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ISE 563 Financial Engineering Homework 2 Spring 2015 Due date, February 11, 2015. Please submit your manuscript in letter size paper. Put your name at the top corner of each page. II. Mean Variance Portfolio Theory 1. (40 pts.) The table shows the rate of return (%) for two risky assets for the last 5 years. Asset 1 2 1 11.34 23.57 2 -17.64 51.96 Year 3 -5.38 -20.45 4 44.72 48.12 5 13.39 6.17 a) Find mean return, variance for each asset, and covariance and correlation among them. b) Find the weights of the minimum variance portfolio. Find the mean and variance of the rate of return. c) Suppose a portfolio mean return equal to 16% is desired. Find the variance of such portfolio. d) Is it possible to build a portfolio having standard deviation smaller than 20%? Show why yes or why not (you do not have to find such portfolio). 2. (60 pts.) An efficient portfolio is to be constructed from three securities with expected returns and covariance matrix given by   0.0625 0.0210 0.0075   0 Σ =  0.0210 0.0784  0.0075 0 0.040   0.20   µ =  0.13  . 0.17 Suppose there is a risk-free asset with rate rf = 0.10. a) Find the weights for the unique efficient portfolio made of these risky assets, the mean return and σ. b) Find the weights of the efficient portfolio that combines the three risky assets with the risk-free asset resulting in a mean return equal to µ = 0.20. Find its standard deviation. c) Is is possible to have an efficient portfolio that combines the three risky assets with the risk-free asset resulting in a standard deviation σ = 0.28? If so, find the weights for each asset. If no, state why. 1. (40 pts.) The table shows the rate of return (%) for two risky assets for the last 5 years. Year 1 2 3 4 5 Asset 1 2 11.34 23.57 -17.64 51.96 -5.38 -20.45 44.72 48.12 13.39 6.17 a) Find mean return, variance for each asset, and covariance and correlation among them. b) Find the weights of the minimum variance portfolio. Find the mean and variance of the rate of return. c) Suppose a portfolio mean return equal to 16% is desired. Find the variance of such portfolio. d) Is it possible to build a portfolio having standard deviation smaller than 20%? Show why yes or why not (you do not have to find such portfolio). 2. (60 pts.) An efficient portfolio is to be constructed from three securities with expected returns and covariance matrix given by Σ = 0.0625 0.0210 0.0075 0.0210 0.0784 0 0.0075 0 0.040 u= 0.20 0.13 0.17 Suppose there is a risk-free asset with rate rf = 0.10. a) Find the weights for the unique efficient portfolio made of these risky assets, the mean return and o. b) Find the weights of the efficient portfolio that combines the three risky assets with the risk-free asset resulting in a mean return equal to y = 0.20. Find its standard deviation. c) Is is possible to have an efficient portfolio that combines the three risky assets with the risk-free asset resulting in a standard deviation o = 0.28? If so, find the weights for each asset. If no, state why.
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