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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 2 Assignment 1: Answer Problem Sheet 1: Q4, Q15 and Problem Sheet 2: Q1, Q5, Q10. Time due: Friday 5:00pm of October 2, 2009 1. Suppose you invest in Honda Motor Company on January 2 for 5,064 yen per share when the exchange rate is $0.0079/yen. On April 20, Honda pays 253.2 yen dividend (reinvested in the stock) when the exchange rate is $0.008/yen and the stock price is 5,003 yen. On December 31, the price of Honda is 6,014 yen per share, and the exchange rate is $0.007/yen. Calculate the rate of return in yen and the rate of return in dollar. 2. Consider the following joint probability distribution of two returns X and Y : Y X-1 1-1 0.1 0.2 0.1 0.2 1 0.1 0.3 For example, P ( X =- 1 and Y = 1) = 0 . 2 . (a) Find the (marginal) distribution of X and Y . Hence, find E ( X ) , V ar ( X ) , E ( Y ) and V ar ( Y ) . (b) Find Cov ( X,Y ) and Corr ( X,Y ) . (c) Are X and Y independent? ie. whether P ( X = x and Y = y ) = P ( X = x ) P ( Y = y ) . 3. Suppose you have the following information on two stocks: Return on Probability Asset A Asset B 1/2- 5% 7% 1/2 20% 22% Calculate the portfolio expected rate of return and risk for the following two portfolios. Also explain the meaning of these two portfolios....
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