8. In a single-factor market, the SML relationship of both the CAPM and the APT states that the risk premium on any security is proportional to beta, or, equivalently, that the security's expected return must be a linear function of beta. Suppose this is not the case, specifically, that expected return rises more than proportionately with beta as in Figure 7.5. (LO 7-1) En FIGURE a. Could this figure be an accurate depiction of the mean-beta relationship in market equilibrium? Hint: Consider the return on a combination of portfolios A and B constructed to match the beta of portfolio C. b. Some researchers have examined the relationship between average returns on diversi- fied portfolios and the ß and ß² of those portfolios. What should they have discovered about the effect of B² on portfolio return? 7.5

8. In a single-factor market, the SML relationship of both the CAPM and the APT states that the risk premium on any security is proportional to beta, or, equivalently, that the security's expected return must be a linear function of beta. Suppose this is not the case, specifically, that expected return rises more than proportionately with beta as in Figure 7.5. (LO 7-1) En FIGURE a. Could this figure be an accurate depiction of the mean-beta relationship in market equilibrium? Hint: Consider the return on a combination of portfolios A and B constructed to match the beta of portfolio C. b. Some researchers have examined the relationship between average returns on diversi- fied portfolios and the ß and ß² of those portfolios. What should they have discovered about the effect of B² on portfolio return? 7.5

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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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?
3. A market consists of two risky assets and no risk-free asset. Let R₁ and R₂ denote the return on each of the risky assets. Using market data the following have been estimated: E[R₁] = 0.10, E[R₂] = 0.15, o² = Var(R₁) = 0.1², o² = Var(R₂) = 0.2² and p1,2 = -1/2 where P1,2 denotes the correlation coefficient for R₁ and R₂. (i) Given that an investor is targeting a total expected return of portfolio, what is the minimum variance that can be achieved? = 0.125 on a (ii) Determine the global minimum variance portfolio and the expected return and variance of return on this portfolio. (iii) Using your answers to parts (i) and (ii) make a rough sketch of the minimum- variance set in - o2 space. You should indicate the efficient frontier and the global minimum variance portfolio. (iv) Without further calculation, explain how you would expect the variance of return calculated in (ii) to change if the two risky assets were independent.
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…
Which of these are true about the Security Market Line and Capital Market Line models? 1. the intercepts are the same 2. the independent variable for the Capital Market Line is beta 3, the Capital Market Line applies to portfolios only O 1 and 2 only O 2 only O 1 and 3 only O 2 and 3 only O 3 only
assume that risk free rate, RF, is currently 8%, the market return, 1m, is 12%, and asset a beta ba, is 1.10. (a) Draw the SML on a set of "non-diversifiable risk Please sent me complete this question for further reliance.
A diagram of the CML and SML for the market M, risk-free asset ry, an inefficient portfolio P, and a complete portfolio C is shown below. The diagram is not to scale. E(r) E(13) CML & CALP E(12) P C E(r) M 01 02 03 P βρ SML M Вм The values of the labeled variables are E[1] = 3.0%, E[12] = 10.3%, E[3] = 16.7%, σ₁ = 17.9%, σ = 30.0%, 03 = 44.3%. What is the standard deviation of nonsystematic risk for the complete portfolio σc under the CAPM? O a. 0.1374 O b. 0.1180 O c. 0.0988 d. 0.1105 O e. 0.0791 O f. 0.0913 Og. 0.0858 O h. 0.1443
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.
Consider the following securities: state Probability A B A B H M L 0.2 0.5 0.3 с 6 10 6 3 7 12 2 5 14 1. The expected payoff of A is: 2. The standard deviation of A is: 3. If the price of A is 3, its expected return is: 4. The covariance between A and B is: 5. The correlation coefficient between A and B is: 6. Is it possible to build a portfolio that has zero variance using A and C? YES/ NO
15. (Singular) Suppose there are two stocks that are uncorrelated. Each of these has variance of 1, and there are expected returns are 7₁ and 72, respectively. The risk-free rate is rf. Find the portfolio of weights w₁ and w₂ for the Markowitz (market) portfolio. Show that for some value of rf there is no Markowitz portfolio.
A risky security has less risk than the overall market. What must the beta of this security be? O 0 but< 1 O 1 O The beta cannot be determined based on the information provided.
Assume that the CAPM assumptions hold. Consider the following statements:i. A stock with a beta below zero will tend to move in the same direction as the market but will tend to move less aggressively in that direction than the market does.ii. Alpha measures the additional risk we take on top of the risk of the market portfolio.

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