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Page 1 of 9 THE AUSTRALIAN NATIONAL UNIVERSITY SCHOOL OF FINANCE AND APPLIED STATISTICS Second Semester Examination 2008 QUANTITATIVE RESEARCH METHODS (STAT1008) Writing Period: 3 hours duration Study Period: 15 minutes duration Permitted Material: Non-programmable calculator, dictionary and 1 A4 page with notes on both sides Instructions to Candidates: Attempt ALL questions. Each question is of equal mark value. Start your solution to each question on a new page. To ensure full marks show all the steps in working out your solution. Marks may be deducted for failure to show appropriate calculations or formulae. Unless otherwise stated, use a significance level of 5%. Selected statistical tables are attached to the back of the examination paper.
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STAT1008 Quantitative Research Methods Final Examination Semester 2, 2008 Page 2 of 9 Question 1 (25 marks) (a) A recent survey of investors with internet access divided them into two groups – those who trade online and those who do not (called traditional investors), and discovered differences between these groups. 65% of the investors studied were traditional investors, and of these, 48% were bullish on the market. 69% of the online investors were bullish on the market. i. (2 marks) If you select an investor at random from the survey group, what is the probability that he or she is bullish on the market? ii. (2 marks) Suppose that you select an investor who is bullish on the market from the total study group. What is the probability that he or she is a traditional investor? iii. (3 marks) Are being bullish on the market and type of investor plausibly independent? Explain your answer carefully. (b) You are trying to set up a portfolio that consists of a corporate bond fund and a common stock fund. The following information about the annual return (per $1000) of each of these investments under different economic conditions is available, along with the probability that each of these economic conditions will occur. State of the Economy Probability Corporate Bonds ($) Common Stocks ($) Recession 0.10 -30 -150 Stagnation 0.15 50 -20 Slow Growth 0.35 90 120 Moderate-High Growth 0.40 102 183 You are given the information that the expected return of corporate bonds is $76.80, and the variance of the return of corporate bonds is 1563.36($ 2 ). i. (6 marks) Compute the expected return and standard deviation for the common stock fund. ii. (4 marks) Compute the covariance between the corporate bond fund and the common stock fund. iii. (5 marks) A portfolio is to be created which involves investing 50% of the funds into each of the investments (corporate bonds and common stocks). Find the expected return and variance of return for this portfolio. iv.
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