Investor Tastes over Risk and Return: Suppose you are considering where toInvest money for the future. A: Like most investors, you care about the expected return on your investment as well as the risk associated with the investment. But different investors are willing to make different kinds of tradeoffs relative to risk and return. (a) On a graph, put risk on the horizontal axis and expected return on the vertical. (For purposes of this exercise, donâ€™t worry about the precise units in which these are expressed.) Where in your graph would you locate â€œsafeâ€ investments like inflation indexed government bonds â€” investments for which you can predict the rate of return with certainty? (b) Pick one of these â€œsafeâ€ investment bundles of risk and return and label it A. Then pick a riskier investment bundle B that an investor could plausibly find equally attractive (given that risk is bad in the eyes of investors while expected returns are good). (c) If your tastes are convex and you only have investments A and B to choose from, would you prefer diversifying your investment portfolio by putting half of your investment in A and half in B? (d) If your tastes are non-convex, would you find such diversification attractive? B: Suppose an investor has utility function u(x1,x2) = (R âˆ’x1)x2 where x1 represents the risk associated with an investment, x2 is the expected return and R is a constant. (a)What is the MRS of risk for return for this investor. (b) Suppose A is a risk free investment, with and suppose that B is risky but our investor is indifferent between A and B. What must the return the risk-free investment be in terms of (c) Do this investorâ€™s tastes satisfy convexity? Illustrate by considering whether this investor would be willing to switch from A or B in part (b) to putting half his investment in A and half in B. (d) Suppose R = 10 for our investor. Imagine he is offered the following 3 investment portfolios: (1) a no-risk portfolio of government bondswith expected return of 2 and 0 risk; (2) a high risk portfolio of volatile stocks with expected return of 10 and risk of 8; or a portfolio that consists half of government bonds and half of volatile stocks, with expected return of 6 and risk of 4. Which would he choose? (e) Suppose a second investor is offered the same three choices. This investor is identical to the first in every way, except that R in his utility function is equal to 20 instead of 10. Which portfolio will he choose? (f ) True or False: The first investorâ€™s tastes are convex while the second oneâ€™s are not. (g)What value of R wouldmake the investor choose the no-risk portfolio?
Assume that you recently graduated with a major in finance and that you have just landed a job as a financial planner with Barney Smith Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a business at the end of 1 year, you have been instructed to plan for a 1-year holding period. Furthermore, your boss has restricted you to the investment alternatives shown in the table with their probabilities and associated outcomes. The relatively high T-bill rate reflects significant inflationary expectations. Barney Smith's economic forecasting staff have developed probability estimates for the state of the economy, and its security analysts have developed a sophisticated computer program that was used to estimate the rate of return on each alternative under each state of the economy. Alta Industries is an electronics firm; Repo Men Inc. collects past-due debts; and Canadian Foam manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" that owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund, and thus obtain average stock market results. Given the situation as described, answer the following questions a. What are investment returns? What is the return on an investment that costs $1,000 and is sold after 1 year for $1,100? b. (1) Why is the T-bill's return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are Alta Industries' returns expected to move with the economy whereas Repo Men's are expected to move counter to the economy? c. Calculate the expected rate of return on each alternative and fill in the blanks in the row for r^ in the table. d. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative, and fill in the blank in the row for Ïƒ in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for Alta Industries, Canadian Foam, and T-bills. e. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks in the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? f. Suppose you created a 2-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. (1) Calculate the expected return (r^p), the standard deviation (Ïƒp), and the coefficient of variation (CVp) for this portfolio and fill in the appropriate blanks in the table. (2) How does the risk of this 2-stock portfolio compare with the risk of the individual stocks if they were held in isolation? g. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen (1) to the risk and (2) to the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer. h. (1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio, and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk? That is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying? i. How is market risk measured for individual securities? How are beta coefficients calculated? j. The expected rates of return and the beta coefficients of the alternatives as supplied by Barney Smith's computer program are as follows: (1) Do the expected returns appear to be related to each alternative's market risk? (2) Is it possible to choose among the alternatives on the basis of the information developed thus far? k. (1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and then graph the relationship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does the fact that Repo Men has an expected return that is less than the T-bill rate make any sense? (4) What would be the market risk and the required return of a 50-50 portfolio of Alta Industries and Repo Men? Of Alta Industries and Canadian Foam? l. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high-and low-risk securities? (2) Suppose instead that investors' risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Inflation remains constant.) What effect would this have on the SML and on returns of high-and low-risk securities?
Assume that you recently graduated with a major in finance. You just landed a job as a financial planner with Merrill Finch Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a business at the end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives in the following table, shown with their probabilities and associated outcomes. (For now, disregard the items at the bottom of the data; you will fill in the blanks later.) aThe estimated returns of U.S. Rubber do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer tires than they would if the economy was stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car they currently own. Under these circumstances, we would expect U.S. Rubberâ€™s stock price to be higher if there is a recession than if the economy is just below average. Merrill Finchâ€™s economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts developed a sophisticated computer program to estimate the rate of return on each alternative under each state of the economy. High Tech Inc. is an electronics firm; Collections Inc. collects past-due debts; and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a â€œmarket portfolioâ€ that owns a market-weighted fraction of all publicly traded stocks; you can invest in that portfolio and thus obtain average stock market results. Given the situation described, answer the following questions: a. 1. Why is the T-billâ€™s return independent of the state of the economy? Do T-bills promise a completely risk-free return? Explain. 2. Why are High Techâ€™s returns expected to move with the economy, whereas Collectionsâ€™s are expected to move counter to the economy? b. Calculate the expected rate of return on each alternative, and fill in the blanks on the row for r^ in the previous table. c. You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like most people, is risk-averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. 1. Calculate this value for each alternative and fill in the blank on the row for Ïƒ in the table. 2. What type of risk is measured by the standard deviation? 3. Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber, and T-bills. d. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks on the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? Explain. e. Suppose you created a two-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. 1. Calculate the expected return r^ p , the standard deviation Ïƒp , and the coefficient of variation (CVP) for this portfolio, and fill in the appropriate blanks in the table. 2. How does the riskiness of this two-stock portfolio compare with the riskiness of the individual stocks if they were held in isolation? f. Suppose an investor starts with a portfolio consisting of one randomly selected stock. 1. What would happen to the riskiness and to the expected return of the portfolio as more randomly selected stocks were added to the portfolio? 2. What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer. g. 1. Should the effects of a portfolio impact the way investors think about the riskiness of individual stocks? 2. If you decided to hold a one-stock portfolio (and consequently were exposed to more risk than diversified investors), could you expect to be compensated for all of your risk; that is, could you earn a risk premium on the part of your risk that you could have eliminated by diversifying? h. The expected rates of return and the beta coefficients of the alternatives supplied by an independent analyst are as follows: 1. What is a beta coefficient, and how are betas used in risk analysis? 2. Do the expected returns appear to be related to each alternativeâ€™s market risk? 3. Is it possible to choose among the alternatives on the basis of the information developed thus far? Use the data given at the start of the problem to construct a graph that shows how the T-billâ€™s, High Techâ€™s, and the marketâ€™s beta coefficients are calculated. Then discuss what betas measure and how they are used in risk analysis. i. The yield curve is currently flat; that is, long-term Treasury bonds also have a 3.0% yield. Consequently, Merrill Finch assumes that the risk-free rate is 3.0%. 1. Write out the security market line (SML) equation; use it to calculate the required rate of return on each alternative; and graph the relationship between the expected and required rates of return. 2. How do the expected rates of return compare with the required rates of return? 3. Does the fact that Collections has an expected return that is less than the T-bill rate make any sense? Explain. 4. What would be the market risk and the required return of a 50â€“50 portfolio of High Tech and Collections? Of High Tech and U.S. Rubber? j. 1. Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 3.0% risk-free rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities? 2. Suppose instead that investorsâ€™ risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities?
a. 1. Why is the T-billâ€™s return independent of the state of the economy? Do T-bills promise a completely risk-free return? Explain. 2. Why are High Techâ€™s returns expected to move with the economy, whereas Collectionsâ€™s are expected to move counter to the economy? b. Calculate the expected rate of return on each alternative, and fill in the blanks on the row for r' in the previous table. c. You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like most people, is risk-averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. 1. Calculate this value for each alternative and fill in the blank on the row for s in the table. 2. What type of risk is measured by the standard deviation? 3. Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber, and T-bills. d. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks on the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? Explain. e. Someone mentioned that you might also want to calculate the Sharpe ratio as a measure of standalone risk. Calculate the missing ratios and fill in the blanks on the row for the Sharpe ratio in the table. Briefly explain what the Sharpe ratio actually measures. f. Suppose you created a two-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. 1. Calculate the expected return (r'p), the standard deviation (Ïƒp), the coefficient of variation (CVP), and the Sharpe ratio for this portfolio, and fill in the appropriate blanks in the table. 2. How does the riskiness of this two-stock portfolio compare with the riskiness of the individual stocks if they were held in isolation? g. Suppose an investor starts with a portfolio consisting of one randomly selected stock. 1. What would happen to the riskiness and to the expected return of the portfolio as more randomly selected stocks were added to the portfolio? 2. What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer. h. 1. Should the effects of a portfolio impact the way investors think about the riskiness of individual stocks? 2. If you decided to hold a one-stock portfolio (and consequently were exposed to more risk than diversified investors), could you expect to be compensated for all of your risk; that is, could you earn a risk premium on the part of your risk that you could have eliminated by diversifying? i. The expected rates of return and the beta coefficients of the alternatives supplied by an independent analyst are as follows: 1. What is a beta coefficient, and how are betas used in risk analysis? 2. Do the expected returns appear to be related to each alternativeâ€™s market risk? 3. Is it possible to choose among the alternatives on the basis of the information developed thus far? Use the data given at the start of the problem to construct a graph that shows how the T-billâ€™s, High Techâ€™s, and the marketâ€™s beta coefficients are calculated. Then discuss what betas measure and how they are used in risk analysis. j. The yield curve is currently flat; that is, long-term Treasury bonds also have a 3.0% yield. Consequently, Merrill Finch assumes that the risk-free rate is 3.0%. 1. Write out the security market line (SML) equation; use it to calculate the required rate of return on each alternative, and graph the relationship between the expected and required rates of return. 2. How do the expected rates of return compare with the required rates of return? 3. Does the fact that Collections has an expected return that is less than the T-bill rate make any sense? Explain. 4. What would be the market risk and the required return of a 50-50 portfolio of High Tech and Collections? Of High Tech and U.S. Rubber? k. 1. Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 3.0% risk-free rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities? 2. Suppose instead that investorsâ€™ risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities? Assume that you recently graduated with a major in finance. You just landed a job as a financial planner with Merrill Finch Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a business at the end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives in the following table, shown with their probabilities and associated outcomes. (For now, disregard the items at the bottom of the data; you will fill in the blanks later.) Merrill Finchâ€™s economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts developed a sophisticated computer program to estimate the rate of return on each alternative under each state of the economy. High Tech Inc. is an electronics firm, Collections Inc. collects past-due debts, and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a â€œmarket portfolioâ€ that owns a market-weighted fraction of all publicly traded stocks; you can invest in that portfolio and thus obtain average stock market results. Given the situation described, answer the following questions.
Assume that you recently graduated with a major in finance, and you just landed a job as a financial planner with Merrill Finch Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a business at the end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives in the following table, shown with their probabilities and associated outcomes. (Disregard for now the items at the bottom of the data; you will fill in the blanks later.) a Note that the estimated returns of U.S. Rubber do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer tires than they would if the economy was stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car they currently own. Under these circumstances, we would expect U.S. Rubber’s stock price to be higher if there is a recession than if the economy was just below average. Merrill Finch’s economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts have developed a sophisticated computer program, which was used to estimate the rate of return on each alternative under each state of the economy. High Tech Inc. is an electronics firm; Collections Inc. collects past-due debts; and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a “market portfolio” that owns a market-weighted fraction of all publicly traded stocks; you can invest in that portfolio, and thus obtain average stock market results. Given the situation as described, answer the following questions. a. (1) Why is the T-bill’s return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are High Tech’s returns expected to move with the economy whereas Collections’ are expected to move counter to the economy? b. Calculate the expected rate of return on each alternative and fill in the blanks on the row for rˆ in the table above. c. You should recognize that basing a decision solely on expected returns is only appropriate for riskneutral individuals. Because your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative, and fill in the blank on the row for s in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber, and T-bills. d. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks on the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? e. Suppose you created a 2-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. (1) Calculate the expected return (rˆp), the standard deviation (sp), and the coefficient of variation (CVp) for this portfolio and fill in the appropriate blanks in the table. (2) How does the riskiness of this 2-stock portfolio compare with the riskiness of the individual stocks if they were held in isolation? f. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen (1) to the riskiness and (2) to the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of the 2 portfolios to illustrate your answer. g. (1) Should portfolio effects impact the way investors think about the riskiness of individual stocks? (2) If you decided to hold a 1-stock portfolio, and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying? h. The expected rates of return and the beta coefficients of the alternatives as supplied by Merrill Finch’s computer program are as follows: (1) What is a beta coefficient, and how are betas used in risk analysis? (2) Do the expected returns appear to be related to each alternative’s market risk? (3) Is it possible to choose among the alternatives on the basis of the information developed thus far? Use the data given at the start of the problem to construct a graph that shows how the T-bill’s, High Tech’s, and the market’s beta coefficients are calculated. Then discuss what betas measure and how they are used in risk analysis. i. The yield curve is currently flat, that is, long-term Treasury bonds also have a 5.5 percent yield. Consequently, Merrill Finch assumes that the risk-free rate is 5.5 percent. (1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and then graph the relationship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does the fact that Collections has an expected return that is less than the T-bill rate make any sense? (4) What would be the market risk and the required return of a 50–50 portfolio of High Tech and Collections? Of High Tech and U.S. Rubber? j. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 5.5 percent risk-free rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities? (2) Suppose instead that investors’ risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities?
1) The expected return on KarolCo. stock is 16.5 percent. If the risk-free rate is 5 percent and the beta of KarolCo is 2.3, then what is the risk premium on the market assuming CAPM is true? a. 2.5% b. 5.0% c. 7.5% d. 10.0% 2) Using the above information, what is the rate of return on the market? a. 2.5% b. 5.0% c. 7.5% d. 10.0% 3) The expected return for Stock Z is 30 percent. If we know the following information about Stock Z: Return Probability Poor 0.2 0.25 Lukewarm ? 0.5 Dynamite! 0.4 0.25 What return will stock Z produce in the Lukewarm state of the world? A) 20% B) 30% C) 40% D) It is impossible to determine. 4) The risks that diversification cannot eliminate are: a. Interest rate risk. b. risk due to a recession. c. inflation risk. d. systematic risk. e. all of the above 5) Kevin purchased a stock a year ago that pays a dividend. He has earned a 50%. The stock was purchased for $16 and is now worth $21. What is the amount of dividends received during the year? a. $5 b. $4 c. $3 d. $2 6) John is investing in the S&P 500. His expected return on the S&P 500 is 10% with a standard deviation of 4%. If John is investing $200,000, then what is the dollar range of returns that John can have with 90 percent confidence at the end of the year? a. $212,000 - $228,000 b. $206,840 - $233,160 c. $204,320 - $235,680 d. $199,400 - $240,600 7) Microsoft’s beta is 1. The risk free rate of return is 2%. If the expected return on the market is 12 percent, then the expected return on Microsoft is: a. 12 percent b. 15 percent c. 8 percent d. 10 percent 8) What is the relationship between present value and future value interest factors? A. The present value and future value factors are equal to each other. B. The present value factor is the exponent of the future value factor. C. The future value factor is the exponent of the present value factor. D. The factors are reciprocals of each other. E. There is no relationship between these two factors. 9) An investment that costs $50,000 will return $15,000 operating cash flows per year for five years. Determine the net present value of the investment if the required rate of return is 14 percent. Should the investment be undertaken? A. Yes, the profit is $25,000. B. No, the accounting return is less than 14%. C. No, the net present value is negative at $11,045. D. Yes, the net present value is positive at $1,496.50. 10) What is the net present value of a project with the following cash flows if the required rate of return is 15 percent? Year Cash Flow 0 ........ -$42,398 1 ......... 13,407 2 ......... 21,219 3 .......... 17,800 A. -$1,574.41 B. -$1,208.19 C. -$842.12 D. -$2,991.34 E. $1,311.16
Assume that you recently graduated with a major in finance and just landed a job in the trust department of a large regional bank. Your first assignment is to invest $100,000 from an estate for which the bank is trustee. Because the estate is expected to be distributed to the heirs in approximately one year, you have been instructed to plan for a one-year holding period. Furthermore, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes. (For now, disregard the items at the bottom of the data; you will fill in the blanks later.) The bankâ€™s economic forecasting staff has developed probability estimates for the state of the economy, and the trust department has a sophisticated computer program that was used to estimate the rate of return on each alternative under each state of the economy. High Tech, Inc., is an electronics firm; Collections, Inc., collects past-due debts; and U.S. Rubber manufactures tires and various other rubber and plastic products. The bank also maintains an â€œindex fundâ€ that includes a market-weighted fraction of all publicly traded stocks; by investing in that fund, you can obtain average stock market results. Given the situation as described, answer the following questions: a. (1) Why is the risk-free return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are High Techâ€™s returns expected to move with the economy whereas Collectionsâ€™ are expected to move counter to the economy? b. Calculate the expected rate of return on each alternative and fill in the row for r in the table. c. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because the beneficiaries of the trust, like virtually everyone, are risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative and fill in the row for Ïƒ in the table. (2) What type of risk does the standard deviation measure? (3) Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber, and T-bills. d. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of total risk than the standard deviation when the alternatives being considered have widely differing expected returns and standard deviations. Calculate the CVs for the different securities and fill in the row for CV in the table. Does the CV measurement produce the same risk rankings as the standard deviation? e. Suppose you created a two-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. (1) Calculate the expected return rP, the standard deviation (Ïƒp), and the coefficient of variation (CVp) for this portfolio and fill in the appropriate rows in the table. (2) How does the riskiness of this two-stock portfolio compare to the riskiness of the individual stocks if they were held in isolation? f. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen? (1) To the riskiness (2) To the expected return of the portfolio as more randomly selected stocks are added to the portfolio? What is the implication for investors? Draw two graphs to illustrate your answer. g. (1) Should portfolio effects influence the way that investors think about the riskiness of individual stocks? (2) If you chose to hold a one-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk? That is, could you earn a risk premium on the part of your risk that you could have eliminated by diversifying? h. The expected rates of return and the beta coefficients of the alternatives as supplied by the bankâ€™s computer program are as follows: (1) What is a beta coefficient, and how are betas used in risk analysis? (2) Do the expected returns appear to be related to each alternativeâ€™s market risk? (3) Is it possible to choose among the alternatives on the basis of the information developed thus far? (4) Use the data given at the beginning of the problem to construct a graph that shows how the T-billâ€™s, High Techâ€™s, and Collectionsâ€™ beta coefficients are calculated. Discuss what beta measures and explain how it is used in risk analysis. i. (1) Write out the SML equation, use it to calculate the required rate of return on each alternative, and then graph the relationship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does the fact that Collections has a negative beta coefficient make any sense? What is the implication of the negative beta? (4) What would be the market risk and the required return of a 50-50 portfolio of High Tech and Collections? Of a 50-50 portfolio of High Tech and U.S. Rubber? j. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 8 percent T-bill rate. What effect would higher inflation have on the SML and on the returns required on high-and low-risk securities? (2) Suppose, instead, that investorsâ€™ risk aversion increased enough to cause the market risk premium to increase by 3 percentage points (inflation remains constant). What effect would this change have on the SML and on returns of high- and low-risksecurities?
Assume that you recently graduated with a major in finance and that you just landed a job as a financial planner with Barney Smith Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a new business that the client plans to start at the end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives shown in the table below. (Disregard for now the items at the bottom of the data; you will fill in the blanks later.) Barney Smith's economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts have developed a sophisticated computer program that was used to estimate the rate of return on each alternative under each state of the economy. Alta Industries is an electronics firm, Repo Men Inc. collects past-due debts, and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" that owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions. The estimated returns of American Foam do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattress may purchase, instead, a cheaper foam mattress. Under these circumstances, we would expect American Foam's stock price to be higher if there is a recession than if the economy was just below average. a. What are investment returns? What is the return on an investment that costs $1,000 and is sold after 1 year for $1,100? b. (1) Why is the T-bill's return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are Alta Industries's returns expected to move with the economy whereas Repo Men's are expected to move counter to the economy? c. Calculate the expected rate of return on each alternative, and fill in the blanks in the row for ^r in the table. d. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative, and fill in the blank in the row for in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for Alta Industries, American Foam, and T-bills. e. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks in the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? (2) How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation? g. Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio's risk and its expected return? What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer h. (1) Should portfolio effects influence how investors think about the risk of individual stocks? (2) If you decided to hold a one-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying? i. How is market risk measured for individual securities? How are beta coefficients calculated? j. Suppose you have the following historical returns for the stock market and for the company P. Q. Unlimited. Explain how to calculate beta, and use the historical stock returns to calculate the beta for PQU. Interpret your results. k. The expected rates of return and the beta coefficients of the alternatives, as supplied by Barney Smith's computer program, are as follows: (1) Do the expected returns appear to be related to each alternative's market risk? (2) Is it possible to choose among the alternatives on the basis of the information developed thus far? l. (1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and then graph the relationship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does it make sense that Repo Men has an expected return that is less than the T-bill rate? (4) What would be the market risk and the required return of a 50-50 portfolio of Alta Industries and Repo Men? Of Alta Industries and American Foam? m. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities? (2) Suppose instead that investors' risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Assume inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities?
a. Suppose Asset A has an expected return of 10% and a standard deviation of 20%. Asset B has an expected return of 16% and a standard deviation of 40%. If the correlation between A and B is 0.35, what are the expected return and standard deviation for a portfolio consisting of 30% Asset A and 70% Asset B? b. Plot the attainable portfolios for a correlation of 0.35. Now plot the attainable portfolios for correlations of +1.0 and -1.0. c. Suppose a risk-free asset has an expected return of 5%. By definition, its standard deviation is zero, and its correlation with any other asset is also zero. Using only Asset A and the risk-free asset, plot the attainable portfolios. d. Construct a plausible graph that shows risk (as measured by portfolio standard deviation) on the x-axis and expected rate of return on the y-axis. Now add an illustrative feasible (or attainable) set of portfolios and show what portion of the feasible set is efficient. What makes a particular portfolio efficient? Don't worry about specific values when constructing the graph-merely illustrate how things look with "reasonable" data. e. Add a set of indifference curves to the graph created for part b. What do these curves represent? What is the optimal portfolio for this investor? Add a second set of indifference curves that leads to the selection of a different optimal portfolio. Why do the two investors choose different portfolios? f. What is the Capital Asset Pricing Model (CAPM)? What are the assumptions that underlie the model? g. Now add the risk-free asset. What impact does this have on the efficient frontier? h. Write out the equation for the Capital Market Line (CML), and draw it on the graph. Interpret the plotted CML. Now add a set of indifference curves and illustrate how an investor's optimal portfolio is some combination of the risky portfolio and the risk-free asset. What is the composition of the risky portfolio? i. What is a characteristic line? How is this line used to estimate a stock's beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk. j. What are two potential tests that can be conducted to verify the CAPM? What are the results of such tests? What is Roll's critique of CAPM tests? k. Briefly explain the difference between the CAPM and the Arbitrage Pricing Theory (APT). l. Suppose you are given the following information: The beta of a company, bi, is 0.9; the risk-free rate, rRF, is 6.8%; and the expected market premium, rM - rRF, is 6.3%. Because your company is larger than average and more successful than average (that is, it has a lower book-to-market ratio), you think the Fama-French three-factor model might be more appropriate than the CAPM. You estimate the additional coefficients from the Fama-French three-factor model: The coefficient for the size effect, ci, is 20.5, and the coefficient for the book-to-market effect, di, is 20.3. If the expected value of the size factor is 4% and the expected value of the book-to-market factor is 5%, then what is the required return using the Fama-French three-factor model? (Assume that ai 5 0.0.) What is the required return using CAPM?
According to the APT, if the risk-free rate is 4%, what should be McCracken’s estimate of the expected return of Orb’s High Growth Fund? Orb Trust (Orb) has historically leaned toward a passive management style of its portfolios. The only model that Orb’s senior management has promoted in the past is the capital asset pricing model (CAPM). Now Orb’s management has asked one of its analysts, Kevin McCracken, CFA, to investigate the use of the arbitrage pricing theory (APT) model. McCracken believes that a two-factor APT model is adequate, where the factors are the sensitivity to changes in real GDP and changes in inflation. McCracken has concluded that the factor risk premium for real GDP is 8% while the factor risk premium for inflation is 2%. He estimates for Orb’s High Growth Fund that the sensitivities to these two factors are 1.25 and 1.5, respectively. Using his APT results, he computes the expected return of the fund. For comparison purposes, he then uses fundamental analysis to also compute the expected return of Orb’s High Growth Fund. McCracken finds that the two estimates of the Orb High Growth Fund’s expected return are equal. McCracken asks a fellow analyst, Sue Kwon, to provide an estimate of the expected return of Orb’s Large Cap Fund based on fundamental analysis. Kwon, who manages the fund, says that the expected return is 8.5% above the risk-free rate. McCracken then applies the APT model to the Large Cap Fund. He finds that the sensitivities to real GDP and inflation are .75 and 1.25, respectively. McCracken’s manager at Orb, Jay Stiles, asks McCracken to compose a portfolio that has a unit sensitivity to real GDP growth but is not affected by inflation. McCracken is confident in his APT estimates for the High Growth Fund and the Large Cap Fund. He then computes the sensitivities for a third fund, Orb’s Utility Fund, which has sensitivities equal to 1.0 and 2.0, respectively. McCracken will use his APT results for these three funds to accomplish the task of creating a portfolio with a unit exposure to real GDP and no exposure to inflation. He calls the fund the “GDP Fund.” Stiles says such a GDP Fund would be good for clients who are retirees who live off the steady income of their investments. McCracken says that the fund would be a good choice if upcoming supply side macroeconomic policies of the government are successful.
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