HW4_Solutions.2006

# HW4_Solutions.2006 - MS&E 242 Investment Science Prof James...

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MS&E 242 Investment Science HW #4 Solutions Prof. James Primbs November 14, 2006 Problem 7.1 a) The equation for the capital market line is: σ σ 5 . 07 . 32 . 07 . 23 . 07 . + = + = r . b) (i). Solve the CML equation with % 39 = r to obtain 64 . = σ (ii). Solving ( ) 39 . 0 23 . 0 1 07 . 0 = + w w , gives 1 = w . Hence, borrow \$1000 at the risk free rate; invest \$2000 in the market. c) Your expected return is ( ) 182 . 0 23 . 0 7 . 0 07 . 0 ) 3 . 0 ( = + . Hence you expect to have (\$1000)(1.182) = \$1182. Problem 7.3 The market has three assets: %, 10 1 = r %, 20 2 = r % 10 3 = r . We are also given that the weights on two portfolios on the minimum-variance set are = 20 . 0 20 . 0 60 . 0 w = 40 . 0 20 . 0 80 . 0 v a) By the 2 fund theorem, we know that the market portfolio must be a combination of w and v. Since the market portfolio must have positive weights on all assets, this means: + 0 0 0 40 . 0

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