Homework Answers
Minimum Variance = (Std Dev (b))2 - (Std dev (b) x Std Dev (a) x Correlation(a,b)) / (Std Dev (a) 2 + Std Dev (b)2 - 2 x Std Dev (b) x Std Dev (a) x Correlation (a,b))
a) 266%
b) 61.53%
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2. Consider two risky assets (A and B), with the following characteristics: E(TA) = 6% and...
Question 4 Below is the risk and return characteristics of two risky assets 10 points Stock...
Question 4 Below is the risk and return characteristics of two risky assets 10 points Stock A Stock B E(R) 4.00%) Std. dev 27.00% 57.00% 11.00% Correlation (A,B):-1 a. Is it possible to construct a portfolio from the two stocks so that the portfolio is risk-free (i.e., the portfolio standard deviation is 0)? Please explain. Yes/No yes You're so smart! b. If so, what is the expected return on this risk-free portfolio? expected return
5. Consider two perfectly negatively correlated risky securities A and B. Your portfolio is currently weighted...
5. Consider two perfectly negatively correlated risky securities A and B. Your portfolio is currently weighted with 50% in A and 50% in B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. The risk-free rate is 3%. (a) (3 points) What are the variance and return for your portfolio? (b) (4 points) What weights would give you the...
We consider different risky portfolios consisting of two risky assets X and Y. Suppose the expected...
We consider different risky portfolios consisting of two risky assets X and Y. Suppose the expected return and standard deviation of the Minimum Variance Portfolio (MVP), M, are 9.05% and 1.04%. There are four other risky portfolios consisting of X and Y: A) Portfolio A: E(rA) = 8.25% and σA = 1.10%. B) Portfolio B: E(rB) = 9.20% and σB = 1.05%. C) Portfolio C: E(rC) = 8.70% and σC = 1.05%. D) Portfolio D: E(rD) = 8.53% and σD...
Question 1: Suppose there are two risky assets, A and B. You collect the following data...
Question 1: Suppose there are two risky assets, A and B. You collect the following data on probabilities of different states happening and the returns of the two risky assets in different states: State Probability Return Asset A Return Asset B State 10.3 7% 14% State 20.4 6% -4% State 30.3 -8% 8% The risk-free rate of return is 2%. (a) Calculate expected returns, variances, standard deviations, covariance, and correlation of returns of the two risky assets. (b) There are...
1. Suppose there is a negative correlation (-0.8) between the two risky assets (LARGE stocks and...
1. Suppose there is a negative correlation (-0.8) between the two risky assets (LARGE stocks and SMALL stocks). Will the variance of the minimum-variance portfolio increase, stay the same, or decrease when we switch from a correlation of 0.4 to a negative correlation of -0.8?
Question 1 Consider two risky assets A and B with E(rA)= 15%, Sigma_A= 32%, E(rB)= 0.09,...
Question 1 Consider two risky assets A and B with E(rA)= 15%, Sigma_A= 32%, E(rB)= 0.09, Sigma_B= 23%, corrA,B= 0.2. The risk free rate is 5%. The optimal risky portfolio of comprised of the two risky assets is to allocate 64% to A and the rest to B. What is the standard deviation of the optimal risky portfolio ? Select one: a. 20.75% b. 23.61% c. 22.86% d. 23.00% Question 2 Continued with previous question. What is the Sharpe ratio...
Question 1. Portfolio Analysis (2 points) a) Assume the following about assets A and B: E[7]0.1,...
Question 1. Portfolio Analysis (2 points) a) Assume the following about assets A and B: E[7]0.1, -0.09, E[TB] =0.08, o -0.04. Which one has lower absolute risk and which one has lower relative risk? (1): b) Find the mean return, E[r.), and variance, oz. of a portfolio consisting of 70% of your total wealth invested in asset A (w4=0.70), and 30% of your total wealth invested in asset B (Wg= 0.30). The correlation between assets A and B (P3) =...
please help and show your work! Consider a market model with three assets: two risky assets...
please help and show your work!
Consider a market model with three assets: two risky assets (#1 and #2) and one risk-free asset (#3). The risk-free rate of interest is r = 3%. The parameters of the risky returns are as follows: 02 = 15%, Mi = 6%, H2 = 9%, 01 = 10%, P12 = -10%. 1. Let u(x) and g(x) with xe (-0,00) denote, respectively, the expected return and volatility of my portfolio if I allocate 100x% of...
There are only two risky assets A and B with expected returns r A = 30...
There are only two risky assets A and B with expected returns r A = 30 % and r The covariance matrix of their returns is = 20 % [0.0576 0.0288] 0.0288 0.0256 (a) Solve for the minimum-variance portfolio of the two risky assets, as well as the expected rate of return and standard deviation of the portfolio. (9 marks) (b) Solve for an efficient portfolio with expected return 29.25 %. (8 marks) (c) Explain how the returns of the...
1. Consider a portfolio P comprised of two risky assets (A and B) whose returns have...
1. Consider a portfolio P comprised of two risky assets (A and B) whose returns have a correlation of zero. Risky asset A has an expected return of 10% and standard deviation of 15%. Risky asset B has an expected return of 7% and standard deviation of 11%. Assuming a risk-free rate of 2.5%, what is the standard deviation of returns on the optimal risky portfolio? a) 9.18% b) .918% c) .84% d) 8.42%
Question 4 Below is the risk and return characteristics of two risky assets 10 points Stock A Stock B E(R) 4.00%) Std. dev 27.00% 57.00% 11.00% Correlation (A,B):-1 a. Is it possible to construct a portfolio from the two stocks so that the portfolio is risk-free (i.e., the portfolio standard deviation is 0)? Please explain. Yes/No yes You're so smart! b. If so, what is the expected return on this risk-free portfolio? expected return
5. Consider two perfectly negatively correlated risky securities A and B. Your portfolio is currently weighted with 50% in A and 50% in B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. The risk-free rate is 3%. (a) (3 points) What are the variance and return for your portfolio? (b) (4 points) What weights would give you the...
Question 1: Suppose there are two risky assets, A and B. You collect the following data on probabilities of different states happening and the returns of the two risky assets in different states: State Probability Return Asset A Return Asset B State 10.3 7% 14% State 20.4 6% -4% State 30.3 -8% 8% The risk-free rate of return is 2%. (a) Calculate expected returns, variances, standard deviations, covariance, and correlation of returns of the two risky assets. (b) There are...
Question 1. Portfolio Analysis (2 points) a) Assume the following about assets A and B: E[7]0.1, -0.09, E[TB] =0.08, o -0.04. Which one has lower absolute risk and which one has lower relative risk? (1): b) Find the mean return, E[r.), and variance, oz. of a portfolio consisting of 70% of your total wealth invested in asset A (w4=0.70), and 30% of your total wealth invested in asset B (Wg= 0.30). The correlation between assets A and B (P3) =...
please help and show your work!
Consider a market model with three assets: two risky assets (#1 and #2) and one risk-free asset (#3). The risk-free rate of interest is r = 3%. The parameters of the risky returns are as follows: 02 = 15%, Mi = 6%, H2 = 9%, 01 = 10%, P12 = -10%. 1. Let u(x) and g(x) with xe (-0,00) denote, respectively, the expected return and volatility of my portfolio if I allocate 100x% of...
There are only two risky assets A and B with expected returns r A = 30 % and r The covariance matrix of their returns is = 20 % [0.0576 0.0288] 0.0288 0.0256 (a) Solve for the minimum-variance portfolio of the two risky assets, as well as the expected rate of return and standard deviation of the portfolio. (9 marks) (b) Solve for an efficient portfolio with expected return 29.25 %. (8 marks) (c) Explain how the returns of the...
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