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Problem+Set+9-1

# Problem+Set+9-1 - (b Find the portfolio of assets(including...

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E120 Principles of Engineering Economics Fall 2010 Problem Set #9 1. Suppose that there are 2 assets with r 1 = 0 . 05, σ 1 = 0, r 2 = 0 . 20, σ 2 = 0 . 15. Find the portfolio mean and variance for the following pair of weights. (Note that asset 1 is a risk- free asset since its standard deviation is zero): (a) w 1 = 0 . 2, w 2 = 0 . 8. (b) w 1 =-0 . 4, w 2 = 1 . 4. 2. Suppose that there are 2 assets with r 1 = 0 . 20, σ 1 = 0 . 40, r 2 = 0 . 10, σ 2 = 0 . 25, σ 12 = 0 . 05. What is the expected return of the portfolio which has a minimum variance? Assume there is no risk-free asset. (Hint: the variance must be greater than or equal to 0) 3. Suppose that there are 2 assets with r 1 = 0 . 20, σ 1 = 0 . 20, r 2 = 0 . 10, σ 2 = 0 . 30, and σ 12 = 0 . 05. (a) If you can choose only one of the assets which one would you choose? Why?
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Unformatted text preview: (b) Find the portfolio of assets (including a risk-free asset with r = 0), with expected return 1 that has minimum variance. What is its standard deviation? Interpret the weights. 4. Suppose that there are three risky assets and one risk-free asset. The risk-free asset has a return of 5%. The risky assets have returns and standard deviations as follows: r 1 = 50%, σ 1 = 60%, r 2 = 30% , σ 2 = 40%, r 3 = 20%, σ 3 = 30%. The covariance values are σ 12 = -0 . 1 5, σ 23 = 0 . 10 , σ 13 = 0 . 12. If you want an expected return of 80%, find the portfolio of assets with minimum variance. Also find the standard deviation of your portfolio....
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