Department of Economics, SUFFOLK UNIVERSITY
Jonathan Haughton
Fall 2012
ECONOMICS 826: Financial Economics
ASSIGNMENT 4
Answers to this assignment are due back by Thursday, October 4, 2012..
1.
Prove that for a two-asset portfolio composed of assets A and B, the minimum-risk portfolio requires
an investment in asset A equal to
𝑥𝐴 =
2
𝜎𝐵
−𝜌𝐴𝐵 𝜎𝐴 𝜎𝐵
2 +𝜎 2 −2𝜌
𝜎𝐴
𝐴𝐵 𝜎𝐴 𝜎𝐵
𝐵
,
where xA is the percent invested in asset A. [Hint: Minimize the variance of 𝑟𝑃 (i.e. the variance of the
portfolio return), noting that ∑ 𝑥𝑖 = 1.]
2.
The Arnaque (A) and Bisou (B) corporations have the following risk and return statistics:
𝐸(𝑟𝐴 ) = 20%; 𝐸(𝑟𝐵 ) = 25%; 𝜎𝐴 = 28%; 𝜎𝐵 = 38%; 𝜌𝐴𝐵 = −1.
a. Determine the minimum-risk portfolio for A and B (i.e. determine the proportions of A and B
that will minimize the risk on the portfolio). [Hint: The result in question 4 will be useful here.]
b. Compute the risk and return on the minimum-risk portfolio.
3.
Assume that we have the following historical returns for Microsoft and Cisco Systems:
Historical returns (% p.a.)
Year
MSFT
CSCO
1
10
9
2
15
12
3
-12
-7
4
20
18
5
7
5
a. Calculate the means and standard deviations of returns for Microsoft, and for Cisco.
b. Suppose the returns for MSFT and CSCO are normally distributed, with the means and standard
deviations computed in a. For each stock, compute 99% confidence intervals of stock prices.
c. Over the past five years you managed your portfolio (which was $1,000 at the beginning) as
follows: At the beginning of each year you divided your money equally between investments in
MSFT and CSCO. At the end of the year you collected your returns and restarted the process of
dividing your entire investment between the two stocks.
a. Using the information in the table, what would have been the return each year on your
total investment?
b. What are the mean return, and standard deviation of returns, for this portfolio?
4.
The return on the market portfolio is 0.12 and the riskless rate is 0.07. Use the CAPM to determine if
the following stocks are mispriced:
Stock
Expected return
Beta
Acme
0.115
0.8
Apex
0.135
1.2
5.
A new perfume manufacturer, Eau Noh, Inc., is expected to generate a return with a standard
deviation of 0.225 and correlation with the market portfolio of 0.8. If the standard deviation on the
yield on the market is 0.12, determine the relative holdings of the market portfolio and Eau Noh, Inc.
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stock to form a portfolio with a beta of 1.8. [Hint: First compute beta, then construct the portfolio.
Note that the beta of a portfolio is a weighted average of the betas of the component assets, with
the weights in proportion to the value of the assets in the portfolio.]
6.
During the most recent 5-year period, the Grate Skott mutual fund earned an average annualized
rate of return of 0.15, and had an annualized standard deviation of 0.30. During this period the
average annual risk-free rate was 0.05, the average annual return on the market index was 0.10, and
the standard deviation of the market return was 0.20. How well did Grate Skott perform on a riskadjusted basis?
7.
A market has only the following three risky assets:
E(r) (% per month)
Risk (i.e. σi) , %
Covariance with market (σim)
Asset 1
2.03
2
1.12
Asset 2
1.79
1
0.90
Asset 3
1.49
1
0.62
Market portfolio
0.92
The market portfolio has 4% invested in Asset 1, 76% in Asset 2, and 20% in Asset 3.
a. What is the expected return of this portfolio?
b. What are the betas of the three risky assets?
c. If the riskless rate of interest is 0.8% (per month), are these three securities priced correctly?
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