Risk and Return with Varying Weights ■ We want to understand all the possible (expected return, volatility) combinations that can be obtained by combining US and JP. - Take an arbitrary portfolio with weights w on US and 1 - w on JP. ■ The expected return of the portfolio is: E[R₂] = w×0.136 + (1 − w)×0.150 ■ Back to p = 27%. The variance of the portfolio return is: Var(Rp) = w²x(0.154)² + (1 − w)²×(0.230)² - +2xwx(1 - w)×0.27×0.154×0.230

Risk and Return with Varying Weights ■ We want to understand all the possible (expected return, volatility) combinations that can be obtained by combining US and JP. - Take an arbitrary portfolio with weights w on US and 1 - w on JP. ■ The expected return of the portfolio is: E[R₂] = w×0.136 + (1 − w)×0.150 ■ Back to p = 27%. The variance of the portfolio return is: Var(Rp) = w²x(0.154)² + (1 − w)²×(0.230)² - +2xwx(1 - w)×0.27×0.154×0.230

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter3: Risk And Return: Part Ii

Section: Chapter Questions

Problem 2P: APT An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk-free...

See similar textbooks

Similar questions

Mean-variance expected utility is given by Eu = e-, where e is expected return, v is the variance of the portfolio and tis risk tolerance. Suppose an investor has risk-loving preferences. What can we say about the value of t? Select one: Ot1 O. t>0 O t=0
2. The following table gives information on the return and variance of assets A and B, whose covariance is 0.0003: A B 0} 0,0009 0,0012 E (R₂) 0,05 0,06 a. Does the portfolio (1/3 of A and 2/3 of B) dominate the portfolio (2/3 of A and 1/3 of B)? b. Does the portfolio (1/2, 1/2) belong to the efficient frontier? c. If there were the possibility of lending and borrowing at 2%, would the portfolio (1/2, 1/2) belong to the new efficient frontier?
5. There are three risky assets with rates of return r₁, 12, and r3, respectively. The covariance matrix and the expected rates of return are [0.4 0.2 0 = Σ 0.2 0.4 0.2 0 0.2 0.4 [0.04] 0.08 0.06 (a) Find the global minimum-variance portfolio. (b) For the required return z = 0.075, find (the weight of) the optimal portfolio with risky assets. For (c) and (d) only, assume there is an additional risk-free asset with return Tf 0.03. = (c) Find the tangent portfolio.
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 two assets. Suppose that the return on asset 1 has expected value 0.05 and standard deviation 0.1 and suppose that the return on asset 2 has expected value 0.02 and standard deviation 0.05. Suppose that the asset returns have correlation 0.4.Consider a portfolio placing weight w on asset 1 and weight 1-w on asset 2; let Rp denote the return on the portfolio. Find the mean and variance of Rp as a function of w.
- Exercise 2 An investor who maximizes a linear mean-variance utility, U(µp, σp) μpaσ, optimally invests half of her wealth in asset 1, having expected re- turn μ₁ = 10% and standard deviation σ1 10%, and half of her wealth in a risk-free asset, having return FR = 4%. = (a) Find the efficient frontier and represent it in the plane (σp, μP) (assuming that the investor feasible portfolios can include a short position in the risk- free asset). (b) Find the risk-aversion parameter a of the investor. (c) Using the same efficient frontier, for which levels of risk-aversion parameter the investor has a negative position in the risk-free asset? =
Q5. You are considering two assets with the following characteristics. Return Standard deviation Weights Asset 1 Asset 2 0.15 0.20 0.10 0.20 0.5 0.5 Compute the standard deviation of two portfolios if r1,2 = 0.40 and -0.60, respectively.
4. Suppose there are three uncorrelated assets. Each has a variance of 1.0 and expected rates of return are 1, 2, and 3, respectively. For this example, short sales are allowed. Do the following: a. Find the minimum variance portfolio for the following desired expected portfolio rates of return: 1.0, 1.5, 2.0, 2.5, and 3.0. b. Sketch these on the return versus risk plot (you will need to use the standard deviation of the portfolio, which clearly equals sqrt(w1^2+w2^2+w3^3), where wi are the weights). c. Suppose we have a risk-free asset with a return of 2%. Modify your plot for b.
* Consider the following portfolio II: long one call with exercise price E₁, long one put with exercise price E2, short one call with exercise price E, and short one put with exercise price E1+E2 E. Consider the case E₁ < E < E2 where E < 2 ⚫ (a) Write down the pay-off function A(S) for the portfolio II. • • (b) What is the value of the pay-off function when S < E₁? (c) What is the value of the pay-off function when E < S < E₂?
What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (SDi), covariance (COVij), and asset weight (Wi) are as shown below? Asset (A) E(R₂) = 25% SDA = 18% WA = 0.75 COVA, B = -0.0009 Select one: A. 13.65% B. 20 U ODN 20.0% C. 18.64% D. 22.5% Asset (B) E(R₂) = 15% SDB = 11% WB = 0.25
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 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 0.45
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