The market has three assets. In addition, PAB = 0. A B 0.2 0.3 1 3 F E(r) 0.1 0 0 (a) If the investor can invest in the risk-free asset and one of the risky assets (either A or B, but not both). Will she choose A or B to construct a portfolio with the risk-free asset? Why? (Hint: you can draw a graph to answer this question.)

The market has three assets. In addition, PAB = 0. A B 0.2 0.3 1 3 F E(r) 0.1 0 0 (a) If the investor can invest in the risk-free asset and one of the risky assets (either A or B, but not both). Will she choose A or B to construct a portfolio with the risk-free asset? Why? (Hint: you can draw a graph to answer this question.)

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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4. Suppose that there are 2 assets with ri 012 = 0.005. = 0.20, 01 = = 0.40, 2 = 0.10, 02 = 0.25 and (a) If ro = 0.02, what are the market portfolio return and variance? What are the corre- sponding weights (i.e. how much to invest in asset 1, asset 2, and the risk-free asset to get the market portfolio)? Answer. (b) If ro 0.05, what are the market portfolio return and variance? What are the corre- sponding weights? Answer.
Consider the following financial market with two risky assets x and y as well as a risk-free asset f: E[r]. x (10%, 8%) •z (6.6%, 6.3%) y (8%, 5%) (0%, 3%) f Is it possible to construct portfolio z with existing assets? Explain.
The optimal proportion of the risky asset in the complete portfolio is given by the equation below y*= E(Rp− Rf) A0² For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse
We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?
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.
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/ where p1,2 denotes the correlation coefficient for R₁ and R₂. (i) Given that an investor is targeting a total expected return of = 0.125 on a portfolio, what is the minimum variance that can be achieved? (ii) Determine the global minimum variance portfolio and the expected return and variance of return on this portfolio.
choose which one ? 3.Assume CAPM holds. What is the correlation between an efficient portfolio and the market portfolio?a.1b.-1c.0d.Not enough information
. Write out the equation for the Capital Market Line(CML), and draw it on the graph. Interpret theplotted CML. Now add a set of indifference curvesand illustrate how an investor’s optimal portfoliois some combination of the risky portfolio and therisk-free asset. What is the composition of the riskyportfolio?
Consider a capital market with two securities. The payoffs of these securities in the two equally likely states of the world are given in the table below. Рayolf Price Security State 1 State 2 PA=2 A 4 2 PB-3 B a. Discuss the concepts of complete capital markets, pure (Arrow-Debreu) securities, and pure factor portfolios. Establish whether the capital market in this case is complete and determine the prices of the pure socurities by arbitrage.
Assuming two risk-free rates for lending and borrowing in the market: r(f) and r(b). Suppose your utility function is described by U = E(r) - 0.5A xo² with A> 0, and you are combining the risk-free asset with the optimal risky asset to maximize the utility. Consider the following two situations: 1. Suppose r(b) = r(f): you form the optimal complete portfolio C1 by borrowing money at r(f) and invest y1 (i.e., y1 represents portfolio weight) in the optimal risky portfolio (P1). Your utility score under this situation is denoted as U1; II. Suppose r(b) >r(f): you form another optimal complete portfolio C2 by borrowing money at r(b) and invest y2 (1.e., y2 represents portfolio weight) in the optimal risky portfolio (P2). Your utility score under this situation is denoted as U2. For simplicity, let's assume the optimal risky portfolios under these two situations are the same (i.e., E(P1)=E(P2) and o(P1) = o(P2)). What are the relationship between y1 and y2, U1 and U2: O a. y1=y2 and U1=U2 O…
Think about whether a risk-free asset should earn a risk-premium beyond the risk-free rate. Thinking about that should give you an idea of the beta for a risk-free asset. Or, look again at the CAPM equation: E(Ri)=Rf+βi[E(RM)−Rf] Given this equation, what beta sets the E(R) of the risk free asset equal to the risk-free rate? A) zero B) 0.5 C) 1.0 D) its random
Consider an economy with a (net) risk-free return r1 = 0:1 and a market portfolio with normally distributed return, with ErM = 0:2 and 2M = 0:02. Suppose investor A has CARA preferences, with risk aversion coe¢ cient equal to 1 and an endowment of 10. a) Write down the maximization problem for the investor. b) Determine the amount invested in the risky portfolio and in the risk-free asset. c) Suppose another investor (B) has a coe¢ cient of absolute risk aversion equal to 2 (and the same endowment 10). Compute his optimal portfolio and compare it to that of investor A. Explain the di§erent results for investors A and B. d) Finally, consider Investor C with mean-variance preferences Ec V ar(c) (and endowment 10). Compute his optimal portfolio and compare it to that of investors A and B (as obtained in questions b and c). Compare your result with those obtained for investors A and B.

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