147493 0147493 6302010 652 0048175 0048175 4926

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Unformatted text preview: $ 6.85 -0.031117 -0.031117 $ 60.69 -0.147493 -0.147493 6/30/2010 $ 6.52 -0.048175 -0.048175 $ 49.26 -0.188334 -0.188334 7/30/2010 $ 7.49 0.148773 0.148773 $ 57.53 0.167885 0.167885 8/31/2010 $ 7.52 0.004005 0.004005 $ 42.84 -0.255345 -0.255345 9/30/2010 $ 8.53 0.134309 0.134309 $ 48.69 0.136555 0.136555 10/29/2010 $ 8.16 -0.043376 -0.043376 $ 56.92 0.169029 0.169029 11/30/2010 $ 7.66 -0.061275 -0.061275 $ 61.83 0.086261 0.086261 12/31/2010 $ 9.07 0.184073 0.184073 $ 58.13 -0.059842 -0.059842 (a) True or false: neither Motorola nor RIM paid a monthly dividend in 2010? Give a brief explanation and provide a formula to justify your answer. Answer: True. By definition: Returns=Capital Gains + Dividend Yield Between periods t-1 and t this is: Notice that in 2010 Motorola and RIM returns = capital gains which means neither stock issued a dividend in 2010. The following table contains the return on 30-day US Treasury Bills issued on December 31st 2010 as well as Motorola and RIM’s average monthly returns; variance of monthly returns; and the covariance of Motorola’s and RIM’s monthly returns for the period February 26th, 1999 to December 31st, 2010: 50 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 30 Day U.S. T-Bill Return (Dec 31st 2010) 0.00081 The following figures are for the period February 26th, 1999 to December 31st, 2010 Average Motorola Monthly Returns Variance of Motorola Monthly Return Average RIM Monthly Returns Variance RIM Monthly Returns Covariance of Motorola and RIM Monthly Returns 0.002616887 0.013877326 0.054275605 0.052027303 0.012945617 (b) Are Motorola stocks riskier than RIM stocks, or the other way around? Give a brief explanation and justify your answer by calculating the risk premium for each stock. Answer: RIM stocks are riskier than Motorola stocks since RIM variance of monthly returns is greater than Motorola’s variance of monthly returns. Notice also that RIM offers a higher return than Motorola since investors have to be compensated for RIM’s higher risk. Rim has the greater risk premium reflecting its greater risk. (c), (d), and (e) answers are not provided because it is solved similarly to the previous questions, but you are encouraged to attempt. It will be a good practice. Option question’s answers: (7.7) The following table contains three risky assets and a risk free asset Asset 1 return Asset 1 variance Asset 2 return Asset 2 variance Asset 3 return Asset 3 variance Covariance (Asset 1, Asset 2) Covariance (Asset 2, Asset 3) Covariance (Asset 1, Asset 3) Risk free asset return 0.02500 0.02600 0.04300 0.03862 0.05600 0.05200 0.000910 0.001300 0.000520 0.003000 51 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (a) Which of two risky assets you will choose to construct a portfolio that has minimum risk and highest return to risk ratio? Answer: Let be the fraction of wealth invested in risky asset 1. Then the portfolio return is ( ) And the portfolio risk is ( √ ) ( ) where To find the portfolio with minimum risk we have to minimize portfolio variance w.r.t , which solves Substituting the values from the table gives ( Assets 1 and 2 Assets 2 and 3 Assets 1 and 3 0.60 0.58 0.66 Portfolio Portfolio Risk to variance return ratio ) return 0.40 0.0322 0.1264 0.2547 0.42 0.0485 0.1510 0.3213 0.34 0.0354 0.1325 0.2673 We will choose asset 2 and 3 since this combination gives the highest risk to return ratio-i.e., it has the highest return per unit of risk. In the portfolio 58% of wealth will be invested in asset 2 and 42% of asset will be invested in asset 3. (b) Which of two risky assets and the risk free asset you will choose to construct the optimal portfolio that has the highest return to risk ratio? Assume the mean-variance utility function of the form . Answer: In this case the portfolio return is ( ( Where ) and We have solved that the optimal denote return on risk free asset and . is ( ( And optimal ) ) ) ( ( ) ( ) ) is 52 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Substituting the values from the table gives ( Assets 1 and 2 Assets 2 and 3 Assets 1 and 3 ) 0.56 0.035 0.5 0.0495 0.55 0.0421 0.44 0.5 0.45 0.1324 0.1526 0.1458 0.2645 0.3243 0.2884 0.61 0.67 0.61 0.0225 0.0339 0.0269 0.0806 0.1015 0.0893 0.2791 0.3341 0.3015 Hence in the optimal portfolio 33% of wealth is invested in asset 2, 33% of wealth invested in asset 3 and 34% of wealth is invested in risk free asset. Notice we choose mix of risky assets 2 and 3 because it gives the highest return per unit of risk. (7.8) You are the Chief Financial Officer (CFO) at Super Corp. the following information is given to you to calculate next month return and associated risk. November October September August $ 190.07 $ 193.49 $ 186.94 $ 189.64 (a) Find return for the month of December. Assume price change occur with equal probability and no dividend payment. Answer: Since we don’t have the price for December we calculate expected return. Hence And ∑ ( { } ) Therefore 53 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (b) Find return for the month of December. Assume price change occur with probability of (.10, .25, .35, .30). Answer: ∑ { } And is probability of return at month and asset at time . price of the Therefore ( ) ( ) ( ) ( ) Hence Now assume return is continuous and return distribution is given by () { (c) Find expected return and variance of the return. Assume . [please show all work]. Answer: Since return is continuous the mean is defined as ∫ We solve this problem by “integration by parts”. Thus let’s and , hence ∫ ⏟ and | ∫ . Using this we have | The variance is 54 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ∫( ) ∫ ∫ ∫ ∫ Applying two times integration by part for the first term and once for the second term and integrating directly the forth term will solve . Substituting the value ( ). 55 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013)...
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This note was uploaded on 03/20/2014 for the course ECON 204 taught by Professor Ajazhussain during the Fall '09 term at University of Toronto- Toronto.

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