FIN321-HW4

# A compute the expected returns and the standard

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a) Compute the expected returns and the standard deviations for both assets. Asset X: Expected Return = .1(.3) + .2(.2) + .4(.15) + .2(.1) + .1(-.5) = .1 = 10% Std. Deviation = sqrt[.1(.3-.1)^2 + .2(.2-.1)^2 + .4(.15-.1)^2 + .2(.1-.1)^2 + .1(-.5-.1)^2 ] = .2074 = 20.74% Asset Y: Expected Return = .1(.12) + .2(.1) + .4(.09) + .2(.08) + .1(-.04) = .08 = 8% Std. Deviation = sqrt[.1(.12-.08)^2 + .2(.1-.08)^2 + .4(.09-.08)^2 + .2(.08-.08)^2 + . 1(-.04-.08) ^2] =.0415 = 4.15% b) Compute the correlation coefficient between the returns on the two assets. Covariance(rA,rB) = .1(.3-.1)(.12-.08) + .2(.2-.1)(.1-.08) + .4(.15-.1)(.09-.08) + .2(.1-.1)(.08-.08) +.1(-.5-.1)(-.04-.08) = .0086 = 86%^2 Correlation Coefficient = .0086/(.2074*.0415) = .9992 c) Can you build a portfolio of assets X and Y with zero risk? Prove that your portfolio is indeed riskless. Zero risk corresponds with a correlation coefficient of -1, meaning that assets X and Y are perfectly negatively correlated. In this case the correlation is opposite to -1, its actual almost +1, indicating that the correlation is positive, meaning the assets move together in any given state of market.

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3. Consider two perfectly negatively correlated risky securities A and 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%. a) What are the weights of A and B in the minimum variance portfolio? wA = .429 wB = .571 b) What is the expected return and standard deviation of the MVP?
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• Spring '13
• JennferJeurgens

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