Homework Answers
Answer is option(b) - .0156
In a single factor model the residual variance of the portfolio
can be calculated as follows:
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1. Assume that oầy = 0.02 and oy = 0.06. Also assume that a portfolio of...
2. If Cov(ex, ey) = 0.01 in the previous question, where op = 0.0156 and xp...
2. If Cov(ex, ey) = 0.01 in the previous question, where op = 0.0156 and xp = (2/3, 1/3)T, what is the residual variance of the portfolio if the single-factor model is not assumed? (a). 0.0112 (b). 0.0156 (c). 0.0200 (d). 0.0333 1. Assume that oầy = 0.02 and oy = 0.06. Also assume that a portfolio of X and Y is constructed, with a 2/3 weight for X and a 1/3 weight for Y. What is the residual variance...
Variance of market portfolio return = 0.07 Given the assumption of a single factor model,...
Variance of market portfolio return = 0.07
Given the assumption of a single factor model, calculate the
following:
The residual variance of each of the above stocks;
The expected return on this 3-stock portfolio;
The beta factor of this 3-stock portfolio;
The variance of this 3-stock portfolio.
be? (10 marks) b) You are given the following table: Securities Weight Beta 1 Expected return 0.7 0.9 0.3 0.4 0.3 2 3 Variance of return 0.06 0.08 0.13 0.6 0.8 1.1...
You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury...
You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 40% and 60%, respectively. X has an expected rate of return of 0.12 and variance of 0.0081, and Y has an expected rate of return of 0.09 and a variance of 0.0016. The coefficient of correlation, rho,...
4. (20 points) Suppose the joint distribution of X and Y is: fxy(x, y) 1 0...
4. (20 points) Suppose the joint distribution of X and Y is: fxy(x, y) 1 0 1 2 3 0.04 0.06 0.01 0.00 0.13 0.13 0.02 0.12 0.04 0.06 0.00 0.11 0.07 0.10 0.06 (a) (4 points) Find the marginal distributions of X and Y. (b) (4 points) Given X = 3, what is the probability that random variable Y is at most 2?. (c) (4 points) Are random variables X and Y independent? Why or why not? (d) (4...
For the following probability distribution x fx) 0 0.01 0.02 0.10 0.35 4 0.20 0.18 0.06...
For the following probability distribution x fx) 0 0.01 0.02 0.10 0.35 4 0.20 0.18 0.06 0.05 0.09 0.03 0.10 Upload a file detailing all of the work needed for these questions. a. b. c. Determine E(x). (2 points) Determine the variance. (2 points) Determine the standard deviation. (1 point)
2. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of...
2. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 2% and a risky portfolio, P constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 40% and 60%, respectively. X has an expected rate of return of 0.10 and variance of 0.0081, and Y has an expected rate of return of 0.06 and a variance of 0.0036. The coefficient of correlation,...
Q2 (e) Assume for simplicity sake that one factor has been deemed appropriate to "explain" returns...
Q2
(e) Assume for simplicity sake that one factor has been deemed appropriate to "explain" returns on stocds (0) How and there is no idiosyncratic risk. Derive the arbitrage pricing theory would you perform a test of the predictions of the capital asset pricing model given historical data (APT) model 2. Consider Tablo 1 Return and Variance a/c to the Stocks Sample Covariance Residual AlphaBeta Expected Variance and Return | with Market | Variance | (96) Return Market 3.60 4.80...
10. You are considering investing $1,000 in a complete portfolio. The complete portfolio is comprised...
10. You are considering investing $1,000 in a complete portfolio. The complete portfolio is comprised of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 10%,...
Problem 17 Intro You've assembled the following portfolio: Stock Beta Portfolio weight 1 1.6 0.2 2...
Problem 17 Intro You've assembled the following portfolio: Stock Beta Portfolio weight 1 1.6 0.2 2 1.1 3 0.7 0.5 The expected market return is 9% and the risk-free rate is 2%. Assume that the CAPM holds. i | Attempt 1/5 for 10 pts. Part 1 What is the beta of the portfolio? No decimals Submit Part 2 IB Attempt 175 for 10 pts. What is the expected return of your portfolio? 3+ decimals Submit Intro We know the following...
Pinulo retums? 1 0 capital asset pricing model given historical data 2. Consider Table 1. (%)...
Pinulo retums? 1 0 capital asset pricing model given historical data 2. Consider Table 1. (%) 3.77 Table 1 Summary Statistics Alpha, Beta, Expected Return and Variance a/c to the Stocks Sample Single Index Model Covariance Residual and Return Alpha Beta with Market Expected Variance Variance Market (%) (%) Return (%) (%) 3.60 3.59 4.80 Market 4.20 0.00 8.70 (a) Consider Table 1. Using the single index model, calculate beta and alpha for stocks 1 and 2. Interpret your findings....
2. If Cov(ex, ey) = 0.01 in the previous question, where op = 0.0156 and xp = (2/3, 1/3)T, what is the residual variance of the portfolio if the single-factor model is not assumed? (a). 0.0112 (b). 0.0156 (c). 0.0200 (d). 0.0333 1. Assume that oầy = 0.02 and oy = 0.06. Also assume that a portfolio of X and Y is constructed, with a 2/3 weight for X and a 1/3 weight for Y. What is the residual variance...
Variance of market portfolio return = 0.07
Given the assumption of a single factor model, calculate the
following:
The residual variance of each of the above stocks;
The expected return on this 3-stock portfolio;
The beta factor of this 3-stock portfolio;
The variance of this 3-stock portfolio.
be? (10 marks) b) You are given the following table: Securities Weight Beta 1 Expected return 0.7 0.9 0.3 0.4 0.3 2 3 Variance of return 0.06 0.08 0.13 0.6 0.8 1.1...
4. (20 points) Suppose the joint distribution of X and Y is: fxy(x, y) 1 0 1 2 3 0.04 0.06 0.01 0.00 0.13 0.13 0.02 0.12 0.04 0.06 0.00 0.11 0.07 0.10 0.06 (a) (4 points) Find the marginal distributions of X and Y. (b) (4 points) Given X = 3, what is the probability that random variable Y is at most 2?. (c) (4 points) Are random variables X and Y independent? Why or why not? (d) (4...
For the following probability distribution x fx) 0 0.01 0.02 0.10 0.35 4 0.20 0.18 0.06 0.05 0.09 0.03 0.10 Upload a file detailing all of the work needed for these questions. a. b. c. Determine E(x). (2 points) Determine the variance. (2 points) Determine the standard deviation. (1 point)
2. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 2% and a risky portfolio, P constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 40% and 60%, respectively. X has an expected rate of return of 0.10 and variance of 0.0081, and Y has an expected rate of return of 0.06 and a variance of 0.0036. The coefficient of correlation,...
Q2
(e) Assume for simplicity sake that one factor has been deemed appropriate to "explain" returns on stocds (0) How and there is no idiosyncratic risk. Derive the arbitrage pricing theory would you perform a test of the predictions of the capital asset pricing model given historical data (APT) model 2. Consider Tablo 1 Return and Variance a/c to the Stocks Sample Covariance Residual AlphaBeta Expected Variance and Return | with Market | Variance | (96) Return Market 3.60 4.80...
Problem 17 Intro You've assembled the following portfolio: Stock Beta Portfolio weight 1 1.6 0.2 2 1.1 3 0.7 0.5 The expected market return is 9% and the risk-free rate is 2%. Assume that the CAPM holds. i | Attempt 1/5 for 10 pts. Part 1 What is the beta of the portfolio? No decimals Submit Part 2 IB Attempt 175 for 10 pts. What is the expected return of your portfolio? 3+ decimals Submit Intro We know the following...
Pinulo retums? 1 0 capital asset pricing model given historical data 2. Consider Table 1. (%) 3.77 Table 1 Summary Statistics Alpha, Beta, Expected Return and Variance a/c to the Stocks Sample Single Index Model Covariance Residual and Return Alpha Beta with Market Expected Variance Variance Market (%) (%) Return (%) (%) 3.60 3.59 4.80 Market 4.20 0.00 8.70 (a) Consider Table 1. Using the single index model, calculate beta and alpha for stocks 1 and 2. Interpret your findings....
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