Investment Analysis and Portfolio Management
Investment Analysis and Portfolio Management
ERASMUS Assignment 2009-2010Semester 11. (a) An investor buys
2000 shares at $10 each. The initial margin requirement is 50% and
the maintenance margin is 30%. If the stock falls to $6, will the
investor receive a margin call?
(b) 1000 shares are purchased on margin at the beginning of the
year for $20 per share. The initial margin requirement was 55%.
Interest of 13% was paid on the margin loan and no margin call was
ever faced. A dividend of $1 per share is received.
i. If the stock were sold for $25 per share at the end of the
year, what is the return for the year?
ii. Calculate the return if the purchase had been made using
cash instead of using a margin account.
(c) Through a margin account, 100 shares are short sold for $10
per share. The initial margin requirement is 45%.
i. If the price of the stock rises to $12 per share, what is the
actual margin in the account?
ii. If the price of the stock falls to $8 per share, what is the
actual margin in the account?
(d) Is it true that the potential loss on a short sale is
infinite? What is the maximum return?
2. The following table provides estimates of the mean returns,
standard deviations and correlations of three assets
ABC
Mean10205
Standard Deviation202510
The risk-free rate of return is 2.
What are the mean and variance of the following portfolios:
a. An equally weighted portfolio of A and B
b. A portfolio consisting of 1/3 B and 2/3 C
c. An equally weighted portfolio of A, B and CPlot the portfolio
frontiers (without short selling) when A is combined with B, when A
is combined with C, and when B is combined with C. Using these
frontiers sketch (you can calculate if you wish) the portfolio set
when portfolios can contain all three assets.
3. The correlation between assets A and B is 0.1. The expected
return of A is 10% and its standard deviation 15%. For B, the
expected return is 15% and the standard deviation 20%.
a. Find the proportions of A and B in the minimum variance
portfolio.
b. What is the value of the minimum standard deviation?
c. What is the expected return on the minimum variance
portfolio?
Now assume a riskfree asset is also available with a return of
5%.
d. What is the composition of the tangency portfolio of risky
assets?
e. What is the market price of risk?
4. Describe the Capital Asset Pricing Model, paying particular
attention to its assumptions. What are its implications for
portfolio choice and portfolio evaluation?5. (i) Define the single
index model. How does it differ from the CAPM?(ii) You have
estimated a beta of 0.85 for H&M Inc using data on returns over
the past 10 years. What factors would you take into account in
adjusting this value?
Assume that returns are generated by a model where the market is
the single factor. The details of the model for three stocks
are:
StockAlphaBeta
Portfolio weight
A2.21.140.2
B0.60.830.5
C3.01.010.3
The expected return on the market is 12% with a standard
deviation of 18%.
(iii) What is the portfolio's expected rate of return?
(iv) What is the standard deviation of the return on the
portfolio?(v) Discuss the limitations of the market model as a
guide to portfolio choice.
Work to be returned by 15 January 2010 to:
Mike Robertson
ERASMUS Secretary
Room 3
University of Exeter Business School
Streatham Court
Rennes Drive
Exeter
EX4 4PU
Phone:+44(0)1392 723416
email: [email protected]
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