III. 1. The average variance of financial assets on a market is 0.4% and the average covariancebetween assets is 0.1%. Compute the variance of a portfolio composed of a. 5 assets: b. 100assets.a. V(Rpf)=..b. V(Rpf)=..2. On a market at equilibrium the effcient frontier has the following equation:E(Rp)=4%+1.2 opfThe standard deviation of the market portfolio equals 5%.a. The expected return on a portfolio A with a beta of 1,2 equals .%.b. How much of the total risk of portfolio B is explained by the market if the correlationbetween A and B equals 0,5? Answer: R? =.%

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1. 1. The average variance of financial assets on a market is 0.4% and the average covariance tween assets is 0.1%. Compute the variance of a portfolio composed of a. 5 assets: b. 100 sets. a. V(Rpf)=........ %

1. 1. The average variance of financial assets on a market is 0.4% and the average covariance tween assets is 0.1%. Compute the variance of a portfolio composed of a. 5 assets: b. 100 sets. a. V(Rpf)=........ %

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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Question

III. 1. The average variance of financial assets on a market is 0.4% and the average covariance
between assets is 0.1%. Compute the variance of a portfolio composed of a. 5 assets: b. 100
assets.
a. V(Rpf)=..
b. V(Rpf)=..
2. On a market at equilibrium the effcient frontier has the following equation:
E(Rp)=4%+1.2 opf
The standard deviation of the market portfolio equals 5%.
a. The expected return on a portfolio A with a beta of 1,2 equals .%.
b. How much of the total risk of portfolio B is explained by the market if the correlation
between A and B equals 0,5? Answer: R? =.
%

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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?
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?
Assume the standard deviation of the market return is 0.2, the standard deviation of asset k is 0.45 and the beta of asset k is 0.675. The correlation coefficient between the return from asset k and the return from the market is: A. 0.473 OB. 0.900 OC. No answer OD. 0.290
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.
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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

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