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Ch 7 Practice

I use the answer for part g to construct a portfolio

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Unformatted text preview: l stocks in January 1st, 2010 for and 2. In each case, interpret and calculate the portfolio return and risk. (i) Use the answer for part (g) to construct a portfolio of 3-month T-Bills and Boeing stocks in January 1st, 2010 for and 2. In each case, interpret and calculate the portfolio return and risk. (j) Suppose an investor wants to construct a portfolio consisting of two risky assets: Case 2 Risky Asset A Risky Asset B Fraction (1 - f) Fraction f Derive the Efficiency Frontier, a single equation that includes the mean portfolio return and portfolio risk of a portfo lio ) is in risky asset B. where fraction is in risky asset A and fraction ( (k) Graph the efficiency frontier for a portfolio where fraction is in Dell stocks and fraction ( for various values of (say . Interpret this graph. ) is in Boeing stocks (l) Suppose an investor wants to construct a portfolio consisting of two risky assets A and B. Calculate the optimal fraction of the portfolio in risky asset B by solving the problem: ̅ Hint: Use the “short method” by substituting expressions for ̅ and . (m) Use the answer for part (l) to construct a portfolio of Dell and Boeing stocks in January 1st, 2010 for In each case, interpret and calculate the portfolio return and risk. and 2. (n) Suppose an investor wants to construct a portfolio consisting of a risk free asset and two risky assets: 3 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. Case 3 \$X Portfolio Risky Free Asset 2 Risky Assets Fraction (1 – β) Fraction β Risky Asset A Risky Asset B Fraction (1 – f) Fraction f Calculate the optimal fraction of the portfolio in risky assets and the optimal fraction allocated to risky asset B by solving the problem: of the risky assets amount ̅ (o) Use the answer for part (n) to construct a portfolio of 3 month T-Bills and Dell and Boeing stocks in January 1st, 2010 for and 2. In each case, interpret and and calculate the portfolio return and risk. (p) Consider an investor who wants to construct a portfolio of two risky assets to minimize portfolio risk. Calculate the optimal fraction of the portfolio in risky asset B by solving the problem: (q) Use your answer to part (p) to construct a minimum risk portfolio of Dell and Boeing stocks. (7.2) Below is a histogram and descriptive statistics of monthly returns on US 30-day T-Bills from Dec 31st 1925 to Dec 31st 2010. Average (Monthly) Return 0.034967738 Variance of (Monthly) Returns 0.000881512 Standard Deviation of (Monthly) Returns 0.029690272 4 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) Are 30-day US T-Bills “risk free”? Give a brief explanation. (b) The following table contains Shell Oil Company’s monthly closing price, monthly returns, and monthly returns without dividends over July 2010 – December 2010: Shell Oil Company Date Price Return Return without Dividend 7/30/2010 53.42 0.106462 0.106462 8/31/2010 51.33 -0.023399 -0.039124 9/30/2010 58.79 0.145334 0.145334 10/29/2010 64.32 0.094064 0.094064 11/30/2010 60.31 -0.049285 -0.062345 12/31/2010 66.67 0.105455 0.105455 What was the dividend in August 2010, November 2010, and December 2010? State all assumptions and show all calculations. (7.3) The following table contains the return on US 30 day T-Bills purchased on Dec 31st 2011 and the average and variance of Shell Oil Company’s monthly returns (August 2005 to December 2011): 30 Day US T-Bill return (issued Dec 31st 2011) 0.0002 Shell Oil Average Monthly return 0.0101 Shell Oil Variance of Monthly return 0.0056 (a) Consider an investor with a mean-variance utility function. What is the parameter of “risk intolerance” if she borrows 10% of her funds to invest in a portfolio of 30-day US T-Bills and Shell Oil stocks in December 2011? State all assumptions and show all calculations. (b) The following table contains the average, variance, and covariance of Shell Oil Company’s and Research in Motion’s (RIM) monthly returns (August 2005 to December 2011) Shell Oil Average Monthly return 0.0101 Shell Oil Variance of Monthly return 0.0056 RIM Average Monthly return 0.0109 RIM Variance of Monthly return 0.0312 5 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. Covariance Shell Oil Company and RIM Monthly return 0.0043 Suppose an investor allocates funds between Shell Oil and RIM stocks. What fraction of this portfolio consists of RIM stocks if her goal is to minimize portfolio risk? State all assumptions and show all calculations. (7.4) The following table contains the sample mean returns and sample standard deviations for MSFT and IBM returns, the sample covariance between MSFT and IBM returns, an...
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