Suppose there are two independent economic factors, M₁ and M2. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 58%. Portfolios A and B are both well diversified.PortfolioBeta on M1Beta on M2A1.7-2.42.3-0.8Expected Return (%)3710BRequired:What is the expected return-beta relationship in this economy?Note: Do not round intermediate calculations. Round your answers to 2 decimal places.Expected return-beta relationship E(rp) =% +BP1+BP2

To determine the expected return-beta relationship in this economy, we will use the Arbitrage…

Answered: Suppose there are two independent…

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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What are the risk premiums of the two factors and what is the risk-free rate?
Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 6%, and all stocks have independent firm- specific components with a standard deviation of 53%. Portfolios A and B are both well-diversified with the following properties: Portfolio A B Beta on F1 1.5 2.5 Beta on F2 Expected Return 1.9 -0.19 31% 28% Required: What is the expected return-beta relationship in this economy? Calculate the risk-free rate, rf, and the factor risk premiums, RP1 and RP2 to complete the equation below. Note: Do not round intermediate calculations. Round your answers to 2 decimal places. = E(rp) rf+(PP1 x RP1) + (BP2 x RP2) % RP1 % RP2 %
Assume that the following two assets are priced according to the zero-beta security market line: asset 1 has expected return of 6% and beta 0.5; asset 2 has expected return 14% and beta 2. (i) A third asset is mispriced by the market: it has beta 1.5 and expected return of 8%. Explain how you can set up a portfolio to exploit the arbitrage opportunity. What is the expected return of such portfolio? [33%] (ii) A fourth asset is mispriced by the market: it has beta 1.2 and expected return of 18%. Explain how you can set up a portfolio to exploit the arbitrage opportunity. What is the expected return of such portfolio? [33%] (iii) What should be the expected return for an asset with beta 0.8?
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 following expected return and the standard deviation of current returns are known: Security (i) Expected Return Standard Deviation βi A 0.20 0.12 1.1 B 0.12 0.10 0.8 T-Bills 0.05 0 0 Market Portfolio 0.20 0.15 1 Required: Determine which of A or B is over-valued or undervalued.
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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…
E(FAssume 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 (Rs) on stock B. The risk-free rate (R;) 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). a o
The CAPM states that the expected (required) return on an asset is : E(Ri)=Rf+βi[E(RM)−Rf] where the term in square brackets is the risk-premium earned by the market portfolio. Therefore, the beta of the market portfolio (βM) must be equal to __________ . A) zero B) 0.5 C) 1.0 D) an unknown estimate
9. Suppose you plan to form your overall investment portfolio in two steps: STEP 1: Choose a portfolio of stocks with a zero position in the risk-free asset. STEP 2: Allocate your money between the portfolio from Step 1 and the risk-free asset. Suppose you can borrow and lend as much as you want at the risk-free rate in Step 2. Let Erp be the expected return of the Step 1 portfolio. Let Var(rp) be the variance of the return of the Step 1 portfolio. Let rf be the risk-free rate. How will you form the Step 1 Portfolio? Set the Step 1 portfolio to maximize Erp SettheStep1portfoliotominimizeVar(rp) Set the Step 1 portfolio to maximize Erp - Var(rp) Set the Step 1 portfolio to maximize the ratio Erp/Var(rp) Set the Step 1 portfolio to maximize the ratio (Erp- rf)/Var(rp) None of the above.
Which ones of the following statements about portfolio beta are correct? O 1. If portfolio beta is between 0 and 1, then the portfolio expected return is between risk-free rate and the market expected return. O 2. If the return of an asset has zero correlation with the market portfolio returns, the beta of this asset must be zero. O 3. A portfolio that has the same portfolio weights as the market portfolio should have a beta of 1. O 4. Diversification is not a way to reduce portfolio beta. O 5. If two portfolios have the same portfolio weights, but different dollar values, their betas are the same.
Calculate the optimal risky portfolio for the following cases when short-sales are allowed. Compute its expected return and the standard deviation of its returns. 1. Two risky assets: Rp = 3, R' = [6, 9], and 4 5 5 20 2. Three risky assets: Rp = 4, R' = [5,9, 8], and [10 0 0 E=0 40 0 0 20 3. Three risky assets: Rp = 5, R' = [12, 9, 8], and 40 10 -5] E= 10 20 0 5 0 30 4. Five risky assets: Rp = 2, R' = [5, 3, 18, 9, 2], and %3D 2 16 0. -12 5 -12 20 16 10 7 14 27 14 9. -13 8. 7 27 13

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