# 4-Answer - 5 E[R VRSN = 9.04 E[R ERTS = 11.62 E[R Portfolio...

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The University of Hong Kong Department of Statistics and Actuarial Science STAT 2309 The Statistics of Investment Risk (First Semester 2009 2010) Problem Sheet 4 Suggested Solution 1. (a) Tangency portfolio: (A B E F) = (0.2375 0.1581 0.4749 0.1295) (b) (c)

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2. (a)
(b) 3. (a) σ 1 = 4.8, σ 2 = 3.1, σ 3 = 4 (b) ߚ = 1.49, ߚ = 1.07, ߚ = 0.47 (c) (stock1, stock2, stock3) = (0.8237 0 0.1763) (d) μ = 2.51%, ߪ = 3.63%

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4. (a) 0.25 (b)(i) x = (0.9120 -0.0077 0.0957) (b)(ii) 0.27 (b)(iii) 0.27 (c) The market is inefficient as the Sharpe ratio of the market portfolio is different from that of the tangency portfolio. (d) ߙ = 1.5, ߙ = -1.5, ߙ = 0 (e) Assuming CAPM is valid. Portfolios A and B are under-priced and over-priced respectively. Hence, a hedge could involve: long portfolio A and short portfolio B.

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Unformatted text preview: 5. E[R VRSN ] = 9.04 E[R ERTS ] = 11.62 E[R Portfolio ] = 10.33 β P = 1.055 E[R P ] = 10.33 6. R i – R f = α i + β i (R m – R f ) + e i 14 – 5 = α i + 0.8(15 – 5) => α i = 1 Since α > 0, it implies that the fund is underpriced and hence one should invest in this fund. 7. 8. Expected return: ൭ 5.6042 8.3586 5.2171 ൱ 9. (a) β 1 = 0.3666, β 2 = 0.9889, β 3 = 1.0196 (b)(i) ∑ CAPM = ቌ 313.29 71.07 71.07 453.69 73.27 197.62 73.27 197.62 334.89 ቍ E[R 1 ] = 4.210, E[R 2 ] = 6.263, E[R 3 ] = 6.365 (b)(ii) Set P = (0 1 -1) and v = 6. (b)(iii) Using PORTimizer, the tangency portfolio is (0.1137 0.8863 0) and given a target portfolio return of 7%, it is recommended that the portfolio consist of: (Risf-free asset, Australia, France, U.S.) = (0.1581, 0.0957, 0.7462, 0)....
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