2. The following table gives information on the return and variance of assets A andB, whose covariance is 0.0003:AB0}0,00090,0012E (R₂)0,050,06a.Does the portfolio (1/3 of A and 2/3 of B) dominate the portfolio (2/3of 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%, wouldthe portfolio (1/2, 1/2) belong to the new efficient frontier?

1. Return and Variance of Assets A and B: - Asset A: Variance (σ²) = 0.0009, Expected Return…

2. The following table gives information on the return and variance of assets A and B, whose covariance is 0.0003: a. b. c. A o} 0,0009 B 0,0012 E (R₂) 0,05 0,06 Does the portfolio (1/3 of A and 2/3 of B) dominate the portfolio (2/3 of A and 1/3 of B)? Does the portfolio (1/2, 1/2) belong to the efficient frontier? If there were the possibility of lending and borrowing at 2%, would the portfolio (1/2, 1/2) belong to the new efficient frontier?

2. The following table gives information on the return and variance of assets A and B, whose covariance is 0.0003: a. b. c. A o} 0,0009 B 0,0012 E (R₂) 0,05 0,06 Does the portfolio (1/3 of A and 2/3 of B) dominate the portfolio (2/3 of A and 1/3 of B)? Does the portfolio (1/2, 1/2) belong to the efficient frontier? If there were the possibility of lending and borrowing at 2%, would the portfolio (1/2, 1/2) belong to the new efficient frontier?

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 return volatility for asset 1 and 2 is 0.2 and 0.3 respectively and the return correlation is 0.7. The portfolio volatility is a) 2.5 b) 3.0 c) 3.5 d) 4
Consider the expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and σ1=0.2 Asset 2: E[r2]=0.3 and σ2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) ρ12= -1, (ii) ρ12=0. (b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.
2) Calculate the envelope set (frontier) for the following four assets and show that the individual assets all lie within this envelope set. 123456 A B E A FOUR-ASSET PORTFOLIO PROBLEM C Variance-covariance 0.01 0.30 0.06 -0.04 0.10 0.01 0.03 0.05 0.03 0.06 0.40 0.02 D 0.05 -0.04 0.02 0.50 F Mean returns 6% 8% 10% 15%
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) = 10% SDA = 8% WA = 0.25 COVAB = 0.006 Select one: A. 13.75% B. 7.72% C. 12.5% D. 8.79% Asset (B) E(RB) = 15% SDB = 9.5% WB = 0.75
The expected value, standard deviation of returns, and coefficient o below.) \table[[Asset A],[Possible Outcomes,Probability,Returns (%)
Uncorrelated assets A and B have standard deviation of return 0.3 and 0.4 respectively. If a denotes the proportion invested in A, which value of a leads to the Minimum Variance Portfolio? A. 0.55 B. 0.64 C. 0.12 D. 0.80 .
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.
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.
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.
The market has three risky assets. The variance-covariance matrix of the risky assets are as follows: r1 r2 r3 r1 0.25 0 -0.2 r2 0 4 0.1 r3 -0.2 0.1 1 Assume the market portfolio is M = 0.2 ◦ r1 + 0.5 ◦ r2 + 0.3 ◦ r3. Further assume E(rM) = 0.08. (1) What is the variance of M?(2) What is the covariance of r2 and M?(3) What is β2?(4) If the rate of return of the risk-free asset is 0.02. Then what is the fair expected rate of return of security 2?(5) An investor wants to invest in a portfolio P = 0.4◦r1+0.6◦r3. What is its “fair” expected rate of return?
(a) XVW Ltd. currently holds a portfolio containing two assets; Asset 1 and Asset 2. If Er1 = 0.25, Er2 = 0.36, Er12 = 0.1, Er2 2 = 0.15 and Er1r2 = 0.125, where ri represents the return in asset i. Determine the optimal proportions in which each asset should be held if the company would like to minimize the variance of their portfolio %3D
3.1 Show that for any portfolio w = equal to (wi,..., wn) the Beta of the portfolio is Bw = wiB1 + + wn Bn, !! ... where B; for i = 1,...,n are Betas of individual assets.

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