Business, 01.03.2021 21:10 lyndah15

g Assets with random rates of return r1, r2 have expected rates ¯r1 = 1, ¯r2 = 2, variances σ1 2 = 1, σ2 2 = 3 and covariance σ1,2 = 1. Consider portfolios consisting of weights w1 = 1 − α and w2 = α of these assets. a) Find weights, expected rate of return ¯rMVP, and volatility σMVP for the minimum variance portfolio. b) Make a sketch in the σ, r¯ plane of the portfolio curve. Label the asset points (σ1, r¯1), (σ2, r¯2), the minimum variance point (σMVP, r¯MVP), and the efficient frontier. c) An individual with utility function U(y) = 16y−y 2 and with unit initial wealth constructs a portfolio consisting of fractions 1 − α and α of these assets. Find the maximum over α of the expected utility E[U(1 + rp(α))], where rp(α) is the portfolio rate of return. d) Calculate σp, ¯rp for the portfolio corresponding to the maximum expected utility, and show that this portfolio is efficient. g

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g Assets with random rates of return r1, r2 have expected rates ¯r1 = 1, ¯r2 = 2, variances σ1 2 = 1...

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