Unformatted text preview: d the return on 30 day US TBills:
July 29th 1988  Dec 31st 2011
Microsoft
IBM
Mean r
0.0247
0.0100
Variance r
0.0115
0.0065
Cov(MSFT, IBM)
0.00375
rf, Dec 31st, 2011
0.0002
(a) Assume that an investor has the meanvariance utility function over expected portfolio returns and portfolio risk: ) in the risk free asset and a fraction in a risky portfolio (portfolio of 2 risky
Suppose that they invest fraction (
assets). When allocating funds in the risky portfolio, they invest fraction (
) in IBM and fraction in MSFT. Calculate
the optimal proportion of funds they allocate in the risk free asset, in IBM and in MSFT. Assume For the remaining parts, Consider a portfolio consisting of the risk free asset and Boeing stock only and suppose
you don’t know the value of . (b) For what value of will an investor allocates all her funds into IBM stocks?
(c) For what value of will an investor allocates more than her funds into IBM stocks?
(d) For what value of will an investor allocates less than her funds into IBM stocks?
(7.5) Consider the following table of returns and probabilities for two risky assets A and B: State Rate of Return A Rate of Return B Probability Strong 10% 5% 0.3 Normal 5% 20% 0.4 Weak 10% 5% (a) Calculate the expected return and risk of asset A.
(b) Calculate the expected return and risk of asset B.
6
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. (c) Calculate the expected covariance of asset A and asset B returns.
(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.
(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.
(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
$
6.85
0.031117
0.031117
$ 60.69
0.147493
0.147493
6/30/2010
$
6.52
0.048175
0.048175
$ 49.26
0.188334
0.188334
7/30/2010
$
7.49
0.148773
0.148773
$ 57.53
0.167885
0.167885
8/31/2010
$
7.52
0.004005
0.004005
$ 42.84
0.255345
0.255345
9/30/2010
$
8.53
0.134309
0.134309
$ 48.69
0.136555
0.136555
10/29/2010
$
8.16
0.043376
0.043376
$ 56.92
0.169029
0.169029
11/30/2010
$
7.66
0.061275
0.061275
$ 61.83
0.086261
0.086261
12/31/2010
$
9.07
0.184073
0.184073
$ 58.13
0.059842
0.059842 (a) True or false: neither Motorola nor RIM paid a monthly dividend in 2010? Give a brief explanation and provide a
formula to justify your answer. The following table contains the return on 30day US Treasury Bills issued on December 31st 2010 as well as Motorola
and RIM’s average monthly returns; variance of monthly returns; and the covariance of Motorola’s and RIM’s monthly
returns for the period February 26th, 1999 to December 31st, 2010:
30 Day U.S. TBill Return (Dec 31st 2010) 0.00081 The following figures are for the period February 26th, 1999 to December 31st, 2010
Average Motorola Monthly Returns
Variance of Motorola Monthly Return
Average RIM Monthly Returns
Variance RIM Monthly Returns
Covariance of Motorola and RIM Monthly Returns 0.002616887
0.013877326
0.054275605
0.052027303
0.012945617
7 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) Are Motorola stocks riskier than RIM stocks, or the other way around? Give a brief explanation and justify your
answer by calculating the risk premium for each stock. An investor has the following meanvariance utility function over expected portfolio returns [ ] and portfolio variance
where is a parameter reflecting the investor’s “attitude towards risk”: (c) Suppose this investor wants to invest in a portfolio consisting of US 30day TBills and RIM stocks. Derive a formula
for the optimal fraction of this portfolio that will be in US 30day TBills and RIM stocks and calculate the value of the
parameter for which the investor invests 100% of her portfolio dollars into RIM stocks. Show all calculations and state
all assumptions.
(d) Suppose
. Suppose this investor wants to invest in a portfolio consisting of US 30day T...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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