BUS3026W_TUTORIAL_2009_SOLS

# BUS3026W_TUTORIAL_2009_SOLS - BUS3026W Finance II 2009...

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BUS3026W Finance II 2009 – Revision Tutorial Due: Not for hand-in ______________________________________________________________ Question 1 For reference purposes, the original portfolio will be indicated by the variable OP while the ABC portfolio will be referenced as ABC . a) i. E(R p ) = (0.9 x 15) + (0.1 x 9) = 13.5 + 0.9 = 14.4% [1] ii. Cov op, ABC = ρ x σ op x σ ABC = 0.4 x 36 x 21 = 302.4 [1] iii. σ 2 p = w 2 op x σ 2 op + w 2 ABC x σ 2 ABC + 2 x w op x w ABC x Cov op = (0.9 2 x 36 2 ) + (0.1 2 x 21 2 ) + (2 x 0.9 x 0.1 x 302.4) = 1049.76 + 4.41 + 54.43 = 1108.6 σ p = 33.30% [2] b) When a portfolio is already fully diversified, there is no benefit to be gained by adding further assets to it unless those assets are mispriced (either giving a return above or below the risk-free rate). If the portfolio is not fully diversified, adding an asset to it will typically improve its reward-to-variability ratio. In our case, the reward-to-variability ratio for the original portfolio is: (15-8)/36 = 0.194 [2] The reward-to-variability ratio for the ABC portfolio is: (9-8)/21 = 0.0476 [2] Finally, the reward-to-variability ratio for the combined portfolio is: (14.4-8)/33.3 = 0.192 [2] The reward-to-variability ratio has therefore decreased by taking on the new shares and the ABC shares should not be kept. [2] c) The weight in OP should be given by: = 21 2 – 302.4 21 2 + 36 2 – 2 (302.4) = 138.6 1132.2 = 12.24% [4] The weight in ABC is then (1 - 0.1224) = 87.76% [1] ) r , 2Cov(r σ σ ) r , Cov(r σ (D) w E D 2 D 2 E E D 2 E MIN - + - =

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The E(R p ) is then: (0.1224 x 15) + (0.8776 x 9) = 9.73%
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BUS3026W_TUTORIAL_2009_SOLS - BUS3026W Finance II 2009...

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