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This paper is not to be removed from the Examination Halls
UNIVERSITY OF LONDON
FN3023 ZB
BSc degrees and Diplomas for Graduates in Economics, Management, Finance
and the Social Sciences, the Diplomas in Economics and Social Sciences and
Access Route
Investment Management
Monday, 19 May 2014 : 14:30 to 17:30
Candidates should answer FOUR of the following EIGHT questions. All questions carry
equal marks.
A calculator may be used when answering questions on this paper and it must comply
in all respects with the specification given with your Admission Notice. The make and
type of machine must be clearly stated on the front cover of the answer book.
PLEASE TURN OVER
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UL14/0234
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1.
(a)
Explain the difference between exchange trading and over-the-counter (OTC) trading of
securities. Discuss the relative benefits for investors of the two forms of trading.
(7 marks)
(b)
Suppose a competitive risk neutral market maker clears the market by offering bid and
ask quotes at which she is willing to trade one share of a stock. Traders are either
uninformed noise traders who are as willing to buy a share as sell a share of the stock,
or informed traders who know exactly the value of stock and who consequently buy
when the value is high and sell if the value is low. The ratio of informed to uninformed
traders is 1 to 5. The value of the stock is 110 if it is high and 90 if it is low, and both are
seen as equally likely by the market maker. Work out the market maker’s bid and ask
quotes in the first round of trading.
(9 marks)
(c)
You seek to implement a return based trading strategy to exploit potential momentum
effects in the stock market. The following table shows the most recent 3-month returns
on 5 stocks in which you seek to trade.
Stock
3-month return
A
5%
B
3%
C
-1%
D
-2%
E
8%
Based on these data, work out a set of weights for your portfolio such that you commit
no capital to your position.
(9 marks)
2.
3.
(a)
Explain what we mean by floating-rate debt. Discuss ways in which these instruments
are helpful to borrowers.
(7 marks)
(b)
A 5-year bond has annual coupon rate of 5% and yield to maturity 6%. What is the
duration of the bond?
(9 marks)
(c)
What is the convexity of the bond in part (b)?
(a)
Explain the difference between hedging using put-option protection and Value-at-Risk
(VaR). Discuss the relative advantages and disadvantages of the two hedge-strategies.
(7 marks)
(b)
A portfolio has a value V that follows a geometric Brownian motion with drift parameter
(instantaneous return) m=0.10 and diffusion parameter (volatility) σ=0.2, which implies
that the log return of the portfolio value from time t to time T, ln VT – ln Vt, is normally
distributed with mean (m – σ2/2)(T-t) and variance σ2(T-t). What is the 1%, 20-day VaR
of the portfolio? Hint: If X is a normally distributed random variable with mean M and
variance S2, then Z = (X-M)/S is a standard normally distributed random variable with
mean 0 and variance 1 with probability Prob(Z ≤ -2.33) = N(-2.33) = 0.01. (9 marks)
(c)
Consider the portfolio in part (b), and assume that the risk free rate (continuously
compounded) is 2%. The costs of a 20-day European call and put options on the
portfolio with exercise price 1,000 are, respectively, 17.766 and 16.671 per 1,000
capital invested at time t (i.e. assuming Vt = 1,000). Create a put-protected portfolio
which – over a 20-day period – will not end up at a value below its current levels Vt.
(9 marks)
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(9 marks)
D1
4.
5.
(a)
Explain the Treynor-Black model outlined in the subject guide.
(b)
A competitive risk neutral market maker clears the market for trading in an asset. There
are two traders, an uninformed noise trader and an informed trader who has perfect
information about the true value of the asset, which is 110 or 90. The market maker
thinks the two prices are equally likely. The uninformed trader buys one unit or sells one
unit of the asset with equal probability. The market maker observes the aggregate
orders from the two traders and clears the market. Work out the optimal trading strategy
and the expected profits for the informed trader.
(9 marks)
(c)
You find that the auto-covariance in price-changes (measured transaction by
transaction) is -0.02. What do you expect is the spread between the bid and ask prices
in this market (measured in dollars and not in percentages)?
(9 marks)
(a)
‘Hedge transactions involving the trading of derivatives have zero net present value, so
will never increase the value of the corporation.’ Discuss this statement, and explain
why hedging of corporate risk nonetheless can add value to corporations. (7 marks)
(b)
A portfolio has a beta of 0.5, and idiosyncratic risk with variance 3%. The variance of
the market portfolio is 10%, and the return on the market portfolio is 8% on average.
The risk free return is 2%. What is the required return on the portfolio in order that it
matches the market portfolio in terms of the Sharpe ratio?
(9 marks)
(c)
Define absolute and relative risk aversion. In asset allocation situations where the
investors split their investments into a safe and a risky asset, how do investors with
constant absolute risk aversion optimally choose their portfolios as their wealth
changes? What about investors with constant relative risk aversion?
(9 marks)
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(7 marks)
D1
6.
(a)
Explain what we mean by the term structure of interest rates. Name three different
types of hypotheses explaining the shape of the term structure of interest rates.
(7 marks)
(b)
The price of a bond is P, and the yield to maturity is r. You estimate that the current
ratio of the change in the bond price, ΔP, over the change in the yield to maturity, Δr, is
-4.5 times the price of the bond P. You also recognise that the ratio ΔP/Δr above is not
constant for varying levels of r and you are trying to work out the numbers for the
current yield to maturity of 5%. If the price of the bond is P=100, what is the (Macaulay)
duration of the bond? Explain how we can make use of bond duration in practice.
(9 marks)
(c)
You are given the following information about a portfolio, denoted A, the market
portfolio, denoted M, and the risk free asset, denoted R.
Expected return
Variance
Beta
Jensen’s alpha
Portfolio A
7.3%
10%
0.88
0.04
Market portfolio M
8%
9%
1
0
Risk free asset R
2%
0
0
0
According to the Treynor-Black model, the optimal mix of the A and M portfolios for
variance-averse investors is given by the formula
In this formula, w is the weight on portfolio A, αA is Jensen’s alpha of portfolio A, βA is
the beta of portfolio A, ErM is the expected return on the market portfolio, rF is the risk
free return, Var(εA) is the idiosyncratic risk of portfolio A, and σM2 is the variance of the
market portfolio. Work out the optimal weight w.
(9 marks)
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7.
(a)
Explain what we mean by collateralised debt/loan obligations. It has been claimed that
these instruments played a role in undermining banks’ lending operations in the period
leading up to the financial crisis in 2007 – explain the argument behind this assertion.
(7 marks)
(b)
An investor has mean-variance preferences which can be expressed as the function
U(µ,σ2) = µ - (ρ/2)σ2, where µ is the expected return on the investor’s portfolios, σ2 is
the variance of the investor’s portfolio, and ρ > 0 is a parameter describing the
investor’s variance aversion. Derive the optimal portfolio for the investor when all
investors have mean-variance preferences and there exists a risk free asset. Also
derive the critical value of ρ which determines the cut-off point between investors who
are net lenders and net borrowers of the risk free asset.
(9 marks)
(c)
In the subject guide there is a discussion about the difficulties of measuring the
performance of hedge funds. The following table is an extract from this material, and
shows the actual performance data on a hedge fund against the S&P 500 index.
Monthly mean return
Monthly standard deviation
Annual Sharpe ratio
S&P 500
1.4%
3.6%
1.39
Hedge Fund
3.6%
5.8%
2.15
Explain what the numbers in the table mean. Explain how the hedge fund achieved
these numbers, and why the real performance of the hedge fund may not be as high as
the numbers indicate.
(9 marks)
8.
(a)
Explain how you can use the single index model to estimate the variance-covariance
matrix of stocks. Why is this method useful in practice?
(7 marks)
(b)
A bond is quoted with a price of 100.20 per 100 face value. The coupon of 3.2% of face
value is paid once a year, and it is 45 days since the last coupon payment. If you were
to trade this bond, what price do you expect to pay for the bond?
(9 marks)
(c)
The expected return on the market index is 8%, with standard deviation 0.3, and the
risk free return is 2%. You consider holding a portfolio that has at most standard
deviation 0.2, subject to the constraint that the portfolio earns an M2 measure of 2%.
What expected return is required to meet your investment objective if the portfolio has
maximum risk?
(9 marks)
END OF PAPER
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