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# 4 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2309 The Statistics of Investment Risk First Semester, 2009-2010 Problem Sheet 4 Assignment 2: Answer Problem Sheet 3: Q2, Q4, Q5 and Problem Sheet 4: Q2, Q6, Q7. Time due: Friday 5:00pm of October 23, 2009 1. (a) Given the following information on 7 assets. Expected Standard Asset return (in %) deviation (in %) μ i σ i A 15 10 B 20 15 C 18 20 D 12 10 E 10 5 F 14 10 G 16 20 Suppose that the returns on the 7 assets have common pairwise correlation of 0.5 and the risk-free interest rate is 5%. What are the optimal weightings of the tangency portfolio if short selling is not allowed? (b) Suppose you hold a portfolio P with expected return E ( R P ) and risk σ P . You are now offered the opportunity to add a new asset Q with expected return E ( R Q ) and risk σ Q to your portfolio. Your investment objective is to maximize the expected return of your portfolio, for a given level of portfolio risk but you are not willing to sell short. Show that you will add the new asset Q to your current portfolio if the following condition met: SR Q > SR P Corr ( R Q , R P ) , where SR P and SR Q are the Sharpe ratios 1 of portfolio P and asset Q respectively. (c) You are a chief investment officer of a Hong Kong pension fund invested in Hong Kong equities and Hong Kong bonds. Your analyst supplies you with the following data on the fund portfolio and an index representing US equities. Current pension US equity fund portfolio market index Expected return 8% 9% Standard deviation 20% 30% Given that the risk-free interest rate is 3% and correlation between the current pension fund portfolio and the US equity market index is 0.5, explain whether you should add US equities to the fund portfolio. 1 The Sharpe ratio of a portfolio P is defined as ( E ( R p ) - R f ) p . 1

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2. A financial analyst provides the following types of information based on the single index market model (SIMM). Expected Beta Residual variance Stock return (in %) coefficient in SIMM μ i β i τ 2 i A 15 1.5 500 B 11 1.1 625 C 9 1.0 600 D 8 0.9 800 E 7 0.7 600 Suppose that the market index has a standard deviation of 20% and the risk-free interest rate is 4%. Assume that short selling is not allowed. Without using PORTimizer, answer the following questions: (a) Find the tangency portfolio.
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4 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS...

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