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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 3 1. You are given the following information on three risky assets: Expected Risk Correlation Asset return (in %) (in %) matrix 1 9 6 1 0.5 0.2 2 3 3 0.5 1 0.4 3 15 15 0.2 0.4 1 (a) Suppose short selling is not allowed. Using PORTimizer to answer the following ques- tions: (i) Trace the efficient frontier consisting of portfolios of the three risky assets and one risk-free asset with 1% risk-free rate. (ii) Suppose you requires an expected return of 8% on your portfolio, what level of risk will the investor accept? (iii) Find the optimal portfolio if your utility is U ( R ) = μ- . 04 σ 2 where μ (in %) and σ (in %) are expected annual return and risk of the portfolio return R . (b) Repeat (a)(i) and (a)(ii) if short selling is allowed. (c) Repeat (a)(iii) if short selling is allowed without using PORTimizer. 2. Today is in September 2009. You are working at HKU and you must join an university retirement scheme in which you are allowed to invest your money in four funds, namely Money Market Fund, Capital Stable Fund, Balanced Fund and Growth Fund. You are not allowed to short sell. Using the average monthly returns, risks and correlations of these four funds computed based on the monthly data from September 2004 to August 2009 obtained from Chapter 4, answer the following questions: (a) Estimate the annualized expected returns and annualized risks of the four funds. Use PORTimizer to answer the following questions: (b) Trace the efficient frontier consisting of portfolios of the four funds. (c) Suppose you can tolerate a maximum annualized risk of 10% on your portfolio. Deter- mine the optimal portfolio and its expected annual return....
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- Spring '11