Consider the following portfolio of assets: Loan Weight 1 0.30 2 0.70 Expected returni ம σ2 13% 11% 9.06% 82.0% P12=-0.87 8.72% 76.0% 012-75.0% What is the variance of the portfolio (round to two decimals)? Note: a^2 denotes the square of a. For example, 2^2 = 4, 3^2=9 (0.3)^2*(82.0%) + (0.7)^2*(76.0%) + (0.3) (0.7)(-0.87) (9.06%) (8.72%) = 30.19 (0.3)^2 (82.0%) + (0.7)^2*(76.0%) + 2(0.3) (0.7)(-0.87) (9.06 %) (8.72%) = 15.75 (0.3)^2*(82.0%) + (0.7)^2*(76.0%) + [(0.3) (0.7)]^2 (-0.87) (9.06%) (8.72%) = 41.59 (0.3) (82.0%) + (0.7) (76.0%) + 2(0.3) (0.7)(-0.87) (9.06 %) (8.72%) = 48.93

Consider the following portfolio of assets: Loan Weight 1 0.30 2 0.70 Expected returni ம σ2 13% 11% 9.06% 82.0% P12=-0.87 8.72% 76.0% 012-75.0% What is the variance of the portfolio (round to two decimals)? Note: a^2 denotes the square of a. For example, 2^2 = 4, 3^2=9 (0.3)^2(82.0%) + (0.7)^2(76.0%) + (0.3) (0.7)(-0.87) (9.06%) (8.72%) = 30.19 (0.3)^2 (82.0%) + (0.7)^2(76.0%) + 2(0.3) (0.7)(-0.87) (9.06 %) (8.72%) = 15.75 (0.3)^2(82.0%) + (0.7)^2*(76.0%) + [(0.3) (0.7)]^2 (-0.87) (9.06%) (8.72%) = 41.59 (0.3) (82.0%) + (0.7) (76.0%) + 2(0.3) (0.7)(-0.87) (9.06 %) (8.72%) = 48.93

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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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?
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%
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B) E(RA)=10% E(RB) = 15% (σA)=8% (GB) = 9.5% WA = 0.25 WB = 0.75 COVA.B = 0.006 What is the standard deviation of this portfolio? O 13.75% O 8.79% O 12.5% O 7.72%
What is the total variance of the following portfolio including 2 assets invested in the ratio of 3:1. Asset A: E(r) = 0.3 , s = 0.6 Asset B: E(r) = 0.4, s = 0.8 Correlation: 0.8 rf = 0.1 A) 1.14 B) 0.88 C) 0.38 D) 1.44
An asset has normally-distributed returns, with mean of 10.6% and standard deviation of 14.8%. What is the 2% VaR (value at risk) return? Enter answer in percents.
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.
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? =. %
The probability distributions of expected returns for the assets are shown in the following table: Asset A Prob Return 0.2 -5% 0.4 10% 0.4 15% a) Calculate the expected return for asset A. b) Calculate the standard deviation for asset A.
Suppose two asset returns are described by a 1-factor model = 2% + 0.6f + ej r2= 2% + 0.6f+ e2 where the volatility of fis 30% and the volatility of e and ez is 20%. What is the covariance of r and r2? (Nearest 0.0001)
Compute the VaR(95%) and ES(95%) of the portfolio managed by Absolute Asset Management if its returns, r, follow the distribution specified below: = 1 10 - |r 100| – 10
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 .
For investment A, the probability of the return being 20.0% is 0.5, 10.0% is 0.4, and -10.0% is 0.1 Compute the standard deviation for the investment with the given information. (Round your answer to one decimal place.) a. 85.00% b. 15.00% c. 34.00% d. 17.00% e. 9.00%

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