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. b. Suppose we form an equally weighted portfolio of stocks A and B. What will be the nonsystematic standard deviation of that portfolio?

2. Suppose that the market model for stocks A and B is estimated with the following results: RA = 1% +0.9RM+EA RB = -2% + 1.1RM+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. b. Suppose we form an equally weighted portfolio of stocks A and B. What will be the nonsystematic standard deviation of that portfolio?

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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Concept explainers

Stock Market Indices

Stock indexes are used to compare the price fluctuations of a group of stocks of similar companies, which are combined based on a similar industry or a particular market capitalization limit or type of market. The price comparison is based on a pre-determined standard method or indicators. These stock indexes are usually considered a base for comparison of a particular stock, and the performance of that particular company can be easily determined.

Question

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.

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Step 2: Standard Deviation of Stocks A, B and Covariance in Between Them

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3. Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
Assume that you are given the following partial covariance and correlation matrices for Securities J, K and the Market. Also assume that the expected risk-free rate for the coming year is 3.0 percent and that the expected risk premium on the market is 7.0 percent. Given this information, determine the required rate of return for Security J for the coming year, using CAPM. J Market Correlation J K Market Covariance J K Market Standard Deviation O 18.48% O 20.20% O 15.48% O 12.71% O 15.04% 0.44 0.86 J 0.014400 J K 0.64 K CAN 0.016900 K 1.00 Market 0.003600 Market
Assume that using the Security Market Line 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 the market portfolio is denoted by RM. Find the ratio of beta of A (bA) to beta of B (bB).
The index model for stocks A and B is estimated from excess return with the following results: RA = -0.01 +0.8RM RB = 0.04 + 1.1RM R-squared 4 = 0.15 R-squared B = 0.3 Market-index risk (oM) is 0.2
16. There are two stocks with the following return and risk values. The correlation between A and B is 0.2. al Expected Standard Return(%) Deviation(%) Stock A 5.5 10 B 7.5 17 What is the standard deviation of the minimum variance portfolio(MVP) that is a) formed by combining assets A and B? (That is, what are the weights of stock A and stock B in MVP?) b) What is the expected return of the portfolio P that is formed by investing 50% on the MVP and 50% on a stock that has an expected return of 10%? c) Assume that the only assets available to investors are the risk free asset and the portfolio P. The risk free rate is 2%. Assume also that there is $100 to be invested. What is the expected return of a NEW portfolio that is formed by combining risk free rate with a weight of -0.5 and portfolio P with a weight of 1.5? What does a negative weight mean? Explain with one sentence
Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA 3.60% +1.20RM + еA RB -1.60% + 1.50RM + еB OM = 16%; R-squareд = 0.25; R-squareB = 0.15 Assume you create portfolio P with investment proportions of 0.70 in A and 0.30 in B. a. What is the standard deviation of the portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Standard deviation % b. What is the beta of your portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Portfolio beta c. What is the firm-specific variance of your portfolio? (Do not round your intermediate calculations. Round your answer to 4 decimal places.) Firm-specific d. What is the covariance between the portfolio and the market index? (Do not round your intermediate calculations. Round your answer to 3 decimal places.) Covariance
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Calculate the coefficients of variation for the following stocks: Stock Expected return Standard deviation of return 1 0.065 0.25 2 0.06 0.17 3 0.14 0.24 What is the coefficient of variation for stock 1? What is the coefficient of variation for stock 2? What is the coefficient of variation for stock 3? f you want to get the best risk-to-reward trade-off, which stock should you buy? Stock 2 Stock 3 Stock 1
Problem 2. Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 2.00% + 1.10RM + A RB = -0.60% + 0.90RM + eB The R-squared of the estimate for stock A is 0.35 and the R-squared of the estimate for stock B is 0.40. The standard deviation of the market is OM = 30%. Assume you create portfolio P with weights of 120% in A and -20% in B. These weights mean that you go long stock A and short stock B. a) What is the standard deviation of the portfolio? [Hint: R-squared is the variance explained by the market risk B²o divided by the variance in the stock o}.] b) What is the beta of the portfolio? c) What is the firm-specific variance of the portfolio? (Round to 3 decimals.)
Give typing answer with explanation and conclusion Assume that two stocks are available. The first stock (Stock A) has an expected return of 25% and a standard deviation of 20%; the second stock (Stock B) has an expected return of 12% and a standard deviation of 10%. If the correlation between the stocks is 0.10, what are the weight of Stock A (WA) and Weight of Stock B(WB) in the minimum-variance portfolio? WA=17.39%, WB=82.61% WA=14.29%, WB=85.71% WA=10.30%, WB=89.70% WA=30.25%, WB=69.75%
You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio X Y Z Market Risk-free Rp 14.0% 13.0 .8.5 12.0 7.2 Ор 39.00% 34.00 24.00 29.00 0 Bp 1.50 1.15 0.90 1.00 0 Assume that the correlation of returns on Portfolio Y to returns on the market is 0.90. What percentage of Portfolio Y's return is driven by the market? Note: Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places. R-squared
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?

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