EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 6, Problem 5PS
Summary Introduction
To calculate: The highest level of risk aversion on which behalf the risk portfolio is preferred for T-bill is to be determined.
Introduction: In the condition of risk averse, the investor chooses the lower return with known risk over higher return with unknown risk. The risk aversion is defined by the impression of the utility function.
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Consider a risky portfolio, A, with an expected rate of return of 0.15 and a standard deviation of 0.15, that lies on a given indifference curve. Which one of the following portfolios might lie on the same indifference curve?
A. E(r) = 0.15; Standard deviation = 0.20
B. E(r) = 0.20; Standard deviation = 0.15
C. E(r) = 0.10; Standard deviation = 0.10
D. E(r) = 0.10; Standard deviation = 0.20
E. E(r) = 0.15; Standard deviation = 0.10
Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills?
If the market portfolio has a required return of 0.12 and a standard deviation of 0.40, and the riskfreerate is 0.04, what is the slope of the security market line?
Chapter 6 Solutions
EBK INVESTMENTS
Ch. 6.A - Prob. 1PCh. 6.A - Prob. 2PCh. 6 - Prob. 1PSCh. 6 - Prob. 2PSCh. 6 - Prob. 3PSCh. 6 - Prob. 4PSCh. 6 - Prob. 5PSCh. 6 - Prob. 6PSCh. 6 - Prob. 7PSCh. 6 - Prob. 8PS
Ch. 6 - Prob. 9PSCh. 6 - Prob. 10PSCh. 6 - Prob. 11PSCh. 6 - Prob. 12PSCh. 6 - Prob. 13PSCh. 6 - Prob. 14PSCh. 6 - Prob. 15PSCh. 6 - Prob. 16PSCh. 6 - Prob. 17PSCh. 6 - Prob. 18PSCh. 6 - Prob. 19PSCh. 6 - Prob. 20PSCh. 6 - Prob. 21PSCh. 6 - Prob. 22PSCh. 6 - Prob. 23PSCh. 6 - Prob. 24PSCh. 6 - Prob. 25PSCh. 6 - Prob. 26PSCh. 6 - Prob. 27PSCh. 6 - Prob. 28PSCh. 6 - Prob. 29PSCh. 6 - Prob. 1CPCh. 6 - Prob. 2CPCh. 6 - Prob. 3CPCh. 6 - Prob. 4CPCh. 6 - Prob. 5CPCh. 6 - Prob. 6CPCh. 6 - Prob. 7CPCh. 6 - Prob. 8CPCh. 6 - Prob. 9CP
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- The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standarddeviation of 20%. Answer the following questions.a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition ofA to make the investors prefer the optimal risky portfolio than the risk free asset? b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expectedreturn and standard deviation of the investor’s optimal complete portfolio?arrow_forwardGiven the non-satiation and risk aversion assumptions, which of the following five portfolios has the most desirable risk and return characteristics and thus will be chosen by investors ? The risk-free rate of return is 6%. (Explain or justify your answer briefly.) Portfolio Average Annual Return (%) Standard Deviation (%) R2 14 21 0.70 K 16 24 0.98 Q 24 28 0.96 17 25 0.92 11 18 0.60arrow_forwardSuppose that the return on the risk-free asset is rRFrRF = 15%, the return on the market portfolio is r̂Mr̂M = 20%, the market risk is σMσM = 10%, and the portfolio risk is σpσp = 15%. Then the expected rate of return on an efficient portfolio equals . Generally, a less risky portfolio would havea lower rate of return.arrow_forward
- According to CAPM, the expected rate of return of a portfolio with a beta of 1.0 and an alpha of 0 is:a. Between rM and rf .b. The risk-free rate, rf .c. β(rM − rf).d. The expected return on the market, rM.arrow_forwardhe risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standarddeviation of 20%. (a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition ofA to make the investors prefer the optimal risky portfolio than the risk free asset? (b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expectedreturn and standard deviation of the investor’s optimal complete portfolio?arrow_forwardConsider the multifactor model APT with three factors. Portfolio A has a beta of 0.8 on factor 1, a beta of 1.1 on factor 2, and a beta of 1.25 on factor 3. The risk premiums on the factor 1, factor 2, and factor 3 are 3%, 5%, and 2%, respectively. The risk-free rate of return is 3%. The expected return on portfolio A is __________ if no arbitrage opportunities exist. A. 23.0% B. 16.5% C. 13.4% D. 13.5%arrow_forward
- Consider a risky portfolio, A, with an expected rate of return of 0.16 and a standard deviation of 0.25, that lies on a given indifference curve. Which one of the following portfolios is not likely to lie on the same indifference curve for a risk-averse investor with a mean- variance utility function? a. Expected return = 0.20; Standard deviation = 0.15 b. Expected return = 0.10; Standard deviation = 0.20 Expected return= 0.15; Standard deviation = 0.20 Expected return = 0.12; Standard deviation = 0.10 Expected return = 0.10; Standard deviation = 0.10 C. d. e.arrow_forwardYou compute the optimal risky portfolio to have the expected return of 12% and standard deviation of 20%. The risk free rate is 4%. What will be the standard deviation of the complete portfolio of risk free asset and the optimal risk portfolio, for a risk averse investor with risk aversion index A=6. O 1.11 О 3.33 O 5.67 O 6.67 O None of abovearrow_forwardAssume the APT equation for portfolios A and B with the following system of equations: E[rA] = λ0 + (λ1)3 + (λ2)0.2 = 11.0 E[rB] = λ0 + (λ1)2 + (λ2)1 = 13.0 Assume the following: . The risk free rate is λ0 = Rf = 5 . The expected return on the market portfolio is RM = 10 . Expected returns are consistent with the CAPM. . (hint: note that λ1 = E[RA] − Rf and λ2 = E[RB] − Rf ). Answer the following: (a) What are λ1 and λ2? (b) What is the CAPM β associated with the pure portfolio associated with factor 1? (c) What is the CAPM β associated with the pure portfolio associated with factor 2?arrow_forward
- The following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement is correct? E[R] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 Figure 1 0.2 0.25 0.3 0.35 0.4 0.45 o (R) E[R] Figure (1) shows an investor with a conservative investment behavior. 0.3 0.25 0.2 0.15 0.1 0.05 0 0 Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset. 0.05 0.1 0.15 In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier. O In Figure (1), more aggressive investment decision led to a higher Sharpe ratio. Figure 2 0.2 0.25 o(R) 0.3 0.35 0.4 0.45arrow_forwardSuppose that optimal risky portfolio has an expected return of 16% and a varianceof 0.04. The risk-free rate is 4%.a) Find the slope of Capital Market Line (Optimal Capital Allocation Line)?b) What is the expected return of a portfolio C, which is on Capital Market Line and has astandard deviation of 0.08?arrow_forwardThe following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement is correct? E[R] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 Figure 1 0.2 0.25 0.3 0.35 o(R) 0.4 0.45 [H]Z 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset. Figure (1) shows an investor with a conservative investment behavior. In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier. In Figure (1), more aggressive investment decision led to a higher Sharpe ratio. 0.15 Figure 2 0.2 0.25 o (R) 0.3 0.35 0.4 0.45arrow_forward
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