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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2309 The Statistics of Investment Risk First Semester, 2009-2010 Problem Sheet 5 1. Given the following information on three stocks: Current Stock Price in One Year when Stock Price Economy is Good Economy is Bad A $3 $10 $8 B $2 $8 $0 C $ P C $9 $12 (a) If P C = 1 , it is found that there is an arbitrage opportunity. Show how it works. (b) Determine the fair value of P C such that arbitrage opportunity disappears. 2. Suppose you have correctly determined that a two-factor APT describes the returns of all well-diversified portfolios, and that the two factors are (a) unexpected change in production (factor 1, F 1 ) and (b) unexpected change in inflation (factor 2, F 2 ). Under the APT model, the expected returns (in %) of all well diversified portfolios over the next year are given by E ( R ) = 5 + 8 β 1- 6 β 2 . The market believes that the standard deviation for both F 1 and F 2 over the next year is equal to 10% and that the two factors are uncorrelated. The risk-free interest rate (for borrowing and lending) over the next year is 5%. You may assume that the error variance in the two-factor model for a well-diversified portfolio is zero. Furthermore, you have identified three well-diversified portfolios, A , B , C with beta coefficients for the two factors given by: Portfolio i β i 1 β i 2 A 0.7- 0.5 B 1.3 0.5 C 2.0- 1.0 (a) Find the expected returns and variance-covariance matrix of portfolios A , B and C , over the next year. (b) Using the three portfolios, construct the factor-mimicking portfolios for factors 1 and 2....
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- Spring '11