Exam Guide
Question 4: Derivative Valuation (35 points)
The date is 20 April. You are a stockbroker at a large Australian firm and specialise in
dealing in derivative markets. As part of your daily routine, you discuss a range of
opportunities and strategies with clients.
(a) You take a call from an investor who has decided to set up a buy/write fund, which is
not allowed to gear/lever. Her strategy is to buy and always hold BHP shares and
write options against the holding. She also states that the fund will earn over 20% per
annum over the next year with no risk of loss.
(i) What type of option trades would the investor seek to enter into, given that she
is already holding BHP shares? Buy/sell, puts/calls or both? Justify your answer.
(ii) Discuss the investor’s comment as to ‘no risk of loss’ with reference to what
assumptions would be required to make this statement true and what will
generate the return from the strategy.
(iii) Outline a strategy that would give a similar result to that outlined above but
using different types of options and underlying security.
(b) Your next call is from the Head of Asset Allocation at a fund manager. She tells you
that they expect the equity market to be extremely volatile over the next three
months and that she thinks there is an equal chance of either a 15% rise or fall over
the period.
(i) Using the following data, suggest an option strategy that would suit the
manager’s view. Draw a payoff diagram that will graphically demonstrate the
outcome of the strategy at maturity for various levels of the All Ordinaries
Index1 (include break-even points and maximum profit/loss).
Current all 2610
June SPI 2626
June SPI Calls June SPI Puts
Strike Bid price Ask price Strike price Bid price Ask price
2450 210 220 2450 50 60
2600 120 130 2600 110 120
2750 55 65 2700 205 215
(3 points)
(3 points)
(3 points)
(6 points)
(ii) Assume that the manager only wanted to protect $10 million of her portfolio
against a fall in the market over the long term. What additional information do
you require to calculate the number of options contracts required to implement
the strategy? (3 points)
1. The All Ordinaries Share Price Index (SPI) also referred as the “All Ordinaries” is the predominate measure
of the overall performance of the Australian sharemarket at any point in time. It is made up of shares of
approximately 250 of the largest Australian companies on ASX, weighted according to each company’s size in
term of market capitalization.
Exam Guide
(c) Your next call is from a trader of options who has a number of different options
positions open. She is about to go on four weeks holiday and asks for your opinion
on her Newscorp positions and if any action needs to be taken prior to departing for
the South Pole.
Long/ Number Security Price Options Option Option
Short Delta Gamma Theta
Short 10,000 Newscorp Ordinary 9.5
Short 15 Newscorp June $9.00 0.24 –0.3 Moderate Moderate
Long 15 Newscorp April $9.50 0.5 0.5 High High
(i) What is the effective exposure to underlying Newscorp shares? (Assume 1000
shares per option contract.) Show your calculations. (4 points)
(ii) Assume that Newscorp shares move sharply higher overnight. How would your
answer to (c)(i) above change and why? (Calculations are not required.) (3 points)
(iii) You notice that the implied volatility of Newscorp options is currently very
high, which is at odds with your view that the share price will stay at the same
level over the next three months. Suggest a course of action (along with
reasons) to the trader that would hedge the portfolio to unexpected price
moves in Newscorp over the period of absence. Use only the type of securities
currently represented in the portfolio. (4 points)
(d) You notice that take-over activity in the equity market has become a current theme
affecting stock prices. Outline how implied volatility would compare to historical
volatility in Western Mining options in the following scenarios. Give reasons why.
(i) A strong market rumour suggests an offer is imminent, but is not formally
announced. (3 points)
(ii) A cash offer, which is expected to succeed, is announced at a price significantly
above current market levels. (3 points)
Exam Guide
Question 5: Portfolio Management (33 points)
You are a consultant to a big institutional client. He shows you the brochure of a product
with the title “Invest your money in stocks but sleep well!” which he has got from his bank.
The product has the following characteristics:
maturity: 1 – 3 years
C, if Imd < Isd
payoff at maturity date:
C
.
1Imd -Isd ′
.
′+ , if Imd 3 Isd
. P1÷
. Isd .
where:
C = invested capital (in USD), minimum: 10 Mio. USD
Isd = Index level at starting date
Imd = Index level at maturity date
Index = S&P500
P1 = positive number, determined at starting date
The client can chose the maturity according to his preferences and the parameter P1 is
determined by the bank.
(a) Explain to your client the characteristics of this product. Sketch the payoff diagram
indicating every level and slope. Describe to your client how the portfolio manager
could implement this strategy. Illustrate your description with the special case where
the manager should not use any stocks or future, under the assumption that all other
necessary assets are available. (9 points)
(b) The client wants to know the meaning of the parameter P1 and which market
parameters or other parameters determine its value. Explain this to him in detail. (6 points)
The bank also offers another product with the following payoff:
C, if Imd < Isd
payoff at maturity date: . Imd -Isd .
C′+1 ′P
. 2÷èIsd ., if Isd ￡ Imd ￡ Imax
. Imax -Isd .
C′+1 ′P
. 2֏Isd ., if Imd > Imax
where:
Imax = certain Index level (determined at issue date) with Imax > Isd
P2 = positive number, determined at starting date
(c) Explain to your client the characteristics of this product and how they differ from
those of the first product. Sketch the payoff diagram indicating every meaningful
level and slope. Describe how the portfolio manager could implement this strategy. (9 points)
(d) What can you say about the parameters P1 and P2 in both the products
(qualitatively)? Do you expect them to be equal or not? If yes, explain why: if not,
indicate which of the two you expect to be higher and why. (6 points)
(e) Does the level of Imax have any impact on P2? Justify your answer. (3 points)
Exam Guide
Question 6: Portfolio Management (21 points)
Pension Fund Z currently allocates its equity investments to three active managers
(Companies A, B, and C) and one passive manager (Company P).
Manager Style Alpha (a) Standard IR Current
deviation of allocation
tracking error(s)
A Active 2.0% 10.0% 0.20 0.2
B Active 1.6% 8.0% 0.20 0.2
C Active 0.5% 5.0% 0.10 0.1
P Passive 0.0% 0.0% – 0.5
The alpha (a ) column in the table indicates the expected “excess return” of the fund
(i.e. the return earned by the fund minus the benchmark return); s indicates the standard
deviation of excess return; and “IR” is an abbreviation for “Information Ratio”, which is
defined as
a /s .
The formulas below give the theoretical allocation to each manager, assuming that there is
no correlation between the excess return and benchmark return for any of the funds and
that excess returns of individual funds are mutually independent.
tIR
. Allocation to active manager: i xi = i
2si
. Allocation to passive manager: P x =-1 .x
p ii
Note that t is a parameter indicating the degree of risk tolerance given for each investor.
Answer the following questions with reference to the information above.
Pension Fund Z thinks that the stock market has been fairly efficient so far. It had
previously decided on a 0.5 allocation to the passive component, but has reviewed its policy
and now wishes to change its allocations between active and passive managers based on the
theoretical formulas shown above.
(a) It is often said that the passive investment component should be increased the more
efficient the market is. Why is this so? Explain by using the theoretical formulas
above. (5 points)
(b) Pension Fund Z’s degree of risk tolerance t is estimated at 20. Find the optimal
allocation ratios for each fund, assuming the excess returns of individual active funds
to be mutually independent. (6 points)
(c) The actual correlation between the excess returns of A and B was positive since they
had similar investment styles. How would this change optimum allocation ratios to
individual managers (A, B, C, and P) from what they were in (b) above? (5 points)
(d) The a and s for each fund are estimated based on past performance, but there may be
some problems raising allocation ratios based on these numbers. Explain why that is. (5 points)
