SINGAPORE INSTITUTE OF MANAGEMENT
UNIVERSITY OF LONDON
PRELIMINARY EXAM 2015
PROGRAMME
:
University of London Degree and Diploma Programmes
MODULE CODE
:
FN3023
MODULE TITLE :
INVESTMENT MANAGEMENT
DATE OF EXAM :
03/03/2015
DURATION
3 Hours
:
TOTAL NUMBER : 5
OF PAGES
(INCLUDING
THIS PAGE)
------------------------------------------------------------------------------------------------------INSTRUCTIONS TO CANDIDATES :-
There are a total of EIGHT questions.
Candidates should answer only FOUR questions.
Each question carries 25 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.
DO NOT TURN OVER THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO.
Candidates are strongly advised to divide their time accordingly.
FN3023 Investment Management
Page 1 of 5
1.
(a) Distinguish between market timing and asset allocation? Explain an approach for measuring the
market timing ability of a fund manager.
(7 marks)
(b) Consider the following data on prices and coupon rates:
Bond price
£104.51 per £100 nominal capital
£104.63 per £100 nominal capital
£91.29 per £100 nominal capital
Coupon rate
10% annual coupon of nominal capital
8% annual coupon of nominal capital
2.5% annual coupon of nominal capital
Time to maturity
1 year
2 years
3 years
Work out the yield on the bonds and the year 1, year 2, and year 3 spot rates. Where you cannot work
out the answer as a number just report the simplest algebraic expression.
(9 marks)
(c) Consider the 3-year bond in question (b) priced at £91.29 per £100 nominal capital and 2.5%
annual coupon. What are the duration and the convexity of this bond? Explain how you can use
duration and convexity to predict bond price changes.
(9 marks)
2.
(a) What do we mean by limit order markets? Explain how the priority rules (with respect to price and
submission time) work in such markets.
(7 marks)
(b) The risk free rate is 4% and the expected return on the market portfolio is 10% with standard
deviation 20%. Suppose you have identified an active portfolio with a beta of 1, an expected return of
13% and a standard deviation of specific risk of 40%. What weight does the Treynor-Black model
suggest should be attached to this portfolio? Draw an appropriate diagram to reflect these numbers.
(9 marks)
(c) You short 1,000 units of a stock. At the end of the first year you need to make a dividend payment,
and also you buy back 400 units of the stock after the dividend transaction has cleared. On the remaining
short position you need to make a further dividend at the end of the second year. You then buy back the
remaining 600 units and the position is cleared. The prices and dividend payments are given below.
Year
Stock price
0
1
2
£100 £80 £70
Dividends per share
£5
£5
You make the transaction on the basis of a 140% initial and maintenance margin requirement (this
corresponds to a margin of 40% in the examples given in the Bodie, Kane, and Marcus Investments
textbook). What is the two-year return on your short transaction?
(9 marks)
FN3023 Investment Management
Page 2 of 5
3.
(a) Suppose the price of two assets A and B, PA and PB respectively, tend to move together. Designating
the quantities traded as XA and XB respectively, if PA < PB, demonstrate how you can construct a trading
strategy that delivers a trading profit for any price P* on convergence.
(7 marks)
(b) A fund is making average return 12% per year over the last 10 years. The standard deviation of the
fund is 30%. The risk free rate is 3%, the average return of the market index is 9%, and the standard
deviation of the market return is 25%. The covariance of the return on the fund with the return on the
market index is 9%. Work out the Sharpe ratio and the Treynor ratio of the fund, and explain whether
the fund is an attractive investment opportunity on the basis of your findings. Do you think there may
be estimation errors in the data you are presented with? Explain.
(9 marks)
(c) Consider a share which is currently valued at 100, but has a true value of either 130 or 80 with equal
probabilities. The market is cleared by a risk neutral competitive market maker who posts a bid price at
which he is prepared to buy from a seller, and an ask price at which he is prepared to sell to a buyer. The
market maker believes there is a 90% chance the next trader is an uninformed trader who is equally
likely to buy or sell for liquidity reasons, and a 10% chance the next trader is an informed trader who
trades on the basis of his or her (perfect) information about the true value of the share. Work out the bid
and ask prices for the next transaction.
(9 marks)
4.
(a) Explain what we mean by efficient markets, and outline the three forms of efficient market
hypothesis.
(7 marks)
(b) You make a stock market investment in 5 stocks, with equal value invested in each stock. The sum
of the betas of the 5 stocks is 7. The market portfolio has standard deviation 30%, and the
idiosyncratic risk term of each stock has variance 2%. The idiosyncratic risk is uncorrelated across the
stocks. What is the standard deviation of the portfolio? Would it matter if the idiosyncratic risk terms
were correlated? Explain. Work out the standard deviation in the extreme case that the idiosyncratic
risk is perfectly correlated across any pair of stocks in the portfolio.
(9 marks)
(c) You hold a portfolio where you estimate the return is risky but that it will be between -20% and
+30%, assume that any number between these extremes is equally likely. The current value of the
portfolio is $20m. You aim to limit your portfolio losses to $1,500,000 with 5% probability (the 5%
VaR is $1,500,000). You can offset losses in excess of this by injecting new money as risk capital.
Outline the details of your risk management strategy.
(9 marks)
FN3023 Investment Management
Page 3 of 5
5.
(a) Explain why the duration method for immunizing bond portfolios is likely to give misleading
results if the change in the term structure is very large, or different for the various spot rates.
(7 marks)
(b) The Black-Scholes value of a European call option on a stock is given by
c = S N(d1) – Xe(-r(T-t)) N(d2)
where S is the current stock price, X is the exercise price, N(X) is the probability that an outcome
drawn from a standard normal probability distribution is less than X, and e(-r(T-t)) is the discounted
value of a risk free payoff of 1 at maturity. Assume S = 100 and put and call options exist with the
same maturity and an exercise price of 100. The following data is given:
e(-r(T-t))
0.95123
d1
0.35
d2
-0.15
N(d1)
0.63683
N(d2)
0.44038
Suppose you wish to create a volatility hedge, using the put and call options above, which is neutral to
small changes in the current stock price but which is sensitive to small changes in the volatility of the
stock. Explain the details of your trading strategy, and specify in particular the number of calls traded
relative to the number of puts.
(9 marks)
(c) Suppose stock returns follow a two-factor structure, and assume your portfolio has a beta of 0.8
with respect to the first factor and a beta of 0.9 with respect to the second factor. There also exists a
risk free asset with return 2%, and two ‘factor portfolios’ which represents the two factor risks – each
has unit beta with respect to their respective factor and zero beta with respect to the other, and no
idiosyncratic risk. The ‘factor portfolio’ representing the first factor risk has expected return 4% and
the ‘factor portfolio’ representing the second factor risk has expected return 8%. Suppose you wish to
immunise your portfolio from factor risk by taking a zero-cost position in the ‘factor portfolios’ and
the risk free asset. First, explain the details of your immunisation strategy. Second, explain what return
you expect on your original un-immunised portfolio, and what return you expect on your immunised
portfolio. Third, explain why you might wish to carry out an immunisation strategy like the one you
have worked out.
(9 marks)
6.
(a) Explain why risk-averse individuals are willing to pay an insurance premium to remove risk.
(7 marks)
(b) A bond portfolio is worth $5,000,000, and you estimate the duration of the portfolio is 7 years.
You are planning to reduce the exposure to interest changes by taking a short position in a 12-year
zero coupon bond. The relevant term structure is level at 5% and the target duration for your net
position is 5 years (i.e. you do not wish to immunise the portfolio completely – just reduce your equity
duration from 7 years to 5 years). Outline the details of your trading.
(9 marks)
(c) Consider the following table of prices for options with 1 year to maturity. The underlying asset is
currently priced at 100.
Exercise price
90
100
Call
33
29
Put
19
24
Can you make arbitrage profits in this market? Explain your answer carefully.
(9 marks)
FN3023 Investment Management
Page 4 of 5
7.
(a) What do we mean by the term structure of interest rates? Explain what the expectations hypothesis
states about the shape of the term structure of interest rates.
(7 marks)
(b) You analyse the performance of a fund, and find that the return over a 1-year period is 21% with
standard deviation of 64%, then over the following 1-year period it is 8% with standard deviation of
12%, and finally if you consider the whole 2-year period you find the average return is 14.5% with
standard deviation of 46% (note: all returns and standard deviations are annualised). The risk free
return is constant and equal to 3% for both periods. Work out the Sharpe ratio for each year separately,
and then for the whole period. Explain why the fund appears to be performing worse over the whole 2year period than in either of the two sub-periods.
(9 marks)
(c) You manage a fund which is currently valued at 100,000 and consists of a broad diversified portfolio
of stocks, and you estimate the portfolio has unit beta (i.e. beta =1). You want to protect the value of
this portfolio such that at the end of a 1-year horizon there is no probability that the value goes below
95,000. The risk free rate is 2% per year, and there are 1-year put and call options on the stock market
index traded with exercise price 95% of the current stock market index. The call is trading at a price of
15%, and the put is trading at a price of 8.14%, of the current index level. Outline the details of your
portfolio protection strategy.
(9 marks)
8.
(a) Contrast the actual performance of fund managers with that expected from the Efficient Markets
hypothesis.
(7 marks)
(b) The 3-month return on 4 stocks is given below.
Stock
A
B
C
D
3-month
return
7%
-2%
4%
3%
Outline a strategy for forming a portfolio of these stocks which seeks to take advantage of momentum
effects.
(9 marks)
(c) A 3-year and 200 day bond with annual coupon 8% is trading at a yield of 8%. If you were to trade
this bond today, you would pay a price equal to 103.54. Work out the clean price quoted in the financial
pages for this bond. Explain why the clean price is not exactly equal to par value in this case even though
the bond is trading at yield to maturity equal to the coupon rate. What should the exact expression for
accrued interest be (hint: the clean price is the dirty price on the day the coupon payment is made)?
(9 marks)
END OF PAPER
FN3023 Investment Management
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