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Sample Examination Paper
Final Examination
Questions
Portfolio Management
Derivative Valuation and Analysis
Fixed Income Valuation and Analysis
Exam Guide
Subject Area
Question Number
Weight
Fixed income valuation and analysis
Q1
20 points
Fixed income valuation and analysis
Q2
25 points
Derivative valuation
Q3
25 points
Derivative valuation
Q4
33 points
Portfolio management
Q5
30 points
Portfolio management
Q6
20 points
Portfolio management
Q7
Portfolio management
Q8
7 points
20 points
180 points
Time allowed : 180 minutes
2
 ACIIA: June 2000
Exam Guide
Answer all questions
Question 1: Bond Valuation and Analysis
(20 points)
You are considering investing in a bond for the next twelve months. You are limiting your
choice of bond to one of the following, both of which pay annual coupons at year end and
have identical credit risk:
(a)
(b)
(c)
(d)
Bond
Maturity
Coupon
YTM
A
2 years
8%
7.842%
B
3 years
9%
8.027%
If the one year, two year and three year spot rates are 7.65%, 7.85% and 8.05%
respectively, determine the prices of bond A and bond B.
Estimate, using duration, the expected change in price of bond B for a 0.2% change
in yield to maturity.
Calculate the difference in the one year holding period return on the bonds, assuming
that spot rates will fall in twelve months’ time by 0.2% across the maturity spectrum.
When estimating holding period return, what are the implications of each of the
following assumptions?
(i)
the yield to maturity or spot rate curve will remain constant; and
(ii) the forward rate curve correctly estimates future spot rates
 ACIIA: June 2000
(4 points)
(5 points)
(6 points)
(5 points)
3
Exam Guide
Question 2: Bond Valuation and Analysis
(25 points)
A pension fund is currently showing a surplus in its asset/liability position (see table below).
Under International Accounting Standards (IAS), which were recently adopted, pension
liabilities must be valued at market interest rates, and, if they are larger than fund assets, the
difference must be posted to the corporate balance sheet as a liability. You have been asked
to invest in bonds in such a way as to avoid this happening. Answer the following questions
about your investment strategy.
Pension Fund Asset/Liability Position
Value
($1 million)
Modified
duration (years)
120
6
Bonds
80
7
Equities
40
4
Pension liabilities
110
12
Surplus
10
–
Pension assets
(a)
(b)
4
Assume that the amount of future pension benefits is fixed in nominal terms and that
you want to maintain a surplus even if there is a movement in interest rates that
causes a change in the liability. You may also assume for the following questions that
interest-rate movement is parallel and that the convexity effect can be ignored.
(i)
If you keep your current asset mix, how many percentage points up or down
will interest rates need to move before the surplus is negative?
(ii) You want to keep the current asset mix ($80 million in bonds, $40 million in
equities), but change the composition of the bond portion so that the current
surplus is maintained even if interest rates move. How many years should the
bonds’ modified duration be?
(iii) If you put all of your assets into bonds, what modified duration will enable you
to maintain the current surplus even if interest rates move?
(iv) Referring to the previous two cases, i.e. (a)(ii) and (a)(iii), discuss the pros and
cons of lengthening the duration of your bond investments.
Pension benefit amounts will be usually indexed to inflation, and you need to take
this factor into account in valuing pension liabilities and in managing bond
portfolios.
(i)
Assume the kind of investments described in Question (a)(iii). If there is
inflation, what effect will it have on assets and liabilities and on the surplus?
(ii) If pension benefit amounts are indexed to inflation, what discount rate should
you use to value liabilities?
(iii) Discuss the kind of bonds you should invest in if pension benefit amounts are
indexed to inflation.
(3 points)
(3 points)
(3 points)
(4 points)
(4 points)
(4 points)
(4 points)
 ACIIA: June 2000
Exam Guide
Question 3: Derivative Valuation and Analysis
(25 points)
You are currently managing a well-diversified stock portfolio with a beta of 1.2 on the
TOPIX* index of Tokyo Stock Exchange stock prices. The TOPIX is now at 1600, oneyear (riskless) interest is 3%, and the aggregate market value of your portfolio is ¥16 billion.
Ignoring dividends, answer the following questions. (Where calculations are necessary,
include the calculations clearly in your answer sheet.)
*TOPIX: The weighted average stock price index of all TSE 1st Section listed stocks.
(a)
(b)
Given a TOPIX value of T one year from now, what will be the Value V of your
portfolio at this time? Express V as a function of T.
(i)
Assume the prices and deltas of a put option on the TOPIX with one year to
maturity are as follows:
Exercise Price
1600
1608
1616
1624
1632
1640
1648
Put Price
72.8
76.3
80
83.3
87.6
91.6
95.7
–0.393
–0.406
–0.419
–0.431
–0.444
–0.457
–0.470
Delta
(c)
Depending on the TOPIX value one year hence, your portfolio may suffer a
loss and you have thought of hedging with a purchase of puts capable of
maintaining the minimum portfolio value (before put premium, of ¥16
billion). Assuming that one TOPIX option corresponds to an amount 10,000
times that of the index, how many puts should you buy at what exercise price?
(ii) How much will this hedge cost?
Since it is difficult to buy puts with one year to maturity on the market, you think of
achieving the same results as in Question 2 by using futures for dynamic hedging.
(i)
Assuming that one-month (risk-free) interest is now 3% (at an annual rate) and
that the TOPIX futures with one month to maturity are at their theoretical
price, how many futures should you sell for the purpose of dynamic hedging?
Assume that the trading unit of the TOPIX futures is 10,000 times the index
and that the amount corresponding to the costs required for the puts purchased
in Question 2 is invested at the risk-free interest rate.
(ii) Assume that immediately afterwards, stock prices rise and TOPIX hits 1632.
Now how many futures should you sell in order to effect dynamic hedging?
The prices and deltas of a put with one year to maturity when TOPIX is at
1632 are as follows:
(iii) The put prices and deltas given in the table for Question (c)(ii) above are the
figures given an estimated volatility of 15%. Explain what the results of
dynamic hedging would be if volatility were actually greater than 15% and
TOPIX fell.
 ACIIA: June 2000
(4 points)
(5 points)
(2 points)
(5 points)
(5 points)
(4 points)
5
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
(ii)
(3 points)
(3 points)
(3 points)
(6 points)
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
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.
6
 ACIIA: June 2000
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/
Short
Number
Security
Price
Options
Delta
Option
Gamma
Option
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)
(d)
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)
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)
(ii)
A strong market rumour suggests an offer is imminent, but is not formally
announced.
A cash offer, which is expected to succeed, is announced at a price significantly
above current market levels.
 ACIIA: June 2000
(3 points)
(3 points)
7
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
payoff at maturity date:
C, if Imd < Isd
 I −I

C × 1 + md sd × P1 , if Imd ≥ Isd
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
P 1 = 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.
(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.
The bank also offers another product with the following payoff:
(9 points)
(6 points)
C, if Imd < Isd
payoff at maturity date:
 I −I

C × 1 + md sd × P2 
Isd

 , if I ≤ I ≤ I
sd
md
max
 I

−I
C × 1 + max sd × P2 
Isd

 , if I > I
md
max
(c)
(d)
(e)
8
where:
Imax = certain Index level (determined at issue date) with Imax > Isd
P2
= positive number, determined at starting date
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.
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.
Does the level of Imax have any impact on P2? Justify your answer.
(9 points)
(6 points)
(3 points)
 ACIIA: June 2000
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
deviation of
tracking error(s)
IR
Current
allocation
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 (α) column in the table indicates the expected “excess return” of the fund
(i.e. the return earned by the fund minus the benchmark return); σ indicates the standard
deviation of excess return; and “IR” is an abbreviation for “Information Ratio”, which is
defined as
α/σ.
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.
• Allocation to active manager:
• Allocation to passive manager:
i xi =
τIR i
2σ i
P x p = 1 − ∑ ix i
Note that τ 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.
(b) Pension Fund Z’s degree of risk tolerance τ is estimated at 20. Find the optimal
allocation ratios for each fund, assuming the excess returns of individual active funds
to be mutually independent.
(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?
(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.
 ACIIA: June 2000
(5 points)
(6 points)
(5 points)
(5 points)
9
Exam Guide
Question 7: Portfolio Management
(8 points)
As a portfolio manager you decide to answer a request for a proposal by a pension fund. Its
committee, responsible for the asset allocation, needs passive management relative to the
following benchmark:
• 50 % SMI (Swiss Market Index / 23 stocks)
• 50 % MSCI Europe ex Switzerland (multi-country Index / 524 stocks / 21 countries)
Assume that the pension fund portfolio will be measured against its benchmark on a
monthly basis. What is the main problem you will face when indexing this portfolio in the
long run? What potential negative impact do you expect and what positive effects, if any,
could you exploit?
(8 points)
Question 8: Portfolio Management
(20 points)
You have divided the market in 4 portfolios following 2 dimensions: Value/Growth and
Small/Large. The weight of each portfolio in the index is given. The risk free rate is 2%.
Furthermore, you have designed the following model:
Portfolios
Weight
Sensitivity to
Factor I
(Market beta)
Sensitivity to
Factor II
(Price/Book)
Sensitivity to
Factor III
(Average
capitalisation)
Small value
5%
0.85
0.8
1
Small growth
5%
0.95
1.3
1
Large value
40%
0.9
2
8
Large growth
50%
1.1
3
10
8%
–2%
0.10%
Risk premium
(a)
(b)
(c)
(d)
10
When using the APT, which portfolio has the highest expected return? Show your
calculations.
Using the APT, what is the expected return of the market and how does it compare
with the returns of the other 4 portfolios?
One of your competitors uses the CAPM. Based on the betas above, which portfolio
will he choose to maximise his expected return?
In order to diversify his perceived risk, another competitor wants to combine the
Small Value and the Large Growth Portfolios. The new portfolio should have an
overall sensitivity to Factor I (market beta) of 1. Show how much the competitor
must invest in Small Value and how much in Large Growth. The portfolio must be
fully invested and without any short sale.
(8 points)
(4 points)
(4 points)
(4 points)
 ACIIA: June 2000
Exam Guide
Question
number
1
Database references
BV o 11 – IIMR – Fi-Fo
CKB references
3.
Bond valuation and analysis
2.2.5.1 Spot rates
2.2.5.3 Forward rates
2
3
4
5
6
7
BV o 3 – SAAJ – Fi
DV o 2 – SAAJ – Fo-Fi
DV o 11 – SIA – Fi
PM o 60 – TCIP – Fi
PM o 3 – SAAJ – Fi
PM o 56 – TCIP – Fi
2.4.1
Basic price/yield relationship
2.5.2
Duration and modified duration
3.
Bond valuation and analysis
2.4.3
Valuation of coupon bonds
2.5.2
Duration and modified duration
4.
Derivatives valuation and analysis
2.1
Futures
2.1.5
Hedging strategies
4.
Derivatives valuation and analysis
2.2
Options
2.2.6
Options strategies
1.
Portfolio management
4.3
Derivatives in portfolio management
4.2.2
Portfolio insurance
1.
Portfolio management
4.1
Managing an equity portfolio
4.1.1
Active management
4.1.2
Passive management
4.1.3
Combined strategies
1.
Portfolio management
5.1
Performance measurement and evaluation
5.1.3
Relative investment performance
5.1.3.2 Indices and benchmarks
8
PM o 52 – TCIP – Fi
 ACIIA: June 2000
1.
Portfolio management
1.5
Arbitrage pricing theory
1.5.4
Arbitrage pricing theory
11