Module 6 - FP513
Bobby owns ABC stock that has mean return of 10.65%, a beta of 1.12, and a standard deviation of 9.05%. He decides to purchase MEJ stock that has a mean return of 11.5%, a beta of 0.98, and a standard deviation of 12.3%. Assume these stocks are weighted in the portfolio 70% for ABC and 30% for MEJ. Also, these stocks exhibit a covariance of 19.86. Calculate the standard deviation for this two-asset portfolio. A) 1.16% B) 10.02% C) 3.23% D) 7.88%
D) 7.88% The answer is 7.88%. To determine the standard deviation of a two-asset portfolio, use this formula: [W2Aσ2A + W2Bσ2B + 2WAWB(COVAB)]1/2 [(0.72 × 9.052) + (0.32 × 12.32) + (2 × 0.7 × 0.3 × 19.86)]1/2 [(0.49 × 81.90) + (0.09 × 151.29) + (8.3412)]1/2 [40.1310 + 13.6161 + 8.3412]1/2 62.08831/2 = 7.8796, or 7.88% Note the standard deviation for the portfolio is lower than the standard deviations for each security. This result directly supports the low correlation between the returns of ABC and MEJ.
The Finite Mutual Fund has a correlation coefficient of 0.90 with the S&P 500 Index. How much of the price movement of the Finite Mutual Fund is explained by the S&P 500 Index? A) 75% B) 100% C) 90% D) 81%
D) 81% R-squared gives us the amount of systematic risk, and we have been given R (correlation coefficient). So, we square 0.90 to come up with an R-squared of 0.81, or 81%.
What is the covariance between OPC and NIR stocks with a standard deviation of 9.13% and 11%, respectively, and a correlation coefficient of 0.85? A) 23.77 B) 28.69 C) 29.05 D) 85.37
D) 85.37 The covariance between the two stocks is 85.37 (9.13 × 11 × 0.85). Covariance measures the extent to which two variables move together, either positively (together) or negatively (opposite).
ABC Mutual Fund has a correlation coefficient of 0.93 with the S&P 500 Index. How much of the price movement of the fund can be explained by the S&P 500 Index? A) 14% B) 7% C) 93% D) 86%
D) 86% The correlation coefficient (R) has been given, so it needs to be squared (R2) in order to come up with the coefficient of determination. (0.932 = 0.8649, or 86%)
Which of these risks is diversifiable? A) Purchasing power risk B) Market risk C) Interest rate risk D) Default risk
D) Default risk Default risk is diversifiable (unsystematic) risk. The others are examples of systematic risk, or nondiversifiable risk.
Which of the following risks is specific to international investing? A) Business risk B) Event risk C) Reinvestment rate risk D) Exchange rate risk
D) Exchange rate risk Exchange rate risk pertains to foreign investments and is the risk for a U.S. investor that the exchange rates between a foreign currency and the U.S. dollar change adversely; that is, when the U.S. investor converts the foreign currency into U.S. dollars, she will get fewer dollars than previously.
Which of these types of risk is associated with the degree to which a company utilizes debt to finance its operations? A) Credit risk B) Default risk C) Business risk D) Financial risk
D) Financial risk Financial risk is associated with the degree to which a company utilizes debt to finance its operations.
You have narrowed your choice down to these three mutual funds which have these annual returns. Which fund should you choose based on risk and return? Fund X | Fund Y | Fund Z Year 1 +15% +7% +12% Year 2 +9% +13% +2% Year 3 +5% +8% +11% A) Fund Z B) Fund X C) Any of these funds because the risk and return are equal D) Fund Y
D) Fund Y This is a problem that can be solved using the coefficient of variation. With the annual returns, calculate the standard deviation and mean return for each of the three funds: Fund X | Fund Y | Fund Z Standard deviation 5.0332 3.2146 5.5076 Mean return 9.6667 9.3333 8.3333 Coefficient of variation 0.5207 0.3444 0.6609 The lowest CV is the correct answer. Sample keystrokes for Fund X (repeat for the other funds) on the HP10BII+: 15 ∑+ 9 ∑+ 5 ∑+ SHIFT, Sx,Sy (8 key) = 5.0332 For the mean return: SHIFT, x,y (7 key) = 9.6667 Calculation as follows for the TI BA II+: Step 1: press "2nd" then "7". This activates the data screen. Step 2: press "2nd" then "CE/C" to clear all your existing work. Step 3: enter the first return "15" into the first "X01" screen and press enter. Step 4: hit the down arrow button "↓" and scroll past "Y01" and hit "↓" one more time until you get to "X02". Step 5: input the next return value which would be "9" and hit enter. Follow this process until you input all 3 values. Step 6: press "2nd" then "8" which is the "STAT" screen. Step 7: press "2nd" then "enter" which is the "SET" screen. Keep hitting the "2nd" and "enter" button until you see "1-V." Step 8: press "↓" to scroll through the calculated statistics. You will hit the "↓" button three times before you reach the standard deviation screen which will start with "Sx" and should equal "5.0332." Step 9: press the up arrow to see the stat above "Sx" which is "x" and should equal "9.67" as the mean. CV = standard deviation ÷ mean CV = 5.0332 ÷ 9.6667 = 0.5207
The Galaxy Fund has a standard deviation of 15, and a mean return of 9%. The Universe Fund has a standard deviation of 22, and a mean return of 13%. The Milky Way Fund has a standard deviation of 18, and a mean return of 11%. Which fund should you choose in order to minimize the risk per unit of return? A) Each fund offers the same risk per unit of return. B) Universe Fund C) Galaxy Fund D) Milky Way Fund
D) Milky Way Fund The Galaxy Fund has a coefficient of variation of 1.67, the Universe Fund has a coefficient of variation of 1.69, and the Milky Way Fund has a coefficient of variation of 1.64. Coefficient of variation = standard deviation ÷ mean return, select the lowest number.
Select the term that measures how far the actual outcomes of a probability distribution deviate from the arithmetic mean. A) Kurtosis B) Lognormal C) Variability D) Skewness
D) Skewness Skewness measures how far the median return is from the mean return in decimal terms.
Based on the information provided, identify the stock that should be acquired if the investor's objective is to minimize the relative total risk per unit of expected return. Stock A Standard deviation = 12.49% Beta = 1.07 Expected return = 4.65% Stock B Standard deviation = 23.51% Beta = 1.98 Expected return = 10.40% Stock C Standard deviation = 14.43% Beta = 1.40 Expected return = 8.75% Stock D Standard deviation = 17.98% Beta = 1.56 Expected return = 9.63% A) Stock A B) Stock B C) Stock D D) Stock C
D) Stock C Coefficient of variation (CV) is a relative measure of total risk (as measured by standard deviation) per unit of expected return. Use the coefficient of variation to solve for the best investment alternative: Stock A: 12.49 ÷ 4.65 = 2.6860 Stock B: 23.51 ÷ 10.40 = 2.2606 Stock C: 14.43 ÷ 8.75 = 1.6491 Stock D: 17.98 ÷ 9.63 = 1.8671 The stock with the lowest CV has the least amount of total risk per unit of expected return.
Select the CORRECT statement regarding investors who only purchase high-beta stocks. A) They prefer stocks with low risk and low positive skewness. B) They prefer stocks with high risk and low positive skewness. C) They prefer stocks with low risk and high positive skewness. D) They prefer stocks with high risk and high positive skewness.
D) They prefer stocks with high risk and high positive skewness. Generally, these types of investors would prefer stocks with high risk (high beta) and high positive skewness that provide the opportunity for high rates of return. Stocks exhibiting high positive skewness have a larger than average number of positive price movements.
All of the following statements correctly explain investment risk except A) a stock's level of risk is a combination of market risk and diversifiable risk. B) investors expect to earn a higher rate of return for assuming a higher level of risk. C) the beta coefficient measures an individual stock's relative volatility to the market. D) systematic risk may be reduced or eliminated by effective portfolio diversification.
D) systematic risk may be reduced or eliminated by effective portfolio diversification. Unsystematic (diversifiable) risk may be effectively managed through portfolio diversification.
If a security has an average return of 14.2% and a standard deviation of 8.4%, then A) the security's returns can be expected to always be positive. B) the security's returns can be expected to be between 8.4% and 14.2% approximately 95% of the time. C) the security's annual volatility can be expected to be within a range approximately 8.4% above and 8.4% below the current fair market value. D) the security's returns can be expected to be between 5.8% and 22.6% approximately 68% of the time.
D) the security's returns can be expected to be between 5.8% and 22.6% approximately 68% of the time. This security can be expected to have a return that does not range beyond one standard deviation on either side of its average return approximately 68% of the time.
A large-cap mutual fund has an average annual return of 11%, a beta of 1.05, and a standard deviation of 16%. What is the coefficient of variation (CV) of this fund? A. 0.12 B. 0.15 C. 0.69 D. 1.45
D. 1.45 The CV is the standard deviation divided by the average annual return. Therefore, 16 ÷ 11 = 1.45.
Eos Company is a privately owned manufacturer of plastics used in the automotive industry. The company is currently financed with a mix of 90% equity and 10% debt. Which of the following risks is experienced by the shareholders of Eos Company? I. Liquidity risk II. Market risk III. Business risk IV. Default risk A. I only B. III only C. II and IV D. I, II, and III
D. I, II, and III Eos Company shareholders own equity in Eos and, therefore, are not subject to default risk. Because Eos is privately held, liquidity risk is relevant. Market risk is a systematic risk, and the automotive industry is particularly subject to market fluctuations. Business risk is the risk associated with individual businesses.
Mysterious Company stock has a mean return of 9% and a standard deviation of 3%. Which statement is CORRECT? A. Approximately 68% of Mysterious Company's returns will fall between 3% and 15%. B. There are 5% of Mysterious Company's returns that will be greater than 15%. C. Half of Mysterious Company's returns will fall below 6%. D. Mysterious Company is unlikely to experience a negative return.
D. Mysterious Company is unlikely to experience a negative return. With a normal probability distribution, 68% of the returns fall within one standard deviation of the mean, 95% within two standard deviations, and 99% within three standard deviations. Therefore, Mysterious Company has less than a 1% chance of experiencing a negative return.
Portfolio A has a standard deviation of 55%, and the market has a standard deviation of 40%. The correlation coefficient between Portfolio A and the market is 0.50. Calculate the percentage of total risk that is unsystematic. A) 75% B) 25% C) 50% D) 100%
The coefficient of determination explains the percentage of change in the dependent variable that can be explained by changes in the independent variable. Therefore, 25% (0.50 × 0.50) of returns are explained by changes in the market. To determine the percentage of returns that are explained by unsystematic risk, subtract the systematic risk from 1. Therefore, the return explained by unsystematic risk is (1 − 0.25) = 0.75, or 75%.
A client has a $1.2 million portfolio consisting of these four stocks: 1. $300,000 | ABC @ 1.1 beta 2. $225,000 | RTR @ 0.7 beta 3. $405,000 | XYZ @ 0.3 beta 4. $270,000 | PDQ @ 1.3 beta What is the beta of the portfolio as a whole? A) 0.8 B) 0.85 C) 1.0 D) 0.91
A) 0.8 The answer is 0.8. This is the weighted average of beta of components, which is calculated as follows: $300,000 ÷ 1,200,000 = 0.25 weighting × 1.1 beta =0.2750 $225,000 ÷ 1,200,000 = 0.1875 weighting × 0.7 beta =0.1313 $405,000 ÷ 1,200,000 = 0.3375 weighting × 0.3 beta =0.1013 $270,000 ÷ 1,200,000 = 0.225 weighting × 1.3 beta =0.2925 Weighted Average Beta: 0.8001
Shari would like to know the weighted beta coefficient for her portfolio. She owns 100 shares of BDL common stock with a beta of 1.3 and total current market value of $8,000; 400 shares of XTP common stock with a beta of 0.9 and total current market value of $13,000; and 200 shares of SPR common stock with a beta of 0.6 and total current market value of $10,000. What is the overall weighted beta coefficient for Shari's portfolio? A) 0.91 B) 1.26 C) 0.99 D) 0.93
A) 0.91 Calculations are shown below: Market Value | Weighting | Beta | Weighted Beta $8,000 ÷$31,000= 0.258 × 1.3 = 0.3354 $13,000 ÷$31,000= 0.419 × 0.9 = 0.3771 $10,000 ÷$31,000= 0.323 × 0.6 = 0.1938 $31,000 0.9063
What is the weighted average beta of a portfolio with 20% in Stock A with a beta of 0.9, 50% in Stock B with a beta of 1.2, and 30% in Stock C with a beta of 1.1? A) 1.11 B) 1.18 C) 1.14 D) 1.20
A) 1.11 You can complete this calculator long-hand in this way: (0.9 x .2) + (1.2 x .5) + (1.1 x .3) = (0.18) + (0.6) + (.33) = 1.11 You can also do this faster using the following keystrokes on the HP 10bII+ (see Financial Calculator Workbook for steps using TI BAII+): 0.9, INPUT, 20, ∑+, 1.2, INPUT, 50, ∑+, 1.1, INPUT, 30, ∑+, DOWNSHIFT, 6 (alternate function is weighted average) = 1.11.
Gary Stevens would like to know the weighted beta for his portfolio. He owns 100 shares of ACE common stock with a beta of 1.1 and total current market value of $5,000; 400 shares of BDF common stock with a beta of 0.70 and total current market value of $8,000; and 200 shares of GIK common stock with a beta of 1.5 and total current market value of $10,000. What is the overall weighted beta coefficient for Gary's portfolio? A) 1.13 B) 1.05 C) 1.01 D) 1.22
A) 1.13 $5,000 + $8000 + $10,000 = $23,000 total value of the portfolio (1.1 x (5,000/23,000)) + (0.7 x (8,000/23,000)) + (1.5 x (10,000/23,000)) (1.1 x 0.217) + (0.7 x 0.347) + (1.5 x 0.4347) 0.2387 + 0.2429 + 0.6520 = 1.1336 = 1.13 Or, you can use these inputs for the HP10BII+: 1.1INPUT (ENTER)5Σ+0.7INPUT (ENTER)8Σ+1.5INPUT (ENTER)10Σ+SHIFT, xw,b = 1.13
Stock XYZ has an average return of 12%; its returns fall within a range of -2% to +26% approximately 68% of the time. Which one of these numbers is closest to the standard deviation of returns of Stock XYZ? A) 14% B) 19% C) 28% D) 8%
A) 14% A standard deviation of 14% means an investor can expect a return on an investment to vary ±14 from the average return approximately 68% of the time.
The Mountain Fund has a standard deviation of 22, a mean return of 15%, and a correlation coefficient with the S&P 400 Mid-Cap Index of 0.85. Mountain Fund is subject to how much systematic risk? A) 72% B) 22% C) 85% D) 90%
A) 72% R-squared gives us the amount of systematic risk, and we have been given R (correlation coefficient). So, we square 0.85 to come up with an R-squared of 0.7225, or 72%.
Which of these statements concerning portfolio diversification is CORRECT? A) By increasing the number of securities in a portfolio, the total risk would be expected to fall at a decreasing rate. B) Diversification reduces the portfolio's expected return because diversification reduces a portfolio's total risk. C) Only systematic risk is reduced as diversification is increased. D) The benefits of diversification are not realized until at least 25 individual securities are included in the portfolio
A) By increasing the number of securities in a portfolio, the total risk would be expected to fall at a decreasing rate. As more and more securities are added to a portfolio, diversification benefits begin to diminish. The main attraction of diversification is the reduction of risk without an accompanying loss of return.
Choose the statement regarding the correlation coefficient that is NOT correct. A) Combining assets with less than perfect positive correlation will not reduce the total risk of the portfolio. B) Perfectly negatively correlated assets have a correlation coefficient of -1.0. C) A correlation coefficient of 0.0 means there is no relationship between the returns of the assets. D) Perfectly positively correlated assets have a correlation coefficient of +1.0.
A) Combining assets with less than perfect positive correlation will not reduce the total risk of the portfolio. Combining assets with less than perfect positive correlation can reduce the total risk of the portfolio. The further the correlation coefficient between the two assets is away from +1.0, the greater the diversification benefits that may be attained.
Which one of these factors has the greatest impact on the standard deviation of a two-asset portfolio? A) Covariance B) The weight of each security in the portfolio C) The portfolio's beta D) The standard deviation of each security in the portfolio
A) Covariance Covariance is the most important variable in minimizing the standard deviation of a portfolio. The weight and standard deviation are not as critical as the covariance of the two securities. Beta is not used in the formula to compute a portfolio's standard deviation.
Which of the following statements concerning a knowledge of the risk/return relationship is CORRECT? I. Future risk/return relationships are not guaranteed to match past risk/return relationships. II. Chances are that past relative relationships will not continue into the future. III. A reduction in risk also means a reduction in the possible return on the investment. IV. The smaller the dispersion of returns, the greater the risk associated with a particular investment. A) I and III B) I only C) II and III D) II, III, and IV
A) I and III Chances are that past relative relationships will continue into the future. The smaller the dispersion of returns, the lower the risk associated with a particular investment.
Mutual fund I has a standard deviation of 4% and an expected return of 10%. Mutual fund J has a standard deviation of 8% and an expected return of 13%. If I and J have a correlation coefficient of -1.0, which of the following statements is CORRECT? A) I and J are perfectly negatively correlated. B) A portfolio combining funds I and J may have an expected return less than 10%. C) J is less risky than I on a risk-adjusted basis. D) There is no combination of I and J such that the portfolio's standard deviation is zero.
A) I and J are perfectly negatively correlated. J's coefficient of variation is 8% ÷ 13% = 0.615. I's coefficient of variation = 4% ÷ 10% = 0.40. I is less risky, on a risk-adjusted basis, than J. Because I and J are perfectly negatively correlated (correlation coefficient of -1.0), there exists a combination of I and J such that the standard deviation is zero. The expected return of a portfolio is the weighted average, which cannot be less than the lowest expected return of the portfolio components.
Which of these statements regarding investment risk is CORRECT? I. A firm's decision to buy back some of its own stock in the open market by borrowing funds through a new bond issue is an example of reinvestment rate risk. II. Rising inflation represents purchasing power risk. III. A decline in a firm's share price as a result of a 20% decline in the S&P 500 Index represents market risk. IV. A reduction in the value of an international stock mutual fund because of a depreciation of the Euro is an example of exchange rate risk. A) II, III, and IV B) IV only C) I and II D) I, II, and III
A) II, III, and IV Only statement I is incorrect. A firm's decision to buy back some of its own stock in the open market by borrowing funds through a new bond issue is an example of financial risk.
Identify the types of bonds that are subject to the most default risk. A) Junk bonds B) U.S. savings bonds C) AA rated general obligation bonds D) U.S. Treasury bonds
A) Junk bonds Junk bonds, sometimes referred to as high-yield bonds, are subjected to the most default risk. Obligations of the U.S. government are free from default risk. AA rated bonds are not free from default risk, but they are less likely to default than junk bonds.
Which one of these alternatives correctly outlines the importance of the portfolio perspective? A) Market participants should analyze the risk-return trade-off of the portfolio, not the risk-return trade-off of the individual investments in a portfolio. B) Market participants should focus on the systematic risk of the components of a portfolio not the unsystematic risk of the components of a portfolio. C) Market participants should analyze the risk-return trade-off of each individual security. D) Market participants should attempt to eliminate the unsystematic risk associated with each security by forming portfolios that will diversify away this risk.
A) Market participants should analyze the risk-return trade-off of the portfolio, not the risk-return trade-off of the individual investments in a portfolio. The key underlying principle of the portfolio perspective is that market participants should analyze the risk-return trade-off of the portfolio as a whole, not the risk-return trade-off of the individual investments in the portfolio.
Consider this information regarding two possible investments: Stocks J and K. Stock J: Expected return: 11.5% Standard deviation: 8% Stock K: Expected return: 8.2% Standard deviation: 6% Identify which of these investments you would prefer and why. A) Stock J because it has the lowest coefficient of variation B) Stock K because it has the highest coefficient of variation C) Stock K because it has the least risk D) Stock J because it has the highest expected return
A) Stock J because it has the lowest coefficient of variation The answer is Stock J because it has the lowest coefficient of variation. The stock with the lower coefficient of variation (CV) provides the least amount of risk for a given level of return. CV = standard deviation of asset ÷ expected return of asset. Stock J: CV = 0.08 ÷ 0.115 = 0.6957 Stock K: CV = 0.06 ÷ 0.082 = 0.7317
Which of the following statements regarding investment theory is NOT correct? A) The beta coefficient may be used to help select a portfolio that is consistent with an investor's willingness to assume unsystematic risk. B) A correlation coefficient of 0.14 between the returns of Stock A and Stock B indicates that very little of Stock A's returns can be attributed to the returns of Stock B. C) In a well-diversified portfolio, diversifiable risk is zero. D) Combining two stocks with a negative covariance can significantly reduce the portfolio's standard deviation
A) The beta coefficient may be used to help select a portfolio that is consistent with an investor's willingness to assume unsystematic risk. Beta is a measure of systematic risk, not unsystematic risk. The beta coefficient may be used to help select a portfolio that is consistent with an investor's willingness to assume systematic risk.
Taylor, a personal friend of yours, has been a practicing veterinarian for eight years. She is 35 years old and has a 3-year-old daughter. Taylor has a moderate risk tolerance, wants to save for retirement, and is considering increasing her investment in the following mutual fund. Taylor has asked you for your recommendation. Risk-free return 7.0% Return of market 12.5% Growth and Income Fund NAV (beginning of year) = $53.00 NAV (end of year) = $52.75 Dividend = $3.25 Capital gains distributed = $2.75 Beta = 0.70 Realized return = 10.85% Which of the following is CORRECT regarding the risk and return of the fund? A) The fund has less risk and less return than the market. B) The fund has less risk and greater return than the market. C) The fund has equal risk and greater return than the market. D) The fund has greater risk and less return than the market.
A) The fund has less risk and less return than the market. A beta of 1 represents the risk of the market. A beta of less than 1 represents risk less than the market's risk, and a beta of greater than 1 represents risk greater than that of the market.
You are comparing two stocks based on the statistics below. Which one is the better investment based on the risk/return relationship? | Stock A | Stock B Average Return 3.00% 9.00% Standard Deviation 3.95 11.86 A) The two stocks have equal risk/reward profiles B) Cannot be determined from the information given C) Stock B because it has a higher return D) Stock A because it has a lower standard deviation
A) The two stocks have equal risk/reward profiles The coefficient of variation is used to evaluate risk/return and is 3.95 ÷ 3.00 = 1.32 for stock A and 11.86 ÷ 9.00 = 1.32 for stock B, so both are equal in the amount of return relative to the risk.
Beverly owns two stocks with a correlation coefficient of zero. Which of these is CORRECT? A) These stocks will move independently of each other. B) These stocks are well diversified because they will move in unison. C) These stocks are not well diversified because they move in unison. D) These stocks are well diversified because as one stock appreciates in value, the other decreases in value.
A) These stocks will move independently of each other. A correlation coefficient of zero means that the two stocks will move independently. Because most stocks are positively correlated, a correlation coefficient of zero should provide more diversification benefits than most pairs of stocks.
Which of the following is the risk that disappears in the portfolio construction process? A) Unsystematic risk B) Systematic risk C) Interest rate risk D) Purchasing power risk
A) Unsystematic risk Unsystematic risk (diversifiable risk) is the risk that is eliminated when the investor builds a well-diversified portfolio.
A beta coefficient of 1.3 indicates that a stock A) is more volatile than the market. B) has more unsystematic risk than the market. C) is less volatile than the market. D) has less unsystematic risk than the market.
A) is more volatile than the market. A beta that is higher than 1.0 indicates that the stock's volatility and risk are higher than that of the market.
A distribution with a mean that is less than its median most likely A) is negatively skewed. B) symmetrical. C) has negative excess kurtosis. D) is positively skewed.
A) is negatively skewed. A distribution with a mean that is less than its median is a negatively skewed distribution. A negatively skewed distribution is characterized by many small gains and a few extreme losses. Note that kurtosis is a measure of the peakedness of a return distribution. In a symmetrical distribution, the mean, median, and mode are all equal.
Investors who want to bear the least amount of risk should acquire stocks with beta coefficients A) less than 0.5. B) greater than 1.5. C) greater than 1.0. D) less than 1.0.
A) less than 0.5. When seeking investments having the least amount of risk, the lowest beta should be selected.
Unsystematic (unique) risk can be reduced by buying A) stocks in numerous unrelated companies. B) stocks in natural resource companies. C) international stocks. D) stock in less-interest-rate-sensitive companies.
A) stocks in numerous unrelated companies. Owning stock in unrelated companies results in holding stocks that have a low correlation coefficient between them. If a portfolio has numerous diversified issues of stocks, an investor can reduce and virtually eliminate the degree of unsystematic (unique) risk in the portfolio. Buying stocks in international companies can help to reduce systematic risk, because those stocks trade in different markets.
Exchange rate risk refers to fluctuations in A) the price of one currency relative to other currencies. B) the value of an investor's portfolio. C) the prices of stocks on the New York Stock Exchange. D) the values of bonds and other debt instruments.
A) the price of one currency relative to other currencies. Relative currency prices and changes to them are the basis of exchange rate risk.
The issuer-specific component of the variability in a stock's total return that is unrelated to overall market variability is known as A) unsystematic risk. B) nondiversifiable risk. C) systematic risk. D) fundamental risk
A) unsystematic risk. Unsystematic risk is unique to a single security, business, industry, or country and may be reduced by diversification.
A portfolio manager considers adding an asset to the portfolio. The manager decides between four equally risky assets: W, X, Y, and Z. The correlations of each asset with the portfolio are as follows: Asset W: 0.90 Asset X: 0.80 Asset Y: 0.40 Asset Z: 0.20 To achieve optimal diversification benefits, which of the assets should be selected by the manager? A. Asset Z B. Asset Y C. Asset W D. Asset X
A. Asset Z Asset Z has the smallest correlation with the portfolio and will therefore provide the largest reduction in portfolio risk.
All of the following are examples of nondiversifiable risks except A. liquidity risk. B. market risk. C. interest rate risk. D. purchasing power risk.
A. liquidity risk. Liquidity risk is a type of unsystematic, or diversifiable, risk.
Adding investments with a negative beta to a well-diversified portfolio that currently has a beta of +1.0 will cause A. the expected performance of the portfolio to improve in bear markets. B. the expected performance of the portfolio to decline in bear markets. C. the portfolio to experience more volatility in times of a bull market. D. the portfolio to experience more volatility in times of a bear market.
A. the expected performance of the portfolio to improve in bear markets. A negative beta means that the investment will move in an opposite direction from the overall market. Therefore, if the market is declining, then the asset should increase in value—thereby increasing the expected performance of the portfolio.
A stock that you are researching has an expected return of 22%, a beta of 1.2, a correlation coefficient of 0.65 with the Russell 2000, an R2 of 0.38 with the S&P 500, and a standard deviation of 28%. Which one of these is the stock's coefficient of variation? A) 33.85 B) 1.27 C) 0.38 D) 18.33
B) 1.27 CV = standard deviation of asset ÷ expected return of asset, 28% ÷ 22% = 1.27.
Your client, Jackson, is considering adding XYZ Mutual Fund to his portfolio. The fund has a correlation coefficient of 0.55 with the S&P 500, and he wants to know how much systematic risk the fund has when compared to this benchmark. You would advise him that the percentage of systematic risk is A) 70% B) 30% C) 55% D) 45%
B) 30% You have been provided with the correlation coefficient (R) and what you need is the coefficient of determination (R2). Keystrokes are 0.55, DOWNSHIFT, "+" key = 0.3025. This means that 30% of the price movement of the fund is explained by the S&P 500, and the other 70% is not. Stated another way, there is 30% systematic risk, and 70% unsystematic risk.
Security A has a standard deviation of 12% and the market has a standard deviation of 16%. The correlation coefficient between Security A and the market is 0.75. What percent of the change in Security A's price can be explained by changes in the market? A) 44% B) 56% C) 12% D) 75%
B) 56% Because the correlation coefficient is 0.75, the coefficient of determination (R2) is 0.5625, or 56%. Therefore, only 56% of investment returns can be explained by changes in the market (i.e., systematic risk represents 56%).
The Gemini Fund has a correlation coefficient of 0.80 with the S&P 500 Index. How much of the price movement of the Gemini Fund can be explained by the S&P 500 Index? A) 75% B) 64% C) 100% D) 80%
B) 64% The correlation coefficient (R) has been given, so it needs to be squared (R2) in order to come up with the coefficient of determination (0.802 = 0.64).
The annual returns of the ABC fund have been +12%. -4%, and +7%. What is the standard deviation of the fund's returns? A) 4.04% B) 8.19% C) 7.79% D) 5.00%
B) 8.19% HP 10bII+ keystrokes: 12, ∑+ 4, +/-, ∑+ 7, ∑+ SHIFT, Sx,Sy (8 key) for standard deviation Calculation is as follows for the TI BA II+: Step 1: press "2nd" then "7". This activates the data screen. Step 2: press "2nd" then "CE/C" to clear all your existing work. Step 3: enter the first return "12" into the first "X01" screen and press enter. Step 4: hit the down arrow button "↓" and scroll past "Y01" and hit "↓" one more time until you get to "X02". Step 5: input the next return value which would be "4,+/-" and hit enter. Follow this process until you input all three values. Step 6: press "2nd" then "8" which is the "STAT" screen. Step 7: press "2nd" then "enter" which is the "SET" screen. Keep hitting the "2nd" and "enter" button until you see "1-V." Step 8: press "↓" to scroll through the calculated statistics. You will hit the "↓" button 3 times before you reach the standard deviation screen which will start with "Sx" and should equal "8.19."
STU Corporation stock has an average rate of return of 24% and a standard deviation of 10%. The risk-free rate of return is 4%. Assuming the historical returns for STU stock are normally distributed, calculate the probability that this stock will have a return in excess of the risk-free rate of return. A) 2.5% B) 97.5% C) 95.0% D) 34.0%
B) 97.5% The answer is 97.5%. The probability of a return above 24% is 50%. The probability of a return between 4% and 24% is 47.5% (95% ÷ 2). Therefore, the probability of a return above 4% is 97.5% (50% + 47.5%).
When analyzing various investment alternatives, investors would generally choose which of these? A) An investment exhibiting a low positive skewness and a leptokurtic distribution B) An investment exhibiting a high positive skewness and a leptokurtic distribution C) An investment exhibiting a high positive skewness and a platykurtic distribution D) An investment exhibiting a low positive skewness and a platykurtic distribution
B) An investment exhibiting a high positive skewness and a leptokurtic distribution Investments exhibiting high positive skewness have a larger than average number of positive price movements. Also, investments exhibiting a leptokurtic distribution have more observations clustered closely around the mean, resulting in a lower variance. Investors prefer a large number of positive returns with low risk.
Choose the best measure of risk for an asset held in a well-diversified portfolio. A) Covariance B) Beta C) Semivariance D) Correlation coefficient
B) Beta Beta is the best measure of risk for an asset held in a well-diversified portfolio.
Which one of these is a measure of a security's risk-adjusted return? A) Covariance B) Coefficient of variation C) Coefficient of determination D) Correlation coefficient
B) Coefficient of variation The coefficient of variation is one of several ways to compute a security's risk-adjusted return. The coefficient of determination measures how much of the movement of a security is attributable to a second security. The correlation coefficient measures the strength of the relationship between two securities. Covariance is used in the computation of a portfolio's standard deviation.
Your Fund Client Fund Three year total return 13.5% 14.75% Average P/E ratio 20% 24% Standard deviation 19% 23% Beta 1.03 1.24 Which fund would you recommend based on each fund's relationship between risk and return? I. Your fund, because its coefficient of variation is 1.41, compared to the client's coefficient of variation of 1.56 II. Client fund, because its higher beta dictates that its return should also be higher, which in fact occurred III. Client fund, because standard deviations and betas change over time and the statistics are close enough so that the fund with the better return should be chosen A) II and III B) I only C) II only D) I and III
B) I only The standard deviation is divided by the total return to obtain the coefficient of variation. A beta is higher does not mean that any higher return is acceptable. The client's fund has higher risk as measured by both standard deviation and beta, but taking this higher risk does not provide sufficient return based on the coefficient of variation calculation.
The Dow Jones Utility Average has recently dropped 30% from its high, and you decide to recommend a utility sector fund to your clients. If they invest in the fund, your clients will be exposed to which of these risks? I. Interest rate risk II. Business risk III. Default risk IV. Financial risk A) II, III, and IV B) I, II, and IV C) II and IV D) I, II, III, and IV
B) I, II, and IV Sector funds are subject to the unsystematic (diversifiable) risks of business risk and financial risk; utility sector funds are also subject to the nondiversifiable interest rate risk because of their high debt to total capital percentage. Stocks are not subject to default risk.
An investment portfolio has the following three stocks: Stock | Investment | Beta Stock 1 $8,000 0.6 Stock 2 $22,000 1.3 Stock 3 $12,000 0.9 Which of the following are CORRECT statements about this portfolio? I. The weighted beta for the portfolio is 0.93. II. The weighted beta for the portfolio is 1.05. III. The portfolio is less risky than the market. IV. The portfolio is riskier than the market. A) II and III B) II and IV C) I and III D) I and IV
B) II and IV The portfolio weighted beta is computed as follows: [(8 ÷ 42) × 0.6] + [(22 ÷ 42) × 1.3] + [(12 ÷ 42) × 0.9] = 0.114 + 0.681 + 0.257 = 1.052, or 1.05. Because the portfolio beta is more than 1.0, the portfolio is considered riskier than the market, which has a portfolio beta of exactly 1.0.
Wendy is concerned that her investment's actual return will not equal its expected return. Point out the type of risk that she is concerned about regarding her investment. A) Purchasing power risk B) Investment risk C) Tax risk D) Business risk
B) Investment risk Investment risk is the uncertainty that an investment's actual, or realized, return will not equal its expected return.
You have narrowed your choice down to these investments with the following characteristics: JJJ | LLL | NNN | YYY Mean return 10 18 7 11 Standard deviation 17 25 10 19 Which fund has the least risk per unit of return? A) YYY Fund B) LLL Fund C) JJJ Fund D) NNN Fund
B) LLL Fund Using the coefficient of variation (CV). JJJ Fund: 17 ÷ 10 = 1.70 LLL Fund: 25 ÷ 18 = 1.39 NNN Fund 10 ÷ 7 = 1.43 YYY Fund 19 ÷ 11 = 1.73 The stock with the lowest CV has the least amount of total risk per unit of expected return.
Which of these is NOT an unsystematic risk? A) Liquidity risk B) Market risk C) Default risk D) Business risk
B) Market risk Unsystematic risk is the risk that affects only one company, country, or sector and its securities. Market risk is an example of a systematic risk.
If two stocks have positive covariance, which of these statements is CORRECT? A) The two stocks must be in the same industry. B) The rates of return tend to move in the same direction relative to their individual means. C) If one stock doubles in price, the other will also double in price. D) The rates of return tend to move in the opposite direction relative to their individual means.
B) The rates of return tend to move in the same direction relative to their individual means. 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.
Which of the following is the most appropriate and accurate indicator for determining a client's risk tolerance level? A) Beta B) There is no single appropriate method for determining risk tolerance. C) Questionnaire D) Standard deviation
B) There is no single appropriate method for determining risk tolerance. A client's risk tolerance level is an intangible and subjective factor. No single method accurately determines that risk level.
An investor is interested in holding a diversified portfolio to reduce unsystematic risk. This can best be accomplished by buying stock in A) foreign companies. B) companies with low correlation coefficients between them. C) companies with strong earnings and revenue growth. D) companies with low betas.
B) companies with low correlation coefficients between them. Holding stocks that have a low correlation coefficient between them will result in a diversified portfolio that reduces and virtually eliminates the degree of unsystematic (business) risk in the portfolio. Buying stocks in international companies and stocks with low betas can help to reduce systematic risk, but only if they have low correlations with other stocks. Buying stocks in companies with strong revenue and earnings growth often results in acquiring significant company-specific risk that is attributable to the underlying business.
The risk associated with the amount of debt a company has issued is A) interest rate risk. B) financial risk. C) systematic risk. D) business risk.
B) financial risk. Financial risk is the risk related to the amount of debt a company has. Business risk is the risk associated with the nature of the business. Interest rate risk is the risk that as interest rates increase, bond prices decrease. Systematic risk is the risk associated with all factors affecting all comparable investments.
A distribution that is more peaked than normal is A) skewed. B) leptokurtic. C) platykurtic. D) convex.
B) leptokurtic. A distribution that is more peaked than normal is leptokurtic. A distribution that is flatter than normal is platykurtic.
A general risk component representing the variability of a stock's total return as it directly relates to overall movements in the general economy is known as A) business risk. B) systematic risk. C) reinvestment rate risk. D) financial risk.
B) systematic risk. Systematic risk, also referred to as market risk, is the variability in a stock's total return that is directly associated with overall movements in the general economy and cannot be eliminated through diversification.
Diversification reduces A) market risk. B) unsystematic risk. C) purchasing power risk. D) systematic risk.
B) unsystematic risk. Unsystematic risk can be diversified away by investing in approximately 10-15 large company stocks in different industries and 25-30 small company stocks in different industries. Systematic risk cannot be reduced by diversification.
Which of the following statements regarding kurtosis is CORRECT? I. Kurtosis describes the degree to which a distribution is not symmetric about its mean. II. Kurtosis measures the peakedness of a distribution reflecting a greater or lesser concentration of returns around the mean. A. I only B. II only C. Both I and II D. Neither I nor II
B. II only The degree to which a distribution is not symmetric about its mean is measured by skewness. Excess kurtosis, which is measured relative to a normal distribution, indicates the peakedness of a distribution, and it reflects the probability of extreme outcomes.
The basic premise of the risk-return tradeoff suggests that risk-averse individuals purchasing investments with higher nondiversifiable risk should expect to earn A. lower rates of return. B. higher rates of return. C. rates of return equal to the market. D. rates of return lower than the market.
B. higher rates of return. Investors are risk averse and require higher rates of return for assuming greater investment risk.
The basic premise of the risk-return tradeoff suggests that risk-averse individuals purchasing investments with higher nondiversifiable risk should expect to earn A. lower rates of return. B. higher rates of return. C. rates of return equal to the market. D. rates of return lower than the market.
B. higher rates of return. The answer is higher rates of return. Investors are risk averse and require higher rates of return for assuming greater investment risk.
Stock XYZ has an average return of 18% with a standard deviation of 21. Within what range could an investor expect a return to fall 68% of the time? A) 0% to 21% B) 3% to 39% C) -3% to 39% D) -3% to 18%
C) -3% to 39% By definition, an investment's return will be within one standard deviation of the mean return 68% of the time. The mean return of 18% plus or minus one standard deviation is 18% - 21% (-3%) and 18% + 21% (39%).
A stock fund had these yearly returns: 20X5 - 14% 20X6 = 7% 20X7 = -3% 20X8 = 18% 20X9 = 9% What is the standard deviation of the returns? A) 6.04 B) 7.13 C) 7.97 D) 8.43
C) 7.97 Calculation as follows for the TI BA II+: Step 1: press "2nd" then "7". This activates the data screen. Step 2: press "2nd" then "CE/C" to clear all your existing work. Step 3: enter the first return "14" into the first "X01" screen and press enter. Step 4: hit the down arrow button "↓" and scroll past "Y01" and hit "↓" one more time until you get to "X02". Step 5: input the next return value which would be "7" and hit enter. Follow this process until you input all 5 values. Step 6: press "2nd" then "8" which is the "STAT" screen. Step 7: press "2nd" then "enter" which is the "SET" screen. Keep hitting the "2nd" and "enter" button until you see "1-V". Step 8: press "↓" to scroll through the calculated statistics. You will hit the "↓" button 3 times before you reach the standard deviation screen which will start with "Sx" and should equal "7.97".
Identify which of these is NOT a source of systematic risk. A) Market risk B) Reinvestment rate risk C) Business risk D) Purchasing power risk
C) Business risk Business risk is a type of unsystematic risk. Unsystematic risks only affect one company, country, or sector and its related securities.
ABC Corporation is a manufacturer of electronic devices used in the manufacturing of airplanes. Five years ago, the corporation floated a $100 million bond issue that would be used to finance improvements at its main manufacturing and distribution center. However, orders for its products have dropped dramatically due to much lower than anticipated demand. The company believes it may miss paying the coupon payment on the bond issue in the upcoming fiscal year. Which of these risks may the owners of ABC Corporation bonds be subject to by holding the bonds? A) Reinvestment rate risk B) Market risk C) Default risk D) Regulation risk
C) Default risk Default risk is the risk that a business will be unable to service its debt obligations.
Bobby has these securities in his portfolio: ABC common stock, XYZ common stock, PQR mutual fund (domestic small cap), DEZ mutual fund (foreign small cap), 30-year Treasury bond, and 5-year Treasury note. Point out the risk that should NOT concern Bobby. A) Reinvestment rate risk B) Systematic risk C) Default risk D) Financial risk
C) Default risk Treasuries are considered default risk-free. Financial risk is the uncertainty introduced from the method by which a firm finances its assets (i.e., debt versus equity financing). Reinvestment rate risk is the risk that as cash flows are received they will be reinvested at lower rates of return than the investment that generated the cash flows. Systematic risk is the risk that all securities are subject to and typically cannot be eliminated through diversification.
Which of these is NOT a type of unsystematic risk? A) Financial risk B) Default risk C) Exchange rate risk D) Country risk
C) Exchange rate risk Exchange rate risk is a type of systematic risk. Systematic risks are those risks that affect the entire market. Systematic risks include market risk, interest rate risk, purchasing power risk, reinvestment rate risk, and exchange rate risk.
Andy owns a yen-denominated bond that matures in 15 years. Andy's bond is subject to which one of these combinations of systematic risk? A) Financial risk and purchasing power risk B) Interest rate risk and default risk C) Exchange rate risk and reinvestment rate risk D) Market risk and business risk
C) Exchange rate risk and reinvestment rate risk Because Andy owns a foreign investment, he would be subject to exchange rate risk. Also, coupon-paying bonds are subject to reinvestment rate risk.
Gordon, age 40, wants to invest in a mutual fund that will provide capital appreciation. He wants a fund that will do as well as the overall market and has a low expense ratio, but he does not want to assume a high risk to achieve his objective. He is considering purchasing one of the following mutual funds: - Fund A: a growth mutual fund that has a beta of 1.10 and invests in medium- to high-grade common stock - Fund B: an index mutual fund that has a beta of 1.00 and invests in common stock that mirrors the S&P 500 Index Which of these funds would best meet Gordon's objective? A) neither alternative is appropriate for his objective B) Fund A, because it can be expected to outperform the market and has an acceptable level of risk C) Fund B, because it has a beta of 1.00, has low expenses, and is less risky D) Fund A, because it invests in lower-risk stocks than Fund B
C) Fund B, because it has a beta of 1.00, has low expenses, and is less risky Fund B can be expected to do as well as the overall market, will have a low expense ratio, and is less risk, as measured by beta, than Fund A.
You are about to recommend the purchase of an additional mutual fund to add to a client's portfolio, with the objective of reducing the portfolio's total risk. Upon analysis of several funds, you determine that the standard deviations of the current portfolio and each of the potential new funds are equal, but that the correlation coefficients of these funds with the current portfolio are as shown in the answer choices below. Which of the funds should you recommend? A) Fund B: correlation coefficient = +0.65 B) Fund A: correlation coefficient = +0.91 C) Fund D: correlation coefficient = -0.08 D) Fund C: correlation coefficient = 0.00
C) Fund D: correlation coefficient = -0.08 According to modern portfolio theory, total portfolio risk, as measured by standard deviation, is lowered by combining securities in a portfolio so that individual securities have negative (or low positive) correlations between each other's rates of return.
Bill and Jane are considering adding additional assets to their investment portfolio. They consider themselves moderate-to-high-risk investors. Based on safety of principal, point out the investment that would offer the couple the least amount of protection from risk. A) Real estate B) High-grade common stock C) Futures D) Balanced mutual funds
C) Futures Based on the risk-return pyramid, futures will offer the couple the least amount of protection. However, due to their high risk, futures may offer the greatest amount of return.
The market's standard deviation is 15 Stock A Stock B Correlation coefficient with market 0.20 0.80 Standard deviation 20 10 Which of the following statements are true and why I The beta of Stock A is lower than the beta of Stock B due to the impact of the correlation coefficients II The beta of Stock A is higher than the beta of Stock B because the standard deviation of Stock A is twice the standard deviation of Stock B III The ratio of Stock As correlation coefficient to Stock Bs correlation coefficient indicates that Stock Bs beta is four times Stock As beta IV The correlation coefficient of Stock A suggests that the price movements of the market are likely to have little relationship with the price movements of Stock A 2 4 1 3 I 4 I 3 4
C) I & IV (1 & 4) According to the formula for beta, Stock A's beta is (20 ÷ 15) × 0.20 = 0.27 and Stock B's beta is (10 ÷ 15) × 0.80 = 0.53. Statement II is incorrect because it does not take into account the relative correlation coefficients. Statement III is incorrect because it does not take into account the relative standard deviations.
Which of these statements concerning portfolio diversification is CORRECT? I. By increasing the number of securities in a portfolio, the total risk would be expected to fall at a decreasing rate. II. Total risk is reduced as diversification is increased. III. The benefits of diversification are not realized until at least 30 individual securities are included in the portfolio. IV. Diversification reduces the portfolio's expected return because diversification reduces a portfolio's total risk. A) III and IV B) I, II, and III C) I and II D) IV only
C) I and II Studies have shown that an investor only needs about 15-20 assets to fully diversify a portfolio. The main attraction of diversification is the reduction of risk without an accompanying loss of return.
Most fixed-income securities are subject to which of the following risks? I. Purchasing power risk II. Liquidity risk III. Default risk IV. Reinvestment rate risk A) I and II B) I, III, and IV C) I, II, III, and IV D) II, III, and IV
C) I, II, III, and IV Fixed-income securities are subject to a number of risks including purchasing power, liquidity, default, and reinvestment rate risk.
Steve and Haley, ages 48 and 45 respectively, invest in large-cap stocks, international stock mutual funds, and rental real estate. They consider themselves moderately aggressive investors. Their investment portfolio is subject to which of these investment risks? I. Investment manager risk II. Financial risk III. Exchange rate risk IV. Default risk A) I only B) II and IV C) I, II, and III D) I, II, III, and IV
C) I, II, and III Their investment portfolio is subject to all of these risks except default risk. Investment manager risk is associated with the skills and philosophy of their mutual fund portfolio managers. Financial risk is the risk that a company's financial structure may negatively affect the value of an equity investment. By holding investments in international stock mutual funds, they are subject to exchange rate risk.
Candi purchases a 30-year zero-coupon corporate bond. The bond was issued by ABC Company, a Fortune 500 company. Her investment is subject to which of these risks? I. Default risk II. Reinvestment rate risk III. Purchasing power risk IV. Interest rate risk A) I, II, and III B) II and III C) I, III, and IV D) I, II, III, and IV
C) I, III, and IV Zero-coupon bonds are not subject to reinvestment rate risk. However, they are subject to purchasing power, interest rate, and default risk.
Which of these are nondiversifiable risks? I. Business risk II. Interest rate risk III. Market risk IV. Purchasing power risk A) I, II, III, and IV B) III only C) II, III, and IV D) I and II
C) II, III, and IV Business risk is a type of diversifiable, or unsystematic, risk.
In a positively skewed distribution, what is the order (from lowest value to highest) for the distribution's mode, mean, and median values? A) Mean, median, mode B) Median, mode, mean C) Mode, median, mean D) Mode, mean, median
C) Mode, median, mean In a positively skewed distribution, the mode is less than the median, which is less than the mean.
Stock A has an expected mean return of 15% and a standard deviation of 22%; Stock B has an expected mean return of 11% and a standard deviation of 13%; and Stock C has an expected mean return of 18% and a standard deviation of 24%. You want to recommend one of these stocks to a client who is most interested in owning stocks that are more likely to deliver the expected mean return. Which stock should you recommend to meet this client's requirement? A) Stock A B) Stock C C) Stock B D) None of these
C) Stock B The coefficient of variation is a measure of the degree of variation of returns compared with the expected mean return. The security with the lowest coefficient of variation is the one most likely to deliver periodic returns closest to its expected return. The coefficients of variation of the three securities are 1.47 for Stock A, 1.18 for Stock B, and 1.33 for Stock C. Stock B should be recommended.
The expected returns and standard deviations of each fund are approximately equal. The correlations between the funds are as shown in the following table. Correlation of Returns Largecap Fund Midcap Fund Smallcap Fund Largecap fund 1 Midcap fund .67 1 Smallcap fund .41 .23 1 Which two funds should you recommend, assuming that your goal is to recommend the two funds that will provide the lowest total portfolio risk and that the portfolio will be equally weighted in the two funds you select? A) The smallcap fund and the largecap fund B) None, since no fund is negatively correlated with another fund C) The midcap fund and the smallcap fund D) The largecap fund and the midcap fund
C) The midcap fund and the smallcap fund A negative correlation is not necessary; low positive correlations are adequate to lower the standard deviation of a portfolio. The fund combination that should be selected, given the objective and the fact that all other factors are equal, is the combination with the lowest correlation—the mid-cap fund and the small-cap fund.
All of these statements concerning the use of the correlation coefficient in reducing portfolio risk are CORRECT except A) combining two securities with zero correlation (statistical independence) reduces portfolio risk, but cannot eliminate it. B) because securities typically have some positive correlation with each other, risk can be reduced, but seldom eliminated. C) combining two securities with perfect negative correlation provides no portfolio risk reduction. D) combining securities with perfect positive correlation provides no portfolio risk reduction.
C) combining two securities with perfect negative correlation provides no portfolio risk reduction. Combining two securities with perfect negative correlation could eliminate risk altogether. This is the principle behind hedging strategies.
Jane's portfolio consists of two stocks, each comprising 50% of the portfolio. Stock 1 has an expected return of 4.5%, a standard deviation of 1.5%, and a beta of 0.65. Stock 2 has an expected return of 8%, a standard deviation of 3%, and a beta of 0.82. If the correlation coefficient between Stock 1 and Stock 2 is 0.75, what is the beta for Jane's portfolio? A. 0.01 B. 0.63 C. 0.74 D. 2.25
C. 0.74 The portfolio beta is a weighted average: (0.50 × 0.65) + (0.50 × 0.82) = 0.74.
Portfolio A has a standard deviation of 55%, and the market has a standard deviation of 40%. Assume that the correlation coefficient between Portfolio A and the market is 0.50. What percentage of the total risk of Portfolio A is unsystematic risk? A. 25% B. 50% C. 75% D. 100%
C. 75% The coefficient of determination (R2) of Portfolio A is 25% (0.25). This is derived by squaring the correlation coefficient (R) of 0.50 (0.50 × 0.50 = 0.25). Therefore, 25% is the percentage of returns of Portfolio A that may be explained by the market (or systematic risk). The remainder of the percentage of returns (movement) of Portfolio A is explained by factors independent of the market (or unsystematic risk). To determine this, subtract the systematic risk from 1.0 (1.0 - 0.25 = 0.75, or 75%).
Which of the following statements is NOT correct concerning the use of the correlation coefficient in reducing portfolio risk? A. Combining securities with perfect positive correlation provides no portfolio risk reduction. B. Combining two securities with zero correlation (statistical independence) reduces portfolio risk, but cannot be eliminated. C. Combining two securities with perfect negative correlation provides no portfolio risk reduction. D. Because securities typically have some positive correlation with each other, risk can be reduced, but seldom eliminated.
C. Combining two securities with perfect negative correlation provides no portfolio risk reduction. The answer is combining two securities with perfect negative correlation provides no portfolio risk reduction. This could eliminate risk altogether and is the principle behind hedging strategies.
You are considering buying a stock that has a mean return of 14% and a standard deviation of 20. You can expect the return to fall within what range 95% of the time? A) -0.06 to 0.34 B) Cannot be determined from the information given C) -0.46 to 0.74 D) -0.26 to 0.54
D) -0.26 to 0.54 A stock with a standard deviation of 20 will deviate from the mean by one standard deviation 68% of the time, two standard deviations 95% of the time, and three standard deviations 99% of the time. So for this stock, plus or minus 40 from the mean of 14% would be -26% and +54%.
An analysis of the monthly returns for the past year of a mutual fund portfolio consisting of two funds revealed these statistics Fund A | Fund B Total return 12% 15% Standard deviation 9% 26% Percentage of portfolio 35% 65% Correlation coefficient (R)0.32 What is the coefficient of determination (R2) of Fund A and Fund B? A) 0.17 B) 0.15 C) 0.90 D) 0.10
D) 0.10 The coefficient of determination is the square of the correlation coefficient (0.32)2 = 0.32 × 0.32 = 0.1024, or 10%.
What is the coefficient of variation for an investment with a standard deviation of 8.65%, an expected return of 11.5%, and a beta of 1.25? A) 1.3290 B) 0.9402 C) 0.1438 D) 0.7522
D) 0.7522 CV = standard deviation of asset ÷ expected return of asset, 8.65% ÷ 11.5% = 0.7522.
Assume your client's portfolio contains these: - $20,000 of Stock A with a beta of 0.90 - $50,000 of Stock B with a beta of 1.20 - $30,000 of stock C with a beta of 1.10 What is the beta coefficient for this portfolio? A) 1.16 B) 1.00 C) 1.05 D) 1.11
D) 1.11 The answer is 1.11. Calculated as follows: 0.20 × 0.90 = 0.18 0.50 × 1.20 = 0.60 0.30 × 1.10 = 0.33 0.18 + 0.60 + 0.33 = 1.11 Using the HP 10bII+: 0.9, INPUT, 20,000, Σ+ 1.2, INPUT, 50,000, Σ+ 1.1, INPUT, 30,000, Σ+ SHIFT, 6 key (x̅w,b) = 1.11
Assuming JHG and DSA stocks have standard deviations of 6.23% and 10.78%, respectively, and a correlation coefficient of 0.17, calculate the covariance between the two stocks. A) 95.06 B) 25.34 C) 26.76 D) 11.42
D) 11.42 The covariance between the two stocks is a positive 11.42 (6.23 × 10.78 × 0.17). Covariance measures the extent to which two variables move together, either positively (together) or negatively (opposite).
Element Corp had these annual returns over the past four years: +12%, +6%, -8%, and +20%. What is the standard deviation for Element Corp. over the past four years? A) 15% B) 12.4% C) 7.5% D) 11.8%
D) 11.8% HP 10bII+ Keystrokes: 12, ∑+ 6, ∑+ 8, +/-, ∑+ 20, ∑+ SHIFT, Sx,Sy (8 key) for standard deviation = 11.8% TI BA II+ Keystrokes: Step 1: press "2nd" then "7". This activates the data screen. Step 2: press "2nd" then "CE/C" to clear all your existing work. Step 3: enter the first return "12" into the first "X01" screen and press enter. Step 4: hit the down arrow button "↓" and scroll past "Y01" and hit "↓" one more time until you get to "X02." Step 5: input the next return value which would be "6" and hit enter. Follow this process until you input all four values. Step 6: press "2nd" then "8" which is the "STAT" screen. Step 7: press "2nd" then "enter" which is the "SET" screen. Keep hitting the "2nd" and "enter" button until you see "1-V." Step 8: press "↓" to scroll through the calculated statistics. You will hit the "↓" button three times before you reach the standard deviation screen which will start with "Sx" and should equal "11.8."
An analysis of the monthly returns for the past year of a mutual fund portfolio consisting of two funds revealed these statistics: Fund A | Fund B Total return 18% 11% Standard deviation 23% 16% Percentage of portfolio 35% 65% Correlation coefficient (R) 0.25 What is the coefficient of determination (R2) of Fund A and Fund B? A) 84.64% B) 21.49% C) 50.00% D) 6.25%
D) 6.25% The coefficient of determination is the square of the correlation coefficient (0.25)2 = 0.25 × 0.25 = 0.0625, or 6.25%.