What is the variance of a portfolio consisting of $2,000 in stock B and $8,000 in stock C? Return if State Occurs State of Probability of State of Stock B Stock C Economy Boom Normal 95% Economy 5% 20% 4% 9% 8%
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Let $w_B$ be the weight of stock B in the portfolio, and $w_C$ be the weight of stock C in the portfolio. $w_B = \frac{2000}{2000 + 8000} = \frac{2000}{10000} = 0.2$ $w_C = \frac{8000}{2000 + 8000} = \frac{8000}{10000} = 0.8$ Let $R_B$ be the return of stock B and Show more…
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You decide to invest in a portfolio consisting of 22 percent Stock A, 45 percent Stock B, and the remainder in Stock C. Based on the following information, what is the variance of your portfolio? State of Economy Probability of State of Economy Return if State Occurs Stock A Stock B Stock C Recession .125 -11.20% -4.60% -13.60% Normal .687 10.50% 10.88% 18.00% Boom .188 21.77% 25.55% 30.25%
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Stocks A, B, and C have expected returns of 7%, 6%, and 10%, respectively and the following variance-covariance matrix:- A B C A 0.1 B 0.001 0.04 C 0.001 -0.04 0.08 (a) Determine the fraction of portfolio to hold in each stock so as to minimize the variance of the portfolio subject to a minimum expected return of the portfolio of 8%. (10 points) (b) Can the variance of the portfolio be smaller than the variance of any individual stock? Explain. (10 points) (c) Find the optimal portfolio if the minimum expected returns for 7% and 9%. Also, plot a curve to show the relationship between expected return and variance (15 points).
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