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Unformatted text preview: az Hussain. Do not distribute. Note: For next version work out formula.
(o) Use the answer for part (n) to construct a portfolio of 3 month TBills and Dell and Boeing stocks in January 1st, 2012
for
and 2. In each case, interpret and calculate the portfolio return and risk.
Answer:
We have: Case 3
$X Portfolio
Return = rp Risk = σp
Risky Free Asset 2 Risky Assets: Dell and Boeing Fraction (1 – β) Fraction β Return = rf Risk = σf Return = rr, Risk = σr Risky Asset A = Boeing Risky Asset B = Dell Fraction (1 – f) Fraction f Let asset B be Dell (since it has the higher return) and let asset A be Boeing. Now, whatever portion
allocated to the two risky assets:
Of the fraction of the portfolio allocated to the two risky assets, the fraction allocated to Dell (asset B):
̅ { ̅ } {
̅̅̅̅̅̅ } ̅̅̅̅̅̅̅̅̅ { } {
Of the fraction of the portfolio is } of the portfolio allocated to the two risky assets, the fraction allocated to Boeing (asset A):
̅̅̅̅̅̅ ̅̅̅̅̅̅̅̅̅ { } { } Second:
The return and risk of the fraction of the portfolio allocated to the two risky assets A and B:
̅̅̅̅̅̅̅̅̅ ( ) (̅̅̅̅̅̅ ̅̅̅̅̅̅̅̅̅)
( )
38 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. Third:
The fraction of the portfolio allocated to Dell and Boeing stocks is:
( Where and ) are from step 2.
The fraction of the portfolio allocated to the risk free asset is:
( Where and ) are from step 2. Notice that the fraction of the portfolio allocated to assets Boeing and Dell are, respectively ( ) and . Using Excel Model Chapter 7.1 we get:
Portfolio of TBills and Dell and Boeing Stocks
Investor A: Investor B: Investor C: Composition of Risky Assets
0.55 0.37 Risky assets return 0.027 0.020 0.017 Risky assets risk 0.134 0.093 0.080 Composition of Portfolio
Fraction for Boeing and
Dell Stocks
Fraction ( ) in 1.47 1.16 0.67 0 0 0.33 1.35 0.64 0.25 3 month TBills
Fraction in Dell stocks 39
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. Fraction in Boeing stocks 0.12 0.52 0.42 Portfolio return 0.039 0.024 0.012 Portfolio risk 0.197 0.108 0.053 ( ) Investor A borrows 47% of her portfolio and invests it all in Dell and Boeing stocks, with 1.35 of her leveraged portfolio
in Dell and 0.12 of her leveraged portfolio Boeing stocks.
Investor B borrows 16% of her portfolio and invests it all in Dell and Boeing stocks, with 0.64 of her leveraged portfolio in
Dell and 0.52 of her leveraged portfolio Boeing stocks.
Investor C invests 67% of her portfolio (no leverage) in Dell and Boeing stocks, 33% in Tbills; 25% of her portfolio is in
Dell and 42% of the portfolio in Boeing stocks.
(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: Answer:
The variance of a portfolio with two risky assets A and B is:
( ) ( ) If the investor wants to minimize risk, she will choose
( (
( )
) such that (minimizing risk is the same as minimizing variance): ) ( ( ) ) Notice that this is independent of the degree of risk aversion.
(q) Use your answer to part (p) to construct a minimum risk portfolio of Dell and Boeing stocks.
40
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:
The risk of a portfolio consisting of assets A and B is minimized by choosing the fraction of portfolio in asset B to be: For Dell and Boeing, letting Boeing be asset A and Dell asset B: Using Excel Model Chapter 7.1, this is: (7.2) Below is a histogram and descriptive statistics of monthly returns on US 30day TBills 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 (a) Are 30 day US TBills “risk free”? Give a brief explanation.
Answer
According to the graph and table above, it appears that US 30 day TBills are risky. However, the graph shows the
distribution of past returns capturing the fact that the returns vary from month to month. That said, 30day US TBills
are risk free: if you purchase a TBill at the beginning of the month and hold on to it for 30 days, you will receive a
guaranteed return on the TBill (although returns vary from month to month). 41
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. (b) The...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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