Unformatted text preview: Allocation in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. [( ) √( ) )
[( ( (
) ) ( )
)
) Solving the above maximization problem yields –
[()
[() [( ) [( ) [() () Substituting the values from the table,
Therefore, Now, we can solve for the expected return and risk of the risky portfolio:
()
√ √ We can now solve for
( ) Therefore,
of the funds should be allocated to the risky asset and (
be allocated to the risk free asset.
Now, funds to be allocated in IBM: ( ) of the funds should ) And, funds to be allocated in MSFT: For the remaining parts, suppose you don’t know the value of . (b) Consider a portfolio consisting of the risk free asset and Boeing stock only. For what value of will an investor
allocate all her funds into Boeing stocks?
Answer:
46
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. If all of the investor’s funds are allocated into IBM stocks, then the risky portfolio ( ) (c) For what value of will an investor allocate more than her funds into IBM stocks?
Answer:
If the investor allocates more than her funds into IBM stocks, then ( ) (d) For what value of will an investor allocate less than her funds into IBM stocks?
Answer:
If the investor allocates less than her funds into Boeing stocks, then ( ) (7.5) Consider the following table of returns and probabilities for two risky assets A and B:
State
Strong
Normal
Weak Rate of Return A
10%
5%
10% Rate of Return B
5%
20%
5% Probability
0.3
0.4 (a) Calculate the expected return and risk of asset A. 47
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:
Since probabilities sum to 1, we see that P(Weak) = 0.3.
The expected return is:
( ) ( ) ( ) The variance is:
( ∑ ) ( ) ( ) ( ) ( ) Thus, expected risk (i.e. expected standard deviation) is
√ √ (b) Calculate the expected return and risk of asset B.
Answer:
The expected return is
( ) ( ) ( ) The variance is
∑ ( ) ( ) ( ) Thus, expected risk (i.e. expected standard deviation) is
√ √ (c) Calculate the expected covariance of asset A and asset B returns.
Answer:
The formula for covariance is ∑
( )( ) ( )( ) ( )( ) ( )( )
48 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. (d) Suppose you want to construct a portfolio consisting of assets A and B that minimizes the expected risk.
Suppose a proportion of the portfolio is in asset A and proportion (
) is in asset B. Calculate the (the
proportion of portfolio in asset A)  which minimizes risk of a portfolio of assets A and B.
Answer:
Similar to part (b) of question (7.3) solves Substituting the values from part (a), (b), and (c)
( )
( ) Hence, 75% of the portfolio should be allocated to asset A and 25% to asset B.
(e) Given the allocation in part (d), will portfolio risk be impacted more by higher riskiness of asset A or asset
B? Show all calculations.
Answer:
This calls for an application of the envelope theorem. The objective was to minimize expected portfolio risk:
( ) ( ) The impact of increased riskiness in asset A is: While the impact of increased riskiness in asset B is:
( ) Hence, higher riskiness of asset A will have a greater impact when: ( )
49 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. ( ) Thus, if more than 50% of the portfolio is allocated to asset A, portfolio risk will be impacted more by grea ter
riskiness in asset A than asset B. In this case, since 75% of the portfolio is in asset A, portfolio risk will be
impacted more from increased riskiness in A than B. Taken to an extreme, the impact on portfolio risk from
greater volatility in any asset can be minimized by choosing infinitesimally small shares, i.e., “diversification”.
(7.6) The following table contains Motorola’s and Research in Motion’s (RIM) Closing Monthly Price, Monthly Returns,
and Monthly Capital Gains in 2010:
Motorola Stocks
Research in Motion (RIM) Stocks
Date
(M/D/Year) Closing Monthly Price Returns Capital Gains Closing Monthly Price Returns Capital Gains
1/29/2010
$
6.15
0.207474
0.207474
$ 62.91
0.068551
0.068551
2/26/2010
$
6.76
0.099187
0.099187
$ 70.88
0.126687
0.126687
3/31/2010
$
7.02
0.038462
0.038462
$ 73.97
0.043595
0.043595
4/30/2010
$
7.07
0.007123
0.007123
$ 71.19
0.037583
0.037583
5/28/2010...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics, Sayed Ajaz Hussain

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