | | | | | | | | | | | Covariance = | 0.069941142 | | | | | Correlation = | 0.923794031 | | | | | | | | | | | Var(Port) = | 0.087479407 Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) = (.50)2(0.177795367) + (.50)2(0.032239975 + 2(.5)(.5)(00.069941142 = 0.087479407 Diff: 3 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical Use the table for the question(s) below. Consider the following covariances between securities: | | Duke | Microsoft | Wal-Mart | Duke | 0.0568 | -0.0193 | 0.0037 | Microsoft | -0.0193 | 0.2420 | 0.1277 | Wal-Mart | 0.0037 | 0.1277 | 0.1413 22) The variance on a portfolio that is made up of a $6000 investments in Microsoft and a $4000 investment in Wal-Mart stock is closest to: Answer: Total invested = $6000 + $4000 = $10,000 XMicrosoft = = .60 XWal-Mart = = .40 Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) = (.60)2(0.2420) + (.40)2(0.1413) + 2(.6)(.4)(0.1277) = 0.1710 Section: 11.2 The Volatility of a Two-Stock Portfolio Skill: Analytical 11.3 The Volatility of a Large Portfolio 1) Which of the following statements is FALSE? A) The variance of a portfolio is equal to the weighted average correlation of each stock within the portfolio. B) The variance of a portfolio is equal to the sum of the covariances of the returns of all pairs of stocks in the portfolio multiplied by each of their portfolio weights. C) The variance of a portfolio is equal to the weighted average covariances of each stock within the portfolio. D) The volatility declines as the number of stocks in a portfolio grows. Section: 11.3 The Volatility of a Large Portfolio Skill: Conceptual 2) Which of the following statements is FALSE? A) The volatility declines as the number of stocks in a portfolio grows. B) An equally weighted portfolio is a portfolio in which the same amount is invested in each stock. C) As the number of stocks in a portfolio grows large, the variance of the portfolio is determined primarily by the average covariance among the stocks. D) When combining stocks into a portfolio that puts positive weight on each stock, unless all of the stocks are uncorrelated with the portfolio, the risk of the portfolio will be lower than the weighted average volatility of the individual stocks. Section: 11.3 The Volatility of a Large Portfolio Skill: Conceptual 3) Which of the following statements is FALSE? A) The expected return of a portfolio is equal to the weighted average expected return, but the volatility of a portfolio is less than the weighted average volatility. B) Each security contributes to the volatility of the portfolio according to its volatility, scaled by its covariance with the portfolio, which adjusts for the fraction of the total risk that is common to the portfolio. C) Nearly half of the volatility of individual stocks can be eliminated in a large portfolio as a result of diversification. D) The overall variability of the portfolio depends on the total co-movement of the stocks within it. Section: 11.3 The Volatility of a Large Portfolio Skill: Conceptual 4) Which of the following formulas is INCORRECT? A) Variance of an equally Weighted Portfolio = (1 - )(Average Variance of Individual Stocks) + (Average covariance between the stocks) B) Variance of a portfolio = C) Variance of a portfolio = D) Variance of a portfolio = Explanation: A) Variance of an equally Weighted Portfolio = (Average Variance of Individual Stocks) + (1 - )(Average covariance between the stocks) Section: 11.3 The Volatility of a Large Portfolio Skill: Conceptual 5) Consider an equally weighted portfolio that contains five stocks. If the average volatility of these stocks is 40% and the average correlation between the stocks is .5, then the volatility of this equally weighted portfolio is closest to: A) .17 B) ..03 C) .41 D) .19 Explanation: B) Variance of an equally Weighted Portfolio = (Average Variance of Individual Stocks) + (1 - )(Average covariance between the stocks) Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Cov(R1,R2) Var = (1/5)(.40)2 + (1 - 1/5)(.5)(.40)(.40) Var = 0.032 + .064 = .096 stdev = = .0309 Section: 11.3 The Volatility of a Large Portfolio Skill: Analytical 6) Consider an equally weighted portfolio that contains 20 stocks. If the average volatility of these stocks is 35% and the average correlation between the stocks is .4, then the volatility of this equally weighted portfolio is closest to: A) .17 B) .41 C) .14 D) .37 Explanation: D) Variance of an equally Weighted Portfolio = (Average Variance of Individual Stocks) + (1 - )(Average covariance between the stocks) Var = (1/20)(.35)2 + (1 - 1/20)(.4)( ( ) Var = .05(.1225) + .95(.4)(.35) = .139125 stdev = = .372995 Section: 11.3 The Volatility of a Large Portfolio Skill: Analytical 7) Consider an equally weighted portfolio that contains 100 stocks. If the average volatility of these stocks is 50% and the average correlation between the stocks is .7, then the volatility of this equally weighted portfolio is closest to: A) .72 B) .63 C) .40 D) .50 Explanation: B) Variance of an equally Weighted Portfolio = (Average Variance of Individual Stocks) + (1 - )(Average covariance between the stocks) Var = (1/100)(.50)2 + (1 - 1/100)(.7)( ( ) Var = .01(.25) + .99(.8)(.50) = .3985 stdev = = .6312 Section: 11.3 The Volatility of a Large Portfolio Skill: Analytical Use the table for the question(s) below. Consider the following covariances between securities: | | Duke | Microsoft | Wal-Mart | Duke | 0.0568 | -0.0193 | 0.0037 | Microsoft | -0.0193 | 0.2420 | 0.1277 | Wal-Mart | 0.0037 | 0.1277 | 0.1413 8) What is the variance on a portfolio that has $2000 invested in Duke Energy, $3000 invested in Microsoft, and $5000 invested in Wal-Mart stock? Answer: | COV | Duke | Microsoft | Wal-Mart | Duke | 0.0568 | -0.0193 | 0.0037 | Microsoft | -0.0193 | 0.2420 | 0.1277 | Wal-Mart | 0.0037 | 0.1277 | 0.1413 | | | | | Weights | 0.2 | 0.3 | 0.5 | XiXj | XDuke | XMicrosoft | XWal-Mart | XDuke | 0.04 | 0.06 | 0.1 | XMicrosoft | 0.06 | 0.09 | 0.15 | XWal-Mart | 0.1 | 0.15 | 0.25 | XiXjCOV(I,j) | Duke | Microsoft | Wal-Mart | Duke | 0.002272 | -0.00116 | 0.000367 | Microsoft | -0.00116 | 0.021776 | 0.019153 | Wal-Mart | 0.000367 | 0.019153 | 0.035318 | | | | | Var(P) = | 0.096086 | | Variance of a portfolio = Diff: 3 Section: 11.3 The Volatility of a Large Portfolio Skill: Analytical 9) What is the variance on a portfolio that has $3000 invested in Duke Energy, $4000 invested in Microsoft, and $3000 invested in Wal-Mart stock? Answer: Variance of a portfolio = | COV | Duke | Microsoft | Wal-Mart | Duke | 0.0568 | -0.0193 | 0.0037 | Microsoft | -0.0193 | 0.2420 | 0.1277 | Wal-Mart | 0.0037 | 0.1277 | 0.1413 | | | | | Weights | 0.3 | 0.4 | 0.3 | XiXj | XDuke | XMicrosoft | XWal-Mart | XDuke | 0.09 | 0.12 | 0.09 | XMicrosoft | 0.12 | 0.16 | 0.12 | XWal-Mart | 0.09 | 0.12 | 0.09 | XiXjCOV(I,j) | Duke | Microsoft | Wal-Mart | Duke | 0.005112 | -0.00232 | 0.00033 | Microsoft | -0.00232 | 0.038714 | 0.015322 | Wal-Mart | 0.00033 | 0.015322 | 0.012715 | | | | | Var(P) = | 0.083205 | | Diff: 3 Section: 11.3 The Volatility of a Large Portfolio Skill: Analytical 11.4 Risk Versus Return: Choosing an Efficient Portfolio 1) Which of the following statements is FALSE? A) We say a portfolio is an efficient portfolio whenever it is possible to find another portfolio that is better in terms of both expected return and volatility. B) We can rule out inefficient portfolios because they represent inferior investment choices. C) The volatility of the portfolio will differ, depending on the correlation between the securities in the portfolio. D) Correlation has no effect on the expected return on a portfolio. Explanation: A) We say a portfolio is an efficient portfolio whenever it is not possible to find another portfolio that is better in terms of both expected return and volatility. Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Conceptual 2) Which of the following statements is FALSE? A) When stocks are perfectly positively correlated, the set of portfolios is identified graphically by a straight line between them. B) An investor seeking high returns and low volatility should only invest in an efficient portfolio. C) When the correlation between securities is less than 1, the volatility of the portfolio is reduced due to diversification. D) Efficient portfolios can be easily ranked, because investors will choose from among them those with the highest expected returns. Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Conceptual 3) Which of the following statements is FALSE? A) We say a portfolio is long those stocks that have negative portfolio weights. B) The efficient portfolios are those portfolios offering the highest possible expected return for a given level of volatility. C) When two stocks are perfectly negatively correlated, it becomes possible to hold a portfolio that bears absolutely no risk. D) The lower the correlation of the securities in a portfolio the lower the volatility we can obtain. Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Conceptual 4) Which of the following statements is FALSE? A) A short sale is a transaction in which you buy a stock that you do not own and then agree to sell that stock back in the future. B) The efficient portfolios are those portfolios offering the lowest possible level of volatility for a given level of expected return. C) A positive investment in a security can be referred to as a long position in the security. D) It is possible to invest a negative amount in a stock or security call a short position. Explanation: A) A short sale is a transaction in which you sell a stock that you do not own and then agree to buy that stock back in the future. Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Conceptual 5) Which of the following statements is FALSE? A) Graphically, the efficient portfolios are those on the northeast edge of the set of possible portfolios, an area which we call the efficient frontier. B) To arrive at the best possible set of risk and return opportunities, we should keep adding stocks until all investment opportunities are represented. C) We say a portfolio is short those stocks that have negative portfolio weights. D) Adding new investment opportunities allows for greater diversification and improves the efficient frontier. Diff: 3 Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Conceptual 6) Suppose you have $10,000 in cash to invest. You decide to sell short $5,000 worth of Kinston stock and invest the proceeds from your short sale, plus your $10,000 into one-year U.S. treasury bills earning 5%. At the end of the year, you decide to liquidate your portfolio. Kinston Industries has the following realized returns: | | P0 | Div1 | P1 | Kinston | $25.00 | $1.00 | $29.00 The return on your portfolio is closest to: A) -0.5% B) 13.5% C) -2.5% D) 14.5% Explanation: C) You short sold $5000/$25 = 200 shares of Kinston and invested the $5,000 + $10,000 in T-notes. In one year you will have (15,000)(1.05) = $15,750 - 200 × ($29 + $1) = $9,750. So, your total return is equal to = -0.025 or -2.5% Diff: 3 Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical Use the table for the question(s) below. Consider the following expected returns, volatilities, and correlations: | Stock | Expected Return | Standard Deviation | Correlation with Duke Energy | Correlation with Microsoft | Correlation with Wal-Mart | Duke Energy | 14% | 6% | 1.0 | -1.0 | 0.0 | Microsoft | 44% | 24% | -1.0 | 1.0 | 0.7 | Wal-Mart | 23% | 14% | 0.0 | 0.7 | 1.0 7) Consider a portfolio consisting of only Duke Energy and Microsoft. The percentage of your investment (portfolio weight) that you would place in Duke Energy stock to achieve a risk-free investment would be closest to: A) 15% B) 40% C) 23% D) 10% Explanation: B) Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Corr(R1,R2)SD1SD2 x1 = .40 Diff: 3 Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical 8) The expected return of a portfolio that is equally invested in Duke Energy and Microsoft is closest to: A) 28% B) 29% C) 24% D) 23% Explanation: B) .5(14%) + .5(44%) = 29% Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical 9) The volatility of a portfolio that is equally invested in Duke Energy and Microsoft is closest to: A) 8% B) 9% C) 11% D) 6% Explanation: B) Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Corr(R1,R2)SD1SD2 = .52(.06)2 + .52(.24)2 + 2(.5)(.5)(-1)(.06)(.24) = .0081 stdev = = .09 Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical 10) The expected return of a portfolio that is consists of a long position of $10000 in Wal-Mart and a short position of $2000 in Microsoft is closest to: A) 21% B) 12% C) 27% D) 18% Explanation: D) = (10,000/8,000)(.23) + (-2000/8,8000)(.44) = (1.25)(.23) + (-.25)(.44) = .1775 Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical 11) The volatility of a portfolio that is consists of a long position of $10000 in Wal-Mart and a short position of $2000 in Microsoft is closest to: A) 9% B) 14% C) 11% D) 12% Explanation: B) Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Corr(R1,R2)SD1SD2 = 1.252(.14)2 + (- 25)2(.24)2 + 2(1.25)(-.25)(0.7)(.14)(.24) = .019525 stdev = = .139732 Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical 12) Consider a portfolio consisting of only Microsoft and Wal-Mart stock. Calculate the expected return on such a portfolio when the weight on Microsoft stock is 0%, 25%, 50%, 75%, and 100% Answer: Rp = x1R1 + x2R2 + ... + xnRn | Weight on Microsoft | Weight on Wal-Mart | Portfolio Return | 0% | 100% | 23% | 25% | 75% | 28% | 50% | 50% | 34% | 75% | 25% | 39% | 100% | 0% | 44% Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical 13) Consider a portfolio consisting of only Microsoft and Wal-Mart stock. Calculate the volatility of such a portfolio when the weight on Microsoft stock is 0%, 25%, 50%, 75%, and 100% Answer: Var(Rp) = x12Var(R1) + x22Var(R2) + 2X1X2Corr(R1,R2)SD1SD2 | Weight on Microsoft | Weight on Wal-Mart | Portfolio Return | Portfolio Variance | Portfolio Volatility | 0% | 100% | 23% | 0.0196 | 0.140 | 25% | 75% | 28% | 0.023445 | 0.153 | 50% | 50% | 34% | 0.03106 | 0.176 | 75% | 25% | 39% | 0.042445 | 0.206 | 100% | 0% | 44% | 0.0576 | 0.240 Diff: 3 Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Analytical 14) What is the efficient frontier and how does it change when more stocks are used to construct portfolios? Answer: The efficient portfolios are those portfolios offering the highest possible expected return for a given level of volatility. The efficient portfolios are those portfolios offering the lowest possible level of volatility for a given level of expected return. Graphically, the efficient portfolios are those on the northwest edge of the set of possible portfolios, an area which we call the efficient frontier. Adding new investment opportunities allows for greater diversification and improves the efficient frontier (moves it to the northwest, thereby providing better risk/return opportunities). To arrive at the best possible set of risk and return opportunities, we should keep adding stocks until all investment opportunities are represented. Section: 11.4 Risk Versus Return: Choosing an Efficient Portfolio Skill: Conceptual 11.5 Risk-Free Saving and Borrowing 1) Which of the following statements is FALSE? A) A portfolio that consists of a long position in the risk-free investment is known as a levered portfolio. B) The optimal portfolio will not depend on the investor's personal tradeoff between risk and return. C) The volatility of the risk-free investment is zero. D) Our total volatility is only a fraction of the volatility of the efficient portfolio, based on the amount we invest in the risk free asset. Section: 11.5 Risk-Free Saving and Borrowing Skill: Conceptual 2) Which of the following statements is FALSE? A) Margin investing is a risky investment strategy. B) Because our return on the risk-free investments is fixed and does not move with (or against) our portfolio, the correlation between the risk-free investment and the portfolio is always equal to one. C) Short selling the risk free investment is equivalent to borrowing money at the risk-free interest rate through a standard loan. D) Margin investing can provide higher expected returns than investing in the efficient portfolio using only the funds we have available. Section: 11.5 Risk-Free Saving and Borrowing Skill: Conceptual 3) Which of the following statements is FALSE? A) The Sharpe ratio measures the ratio of volatility-to-reward provided by a portfolio. B) Borrowing money to invest in stocks is referred to as buying stocks on margin. C) The Sharpe ratio is the number of stand deviations the portfolio's return would have to fall to under-perform the risk-free investment. D) The slope of the line through a given portfolio is often referred to as the Sharpe ratio of the portfolio. Explanation: A) The Sharpe ratio measures the ratio of reward-to-volatility provided by a portfolio. Section: 11.5 Risk-Free Saving and Borrowing Skill: Conceptual 4) Which of the following statements is FALSE? A) The tangent portfolio is efficient and that, once we include the risk-free investment, all efficient portfolios are combinations of the risk-free investment and the tangent portfolio. B) The optimal portfolio of risky investments depends on how conservative or aggressive the investor is. C) By combining the efficient portfolio with the risk-free investment, an investor will earn the highest possible expected return for any level of volatility her or she is willing to bear. D) The efficient portfolio is the tangent portfolio, the portfolio with the highest Sharpe ratio in the economy. Section: 11.5 Risk-Free Saving and Borrowing Skill: Conceptual 5) Which of the following statements is FALSE? A) If we increase the fraction invested in the efficient portfolio beyond 100%m we are short selling the risk-free investment. B) As we increase the fraction invested in the efficient portfolio, we increase our risk premium but not our risk proportionately. C) To earn the highest possible expected return for any level of volatility we must find the portfolio that generates the steepest possible line when combined with the risk-free investment. D) Every investor should invest in the tangent portfolio independent of his or her taste for risk. Section: 11.5 Risk-Free Saving and Borrowing Skill: Conceptual 6) Which of the following statements is FALSE? A) An investor's preferences will determine only how much to invest in the tangent or efficient portfolio versus the risk-free investment. B) Conservative investors will invest a small amount in the tangent or efficient portfolio, choosing a portfolio on the line near the risk-free investment C) Only aggressive investors will choose to hold the portfolio of risky assets, the tangent or efficient portfolio. D) Aggressive investors will invest more in the tangent portfolio choosing a portfolio that is near the tangent portfolio or even beyond it by buying stocks on margin. Section: 11.5 Risk-Free Saving and Borrowing Skill: Conceptual 7) Which of the following equations is INCORRECT? A) E[Rxp] = rf + x(E[Rp] - rf) B) E[Rxp] = (1 - x)rf + xE[Rp] C) Sharpe ratio = D) SD( Rxp) = xSD(Rp) Explanation: C) Sharpe ratio = Section: 11.5 Risk-Free Saving and Borrowing Skill: Conceptual Use the information for the question(s) below. Suppose you have $10,000 in cash and you decide to borrow another $10,000 at a 6% interest rate to invest in the stock market. You invest the entire $20,000 in an exchange traded fund (ETF) with a 12% expected return and a 20% volatility. 8) The expected return on your of your investment is closest to: A) 18% B) 20% C) 12% D) 24% Explanation: A) E[Rxp] = rf + x(E[Rp] - rf) = .06 + 2(.12 - .06) = .18 or 18% Section: 11.5 Risk-Free Saving and Borrowing Skill: Analytical 9) The volatility of your of your investment is closest to: A) 40% B) 20% C) 30% D) 24% Explanation: A) SD( Rxp) = xSD(Rp) = 2(.20) = .40 Section: 11.5 Risk-Free Saving and Borrowing Skill: Analytical 10) Assume that the EFT you invested in returns -10%, then the realized return on your investment is closest to: A) -20% B) -10% C) -24% D) -26% Explanation: D) Value of portfolio = $20,000( 1 + -.10) = $18,000 - $10,600 loan & interest = 7,400 So, return = (7400 - 10000)/10000 = -26% Section: 11.5 Risk-Free Saving and Borrowing Skill: Analytical Use the information for the question(s) below. Suppose that you currently have $250,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The efficient (tangent) portfolio has an expected return of 17% and a volatility of 12%. The risk-free rate of interest is 5%. 11) The Sharpe ratio for your portfolio is closest to: A) 1.2 B) 0.6 C) 1.0 D) 0.7 Explanation: D) Sharpe ratio = = = .7 Section: 11.5 Risk-Free Saving and Borrowing Skill: Analytical 12) The Sharpe ratio for the efficient portfolio is closest to: A) 0.7 B) 1.0 C) 1.4 D) 1.2 Explanation: B) Sharpe ratio = = = 1.0 Section: 11.5 Risk-Free Saving and Borrowing Skill: Analytical 13) You want to maximize your expected return without increasing your risk. Without increasing your volatility beyond its current 10%, the maximum expected return you could earn is closest to: A) .12.0% B) 12.5% C) 13.4% D) 15.0% Explanation: D) SD( Rxp) = xSD(Rp) .10 = x(.12) x = .10/.12 x = .833333 So, E[Rxp] = rf + x(E[Rp] - rf) = .05 + .8333(.17 -.05) = .15 or 15% Section: 11.5 Risk-Free Saving and Borrowing Skill: Analytical 14) Suppose that you want to maximize your expected return without increasing your risk. How can you achieve this goal? Without increasing your risk, what is the maximum expected return you can expect? y investing in a combination of the risk-free asset and the efficient portfolio. We find the weights and expected returns as follows: SD( Rxp) = xSD(Rp) .10 = x(.12) x = .10/.12 x = .833333 invested in the efficient portfolio So, E[Rxp] = rf + x(E[Rp] - rf) = .05 + .8333(.17 - .05) = .15 or 15% Section: 11.5 Risk-Free Saving and Borrowing Skill: Analytical 11.6 The Efficient Portfolio and Required Returns 1) Which of the following statements is FALSE? A) A portfolio is efficient if it has the highest possible Sharpe ratio; that is it is efficient if it provides the largest increase in expected return possible for a given increase in volatility. B) The required return for an investment is equal to a risk premium that is equal to the risk premium of the investor's current portfolio scaled by . C) Increasing the investment in investment I will increase the Sharpe ratio of portfolio P if its expected return E[Ri] exceeds the required return ri, which is given by ri = rf + × (E[Rp] - rf). D) If a security i's expected return is less than the required return ri, we should reduce our holding of security i. Section: 11.6 The Efficient Portfolio and Required Returns Skill: Conceptual 2) Which of the following statements is FALSE? A) The Sharpe ratio if the portfolio tells us how much our expected return will increase for a given increase in volatility. B) We should continue to trade securities until the expected return of each security equals its required return. C) The required return is the expected return that is necessary to compensate for the risk that an investment will contribute to the portfolio. D) If security i’s required return exceeds its expected return, then adding more of it will improve the performance of the portfolio. Section: 11.6 The Efficient Portfolio and Required Returns Skill: Conceptual 3) Which of the following statements is FALSE? A) Because all other risk is diversifiable, it is an investment’s beta with respect to the efficient portfolio that measures its sensitivity to systematic risk, and therefore determines its cost of capital. B) If a security's expected return exceeds its required return given our current portfolio, then we can improve the performance of our portfolio by adding more of the security. C) The appropriate risk premium for an investment can be determined from its beta with the efficient portfolio. D) As we buy shares of a security i, its correlation with our portfolio P will increase, ultimately raising its required return until E[Ri] = Rp. Section: 11.6 The Efficient Portfolio and Required Returns Skill: Conceptual Use the following information to answer the question(s) below. | Firm | Portfolio Weight | Volatility | Correlation w/ Market Portfolio | Taggart Transcontinental | 0.25 | 14% | 0.7 | Wyatt Oil | 0.35 | 18% | 0.6 | Rearden Metal | 0.40 | 15% | 0.5 The volatility of the market portfolio is 10%, the expected return on the market is 12%, and the risk-free rate of interest is 4%. 4) The Sharpe Ratio for the market portfolio is closest to: A) 0.40 B) 0.48 C) 0.56 D) 0.80 Explanation: D) Sharpe Ratio = = = 0.80 Section: 11.6 The Efficient Portfolio and Required Returns Skill: Analytical Use the information for the question(s) below. You are presently invested in the Luther Fund, a broad based mutual fund that invest in stocks and other securities. The Luther Fund has an expected return of 14% and a volatility of 20%. Risk-free Treasury bills are currently offering returns of 4%. You are considering adding a precious metals fund to your current portfolio. The metals fund has an expected return of 10%, a volatility of 30%, and a correlation of -.20 with the Luther Fund. 5) The beta of the precious metals fund with the Luther Fund is closest to: A) -0.3 B) -0.6 C) 0.3 D) 0.6 Explanation: A) = = = -0.3 Section: 11.6 The Efficient Portfolio and Required Returns Skill: Analytical 6) The expected return on the precious metals fund is closest to: A) -3% B) 4% C) 1% D) 10% Explanation: C) = = = -0.3 ri = rf + × (E[Rp] - rf) = .04 + (-0.3)(.14 - .04) = .01 Section: 11.6 The Efficient Portfolio and Required Returns Skill: Analytical Use the information for the question(s) below. Sisyphean industries is seeking to raise capital from a large group of investors to fund a new project. Suppose that the efficient portfolio has an expected return of 14% and a volatility of 20%. Sisyphean's new project is expected to have a volatility of 40% and a 70% correlation with the efficient portfolio. The risk-free rate is 4%. 7) The beta for Sisyphean's new project is closest to: A) 1.25 B) 1.40 C) 0.70 D) 1.75 Explanation: B) = = = 1.4 Section: 11.6 The Efficient Portfolio and Required Returns Skill: Analytical 8) The required return for Sisyphean's new project is closest to: A) 24% B) 14% C) 18% D) 10% Explanation: C) = = = 1.4 ri = rf + × (E[Rp] - rf) = .04 + (1.4)(.14 - .04) = .18 Section: 11.6 The Efficient Portfolio and Required Returns Skill: Analytical Use the information for the question(s) below. You are presently invested in the Luther Fund, a broad based mutual fund that invest in stocks and other securities. The Luther Fund has an expected return of 14% and a volatility of 20%. Risk-free Treasury bills are currently offering returns of 4%. You are considering adding a precious metals fund to your current portfolio. The metals fund has an expected return of 10%, a volatility of 30%, and a correlation of -.20 with the Luther Fund. 9) Will adding the precious metals fund improve your portfolio? Answer: Yes = = = -0.3 ri = rf + × (E[Rp] - rf) = .04 + (-0.3)(.14 - .04) = .01 < .10 (the expected return on metals fund) Since the required return is less than the expected return, you can benefit from adding the precious metals fund to your portfolio. Section: 11.6 The Efficient Portfolio and Required Returns Skill: Analytical Use the following information to answer the question(s) below. Suppose that all stocks can be grouped into two mutually exclusive portfolios (with each stock appearing in only one portfolio): growth stocks and value stocks. Assume that these two portfolios are equal in size (market value), the correlation of their returns is equal to 0.6, and the portfolios have the following characteristics: | | Expected Return | Volatility | Value Stocks | 0.12 | 14% | Growth Stocks | 0.15 | 24% The risk free rate is 3.5%. 10) The Sharpe ratio for the value stock portfolio is closest to: A) .53 B) .58 C) .61 D) .79 Explanation: C) Sharpe Ratio = = = 0.607143 Section: 11.6 The Efficient Portfolio and Required Returns Skill: Analytical 11.7 The Capital Asset Pricing Model Use the following information to answer the question(s) below. Your investment portfolio consists of $10,000 worth of Google stock. Suppose that the risk-free rate is 4%, Google stock has an expected return of 14% and a volatility of 35%, and the market portfolio has an expected return of 12% and a volatility of 18%. Assume that the CAPM assumptions hold. 1) What alternative investment has the lowest possible volatility while having the same expected return as Google? A) -25% in the risk-free asset and +125% in the market portfolio B) -20% in the risk-free asset and +120% in the market portfolio C) 0% in the risk-free asset and +100% in the market portfolio D) 20% in the risk-free asset and +80% in the market portfolio Explanation: A) r = wm(rm) + 1 - wm)(rf) → .14 = wm(.12) + (1 - wm)(.04) → .08wm = .10 → wm = 1.25 → wrf = -.25 Section: 11.7 The Capital Asset Pricing Model Skill: Analytical 2) The volatility of the alternative investment that has the lowest possible volatility while having the same expected return as Google is closest to: A) 18.0% B) 22.5% C) 23.4% D) 35.0% Explanation: B) r = wm(rm) + (1 - wm)(rf) → .14 = wm(.12) + (1 - wm)(.04) → .08wm = .10 → wm = 1.25 → wrf = -.25 SD(rxp) = x SD(rp) = 1.25(.18) = .225 Section: 11.7 The Capital Asset Pricing Model Skill: Analytical 3) What alternative investment has the highest possible expected return while having the same volatility as Google? A) -25% in the risk-free asset and +125% in the market portfolio B) -20% in the risk-free asset and +120% in the market portfolio C) -94% in the risk-free asset and +194% in the market portfolio D) 6% in the risk-free asset and +94% in the market portfolio Explanation: C) SD(rxp) = x SD(rp) = x(.18) = .35 → x = 1.944444 Section: 11.7 The Capital Asset Pricing Model Skill: Analytical 4) The expected return on the alternative investment having the highest possible expected return while having the same volatility as Google is closest to? A) 21.6% B) 19.6% C) 23.4% D) 35.0% Explanation: B) SD(rxp) = x SD(rp) = x(.18) = .35 → x = 1.944444 r = wm(rm) + (1 - wm)(rf) = 1.944444 (.12) + (-0.944444)(.04) = .1956 Section: 11.7 The Capital Asset Pricing Model Skill: Analytical Use the following information to answer the question(s) below. Suppose that all stocks can be grouped into two mutually exclusive portfolios (with each stock appearing in only one portfolio): growth stocks and value stocks. Assume that these two portfolios are equal in size (market value), the correlation of their returns is equal to 0.6, and the portfolios have the following characteristics: | | Expected Return | Volatility | Value Stocks | 0.12 | 14% | Growth Stocks | 0.15 | 24% The risk free rate is 3.5%. 5) The expected return on the market portfolio (which is a 50-50 combination of the value and growth portfolios) is closest to: A) 12.0% B) 13.5% C) 15.0% D) 19.0% Explanation: B) expected return = .50(12%) + .50(15%) = 13.5% Section: 11.7 The Capital Asset Pricing Model Skill: Analytical 6) The volatility on the market portfolio (which is a 50-50 combination of the value and growth portfolios) is closest to: A) 13.5% B) 15.2% C) 17.1% D) 19.0% Explanation: C) σp2 = x12 [(SD(R1))]2 + x22 [(SD(R2))]2 + 2x1x2 Corr(R1, R2)SD(R1)SD(R2) = [(.5)]2 [(.14)]2 + [(.5)]2 [(.24)]2 + 2(.5)(.5)(.6) ... Section: 11.7 The Capital Asset Pricing Model Skill: Analytical 7) Which of the following statements is FALSE? A) Because all investors should hold the risky securities in the same proportions as the efficient portfolio, their combined portfolio will also reflect the same proportions as the efficient portfolio. B) When the CAPM assumptions hold, choosing an optimal portfolio is relatively straightforward: it is the combination of the risk-free investment and the market portfolio. C) Graphically, when the tangent line goes through the market portfolio, it is called the security market line (SML). D) A portfolio's risk premium and volatility are determined by the fraction that is invested in the market. Explanation: C) Graphically, when the tangent line goes through the market portfolio, it is called the capital market line (CML). Section: 11.7 The Capital Asset Pricing Model Skill: Conceptual 8) Which of the following is NOT an assumption used in deriving the Capital Asset Pricing Model (CAPM)? A) Investors have homogeneous expectations regarding the volatilities, correlation, and expected returns of securities. B) Investors have homogeneous risk adverse preferences toward taking on risk. C) Investors hold only efficient portfolios of traded securities, that is portfolios that yield the maximum expected return for the given level of volatility. D) Investors can buy and sell all securities at competitive market prices without incurring taxes or transactions cost and can borrow and lend at the risk-free interest rate. Section: 11.7 The Capital Asset Pricing Model Skill: Conceptual 9) Which of the following statements is FALSE? A) Short-term margin loans from a broker are often 1% to 2% lower than the rates paid on short-term Treasury securities. B) In the real world investors have different information and expectations regarding securities. C) The SML is still valid when interest rates differ. D) When borrowing and lending occur at different rates there are different tangent portfolios identified. Section: 11.7 The Capital Asset Pricing Model Skill: Conceptual 10) Which of the following statements is FALSE? A) A combination of portfolios on the efficient frontier of risky investments is also on the efficient frontier of risky investments. B) The conclusion of the CAPM that investors should hold the market portfolio combined with the risk-free investment depends on the quality of an investor's information. C) The SML holds with some rate r* between rs and rb in place of rf, where r* depends on the proportion of savers and borrowers in the economy. D) In reality, investors have different information and spend varying amounts of effort on research for assorted stocks. Section: 11.7 The Capital Asset Pricing Model Skill: Conceptual 11) Which of the following statements is FALSE? A) When an investor chooses her optimal portfolio, she will do so by finding the tangent line using the risk-free rate that corresponds to her investment horizon. B) If the market portfolio is not efficient, savvy investors who recognize that the market portfolio is not optimal will push prices and expected returns back into balance. C) Even though different investors may research different stocks, their information will not impact the market portfolio since there is no way to share this information with other investors. D) In the real world borrowers pay higher interest rates than savers receive. Section: 11.7 The Capital Asset Pricing Model Skill: Conceptual 11.8 Determining the Risk Premium Use the following information to answer the question(s) below. | Firm | Portfolio Weight | Volatility | Correlation w/ Market Portfolio | Taggart Transcontinental | 0.25 | 14% | 0.7 | Wyatt Oil | 0.35 | 18% | 0.6 | Rearden Metal | 0.40 | 15% | 0.5 The volatility of the market portfolio is 10%, the expected return on the market is 12%, and the risk-free rate of interest is 4%. 1) The beta for Taggart Transcontinental is closest to: A) 0.75 B) 0.80 C) 1.00 D) 1.10 Explanation: C) βTT = = = 0.98 Section: 11.8 Determining the Risk Premium Skill: Analytical 2) The beta for Wyatt Oil is closest to: A) 0.75 B) 0.80 C) 1.00 D) 1.10 Explanation: D) βWO = = = 1.08 Section: 11.8 Determining the Risk Premium Skill: Analytical 3) The expected return for Wyatt Oil is closest to: A) 11.4% B) 11.8% C) 12.0% D) 12.6% Explanation: D) βWO = = = 1.08 ri = rf + βi(Rm - rf) = .04 + 1.08(.12 - .04) = .1264 or 12.64% Section: 11.8 Determining the Risk Premium Skill: Analytical 4) The expected return for Rearden Metal is closest to: A) 10.0% B) 11.4% C) 11.8% D) 12.0% Explanation: A) βRM = = = 0.75 ri = rf + βi(Rm - rf) = .04 + 0.75(.12 - .04) = .10 or 10.00% Section: 11.8 Determining the Risk Premium Skill: Analytical 5) The beta for the market is closest to: A) 0.80 B) 1.00 C) 1.10 D) 1.25 Explanation: B) βWO = = = 1.00 Section: 11.8 Determining the Risk Premium Skill: Analytical 6) The beta for the portfolio of the three stocks is closest to: A) 0.92 B) 0.94 C) 1.00 D) 1.02 Explanation: A) βTT = = = 0.98 βWO = = = 1.08 βRM = = = 0.75 βport = = (.25)0.98 + (.35)1.08 + (.40)0.75 = .9230 Section: 11.8 Determining the Risk Premium Skill: Analytical 7) The expected return on the portfolio of the three stocks is closest to: A) 10.0% B) 11.4% C) 11.8% D) 12.0% Explanation: B) βTT = = = 0.98 βWO = = = 1.08 βRM = = = 0.75 βport = = (.25)0.98 + (.35)1.08 + (.40)0.75 = .9230 ri = rf + βi(Rm - rf) = .04 + 0.9230(.12 - .04) = .113840 or 11.38% Diff: 3 Section: 11.8 Determining the Risk Premium Skill: Analytical 8) The Sharpe Ratio for Rearden Metal is closest to: A) 0.40 B) 0.56 C) 0.80 D) 1.00 Explanation: A) βRM = = = 0.75 ri = rf + βi(Rm - rf) = .04 + 0.75(.12 - .04) = .10 or 10.00% Sharpe Ratio = = = 0.40 Diff: 3 Section: 11.8 Determining the Risk Premium Skill: Analytical 9) The Sharpe Ratio for Wyatt Oil is closest to: A) 0.40 B) 0.48 C) 0.56 D) 0.80 Explanation: B) βWO = = = 1.08 ri = rf + βi(Rm - rf) = .04 + 1.08(.12 - .04) = .1264 or 12.64% Sharpe Ratio = = = 0.48 Diff: 3 Section: 11.8 Determining the Risk Premium Skill: Analytical 10) Suppose that Google Stock has a beta of 1.06 and Boeing stock has a beta of 1.31. The beta on a portfolio that consists of 30% Google stock and 70% Boeing stock is closest to: A) 1.06 B) 1.14 C) 1.19 D) 1.24 Explanation: D) βport = = (.30)1.06 + (.70)1.31 = 1.2350 Section: 11.8 Determining the Risk Premium Skill: Analytical 11) Suppose that Google Stock has a beta of 1.06 and Boeing stock has a beta of 1.31. If the risk-free interest rate is 4% and the expected return from the market portfolio is 12%, then the expected return on a portfolio that consists of 30% Google stock and 70% Boeing stock is closest to: A) 12.5% B) 13.1% C) 13.5% D) 13.9% Explanation: D) βport = = (.30)1.06 + (.70)1.31 = 1.2350 ri = rf + βi(Rm - rf) = .04 + 1.235(.12 - .04) = .1388 or 13.88% Section: 11.8 Determining the Risk Premium Skill: Analytical Use the following information to answer the question(s) below. Suppose that all stocks can be grouped into two mutually exclusive portfolios (with each stock appearing in only one portfolio): growth stocks and value stocks. Assume that these two portfolios are equal in size (market value), the correlation of their returns is equal to 0.6, and the portfolios have the following characteristics: | | Expected Return | Volatility | Value Stocks | 0.12 | 14% | Growth Stocks | 0.15 | 24% The risk free rate is 3.5%. 12) The Sharpe ratio for the market (which is a 50-50 combination of the value and growth portfolios) portfolio is closest to: A) .53 B) .58 C) .61 D) .79 Explanation: B) expected return = .50(12%) + .50(15%) = 13.5% σp2 = x12 [(SD(R1))]2 + x22 [(SD(R2))]2 + 2x1x2 Corr(R1, R2)SD(R1)SD(R2) = [(.5)]2 [(.14)]2 + [(.5)]2 [(.24)]2 + 2(.5)(.5)(.6) ... Sharpe Ratio = = = 0.583410 Diff: 3 Section: 11.8 Determining the Risk Premium Skill: Analytical 13) Which of the following equations is INCORRECT? A) E[RxCML] = rf + x(E[RMkt] + rf) B) ri = rf + b(E[RMkt] - rf) C) SD(RxCML) = xSD(RMkt) D) E[RxCML] = (1 - x)rf + xE[RMkt] Explanation: A) E[RxCML] = rf + x(E[RMkt] - rf) Section: 11.8 Determining the Risk Premium Skill: Analytical Use the information for the question(s) below. Tom's portfolio consists solely of an investment in Merck stock. Merck has an expected return of 13% and a volatility of 25%. The market portfolio has an expected return of 12% and a volatility of 18%. The risk-free rate is 4%. Assume that the CAPM assumptions hold in the market. 14) Assuming that Tom wants to maintain the current volatility of his portfolio, then the amount that Tom should invest in the market portfolio to maximize his expected return is closest to: A) 72% B) 92% C) 110% D) 140% Explanation: D) SD(RxCML) = xSD(RMkt) .25 = x(.18) → x = .25/.18 = 1.39 Section: 11.8 Determining the Risk Premium Skill: Analytical 15) Assuming that Tom wants to maintain the current volatility of his portfolio, then the maximum expected return that Tom could achieve by investing in the market portfolio and risk-free investment is closest to: A) 13% B) 15% C) 16% D) 12% Explanation: B) SD(RxCML) = xSD(RMkt) .25 = x(.18) → x = .25/.18 = 1.39 E[RxCML] = rf + x(E[RMkt] - rf) E[RxCML] = .04 + 1.39(.12 - .04) = .1512 Section: 11.8 Determining the Risk Premium Skill: Analytical 16) Assuming that Tom wants to maintain the current expected return on his portfolio, then the amount that Tom should invest in the market portfolio to minimize his volatility is closest to: A) 100% B) 90% C) 125% D) 110% Explanation: D) E[RxCML] = rf + x(E[RMkt] - rf) .13 = .04 + x(.12 - .04) x = .09/.08 = 1.125 Section: 11.8 Determining the Risk Premium Skill: Analytical 17) Assuming that Tom wants to maintain the current expected return on his portfolio, then the minimum volatility that Tom could achieve by investing in the market portfolio and risk-free investment is closest to: A) 20% B) 25% C) 22% D) 18% Explanation: A) E[RxCML] = rf + x(E[RMkt] - rf) .13 = .04 + x(.12 - .04) x = .09/.08 = 1.125 SD(RxCML) = xSD(RMkt) 1.125(.18) = .2025 Section: 11.8 Determining the Risk Premium Skill: Analytical 18) You currently own $100,000 worth of Wal-Mart stock. Suppose that Wal-Mart has an expected return of 14% and a volatility of 23%. The market portfolio has an expected return of 12% and a volatility of 16%. The risk-free rate is 5%. Assuming the CAPM assumptions hold, what alternative investment has the lowest possible volatility while having the same expected return as Wal-Mart? What is the volatility of this portfolio? Answer: E[RxCML] = rf + x(E[RMkt] - rf) .14 = .05 + x(.12 - .05) x = .09/.07 = 1.286. So the portfolio is long 129% market and short 29% risk-free asset SD(RxCML) = xSD(RMkt) 1.286(.16) = .2057 = 20.6% Section: 11.8 Determining the Risk Premium Skill: Analytical 19) You currently own $100,000 worth of Wal-Mart stock. Suppose that Wal-Mart has an expected return of 14% and a volatility of 23%. The market portfolio has an expected return of 12% and a volatility of 16%. The risk-free rate is 5%. Assuming the CAPM assumptions hold, what alternative investment has the highest possible expected return while having the same volatility as Wal-Mart? What is the expected return of this portfolio? Answer: SD(RxCML) = xSD(RMkt) .23 = x(.16) → x = .23/.16 = 1.4375, so long 144% market and short 44% risk-free E[RxCML] = rf + x(E[RMkt] - rf) E[RxCML] = .05 +1.4375(.12 - .05) = .2081 or 20.8% Section: 11.8 Determining the Risk Premium Skill: Analytical 20) Which of the following statements is FALSE? A) The risk premium of a security is equal to the market risk premium (the amount by which the market's expected return exceeds the risk-free rate), divided by the amount of market risk present in the security's returns measured by its beta with the market. B) We refer to the beta of a security with the market portfolio simply as the securities beta. C) There is a linear relationship between a stock's beta and its expected return. D) A security with a negative beta has a negative correlation with the market, which means that this security tend to perform will when the rest of the market is doing poorly. Explanation: A) The risk premium of a security is equal to the market risk premium (the amount by which the market’s expected return exceeds the risk-free rate), multiplied by the amount of market risk present in the security’s returns measured by its beta with the market. Section: 11.8 Determining the Risk Premium Skill: Conceptual 21) Which of the following statements is FALSE? A) The expected return of a portfolio should correspond to the portfolio's beta. B) Graphically the line through the risk-free investment and the market portfolio is called the capital market line (CML). C) The beta of a portfolio is the weighted average beta of the securities in the portfolio. D) By holding a negative beta security, an investor can reduce the overall market risk of her portfolio. Section: 11.8 Determining the Risk Premium Skill: Conceptual 22) Which of the following statements is FALSE? A) To improve the performance of their portfolios, investors who are holding the market portfolio will compare the expected return of each security with its required return from the security market line. B) The Sharpe ratio of a portfolio will increase if we sell stocks with positive alphas. C) When a stock's alpha is not zero, investors can improve upon the performance of the market portfolio. D) When the market portfolio is efficient, all stocks are on the security market line and have an alpha of zero. Explanation: B) The Sharpe ratio of a portfolio will decrease if we sell stocks with positive alphas. Section: 11.8 Determining the Risk Premium Skill: Conceptual 23) Which of the following statements is FALSE? A) We can improve the performance of our portfolio by selling stocks with negative alphas. B) The market portfolio is on the SML, and according to the CAPM, since all other portfolios are inefficient they will not fall on the SML. C) The difference between a stock's expected return and its required return according to the security market line is called the stock's alpha. D) The risk premium for any security is proportional to its beta with the market. Section: 11.8 Determining the Risk Premium Skill: Conceptual 24) Which of the following statements is FALSE? A) The market portfolio is the efficient portfolio. B) Many practitioners believe it is sensible to use the CAPM and the security market line as a practical means to estimate a stock's required return and therefore a firm's equity cost of capital. C) If we plot individual securities according to their expected return and beta, the CAPM implies that they should all fall along the CML. D) As savvy investors attempt to trade to improve their portfolios, they raise the price and lower the expected return of the positive alpha stocks, and they depress the price and raise the expected return of negative alpha stocks, until the stocks are once again on the security market line and the market portfolio is efficient. Section: 11.8 Determining the Risk Premium Skill: Conceptual 25) The beta for the market portfolio is closest to: A) 1 B) 0 C) Unable to answer this question without knowing the markets expected return D) Unable to answer this question without knowing the markets volatility Explanation: A) Beta of the Market Portfolio = bmkt = = Corr(Rmkt,Rmkt) = 1 (since the market is perfectly correlated with itself.) Section: 11.8 Determining the Risk Premium Skill: Analytical 26) The beta for the risk free investment is closest to: A) 1 B) 0 C) Unable to answer this question without knowing the risk free rate D) Unable to answer this question without knowing the markets volatility Explanation: B) Beta of the Market Portfolio = brf = = since the risk free investment has zero volatility, the Beta must equal zero. Section: 11.8 Determining the Risk Premium Skill: Analytical Use the information for the question(s) below. Suppose that the risk-free rate is 5% and the market portfolio has an expected return of 13% with a volatility of 18%. Monsters Inc. has a 24% volatility and a correlation with the market of .60, while California Gold Mining has a 32% volatility and a correlation with the market of -.7. Assume the CAPM assumptions hold. 27) Monsters' beta with the market is closest to: A) 1.3 B) 1.0 C) 0.6 D) 0.8 Explanation: D) bMonsters = = = .80 Section: 11.8 Determining the Risk Premium Skill: Analytical 28) Monsters' required return is closest to: A) 10.0% B) 13.0% C) 11.5% D) 15.5% Explanation: C) bMonsters = = = .80 ri = rf + b(E[RMkt] - rf) = .05 + .8(.13 - .05) = .114 Section: 11.8 Determining the Risk Premium Skill: Analytical 29) Suppose that Monsters' expected return is 12%. Then Monsters' alpha is closest to: A) -2.0% B) -1.0% C) 1.0% D) 0.5% Explanation: D) bMonsters = = = .80 ri = rf + b(E[RMkt] - rf) = .05 + .8(.13 - .05) = .114 so alpha = .12 - 11.4 = 0.6% Section: 11.8 Determining the Risk Premium Skill: Analytical 30) California Gold Mining's beta with the market is closest to: A) 0.9 B) 1.25 C) -0.9 D) -1.25 Explanation: D) bCGM = = = -1.24 Section: 11.8 Determining the Risk Premium Skill: Analytical 31) California Gold Mining's required return is closest to: A) -5% B) 13% C) 15% D) 5% Explanation: A) bCGM = = = -1.24 ri = rf + b(E[RMkt] - rf) = .05 + -1.24(.13 - .05) = -.05 or -5% Section: 11.8 Determining the Risk Premium Skill: Analytical 32) Suppose that California Gold Mining's expected return is 2%. Then California Gold Mining's alpha is closest to: A) -3% B) -13% C) 7% D) -11% Explanation: C) bCGM = = = -1.24 ri = rf + b(E[RMkt] - rf) = .05 + -1.24(.13 - .05) = -.05 or -5% Alpha = .02 - -.05 = 7% Section: 11.8 Determining the Risk Premium Skill: Analytical Use the table for the question(s) below. Consider the following three individuals portfolios consisting of investments in four stocks: | Stock | Beta | Peter's Investment | Paul's Investment | Mary's Investment | Eenie | 1.3 | 2500 | 5000 | 10000 | Meenie | 1.0 | 2500 | 5000 | 10000 | Minie | 0.8 | 2500 | 5000 | -5000 | Moe | -0.5 | 2500 | -5000 | -5000 33) The beta on Peter's Portfolio is closest to: A) 0.7 B) 0.8 C) 1.8 D) 1.0 Explanation: A) bportfolio = Σxibi | Stock | Beta | Peter's Investment | Paul's Investment | Mary's Investment | Peter's Weights | Paul's Weights | Mary's Weights | Eenie | 1.3 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Meenie | 1.0 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Minie | 0.8 | 2500 | 5000 | -5000 | 25% | 50% | -50% | Moe | -0.5 | 2500 | -5000 | -5000 | 25% | -50% | -50% | | | | | Port Beta= | 0.65 | 1.80 | 2.15 Section: 11.8 Determining the Risk Premium Skill: Analytical 34) Assuming that the risk-free rate is 4% and the expected return on the market is 12%, then required return on Peter's Portfolio is closest to: A) 10% B) 12% C) 9% D) 8% Explanation: C) bportfolio = Σxibi ri = rf + b(E[RMkt] - rf) = .04 + .65(.12 - .04) = .092 | Stock | Beta | Peter's Investment | Paul's Investment | Mary's Investment | Peter's Weights | Paul's Weights | Mary's Weights | Eenie | 1.3 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Meenie | 1.0 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Minie | 0.8 | 2500 | 5000 | -5000 | 25% | 50% | -50% | Moe | -0.5 | 2500 | -5000 | -5000 | 25% | -50% | -50% | | | | | Port Beta= | 0.65 | 1.80 | 2.15 Section: 11.8 Determining the Risk Premium Skill: Analytical 35) The beta on Paul's Portfolio is closest to: A) 1.5 B) 1.8 C) 1.3 D) 1.0 Explanation: B) bportfolio = Σxibi | Stock | Beta | Peter's Investment | Paul's Investment | Mary's Investment | Peter's Weights | Paul's Weights | Mary's Weights | Eenie | 1.3 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Meenie | 1.0 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Minie | 0.8 | 2500 | 5000 | -5000 | 25% | 50% | -50% | Moe | -0.5 | 2500 | -5000 | -5000 | 25% | -50% | -50% | | | | | Port Beta= | 0.65 | 1.80 | 2.15 Section: 11.8 Determining the Risk Premium Skill: Analytical 36) Assuming that the risk-free rate is 4% and the expected return on the market is 12%, then required return on Peter's portfolio is closest to: A) 20% B) 22% C) 18% D) 16% Explanation: C) bportfolio = Σxibi ri = rf + b(E[RMkt] - rf) = .04 + 1.8(.12 - .04) = .184 | Stock | Beta | Peter's Investment | Paul's Investment | Mary's Investment | Peter's Weights | Paul's Weights | Mary's Weights | Eenie | 1.3 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Meenie | 1.0 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Minie | 0.8 | 2500 | 5000 | -5000 | 25% | 50% | -50% | Moe | -0.5 | 2500 | -5000 | -5000 | 25% | -50% | -50% | | | | | Port Beta= | 0.65 | 1.80 | 2.15 Section: 11.8 Determining the Risk Premium Skill: Analytical 37) Assuming that the risk-free rate is 4% and the expected return on the market is 12%, then calculate the required return on Mary's portfolio. portfolio = Σxibi ri = rf + b(E[RMkt] - rf) = .04 + 2.15(.12 - .04) = .212 | Stock | Beta | Peter's Investment | Paul's Investment | Mary's Investment | Peter's Weights | Paul's Weights | Mary's Weights | Eenie | 1.3 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Meenie | 1.0 | 2500 | 5000 | 10000 | 25% | 50% | 100% | Minie | 0.8 | 2500 | 5000 | -5000 | 25% | 50% | -50% | Moe | -0.5 | 2500 | -5000 | -5000 | 25% | -50% | -50% | | | | | Port Beta= | 0.65 | 1.80 | 2.15 Section: 11.8 Determining the Risk Premium Skill: Analytical 38) Suppose that the risk-free rate is 5% and the market portfolio has an expected return of 13% with a volatility of 18%. Luther Industries has a volatility of 24% and a correlation with the market of .5. If you assume that the CAPM assumptions hold, then what is the expected return on Luther stock? Answer: bMonsters = = = .66667 ri = rf + b(E[RMkt] - rf) = .05 + .66667(.13 - .05) = .103333 Section: 11.8 Determining the Risk Premium Skill: Analytical 39) Which of the following statements is FALSE? A) Investors may have different information regarding expected returns, correlations, and volatilities, but they correctly interpret that information and the information contained in market prices and they adjust their estimates of expected returns in a rational way. B) Investors may learn different information through their own research and observations, but as long as they understand the differences in information and learn from other investors by observing prices, the CAPM conclusions still stand. C) Every investor, regardless of how much information he has access to, can guarantee himself an alpha of zero by holding the market portfolio. D) The CAPM requires making the strong assumption of homogeneous expectations. Section: 11.8 Determining the Risk Premium Skill: Conceptual 40) Which of the following statements is FALSE? A) Because of the higher and uncompensated risk involved, no investor should choose a portfolio with a negative alpha. B) Because the average portfolio of all investors is the market portfolio, the average alpha for all investors is zero. C) The market portfolio can be inefficient if a significant number of investors misinterpret information and believe they are earning a positive alpha when they are actually earning a negative alpha. D) If no investor earns a positive alpha, then no investor can earn a negative alpha, and the market portfolio must be efficient. Section: 11.8 Determining the Risk Premium Skill: Conceptual 41) Explain how having different interest rates for borrowing and lending affects the CAPM and the SML. Answer: The basic conclusions of the CAPM will still hold. However, investors will now be faced with a group of efficient portfolios of risky assets along the efficient frontier. An individual investors optimal efficient portfolio will be the one identified by the line tangent to the efficient frontier that intersects at their appropriate interest rate. The market portfolio will become the average of all the individual efficient portfolios, and an average interest rate can be used to generalize the CAPM and SML to all investors using the market portfolio. Section: 11.8 Determining the Risk Premium Skill: Conceptual [Show More]

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