CFA Level 1 - Portfolio Management Session 12 - Reading 44

CFA Level 1 - Portfolio Management Session 12 - Reading 44 (Notes, Practice Questions, Sample Questions) 1. Over the long term, the annual returns and standard deviations of returns for major asset classes have shown: A)a positive relationship. B)a negative relationship. C)no clear relationship. {Explanation}: (A) In most markets and for most asset classes, higher average returns have historically been associated with higher risk (standard deviation of returns). 2. 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 B decreases to 0.188 and the covariance remains the same, the correlation between the two bonds will: A)remain the same. B)increase. C)decrease. {Explanation}: (C) P1,2 = 0.048/(0.0260.5 × 0.1880.5) = 0.69 which is lower than the original 0.79 3. 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}: (C) 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 4. 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}: (B) The formula is: (correlation)(standard deviation of A)(standard deviation of B) = (0.20)(0.122)(0.089) = 0.0022 5. Stock A has a standard deviation of 10.00. Stock B also has a standard deviation of 10.00. If the correlation coefficient between these stocks is - 1.00, what is the covariance between these two stocks? A)-100.00. B)1.00. C)0.00. {Explanation}: (A) Covariance = correlation coefficient × standard deviationStock 1 × standard deviationStock 2 = (- 1.00)(10.00)(10.00) = - 100.00 6. 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)0.3750. B)0.0264. C)0.0352. {Explanation}: (B) cov1,2 = 0.75 × 0.16 × 0.22 = 0.0264 = covariance between A and B 7. If two stocks have positive covariance, which of the following statements is CORRECT? A)The rates of return tend to move in the same direction relative to their individual means. B)The two stocks must be in the same industry. C)If one stock doubles in price, the other will also double in price. {Explanation}: (A) This is a correct description of positive covariance. If one stock doubles in price, the other will also double in price is true if the correlation coefficient = 1. The two stocks need not be in the same industry 8. A measure of how well the returns of two risky assets move together is the: A)standard deviation. B)covariance. C)range. {Explanation}: (B) This is a correct description of covariance. A positive covariance means the returns of the two securities move in the same direction. A negative covariance means that the returns of two securities move in opposite directions. A zero covariance means there is no relationship between the behaviors of two stocks. The magnitude of the covariance depends on the magnitude of the individual stock’s standard deviations and the relationship between their co-movements. The covariance is an absolute measure of movement and is measured in return units squared. 9. 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)0.40. B)0.91. C)0.00016. {Explanation}: (A) 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 10. The standard deviation of the rates of return is 0.25 for Stock J and 0.30 for Stock K. The covariance between the returns of J and K is 0.025. The correlation of the rates of return between J and K is: A)0.33. B)0.10. C)0.20. {Explanation}: (A) CovJ,K = (rJ,K)(SDJ)(SDK), where r = correlation coefficient and SDx = standard deviation of stock x Then, (rJ,K) = CovJ,K / (SDJ × SDK) = 0.025 / (0.25 × 0.30) = 0.333 11. Which of the following statements regarding the covariance of rates of return is least accurate? A)It is a measure of the degree to which two variables move together over time. B)It is not a very useful measure of the strength of the relationship, there is absent information about the volatility of the two variables. C)If the covariance is negative, the rates of return on two investments will always move in different directions relative to their means. {Explanation}: (C) Negative covariance means rates of return will tend to move in opposite directions on average. 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 12. 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)0.0002. C)0. {Explanation}: (A) 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 13. If the standard deviation of stock A is 13.2 percent, the standard deviation of stock B is 17.6 percent, and the covariance between the two is 0, what is the correlation coefficient? A)+1. B)0.31. C)0. {Explanation}: (C) Since covariance is zero, the correlation coefficient must be zero 14. If the standard deviation of stock A is 7.2%, the standard deviation of stock B is 5.4%, and the covariance between the two is -0.0031, what is the correlation coefficient? A)-0.19. B)-0.80. C)-0.64. {Explanation}: (B) The formula is: (Covariance of A and B)/[(Standard deviation of A)(Standard Deviation of B)] = (Correlation Coefficient of A and B) = (-0.0031)/[(0.072)(0.054)] = -0.797 15. If the standard deviation of returns for stock A is 0.60 and for stock B is 0.40 and the covariance between the returns of the two stocks is 0.009 what is the correlation between stocks A and B? A)0.0020. B)0.0375. C)26.6670. {Explanation}: (B) CovA,B = (rA,B)(SDA)(SDB), where r = correlation coefficient and SDx = standard deviation of stock x Then, (rA,B) = CovA,B / (SDA × SDB) = 0.009 / (0.600 × 0.400) = 0.0375 16. Stock A has a standard deviation of 10%. Stock B has a standard deviation of 15%. The covariance between A and B is 0.0105. The correlation between A and B is: A)0.70. B)0.55. C)0.25. {Explanation}: (A) CovA,B = (rA,B)(SDA)(SDB), where r = correlation coefficient and SDx = standard deviation of stock x Then, (rA,B) = CovA,B / (SDA × SDB) = 0.0105 / (0.10 × 0.15) = 0.700 17. Risk aversion means that if two assets have identical expected returns, an individual will choose the asset with the: A)higher standard deviation. B)shorter payback period. C)lower risk level. {Explanation}: (C) 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. This means that there is a positive relationship between expected returns (ER) and expected risk (Es) and the risk return line (capital market line [CML] and security market line [SML]) is upward sloping. Standard deviation is a way to quantify risk. The payback period is used to evaluate capital projects, not investment returns. 18. Which of the following statements about risk aversion is CORRECT? A)Given a choice between two assets with equal rates of return, the investor will always select the asset with the lowest level of risk. B)Risk averse investors will not take on risk. C)Risk aversion implies that the risk-return line, the CML, and the SML are downward sloping curves. {Explanation}: (A) Risk aversion implies that an investor will not assume risk unless compensated. 19. 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}: (A) 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 20. 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 = 0.04666; Standard Deviation = 21.60%. C)Variance = 0.03836; Standard Deviation = 19.59%. {Explanation}: (C) (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% 21. Which of the following measures is NOT considered when calculating the risk (variance) of a two-asset portfolio? A)The beta of each asset. B)Each asset’s standard deviation. C)Each asset weight in the portfolio. {Explanation}: (A) The formula for calculating the variance of a two-asset portfolio is: σp2 = WA2σA2 + WB2σB2 + 2WAWBCov(a,b) 22. 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)0.3742. B)0.5795. C)0.3400. {Explanation}: (B) 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 23. 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)0.25 B)0.39 C)0.54 {Explanation}: (A) 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 24. 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)0.0020. B)0.0026. C)0.0007. {Explanation}: (C) 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 25. 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)0.1832. B)0.1600. C)0.0256. {Explanation}: (B) The formula for the standard deviation of a 2-stock portfolio is: s = [WA2sA2 + WB2sB2 + 2WAWBsAsBrA,B]1/2 s = [(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% 26. 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)0.426. C)0.370. {Explanation}: (C) 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 27. Which one of the following statements about correlation is NOT correct? A)The covariance is equal to the correlation coefficient times the standard deviation of one stock times the standard deviation of the other stock. B)Positive covariance means that asset returns move together. C)If two assets have perfect negative correlation, it is impossible to reduce the portfolio's overall variance. {Explanation}: (C) This statement should read, "If two assets have perfect negative correlation, it is possible to reduce the portfolio's overall variance to zero." 28. 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)most if she put half your money in XYZ Co. and half in Branton Co. B)more if she bought Branton Co. C)more if she bought XYZ Co. {Explanation}: (B) 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 = ΥBranton = σXYZ so you want to pick the lowest covariance which is between Randy and Branton 29. 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)increase. B)decrease. C)decrease only if the correlation is negative. {Explanation}: (B) If the correlation coefficient is less than 1, there are benefits to diversification. Thus, adding the stock will reduce the portfolio's standard deviation 30. As the correlation between the returns of two assets becomes lower, the risk reduction potential becomes: A)smaller. B)greater. C)decreased by the same level. {Explanation}: (B) 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 31. 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)0.00. B)+1.00. C)+0.50. {Explanation}: (B) Adding any stock that is not perfectly correlated with the portfolio (+1) will reduce the risk of the portfolio 32. 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)63% 37% B)0% 100% C)100% 0% {Explanation}: (C) 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 33. Which one of the following statements about correlation is NOT correct? A)Potential benefits from diversification arise when correlation is less than +1. B)If the correlation coefficient were -1, a zero variance portfolio could be constructed. C)If the correlation coefficient were 0, a zero variance portfolio could be constructed {Explanation}: (C) A correlation coefficient of zero means that there is no relationship between the stock's returns. The other statements are true 34. 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}: (A) There are benefits to diversification as long as the correlation coefficient between the assets is less than 1 35. 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)30% in Stock A and 70% in Stock B. B)100% in Stock B. C)50% in Stock A and 50% in Stock B. {Explanation}: (B) Since the stocks are perfectly correlated, there is no benefit from diversification. So, invest in the stock with the lowest risk 36. Which of the following statements about portfolio theory is least accurate? A)Assuming that the correlation coefficient is less than one, the risk of the portfolio will always be less than the simple weighted average of individual stock risks. B)For a two-stock portfolio, the lowest risk occurs when the correlation coefficient is close to negative one. C)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 not decrease the overall portfolio standard deviation {Explanation}: (C) 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 37. Which of the following statements about the efficient frontier is least accurate? A)Portfolios falling on the efficient frontier are fully diversified. B)Investors will want to invest in the portfolio on the efficient frontier that offers the highest rate of return. C)The efficient frontier shows the relationship that exists between expected return and total risk in the absence of a risk-free asset. {Explanation}: (B) The optimal portfolio for each investor is the highest indifference curve that is tangent to the efficient frontier