Reading 20 Portfolio Risk and Return Part I - Answers.pdf

Question #1 of 66 Question ID: 1573189 In a two-asset portfolio, reducing the correlation between the two assets moves the efficient frontier in which direction? The efficient frontier is stable unless return expectations change. If ex...

Question #1 of 66 Question ID: 1573189 In a two-asset portfolio, reducing the correlation between the two assets moves the efficient frontier in which direction? The efficient frontier is stable unless return expectations change. If expectations A) change, the efficient frontier will extend to the upper right with little or no change in risk. The efficient frontier is stable unless the asset’s expected volatility changes. This B) depends on each asset’s standard deviation. The frontier extends to the left, or northwest quadrant representing a reduction C) in risk while maintaining or enhancing portfolio returns. Explanation Reducing correlation between the two assets results in the efficient frontier expanding to the left and possibly slightly upward. This reflects the influence of correlation on reducing portfolio risk. (Module 20.4, LOS 20.g) Question #2 of 66 Question ID: 1573142 The particular portfolio on the efficient frontier that best suits an individual investor is determined by: A) the individual's utility curve. B) the current market risk-free rate as compared to the current market return rate. C) the individual's asset allocation plan. Explanation The optimal portfolio for each investor is the highest indifference curve that is tangent to the efficient frontier. The optimal portfolio is the portfolio that gives the investor the greatest possible utility. (Module 20.2, LOS 20.c) Question #3 of 66 Question ID: 1573196 According to the CAPM, a rational investor would be least likely to choose as his optimal portfolio: A) a 100% allocation to the risk-free asset. B) the global minimum variance portfolio. C) a 130% allocation to the market portfolio. Explanation According to the CAPM, rational, risk-averse investors will optimally choose to hold a portfolio along the capital market line. This can range from a 100% allocation to the risk- free asset to a leveraged position in the market portfolio constructed by borrowing at the risk-free rate to invest more than 100% of the portfolio equity value in the market portfolio. The global minimum variance portfolio lies below the CML and is not an efficient portfolio under the assumptions of the CAPM. (Module 20.4, LOS 20.g) Question #4 of 66 Question ID: 1573162 If the standard deviation of returns for stock X is 0.60 and for stock Y is 0.40 and the covariance between the returns of the two stocks is 0.009, the correlation between stocks X and Y is closest to: A) 26.6670. B) 0.0375. C) 0.0020. Explanation CovX,Y = (rX,Y)(sX)(sY), where r = correlation coefficient, sx = standard deviation of stock X , and sY = standard deviation of stock Y Then, (rX,Y) = CovX,Y / (SDX × SDY) = 0.009 / (0.600 × 0.400) = 0.0375 (Module 20.3, LOS 20.d) Question #5 of 66 Question ID: 1573193 Which of the following portfolios falls below the Markowitz efficient frontier? Portfolio Expected Return Expected Standard Deviation A 7% 14% B 9% 26% C 15% 30% D 12% 22% A) B. B) C. C) D. Explanation Portfolio B is not on the efficient frontier because it has a lower return, but higher risk, than Portfolio D. (Module 20.4, LOS 20.g) Question #6 of 66 Question ID: 1573176 As the correlation between the returns of two assets becomes lower, the risk reduction potential becomes: A) decreased by the same level. B) greater. C) smaller. Explanation Perfect positive correlation (r = +1) of the returns of two assets offers no risk reduction, whereas perfect negative correlation (r = -1) offers the greatest risk reduction. (Module 20.4, LOS 20.f) Question #7 of 66 Question ID: 1573169 What is the variance of a two-stock portfolio if 15% is invested in stock A (variance of 0.0071) and 85% in stock B (variance of 0.0008) and the correlation coefficient between the stocks is –0.04? A) 0.0007. B) 0.0020. C) 0.0026. Explanation The variance of the portfolio is found by: [W12 σ12 + W22 σ22 + 2W1W2σ1σ2r1,2], or [(0.15)2(0.0071) + (0.85)2(0.0008) + (2) (0.15)(0.85)(0.0843)(0.0283)(–0.04)] = 0.0007. (Module 20.3, LOS 20.e) Question #8 of 66 Question ID: 1573149 Becky Scott and Sid Fiona have the same expectations about the risk and return of the market portfolio; however, Scott selects a portfolio with 30% T-bills and 70% invested in the market portfolio, while Fiona holds a leveraged portfolio, having borrowed to invest 130% of his portfolio equity value in the market portfolio. Regarding their preferences between risk and return and their indifference curves, it is most likely that: Scott is willing to take on more risk to increase her expected portfolio return A) than Fiona is. B) Scott is risk averse but Fiona is not. C) Fiona’s indifference curves are flatter than Scott’s. Explanation Even risk-averse investors will prefer leveraged risky portfolios if the increase in expected return is enough to offset the increase in portfolio risk. Scott's portfolio selection implies that she is more risk averse than Fiona, has steeper indifference curves, and is willing to take on less additional risk for an incremental increase in expected returns than Fiona. (Module 20.2, LOS 20.c) Question #9 of 66 Question ID: 1573154 Stock 1 has a standard deviation of 10. Stock 2 also has a standard deviation of 10. If the correlation coefficient between these stocks is –1, what is the covariance between these two stocks? A) 0.00. B) –100.00. C) 1.00. Explanation Covariance = correlation coefficient × standard deviationStock 1 × standard deviationStock 2 = (–1.00) (10.00)(10.00) = –100.00. (Module 20.3, LOS 20.d) Question #10 of 66 Question ID: 1573148 Which of the following statements about the efficient frontier is least accurate? Investors will want to invest in the portfolio on the efficient frontier that offers A) the highest rate of return. B) Portfolios falling on the efficient frontier are fully diversified. The efficient frontier shows the relationship that exists between expected C) return and total risk in the absence of a risk-free asset. Explanation The optimal portfolio for each investor is the highest indifference curve that is tangent to the efficient frontier. (Module 20.2, LOS 20.c) Question #11 of 66 Question ID: 1573135 Historically, which of the following asset classes has exhibited the smallest standard deviation of monthly returns? A) Large-capitalization stocks. B) Long-term corporate bonds. C) Treasury bills. Explanation Based on data for securities in the United States from 1926 to 2008, Treasury bills exhibited a lower standard deviation of monthly returns than both large-cap stocks and long-term corporate bonds. (Module 20.1, LOS 20.a) Question #12 of 66 Question ID: 1573198 In the Markowitz framework, risk is defined as the: A) variance of returns. B) probability of a loss. C) beta of an investment. Explanation The Markowitz framework assumes that all investors view risk as the variability of returns. The variability of returns is measured as the variance (or equivalently standard deviation) of returns. The capital asset pricing model (CAPM) employs beta as the measure of an investment's systematic risk. (Module 20.4, LOS 20.g) Question #13 of 66 Question ID: 1573166 Calculating the variance of a two-asset portfolio least likely requires inputs for each asset's: A) beta. B) weight in the portfolio. C) standard deviation. Explanation Beta is not an input to calculate the variance of a two-asset portfolio. The formula for calculating the variance of a two-asset portfolio is: 2 2 2 2 2 σ = w σ + w σ + 2wA wB CovAB P A A B B (Module 20.3, LOS 20.e) Question #14 of 66 Question ID: 1573191 Which of the following portfolios falls below the Markowitz efficient frontier? Portfolio Expected Return Expected Standard Deviation A 12.1% 8.5% B 14.2% 8.7% C 15.1% 8.7% A) Portfolio A. B) Portfolio C. C) Portfolio B. Explanation Portfolio B is inefficient (falls below the efficient frontier) because for the same risk level (8.7%), you could have portfolio C with a higher expected return (15.1% versus 14.2%). (Module 20.4, LOS 20.g) Question #15 of 66 Question ID: 1573195 Which of the following inputs is least likely required for the Markowitz efficient frontier? The: A) level of risk aversion in the market. B) covariation between all securities. C) expected return of all securities. Explanation The level of risk aversion in the market is not a required input. The model requires that investors know the expected return and variance of each security as well as the covariance between all securities. (Module 20.4, LOS 20.g) Question #16 of 66 Question ID: 1573180 There are benefits to diversification as long as: A) the correlation coefficient between the assets is less than 1. B) there is perfect positive correlation between the assets. C) there must be perfect negative correlation between the assets. Explanation There are benefits to diversification as long as the correlation coefficient between the assets is less than 1. (Module 20.4, LOS 20.f) Question #17 of 66 Question ID: 1573190 On a graph of risk, measured by standard deviation and expected return, the efficient frontier represents: A) the set of portfolios that dominate all others as to risk and return. the group of portfolios that have extreme values and therefore are “efficient” in B) their allocation. C) all portfolios plotted in the northeast quadrant that maximize return. Explanation The efficient set is the set of portfolios that dominate all other portfolios as to risk and return. That is, they have highest expected return at each level of risk. (Module 20.4, LOS 20.g) Question #18 of 66 Question ID: 1573187 Which one of the following portfolios cannot lie on the efficient frontier? Portfolio Expected Return Standard Deviation A 20% 35% B 11% 13% C 8% 10% D 8% 9% A) Portfolio D. B) Portfolio C. C) Portfolio A. Explanation Portfolio C cannot lie on the frontier because it has the same return as Portfolio D, but has more risk. (Module 20.4, LOS 20.g) Question #19 of 66 Question ID: 1573188 Which one of the following portfolios does not lie on the efficient frontier? Portfolio Expected Return Standard Deviation A 7 5 B 9 12 C 11 10 D 15 15 A) C. B) B. C) A. Explanation Portfolio B has a lower expected return than Portfolio C with a higher standard deviation. (Module 20.4, LOS 20.g) Question #20 of 66 Question ID: 1573155 The correlation coefficient between stocks A and B is 0.75. The standard deviation of stock A's returns is 16% and the standard deviation of stock B's returns is 22%. What is the covariance between stock A and B? A) 0.0352. B) 0.3750. C) 0.0264. Explanation cov1,2 = 0.75 × 0.16 × 0.22 = 0.0264 = covariance between A and B. (Module 20.3, LOS 20.d) Question #21 of 66 Question ID: 1573179 Which one of the following statements about correlation is NOT correct? A) Potential benefits from diversification arise when correlation is less than +1. If the correlation coefficient were 0, a zero variance portfolio could be B) constructed. If the correlation coefficient were -1, a zero variance portfolio could be C) constructed. Explanation A correlation coefficient of zero means that there is no relationship between the stock's returns. The other statements are true. (Module 20.4, LOS 20.f) Question #22 of 66 Question ID: 1573192 Which of the following statements about the efficient frontier is least accurate?  A portfolio that plots above efficient frontier is not attainable, while a portfolio A) that plots below the efficient frontier is inefficient. The efficient frontier is the set of portfolios with the greatest expected return B) for a given level of risk. C) The slope of the efficient frontier increases steadily as risk increases. Explanation The slope of the efficient frontier decreases steadily as risk and return increase. The efficient frontier is the set of portfolios with the greatest expected return for a given level of risk as measured by standard deviation of returns. That is, for a given level of risk, an expected return greater than that of the portfolio on the efficient frontier is not attainable, and a portfolio with a lower expected return is inefficient. (Module 20.4, LOS 20.g) Question #23 of 66 Question ID: 1573133 Over the long term, the annual returns and standard deviations of returns for major asset classes have shown: A) a negative relationship. B) a positive relationship. C) no clear relationship. Explanation In most markets and for most asset classes, higher average returns have historically been associated with higher risk (standard deviation of returns). (Module 20.1, LOS 20.a) Question #24 of 66 Question ID: 1573157 An analyst gathered the following data for Stock A and Stock B: Time Period Stock A Returns Stock B Returns 1 10% 15% 2 6% 9% 3 8% 12% What is the covariance for this portfolio? A) 6. B) 3. C) 12. Explanation The formula for the covariance for historical data is: cov1,2 = {Σ[(Rstock A − Mean RA)(Rstock B − Mean RB)]} / (n − 1) Mean RA = (10 + 6 + 8) / 3 = 8, Mean RB = (15 + 9 + 12) / 3 = 12 Here, cov1,2 = [(10 − 8)(15 − 12) + (6 − 8)(9 − 12) + (8 − 8)(12 − 12)] / 2 = 6 (Module 20.3, LOS 20.d) Question #25 of 66 Question ID: 1573164 Betsy Minor is considering the diversification benefits of a two stock portfolio. The expected return of stock A is 14 percent with a standard deviation of 18 percent and the expected return of stock B is 18 percent with a standard deviation of 24 percent. Minor intends to invest 40 percent of her money in stock A, and 60 percent in stock B. The correlation coefficient between the two stocks is 0.6. What is the variance and standard deviation of the two stock portfolio? A) Variance = 0.02206; Standard Deviation = 14.85%. B) Variance = 0.03836; Standard Deviation = 19.59%. C) Variance = 0.04666; Standard Deviation = 21.60%. Explanation (0.40)2(0.18)2 + (0.60)2(0.24)2 + 2(0.4)(0.6)(0.18)(0.24)(0.6) = 0.03836. 0.038360.5 = 0.1959 or 19.59%. (Module 20.3, LOS 20.e) Question #26 of 66 Question ID: 1573175 A portfolio manager adds a new stock that has the same standard deviation of returns as the existing portfolio but has a correlation coefficient with the existing portfolio that is less than +1. Adding this stock will have what effect on the standard deviation of the revised portfolio's returns? The standard deviation will: A) decrease only if the correlation is negative. B) decrease. C) increase. Explanation If the correlation coefficient is less than 1, there are benefits to diversification. Thus, adding the stock will reduce the portfolio's standard deviation. (Module 20.4, LOS 20.f) Question #27 of 66 Question ID: 1573186 Of the six attainable portfolios listed, which portfolios are not on the efficient frontier? Portfolio Expected Return Standard Deviation A 26% 28% B 23% 34% C 14% 23% D 18% 14% E 11% 8% F 18% 16% A) A, B, and C. B) B, C, and F. C) C, D, and E. Explanation Portfolio B cannot lie on the frontier because its risk is higher than that of Portfolio A's with lower return. Portfolio C cannot lie on the frontier because it has higher risk than Portfolio D with lower return. Portfolio F cannot lie on the frontier cannot lie on the frontier because its risk is higher than Portfolio D. (Module 20.4, LOS 20.g) Question #28 of 66 Question ID: 1573140 The basic premise of the risk-return trade-off suggests that risk-averse individuals purchasing investments with higher non-diversifiable risk should expect to earn: A) lower rates of return. B) rates of return equal to the market. C) higher rates of return. Explanation Investors are risk averse. Given a choice between two assets with equal rates of return, the investor will always select the asset with the lowest level of risk. This means that there is a positive relationship between expected returns (ER) and expected risk (Eσ) and the risk return line (capital market line [CML] and security market line [SML]) is upward sweeping. (Module 20.2, LOS 20.c) Question #29 of 66 Question ID: 1573151 A bond analyst is looking at historical returns for two bonds, Bond 1 and Bond 2. Bond 2's returns are much more volatile than Bond 1. The variance of returns for Bond 1 is 0.012 and the variance of returns of Bond 2 is 0.308. The correlation between the returns of the two bonds is 0.79, and the covariance is 0.048. If the variance of Bond 1 increases to 0.026 while the variance of Bond 2 decreases to 0.188 and the covariance remains the same, the correlation between the two bonds will: A) decrease. B) increase. C) remain the same. Explanation P1,2 = 0.048/(0.0260.5 × 0.1880.5) = 0.69 which is lower than the original 0.79. (Module 20.3, LOS 20.d) Question #30 of 66 Question ID: 1573150 Smith has more steeply sloped risk-return indifference curves than Jones. Assuming these investors have the same expectations, which of the following best describes their risk preferences and the characteristics of their optimal portfolios? Smith is: less risk averse than Jones and will choose an optimal portfolio with a lower A) expected return. more risk averse than Jones and will choose an optimal portfolio with a higher B) expected return.  more risk averse than Jones and will choose an optimal portfolio with a lower C) expected return. Explanation Steeply sloped risk-return indifference curves indicate that a greater increase in expected return is required as compensation for assuming an additional unit of risk, compared to less-steep indifference curves. The more risk-averse Smith will choose an optimal portfolio with lower risk and a lower expected return than the less risk-averse Jones's optimal portfolio. (Module 20.2, LOS 20.c) Question #31 of 66 Question ID: 1573185 The efficient frontier is best described as the set of attainable portfolios that gives investors: A) the highest expected return for any given level of risk. B) the lowest risk for any given level of risk tolerance. C) the highest diversification ratio for any given level of expected return. Explanation The efficient frontier is the set of efficient portfolios that gives investors the highest expected return for any given level of risk, or the lowest risk for any given level of expected return. Efficient portfolios have low diversification ratios. (Module 20.4, LOS 20.g) Question #32 of 66 Question ID: 1573147 Which of the following statements about the optimal portfolio is NOT correct? The optimal portfolio: A) is the portfolio that gives the investor the maximum level of return. B) may be different for different investors. lies at the point of tangency between the efficient frontier and the indifference C) curve with the highest possible utility. Explanation This statement is incorrect because it does not specify that risk must also be considered. (Module 20.2, LOS 20.c) Question #33 of 66 Question ID: 1573171 Two assets are perfectly positively correlated. If 30% of an investor's funds were put in the asset with a standard deviation of 0.3 and 70% were invested in an asset with a standard deviation of 0.4, what is the standard deviation of the portfolio? A) 0.151. B) 0.370. C) 0.426. Explanation σ portfolio = [W12σ12 + W22σ22 + 2W1W2σ1σ2r1,2]1/2 given r1,2 = +1 σ = [W12σ12 + W22σ22 + 2W1W2σ1σ2]1/2 = (W1σ1 + W2σ2)2]1/2 σ = (W1σ1 + W2σ2) = (0.3)(0.3) + (0.7)(0.4) = 0.09 + 0.28 = 0.37 (Module 20.3, LOS 20.e) Question #34 of 66 Question ID: 1573161 If the standard deviation of stock X is 7.2%, the standard deviation of stock Y is 5.4%, and the covariance between the two is –0.0031, their correlation coefficient is closest to: A) -0.80. B) -0.19. C) -0.64. Explanation Correlation = (covariance of X and Y) / [(standard deviation of X)(standard deviation of Y)] = –0.0031 / [(0.072)(0.054)] = –0.797. (Module 20.3, LOS 20.d) Question #35 of 66 Question ID: 1573183 Kendra Jackson, CFA, is given the following information on two stocks, Rockaway and Bridgeport. Covariance between the two stocks = 0.0325 Standard Deviation of Rockaway's returns = 0.25 Standard Deviation of Bridgeport's returns = 0.13 Assuming that Jackson must construct a portfolio using only these two stocks, which of the following combinations will result in the minimum variance portfolio? A) 100% in Bridgeport. B) 50% in Bridgeport, 50% in Rockaway. C) 80% in Bridgeport, 20% in Rockaway. Explanation First, calculate the correlation coefficient to check whether diversification will provide any benefit. rBridgeport, Rockaway = covBridgeport, Rockaway / [( σBridgeport) × (σRockaway) ] = 0.0325 / (0.13 × 0.25) = 1.00 Since the stocks are perfectly positively correlated, there are no diversification benefits and we select the stock with the lowest risk (as measured by variance or standard deviation), which is Bridgeport. (Module 20.4, LOS 20.g) Question #36 of 66 Question ID: 1573134 Over long periods of time, compared to fixed income securities, equities have tended to exhibit: A) higher average annual returns and higher standard deviation of returns. B) higher average annual returns and lower standard deviation of returns. C) lower average annual returns and higher standard deviation of returns. Explanation Based on data for securities in the United States from 1926 to 2008, both small-cap stocks and large-cap stocks have exhibited higher average annual returns and higher standard deviations of returns than long-term corporate bonds and long-term government bonds. Results over long periods of time have been similar in other developed markets. (Module 20.1, LOS 20.a) Question #37 of 66 Question ID: 1573158 The covariance of the market's returns with the stock's returns is 0.008. The standard deviation of the market's returns is 0.1 and the standard deviation of the stock's returns is 0.2. What is the correlation coefficient between the stock and market returns? A) 0.00016. B) 0.40. C) 0.91. Explanation CovA,B = (rA,B)(SDA)(SDB), where r = correlation coefficient and SDx = standard deviation of stock x Then, (rA,B) = CovA,B / (SDA × SDB) = 0.008 / (0.100 × 0.200) = 0.40 Remember: The correlation coefficient must be between -1 and 1. (Module 20.3, LOS 20.d) Question #38 of 66 Question ID: 1573173 An investor's portfolio currently has an expected return of 11% with a variance of 0.0081. She is considering replacing 20% of the portfolio with a security that has an expected return of 12% and a standard deviation of 0.07. If the covariance between the returns on the existing portfolio and the returns on the added security is 0.0058, the variance of returns on the new portfolio will be closest to: A) 0.00545. B) 0.00724. C) 0.00984. Explanation 0.82(0.0081) + 0.22 (0.072) + 2(0.8)(0.2)(0.0058) = 0.00724. (Module 20.3, LOS 20.e) Question #39 of 66 Question ID: 1573156 If two stocks have positive covariance: A) they are likely to be in the same industry. B) they exhibit a strong correlation of returns. C) their rates of return tend to change in the same direction. Explanation For two stocks with positive covariance, their prices will tend to move together over time and they will tend to produce rates of return greater than their mean returns at the same time and produce rates of return less than their mean returns at the same time. Positive covariance does not necessarily imply strong positive correlation. Two stocks need not be in the same industry to have a positive covariance. (Module 20.3, LOS 20.d) Question #40 of 66 Question ID: 1573181 Stock A has a standard deviation of 0.5 and Stock B has a standard deviation of 0.3. Stock A and Stock B are perfectly positively correlated. According to Markowitz portfolio theory how much should be invested in each stock to minimize the portfolio's standard deviation? A) 100% in Stock B. B) 30% in Stock A and 70% in Stock B. C) 50% in Stock A and 50% in Stock B. Explanation Since the stocks are perfectly correlated, there is no benefit from diversification. So, invest in the stock with the lowest risk. (Module 20.4, LOS 20.f) Question #41 of 66 Question ID: 1573139 Three portfolios have the following expected returns and risk: Portfolio Expected return Standard deviation Jones 4% 4% Kelly 5% 6% Lewis 6% 5% A risk-averse investor choosing from these portfolios could rationally select: A) Jones, but not Kelly or Lewis. B) Jones or Lewis, but not Kelly. C) Lewis, but not Kelly or Jones. Explanation Risk aversion means that to accept greater risk, an investor must be compensated with a higher expected return. A risk-averse investor will not select a portfolio if another portfolio offers a higher expected return with the same risk, or lower risk with the same expected return. Thus a rational investor would always choose Lewis over Kelly, because Lewis has both a higher expected return and lower risk than Kelly. Neither Lewis nor Kelly is necessarily preferable to Jones, because although Jones has a lower expected return, it also has lower risk. Therefore, either Jones or Lewis might be selected by a rational investor, but Kelly would not be. (Module 20.2, LOS 20.b) Question #42 of 66 Question ID: 1573168 An investor has a two-stock portfolio (Stocks A and B) with the following characteristics: σA = 55% σB = 85% CovarianceA,B = 0.09 WA = 70% WB = 30% The variance of the portfolio is closest to: A) 0.39. B) 0.25. C) 0.54. Explanation The formula for the variance of a 2-stock portfolio is: s2 = [WA2σA2 + WB2σB2 + 2WAWBσAσBrA,B] Since σAσBrA,B = CovA,B, then s2 = [(0.72 × 0.552) + (0.32 × 0.852) + (2 × 0.7 × 0.3 × 0.09)] = [0.1482 + 0.0650 + 0.0378] = 0.2511. (Module 20.3, LOS 20.e) Question #43 of 66 Question ID: 1573163 An investment advisor is considering a portfolio that is 60% invested in a broad-based stock index fund with the remainder invested in a taxable bond fund. The stock index fund has an expected return of 7% and variance of 0.04, while the bond fund has an expected return of 3% and a variance of 0.0081. If the covariance of returns between the bond and index funds is 0.0108, the standard deviation of returns for the overall portfolio is closest to: A) 1.58%. B) 14.45%. C) 12.56%. Explanation The standard deviation of returns for the overall portfolio is as follows: 2 2 √0.6 (0.04) + 0.4 (0.0081) + 2 (0.6) (0.4) (0.0108) = 14.4499% (Module 20.3, LOS 20.d) Question #44 of 66 Question ID: 1573167 Assets A (with a variance of 0.25) and B (with a variance of 0.40) are perfectly positively correlated. If an investor creates a portfolio using only these two assets with 40% invested in A, the portfolio standard deviation is closest to: A) 0.3400. B) 0.3742. C) 0.5795. Explanation The portfolio standard deviation = [(0.4)2(0.25) + (0.6)2(0.4) + 2(0.4)(0.6)1(0.25)0.5(0.4)0.5]0.5 = 0.5795 (Module 20.3, LOS 20.e) Question #45 of 66 Question ID: 1573160 If the standard deviation of stock A is 10.6%, the standard deviation of stock B is 14.6%, and the covariance between the two is 0.015476, what is the correlation coefficient? A) +1. B) 0. C) 0.0002. Explanation The formula is: (Covariance of A and B) / [(Standard deviation of A)(Standard Deviation of B)] = (Correlation Coefficient of A and B) = (0.015476) / [(0.106)(0.146)] = 1. (Module 20.3, LOS 20.d) Question #46 of 66 Question ID: 1573177 Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than which of the following? A) +0.50. B) 0.00. C) +1.00. Explanation Adding any stock that is not perfectly correlated with the portfolio (+1) will reduce the risk of the portfolio. (Module 20.4, LOS 20.f) Question #47 of 66 Question ID: 1573143 Investors who are less risk averse will have what type of indifference curves for risk and expected return? A) Flatter. B) Inverted. C) Steeper. Explanation Investors who are less risk averse will have flatter indifference curves, meaning they are willing to take on more risk for a slightly higher return. Investors who are more risk averse require a much higher return to accept more risk, producing steeper indifference curves. (Module 20.2, LOS 20.c) Question #48 of 66 Question ID: 1573172 A portfolio manager invests 40% of a portfolio in Asset X, which has an expected standard deviation of returns of 15%, and the remainder in Asset Y, which has an expected standard deviation of returns of 25%. If the covariance of returns between assets X and Y is 0.0158, the expected standard deviation of portfolio returns is closest to: A) 2.7%. B) 16.3%. C) 18.4%. Explanation The expected standard deviation of portfolio returns is: [0.402 × 0.152 + 0.602 × 0.252 + 2(0.40 × 0.60 × 0.0158)]1/2 = 18.35%. (Module 20.3, LOS 20.e) Question #49 of 66 Question ID: 1573145 According to Markowitz, an investor's optimal portfolio is determined where the: A) investor's utility curve meets the efficient frontier. B) investor's highest utility curve is tangent to the efficient frontier. C) investor's lowest utility curve is tangent to the efficient frontier. Explanation The optimal portfolio for an investor is determined as the point where the investor's highest utility curve is tangent to the efficient frontier. (Module 20.2, LOS 20.c) Question #50 of 66 Question ID: 1573184 Which of the following statements best describes an investment that is not on the efficient frontier? A) There is a portfolio that has a lower return for the same risk. B) The portfolio has a very high return. C) There is a portfolio that has a lower risk for the same return. Explanation The efficient frontier outlines the set of portfolios that gives investors the highest return for a given level of risk or the lowest risk for a given level of return. Therefore, if a portfolio is not on the efficient frontier, there must be a portfolio that has lower risk for the same return. Equivalently, there must be a portfolio that produces a higher return for the same risk. (Module 20.4, LOS 20.g) Question #51 of 66 Question ID: 1573174 A portfolio currently holds Randy Co. and the portfolio manager is thinking of adding either XYZ Co. or Branton Co. to the portfolio. All three stocks offer the same expected return and total risk. The covariance of returns between Randy Co. and XYZ is +0.5 and the covariance between Randy Co. and Branton Co. is -0.5. The portfolio's risk would decrease: A) more if she bought Branton Co. B) more if she bought XYZ Co. C) most if she put half your money in XYZ Co. and half in Branton Co. Explanation In portfolio composition questions, return and standard deviation are the key variables. Here you are told that both returns and standard deviations are equal. Thus, you just want to pick the companies with the lowest covariance, because that would mean you picked the ones with the lowest correlation coefficient. σportfolio = [W12 σ12 + W22 σ22 + 2W1 W2 σ1 σ2 r1,2]½ where σRandy =YBranton = σXYZ so you want to pick the lowest covariance which is between Randy and Branton. (Module 20.4, LOS 20.f) Question #52 of 66 Question ID: 1573178 Stock A has a standard deviation of 4.1% and Stock B has a standard deviation of 5.8%. If the stocks are perfectly positively correlated, which portfolio weights minimize the portfolio's standard deviation? Stock A Stock B A) 0% 100% B) 100% 0% C) 63% 37% Explanation Because there is a perfectly positive correlation, there is no benefit to diversification. Therefore, the investor should put all his money into Stock A (with the lowest standard deviation) to minimize the risk (standard deviation) of the portfolio. (Module 20.4, LOS 20.f) Question #53 of 66 Question ID: 1573152 If the standard deviation of returns for stock A is 0.40 and for stock B is 0.30 and the covariance between the returns of the two stocks is 0.007 what is the correlation between stocks A and B? A) 17.14300. B) 0.00084. C) 0.05830. Explanation CovA,B = (rA,B)(SDA)(SDB), where r = correlation coefficient and SDx = standard deviation of stock x Then, (rA,B) = CovA,B / (SDA × SDB) = 0.007 / (0.400 × 0.300) = 0.0583 (Module 20.3, LOS 20.d) Question #54 of 66 Question ID: 1573197 Which of the following possible portfolios is least likely to lie on the efficient frontier? Portfolio Expected Return Standard Deviation X 9% 12% Y 11% 10% Z 13% 15% A) Portfolio Z. B) Portfolio Y. C) Portfolio X. Explanation Portfolio X has a lower expected return and a higher standard deviation than Portfolio Y. X must be inefficient. (Module 20.4, LOS 20.g) Question #55 of 66 Question ID: 1573141 A line that represents the possible portfolios that combine a risky asset and a risk free asset is most accurately described as a: A) capital allocation line. B) capital market line. C) characteristic line. Explanation The line that represents possible combinations of a risky asset and the risk-free asset is referred to as a capital allocation line (CAL). The capital market line (CML) represents possible combinations of the market portfolio with the risk-free asset. A characteristic line is the best fitting linear relationship between excess returns on an asset and excess returns on the market and is used to estimate an asset's beta. (Module 20.2, LOS 20.c) Question #56 of 66 Question ID: 1573194 An investor has identified the following possible portfolios. Which portfolio cannot be on the efficient frontier? Portfolio Expected Return Standard Deviation V 18% 35% W 12% 16% X 10% 10% Y 14% 20% Z 13% 24% A) X. B) Z. C) Y. Explanation Portfolio Z must be inefficient because its risk is higher than Portfolio Y and its expected return is lower than Portfolio Y. (Module 20.4, LOS 20.g) Question #57 of 66 Question ID: 1573136 An analyst gathers the following data about the returns for two stocks. Stock A Stock B E(R) 0.04 0.09 σ2 0.0025 0.0064 CovA,B= 0.001 The correlation between the returns of Stock A and Stock B is closest to: A) 0.25. B) 0.50. C) 0.63. Explanation The correlation between the two stocks is: ρA,B = COVA,B / (σA × σB) = 0.001 / (0.05 × 0.08) = 0.001 / (0.004) = 0.25 Note that the formula uses the standard deviations, not the variances, of the returns on the two securities. (Module 20.1, LOS 20.a) Question #58 of 66 Question ID: 1573170 An investor calculates the following statistics on her two-stock (A and B) portfolio. σA = 20% σB = 15% rA,B = 0.32 WA = 70% WB = 30% The portfolio's standard deviation is closest to: A) 0.1600. B) 0.1832. C) 0.0256. Explanation The formula for the standard deviation of a 2-stock portfolio is: σ = [WA2σA2 + WB2σB2 + 2WAWBσAσBρA,B]1/2 σ = [(0.72 × 0.22) + (0.32 × 0.152) + ( 2 × 0.7 × 0.3 × 0.2 × 0.15 × 0.32)]1/2 = [0.0196 + 0.002025 + 0.004032]1/2 = 0.02565701/2 = 0.1602, or approximately 16.0%. (Module 20.3, LOS 20.e) Question #59 of 66 Question ID: 1573146 The optimal portfolio in the Markowitz framework occurs when an investor achieves the diversified portfolio with the: A) highest return. B) lowest risk. C) highest utility. Explanation The optimal portfolio in the Markowitz framework occurs when the investor achieves the diversified portfolio with the highest utility. (Module 20.2, LOS 20.c) Question #60 of 66 Question ID: 1573182 Which of the following statements about portfolio theory is least accurate? Assuming that the correlation coefficient is less than one, the risk of the A) portfolio will always be less than the simple weighted average of individual stock risks. For a two-stock portfolio, the lowest risk occurs when the correlation coefficient B) is close to negative one. When the return on an asset added to a portfolio has a correlation coefficient of C) less than one with the other portfolio asset returns but has the same risk, adding the asset will not decrease the overall portfolio standard deviation. Explanation When the return on an asset added to a portfolio has a correlation coefficient of less than one with the other portfolio asset returns but has the same risk, adding the asset will decrease the overall portfolio standard deviation. Any time the correlation coefficient is less than one, there are benefits from diversification. The other choices are true. (Module 20.4, LOS 20.f) Question #61 of 66 Question ID: 1573137 Risk aversion means that an individual will choose the less risky of two assets: A) even if it has a lower expected return. B) in all cases. C) if they have the same expected return. Explanation Investors are risk averse. Given a choice between assets with equal rates of expected return, the investor will always select the asset with the lowest level of risk. Risk aversion does not imply that an investor will choose the less risky of two assets in all cases, or that an investor is unwilling to accept greater risk to achieve a greater expected return. (Module 20.2, LOS 20.b) Question #62 of 66 Question ID: 1573165 Using the following correlation matrix, which two stocks would combine to make the lowest- risk portfolio? (Assume the stocks have equal risk and returns.) Stock A B C A +1 -- -- B - 0.2 + 1 -- C + 0.6 - 0.1 + 1 A) A and B. B) A and C. C) C and B. Explanation Portfolios A and B have the lowest correlation coefficient and will thus create the lowest- risk portfolio. The standard deviation of a portfolio = [W12σ12 + W22σ22 + 2W1W2σ1σ2r1,2]1/2 The correlation coefficient, r1,2, varies from + 1 to - 1. The smaller the correlation coefficient, the smaller σportfolio can be. If the correlation coefficient were - 1, it would be possible to make σportfolio go to zero by picking the proper weightings of W1 and W2. (Module 20.3, LOS 20.e) Question #63 of 66 Question ID: 1573138 A stock has an expected return of 4% with a standard deviation of returns of 6%. A bond has an expected return of 4% with a standard deviation of 7%. An investor who prefers to invest in the stock rather than the bond is best described as: A) risk averse. B) risk neutral. C) risk seeking. Explanation Given two investments with the same expected return, a risk averse investor will prefer the investment with less risk. A risk neutral investor will be indifferent between the two investments. A risk seeking investor will prefer the investment with more risk. (Module 20.2, LOS 20.b) Question #64 of 66 Question ID: 1573159 Which of the following statements regarding the covariance of rates of return is least accurate? Covariance is positive if two variables tend to both be above their mean values A) in the same time periods. If the covariance is negative, the rates of return on two investments will always B) move in different directions relative to their means.  Covariance is not a very useful measure of the strength of the relationship C) between rates of return. Explanation Negative covariance means rates of return for one security will tend to be above its mean return in periods when the other is below its mean return, and vice versa. Positive covariance means that returns on both securities will tend to be above (or below) their mean returns in the same time periods. For the returns to always move in opposite directions, they would have to be perfectly negatively correlated. Negative covariance by itself does not imply anything about the strength of the negative correlation, it must be standardized by dividing by the product of the securities' standard deviations of return. (Module 20.3, LOS 20.d) Question #65 of 66 Question ID: 1573153 If the standard deviation of asset A is 12.2%, the standard deviation of asset B is 8.9%, and the correlation coefficient is 0.20, what is the covariance between A and B? A) 0.0001. B) 0.0022. C) 0.0031. Explanation The formula is: (correlation)(standard deviation of A)(standard deviation of B) = (0.20) (0.122)(0.089) = 0.0022. (Module 20.3, LOS 20.d) Question #66 of 66 Question ID: 1573144 The graph below combines the efficient frontier with the indifference curves for two different investors, X and Y. Which of the following statements about the above graph is least accurate? A) Investor X's expected return is likely to be less than that of Investor Y. The efficient frontier line represents the portfolios that provide the highest B) return at each risk level. C) Investor X is less risk-averse than Investor Y. Explanation Investor X has a steep indifference curve, indicating that he is risk-averse. Flatter indifference curves, such as those for Investor Y, indicate a less risk-averse investor. The other choices are true. A more risk-averse investor will likely obtain lower returns than a less risk-averse investor. (Module 20.2, LOS 20.c)