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Unformatted text preview: January 1st 2012 the 3Month US TBill 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 20122013) 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 TBills 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 TBills: 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 3month TBills and Boeing stocks in January 1st, 2012 for
and 2. In each case, interpret and calculate the portfolio return and risk.
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ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Answer:
On January 1st 2010 the 3Month US TBill 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 TBills 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 TBills: 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:
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ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 20122013) 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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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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