Consider the following single index specification: R¡ = a¡ + ß¡ RM + ei. Where R, is the return on security i (X or Y), R is the return on index M (a broad market index) and e; is a zero-mean white noise random variable not correlated with anything. Assume that the single index specification correctly describes returns of all securities and the risk- free rate is constant at 4%. Furthermore, you have the following descriptive statistics for returns of Stock X, Y, and index M. Stock X Stock Y Index M Expected return 13% 9% 10% Return Standard Deviation 30% 15% 20% Bi 1.5 0.5 1

Consider the following single index specification: R¡ = a¡ + ß¡ RM + ei. Where R, is the return on security i (X or Y), R is the return on index M (a broad market index) and e; is a zero-mean white noise random variable not correlated with anything. Assume that the single index specification correctly describes returns of all securities and the risk- free rate is constant at 4%. Furthermore, you have the following descriptive statistics for returns of Stock X, Y, and index M. Stock X Stock Y Index M Expected return 13% 9% 10% Return Standard Deviation 30% 15% 20% Bi 1.5 0.5 1

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 the following single factor specification: R₁ = a¡ + ßi, Rµ + €i. Where R; is the return on security i, RM is the return on index M (a broad market index) and e, is a zero- mean white noise random variable not correlated with anything. Assume that the single factor specification above correctly describes the return generating processes of all securities. Furthermore, you have the following descriptive statistics for returns of well-diversified Portfolios X, Y, and index M. Portfolio X Portfolio Y Index M Risk-Free Expected return 14% 17% ?? ?? B₁ 1.2 1.6 1 0 a. Assume that the corresponding single factor APT correctly prices Portfolios X and Y. In other words, the expected returns of Portfolios X and Y shown above - 14% and 17% respectively - are equal to their APT-predicted expected returns. Calculate the expected return of Index M and risk-free rate. b. Another well-diversified portfolio Z has a beta, ßz, of 0.8 while its expected return is 10%. Form a portfolio consisting…
Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be halfof the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratioof betaof A(A) tobeta of B(B). Thank you for your help.
Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 1.4 14 % 23 % B 1.6 16 14 C 1.8 18 17 a. If σM = 22%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (bA) to beta of B (bB). please show all workings and not merely : Ra = 1/2 rbRf = 1/4 Ra
Assume that security returns are generated by the single-index model, Ri = alphai + BetaiRM + ei where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data. Security Betai E(Ri) sigma(ei) A 1.4 15% 28% B 1.6 17% 14% C 1.8 19% 23% a. If simaM = 24%, calculate the variance of returns of securities A, B, and C (round to whole number). Variance Security A Security B Security C b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C (enter the variance answers as a whole number decimal and the mean as a whole number percentage)? Mean Variance Security A ?% Security B ?% Security C ?%
Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (bA) to beta of B (bB). (please show all workings)
Questions C and D is required. Thank you.c) Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B (B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i ( , where are standard deviations of asset i and market portfolio, is the correlation between asset i and the market portfolio)
Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (βA) to beta of B (βB).
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). 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. (Hint: Beta of asset i (??) = ???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)
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). 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. (Hint: Beta of asset i (??) =???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)Question 2. Foreign exchange marketsStatoil, the national…
The market portfolio (M) has the expected rate of return E(rM) = 0.12. Security A is traded in the market. We know that E(rA) = 0.17 and βA = 1.5. (1) What is the rate of return of the risk-free asset (rf)? (2) Security B is also traded in the market. βB = 0.8. Then what is “fair” expected rate of return of security B according to the CAPM? (3) Security C is a third security traded in the market. βC = 0.6, and from the market price, investors calculate E(rC) = 0.1. Is C overpriced or underpriced? What is αC?
Which of the following statements regarding the graph of the SML is most accurate? Select one O A. O B. B-1.0 The beta of Portfolios A, B, and C are identical as they fall directly on the line. The expected return of Portfolio C is the difference between the market's expected return and the risk-free rate. O C. Portfolio A has lower systematic risk than Portfolio B. OD. The slope of the line is the market risk premium.

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