Eco 204 s ajaz hussain do not distribute june 30th

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Unformatted text preview: January 1st 2012 the 3-Month US T-Bill interest rate was 0.03% or 0.0006. Now: 25 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. June 30th 1988 - Dec 31st 2011 Dell Boeing Mean r 0.028 0.011 Risk σ 0.145 0.080 Cov(Dell, Boeing) 0.0021 rf, Jan 1st 2012 0.0003 Dell’s average return is greater than the risk free return. Thus, the fraction of a portfolio consisting of Dell stocks and US 3 Month T-Bills issued on 01/01/2012 and held to maturity is: (̅̅̅̅̅̅ ) Using Excel Model Chapter 7.1 we get: Note: You’ll get a different answer from using the rounded returns in the table above. for 3 Investors Investor A: Investor B: Investor C: 0.66 0.33 0.037 0.019 0.0094 0.192 0.096 0.048 Investor A borrows 33% of her portfolio money and invests 1.33 times her portfolio in Dell stocks, earning a higher return than Dell’s average returns and taking on more risk compared to investing just her money in Dell stocks. Investor B invests 66% of her portfolio money in Dell stocks, earning a lower return than Dell’s average returns and taking on less risk compared to investing all her money in Dell stocks. Investor C invests 33% of her portfolio money in Dell stocks, earning a lower return than Dell’s average returns and taking on less risk compared to investing all her money in Dell stocks. Notice that investor C has the highest percentage of the portfolio in T-Bills: this is because she is the most risk averse of the three investors (she has the highest degree of risk aversion parameter ). Another way to see this is: As then -i.e. investor becomes less willing to invest in risky asset as c increases. (i) Use the answer for part (g) to construct a portfolio of 3-month T-Bills and Boeing stocks in January 1st, 2012 for and 2. In each case, interpret and calculate the portfolio return and risk. 26 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. Answer: On January 1st 2010 the 3-Month US T-Bill interest rate was 0.06% or 0.006. Now: June 30th 1988 - Dec 31st 2009 Dell Boeing Mean r 0.028 0.011 Risk σ 0.145 0.080 Cov(Dell, Boeing) 0.0021 rf, Jan 1st 2010 0.0003 Boeing’s average return is greater than the risk free return. Thus, the fraction of a portfolio consisting of Boeing stocks and US 3 Month T-Bills issued on 01/01/2012 and held to maturity is: (̅̅̅̅̅̅̅̅̅ ) Using Excel model 14.8 we get: Note: You’ll get a different answer from using the rounded returns in the table above. for 3 Investors Investor A: Investor B: Investor C: 0.84 0.42 0.018 0.009 0.005 0.134 0.067 0.034 Investor A borrows 68% of her portfolio money and invests 1.68 times her portfolio in Boeing stocks, earning a higher return than Boeing’s average returns and taking on more risk compared to investing just her money in Boeing stocks. Investor B invests 84% of her portfolio money in Boeing stocks, earning a lower return than Boeing’s average returns and taking on less risk compared to investing all her money in Boeing stocks. Investor C invests 42% of her portfolio money in Boeing stocks, earning a lower return than Boeing’s average returns and taking on less risk compared to investing all her money in Boeing stocks. Notice that investor C has the highest percentage of the portfolio in T-Bills: this is because she is the most risk averse of the three investors (she has the highest degree of risk aversion parameter ). (j) Suppose an investor wants to construct a portfolio consisting of two risky assets: 27 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 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 portfolio ) is in risky asset A. where fraction is in risky asset B and fraction ( Answer: First some notation: return and risk of “risk asset A” return and risk of “risky asset B” return and risk of portfolio with fraction in risky asset B and fraction ( ) in risky asset A Portfolio return is a weighted average of the two risky assets return: ( ) ( ) Note: it’s convenient to label the risky asset with the higher return as “risky asset B”. Notice that this equation cannot be plotted in the ( Here’s how: consider the risk of the portfolio: ) space. To do so, we need to introduce into the equation. √ is the variance of the portfolio with fraction in risky asset A and fraction ( ( ) in risky asset B: ) Use the formula for the variance of a linear combina...
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