Consider the following two assets. Returns on asset 1 has a mean of and standard...
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Consider the following two assets. Returns on asset 1 has a mean of μ₁ and standard deviation of σ1. Returns on asset 2 has a mean of μ2 and standard deviation of σ2. The correlation coefficient p1,2 measures how the two assets' returns are correlated, and it takes on values between -1 and +1. An investor puts W₁ fraction of her wealth into stock 1, and W₂ = 1- W₁ fraction of her wealth into stock 2. 1. Using the equation on the standard deviation of portfolio returns, argue that the portfolio risk is in- creasing in P1,2- 2. When P1,2 1, argue using mathematical formulas that the portfolio standard deviation is equal to the weighted average of the standard deviation of the individual stocks in the portfolio. (Hint, Square of Summation). 3. Now suppose P1,2 -1. If the investor wants to minimize her risk in investing in this portfolio, how should she choose W₁ and W₂ =1-W₁? (Hint, Square of Difference). Consider the following two assets. Returns on asset 1 has a mean of μ₁ and standard deviation of σ1. Returns on asset 2 has a mean of μ2 and standard deviation of σ2. The correlation coefficient p1,2 measures how the two assets' returns are correlated, and it takes on values between -1 and +1. An investor puts W₁ fraction of her wealth into stock 1, and W₂ = 1- W₁ fraction of her wealth into stock 2. 1. Using the equation on the standard deviation of portfolio returns, argue that the portfolio risk is in- creasing in P1,2- 2. When P1,2 1, argue using mathematical formulas that the portfolio standard deviation is equal to the weighted average of the standard deviation of the individual stocks in the portfolio. (Hint, Square of Summation). 3. Now suppose P1,2 -1. If the investor wants to minimize her risk in investing in this portfolio, how should she choose W₁ and W₂ =1-W₁? (Hint, Square of Difference).
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The equation for the standard deviation of portfolio returns is given by p sqrtW W W 2WW WP In this equation p represents the standard deviation of th... View the full answer
Related Book For
Essentials Of Business Statistics
ISBN: 9780078020537
5th Edition
Authors: Bruce Bowerman, Richard Connell, Emily Murphree, Burdeane Or
Posted Date:
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