Consider 3 stocks A, B, and C and the risk-free rate RF-0.5%. The logarithmic rates of return are as llows: RA,t(%) RB,t (%) Rc,t(%) 1 6 7 4 2 6 9 2 3 -2 3 8 4 2 6 3 a) Compute the mean returns the holding returns for the entire period. b) Determine the risk of each stock. c) Measure the correlation between A and B, A and C, and B and C. 5 5 6 -1 6 8075 -5

Consider 3 stocks A, B, and C and the risk-free rate RF-0.5%. The logarithmic rates of return are as llows: RA,t(%) RB,t (%) Rc,t(%) 1 6 7 4 2 6 9 2 3 -2 3 8 4 2 6 3 a) Compute the mean returns the holding returns for the entire period. b) Determine the risk of each stock. c) Measure the correlation between A and B, A and C, and B and C. 5 5 6 -1 6 8075 -5

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Consider information given in the table below and answers the question asked thereafter: State Probability return on stock A Return on stock B A 0.15 10% 9% B 0.15 6% 15% C 0.10 20% 10% D 0.18 5% -8% E 0.12 -10% 20% F 0.30 8% 5% Calculate covariance and coefficient of correlation between the returns of thestocks A and B.v. Now suppose you have $100,000 to invest and you want to a hold a portfoliocomprising of $45,000 invested in stock A and remaining amount in stock B.Calculate risk and return of your portfolio.
2. Suppose that three stocks (A, B, and C) and two common systematic risk factors (1 and 2) have the following relationship: E(RA) = (0.80) F1 + (0.90) F2 E(RB)= (-0.20) F1 + (1.30) F2 E(RC)= (1.80) F1 + (0.50) F2 a. Compute the expected returns if F1 = 4% and F2 = 5% b. Assuming that all three stocks are currently priced at $35 and will not pay a dividend over the next year, compute the expected prices a year from now c. Now, suppose you "know" that in one year the actual prices of stocks A, B, and C will be $37.20, $37.80, and $38.50. How can you best take advantage of what you consider to be a market mispricing? d. How will the current prices adjust?
QG. The following information is available about the stocks of two companies A and B: Stock A Stock B Expected Return (%) Probability -5 12 15 20 0.05 0.55 0.35 0.05 Expected Return (%) Probability 5 15 18 20 0.05 0.65 0.20 0.10 Stock Standard Deviation of Returns (%) A B 25 35 The coefficient of correlation between the returns on A and B is 0.05. A portfolio is constructed by allocating the funds between A and B in the ratio of 2:3. Calculate the expected return on the portfolio. b. Calculate the portfolio risk.
Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + .7RM + eARB = −2% + 1.2RM + eBσM = 20%; R-squareA = .20; R-squareB = .12What is the covariance between each stock and the market index?
Plz show the formula step by step. There is the following table shows the probabilities of occurrence of 3 states and the expected rate of returns on stocks A and B State Probability Expected rate ofReturns on Stock A Expected rate ofReturns on Stock B Boom 0.5 0.25 0.20 Neutral 0.3 0.15 0.10 Recession 0.2 0.05 0.02 (A) Calculate the expected rates of returns and standard deviations of stocks A and B. The colleague has given you his forecasts of stocks C and D as follows: State Probability Expected rate ofReturns on Stock C Expected rate ofReturns on Stock D Boom 0.7 0.40 -0.10 Bust 0.3 -0.05 0.30 She would like to invest 80% of his money in stock C and 20% of her money in stock D to construct a portfolio.(B) Calculate the portfolio's expected rate of returns and its standard deviation
2. Suppose that the market model for stocks A and B is estimated with the following results: RA = 1% +0.9*RM+EA RB = -2% + 1.1*RM+EB The standard deviation of the markets returns is 20% and firm specific risk (standard deviation) equals 30% for A and 10% for B. a. Compute the risk (standard deviation) of each stock and the covariance between them. Suppose we form an equally weighted portfolio of stocks A and B. What will be the nonsystematic standard deviation of that portfolio? b.
Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 0.03 + 0.7 RM + eA RB = -0.02+ 1.2 RM + eB σM =0.20; R-square A = 0.25 R-square B = 0.20 What is the standard deviation of A & B, respectively? Group of answer choices 0.54, 0.28 0.28, 0.54 0.45, 0.50 0.50, 0.45
Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .092, E(RB) = 152, đA = .362, and Og = .622. %3D Calculate the expected return of a portfolio that is composed of 37 percent A and 63 percent B when the correlation between the returns on A and B is .52. (Do not a-1. round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Calculate the standard deviation of a portfolio that is composed of 37 percent A and 63 percent B when the correlation coefficient between the returns on A and B is .52. а-2. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Calculate the standard deviation of a portfolio with the same portfolio weights as in h part (a) when the correlation coefficient between the returns on A and B is -.52. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a-1.…
Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + .7RM + eARB = −2% + 1.2RM + eBσM = 20%; R-squareA = .20; R-squareB = .12What are the covariance and the correlation coefficient between the two stocks?
The index model has been estimated using historical excess return data for stocks A, B, and C, with the following results: RA = 0.02 + 0.9RM + eA RB = 0.04 + 1.2RM + eB RC = 0.10 + 1.ORM + eC OM oM = 0.22 o(eA) = 0.21 o(eB ) = 0.11 o(eC ) = 0.23 a. What are the standard deviations of stocks A, B, and C? b. Break down the variances of stocks A, B, and C into their systematic and firm-specific components. c. What is the covariance between the returns on each pair of stocks? d. What is the covariance between each stock and the market index?
c) Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). (10 marks)d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (10 marks)(Hint: Beta of asset i (??) =???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)
Suppose that three stocks (A, B, and C} and two common risk factors (1 and 2) have the following relationship: E(RA) = (1.1)A1 + (0.8)A2 E(RB) = (0.7)A1 + (0.6)A2 E(RC) = (0.3)A1 + (0.4)A2 a. If A1 = 4 percent and A2 = 2 percent, what are the prices expected next year for each of the stocks? Assume that all three stocks currently sell for $30 and will not pay a dividend in the next year. b. Suppose that you know that next year the prices for Stocks A, B, and C will actually be $31.50, $35.00, and $30.50. Create and demonstrate a riskless, arbitrage investment to take advantage of these mispriced securities. What is the profit from your investment? You may assume that you can use the proceeds from any necessary short sale. Problems 13 and 14 refer to the data contained in Exhibit 7.23, which lists 30 monthly excess returns to two different actively managed stock portfolios (A and B) and three different common risk factors (1, 2, and 3). {Note: You may find it…

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