BEE 3016
UNIVERSITY OF EXETER
SCHOOL OF BUSINESS AND ECONOMICS
MAY/JUNE 2006
INVESTMENT ANALYSIS AND PORTFOLIO MANAGEMENT
Duration: THREE HOURS
FORMULA BOOKS ARE NOT PERMITTED
Answer THREE out of EIGHT questions
Calculators permitted
Question 1.
The following table provides estimates of the expected returns, standard deviations
and correlations of three assets
Asset
Expected return
Standard deviation
Correlations
A
10
5
B
8
4
C
6
3
 AB  0
 AC  0.3
 BC  1
(i) Calculate the mean return and the variance of return for the following portfolios:
a.
b.
c.
d.
An equally-weighted portfolio of A and B,
An equally weighted portfolio of A, B and C,
1/10 in A, 11/10 in B and a short sale of C,
As (c) but with 25% of the portfolio financed by borrowing at 4%.
[15 marks]
(ii) Construct the portfolio frontier:
a. When the only assets available are A and B,
b. When the only assets available are B and C.
In each case, determine the composition of the minimum variance portfolio, making
clear whether short sales are needed to achieve this.
[10 marks]
(iii) What must be the equilibrium return on short term treasury bills when assets A, B,
and C are all available? Explain what would happen if the government did not set the
return at this value.
[8 marks]
Question 2.
(i) Describe the single index model and its assumptions. Which of the assumptions are
necessarily satisfied when the model is estimated by least squares?
[8 marks]
Estimation of the single index model for the three stocks in a portfolio provides the
data in the table.
Stock
Alpha
Beta
A
B
C
3
2
1
1.2
0.7
1.1
e
4
6
2
i
Portfolio weight
0.3
0.4
0.3
The expected return on the market is 10% with a standard deviation of 16%. The risk
free rate is 5%.
(ii) What is the expected return for the portfolio?
[5 marks]
(iii) What is the standard deviation of the return on the portfolio? If you assumed this
portfolio were “well diversified” how would the answer change?
[10 marks]
(iv) Discuss the limitations of the single index model as a guide to portfolio choice.
[10 marks]
Question 3.
a. State and explain the assumptions of the Capital Asset Pricing Model.
[8 marks]
b. Assume that a risk free asset is available. State and derive the capital market line
and security market line.
[8 marks]
c. You collect data on the annual returns for a number of stocks in 2005. You observe
that some of the stocks lie above the security market line and some lie below. Is this
evidence that the CAPM does not apply?
[8 marks]
d. Will a risk-averse investor choose only stocks with low betas? Explain your
reasoning.
[9 marks]
Question 4.
a. Describe call and put options, making sure that you distinguish between American
and European.
[4 marks]
b. Derive the put-call parity relationship.
[6 marks]
c. Using the binomial pricing model, calculate the value of a call option on a stock
that currently sells for £10 but may rise in one year to £12 or fall to £8 assuming that
the annual risk free rate of return is 5% and the exercise price is £10.
[8 marks]
d. Repeat the analysis in part c when the year is split into three periods of four
months.
[9 marks]
e. Is the binomial pricing model of any value in investment analysis?
[6 marks]
Question 5.
a. Is stock price maximization good or bad for society?
[5 marks]
b. When we estimate the covariance between the NYSE, DJIA and S&P indexes we
find high levels of correlation but none of the correlation equals 1. Explain why the
correlations are high. What are the main differences in these three indices? [5 marks]
c. Explain the difference between APT and the CAPM with respect to the market
portfolio.
[5 marks]
d. Suppose you are considering the purchase of shares in the XYZ mutual fund. As
part of your investment analysis, you regress XYZ’s returns for the past five years
against the three factors specified in the Fama-French model. This procedure
generates the following coefficient estimates: market factor = 1.2, SMB factor = -0.3,
HML factor = 1.4. Explain what each of these coefficient values means. What types
of stocks is XYZ likely to be holding?
[8 marks]
e. Four factors affect the value of a futures contract on a stock index. Three of these
factors are: the current price of the stock index, the time remaining until the contract
maturity (delivery) data, and the dividends on the stock index. Identify the fourth
factor and explain how and why changes in this factor affect the value of the futures
contract.
[10 marks]
Question 6.
a. You are given the following information on 5 portfolios at different periods.
Month
Portfolio
February
March
May
August
December
B
F
T
C
E
Portfolio
Return %
11.5
10.0
14.0
12.0
15.9
Market Return
%
4.0
8.5
9.6
15.3
12.4
Portfolio Beta
0.95
1.25
1.45
0.70
-0.30
(i) Compute the abnormal rates of return for the five portfolios, ignoring differential
systematic risk.
[6 marks]
(ii) Compute the abnormal rate of return for the five portfolios taking into account
their systematic risk.
[6 marks]
(iii) Compare the two sets of estimates of abnormal returns and discuss the reason for
the difference in each case.
[6 marks]
b. State whether each of the following statements is true or false (there is no need to
explain your answer).
[15 marks]
1.
Shareholders should take actions that are detrimental to bondholders.
2.
For a firm, maximizing stock price is the same thing as maximizing profit.
3.
Two measures of the risk premium are the standard deviation and the variance.
4.
In the APT model, the identity of all the factors is known.
5.
A good portfolio is a collection of individually good assets.
6.
The correlation coefficient and the covariance are measures of the extent to
which two random variables move together.
7.
Like hedging, arbitrage results in increased returns with a disproportional
increase in risk.
8.
Beta is a measure of unsystematic risk.
9.
Under the CAPM framework, the introduction of lending and borrowing at
differential rates leads to a non-linear capital market line.
10. Studies have shown the beta is more stable for portfolios than for individual
securities.
11. If an incorrect proxy market portfolio such as the S&P index is used when
developing the security market line, the slope of the line will tend to be
underestimated.
12. Empirical tests of the APT model have found that as the size of a portfolio
increased so did the number of factors.
13. The random walk hypothesis contends that stock prices occur randomly.
14. The strong form of the efficient market hypothesis contends that only insiders
can earn abnormal returns.
15. Forward contracts are individually designed agreements, and can be tailored to
the specific needs of the ultimate end-user.
Question 7.
State the correct choice and very briefly explain your answer (less than 30 words).
Each question carries 3 marks.
1.
The ability to sell an asset quickly at a fair price is associated with
a) Business risk.
b)
Liquidity risk.
c) Exchange rate risk.
d)
Financial risk.
e) Market risk.
2.
The main trade off between forward and future contracts is
a) Design flexibility.
b)
Credit risk.
c) Liquidity risk.
d)
All of the above.
e) Choices a and b only
3.
In a two stock portfolio, if the correlation coefficient between two stocks
were to decrease over time every thing else remaining constant the
portfolio's risk would
a) Decrease.
b)
Remain constant.
c) Increase.
d)
Be a negative value.
e) Fluctuate positively and negatively.
4.
The market portfolio consists of all
a) New York Stock Exchange stocks. b)
c) High grade stocks and bonds.
d)
e) U.S. and non-U.S. stocks and bonds.
Stocks and bonds.
Risky assets.
5.
The correlation coefficient between the market return and a risk-free asset
would
a) be + .
b)
be - .
c) be +1.
d)
be –1.
e) be Zero.
6.
The expected return for a stock, calculated using the CAPM, is 10.5%. The
market return is 9.5% and the beta of the stock is 1.50. Calculate the implied
risk-free rate.
a) 7.50%
b)
13.91%
c) 17.50%
d)
21.88%
e) 14.38%
7.
The fact that tests have shown the CAPM intercept to be greater than the
RFR is consistent with a
a) Zero beta model.
b)
Higher borrowing rate.
c) APT.
d)
(a) or (b)
e) (b) or (c)
8.
To date, the results of empirical tests of the Arbitrage Pricing Model have
been
a) Clearly favourable.
b)
Clearly unfavourable.
c)
e)
Mixed.
Biased.
d)
Unavailable.
9.
A portfolio manager without superior analytical skills should
a) Determine and quantify the risk preferences of a client.
b) Minimize transaction costs.
c) Maintain the specified risk level.
d) Ensure that the portfolio is completely diversified.
e) All of the above.
10.
As a contract approaches maturity, the spot price and forward price
a) Increase.
b)
Diverge.
c) Maintain a fixed price differential. d)
Converge.
e) Have a random relationship.
Question 8.
a. Suppose that the market consists of two stocks, A and B. You are given the
following information:
Risk free rate: 5%.
Expected Returns: E(RA) = 14%, E(RB) = 8%.
Standard Deviation: SD(RA) = 6%, SD(RB) = 3%.
Covariance(RA, RB) = -9.
(i) Find the optimal weights. Is shortselling necessary for your optimal portfolio?
Why or why not?
[12 marks]
(ii) Find the expected portfolio mean and the portfolio variance.
[4 marks]
b. Consider the following two investment outcomes. Examine whether A
stochastically dominates B with respect to first, second and third order stochastic
dominance.
[17 marks]
Outcome
6
7
8
10
12
A
Probability
1/4
1/20
1/4
1/5
1/4
B
Outcome
5
9
10
12
Probability
1/4
1/4
1/4
1/4