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Discipline of Finance
FINC3012 – Derivative Securities
Assignment
1. Due date and time: 18 October 2023 by 23:59.
2. Please include a cover sheet containing your group name and the student number of each
member in your group. Cover sheet does not contribute to the total number of pages for the
assignment.
3. Assignments must be typed and submitted via Turnitin through Canvas.
4. Maximum length is 10 pages with font size 11pt or larger. Cover sheet and references (if any)
do not contribute to the assignment length.
5. This is not intended to be a formal report, so please do not write background information,
definitions presented in lectures, and other facts not explicitly required in answering the ques-
tions.
6. Please keep your answers as brief as possible and only write information explicitly relevant to
the questions asked. Marks will not be awarded to (parts of) answers not explicitly relevant
to the questions asked nor will marks be based on the lengths of the answers. If you do not
follow this instruction, you may exceed the maximum page count for the assignment.
7. Penalty of 5% per calendar day, or part thereof, will apply to late submissions.
8. Do not attach printouts of Excel spreadsheet to the assignment.
Background Information
The purpose of this assignment is to introduce you to a real world derivative that is currently
offered by a major Australian bank. It is an example of a total return swap (TRS) and is based
on an interest rate index and constructed as follows:
A. At inception of the index, $1,000 is deposited for 4 weeks at the prevailing BBSW1M rate.
B. For each of the next 3 weeks, additional $1,000 deposits are made, each for 4 weeks maturity
and at the prevailing BBSW1M rate at the time. This results in 4 separate deposits, each with
initial amount $1,000 and maturity of 4 weeks, but with maturities offset by 1 week.
C. As each deposit matures, the total amount of the deposit including interest is rolled over into
another 4 week deposit at the prevailing BBSW1M rate.
D. On any given date t, the value of the portfolio of deposits is computed as follows
Vt =
4∑
i=1
Ai(1 +Ri · 28/365)
1 +Ri · di/365 ,
where Ai are the current deposit amounts, Ri are the BBSW1M rates at which the i-th deposit
was made (or rolled over), and di is the remaining number of days to maturity for the i-th
deposit.
E. The index value at inception is set to I0 = 1, 000, and updated each day according to the rule
It+1 = It · Vt+1/Vt.
2F. For simplicity, assume that the second to fourth $1,000 amounts do not earn any interest until
they are deposited, so that Ri = 0 for these amounts in the above expression for Vt over the
initial 4 week period.
You may assume that the index is maintained and published daily by a well-known financial data
vendor, and has been in existence for well over 10 years.
Suppose you work on an interest rate desk at a bank, and a client, who is a fixed income fund
manager, wishes to enter into a TRS where they receive the return on the above index every 4
weeks on the notional amount of $100,000,000. The client will give the bank $100,000,000 at the
start of the TRS, and the bank must return the $100,000,000 to the client at the end of the TRS.
You have been given the task of analysing the risks associated with the TRS and to propose a
method for managing the risks. After some investigation, you discover that the bank’s treasury
department will pay BBSW1M plus 18 basis points on any cash you leave with them for 4 weeks,
and will pay the official cash rate of 1.5% for overnight deposits. You realize that you can mimic
the 4 deposits underlying the index with the bank’s treasury, and hence potentially make the 18
basis point margin the treasury pays above the BBSW1M rate.
You have collected the BBSW1M rate each week for the past 4 years, and have decided to test your
idea with this data. Please download the file BBSW1M.xlsx from Canvas that contains (fictitious)
BBSW1M and official cash rates to use for the assignment. You may assume that the value of the
index 4 years ago was I = 1, 386.82, and the notional amounts, the times to maturity, and the
BBSW1M rates for the 4 deposits underlying the index at that time were as follows:
Deposit number Notional Weeks to maturity BBSW1M
1 1,324.24 4 1.7634%
2 1,316.15 3 1.7628%
3 1,346.82 2 1.7626%
4 1,362.90 1 1.7701%
Note that “Week 0” in the file BBSW1M.xlsx corresponds to the time at which Deposit number 1
in the above table has exactly 28 days to maturity.
For overnight deposits with treasury, you may assume for simplicity that the interest earned over
n weeks is given by the expression
Interest = A
(
1 +R · 7365
)n
−A,
where A is the deposit amount and R is the official cash rate, so that it is weekly compounded.1
You realize that there are 3 distinct stages, with different risk characteristics, that make up your
strategy, viz. “entry” stage, “continuation” stage, and “exit” stage. You may assume that the
value of the deposits you have with the treasury can be valued similarly to the way the portfolio
in the index is valued so that
V¯t =
4∑
i=1
Ai(1 + (Ri +m) · 28/365)
1 +Ri · di/365 , (1)
where m is the margin above BBSW1M paid by the treasury.
1In practice, interest on overnight deposit is compounded daily, but in order the keep calculations as simple as
possible, it has been made weekly compounding for the purposes of this assignment.
3Questions
If a question asks you compute numerical values, then you must provide a brief explanation of how
you computed these values to earn full marks. If you do not provide any explanation and your
values are incorrect, then you will not be awarded any marks. [55 marks]
1. Using the data in the file BBSW1M.xlsx and the index data in the table above, compute the
values of the portfolio underlying index and hence the index values for each week given in the
file. Fill in the table below with the values you computed:
Week 0 4 12 199
Vt – – – –
It – – – –
Round the portfolio values to 4 decimal places, and the index values to 2 decimal places in the
table. [10 marks]
2. Analyse the initial entry stage of the hedging strategy by following the steps outlined below.
Recall that any amount that has not been deposited already for 4 weeks at the BBSW1M rate
must be deposited at the overnight rate. [30 marks]
(a) Since it is important to match the relative sizes of the 4 deposits underlying the index, you
need to be careful when dividing the total amount into the 4 constituent deposits in the
initial entry stage. Assuming that the official cash rate remains constant at 1.5% over any
4 week period, and noting that any amount not deposited for 4 weeks must be deposited on
a weekly basis at the overnight cash rate, explain how to compute the 4 notional amounts
into which you need to divide the $100,000,000. For simplicity, you may also assume that
one of the deposits has just been rolled, so that it has 4 weeks to maturity. [8 marks]
(b) Using the results from part (a), compute the 4 hedge notional amounts that you need to
divide $100,000,000 into at Week 0 and Week 195. Note that to compute the hedge notional
amounts at Week 195, you will first need to roll the 4 deposits underlying the index from
Week 0 to Week 195. [8 marks]
(c) Compute the profit/loss over each of the 196 rolling 4 week historical periods, assuming
that the strategy is initiated at the beginning of the period. That is, paying the return
on the index to the client and earning the return on the deposits with treasury where
the terminal value of the hedge portfolio is computed using V¯t in (1). Include in your
answer the interest paid to the client, the terminal value of the hedge portfolio V¯t, and the
profit/loss on the TRS for the initial and the final 4 week periods. [8 marks]
(d) Compute the mean and the standard deviation of the profit/loss from the 196 historical
periods, and plot the histogram with minimum profit/loss -$2,500, maximum $7,000, and
with increments of $500. [3 marks]
(e) By analysing the data, briefly describe and explain the situations under which the entry
stage of the strategy leads to profit and to loss. [3 marks]
3. Analyse the continuation stage of the hedging strategy by following the steps outlined below.
For this stage, you may assume that the 4 hedge deposit amounts with treasury are in the
same proportions to the corresponding deposits underlying the index. In order to ensure that
the notional amounts for the 4 hedge deposits remain consistent with those underlying the
index, assume that only the component of interest earned at the BBSW1M rate is rolled for
each hedge deposit, and the component of interest earned from the treasury margin of 18 basis
4points is not rolled at the maturity of each deposit, but removed instead and deposited weekly
at the overnight cash rate. This means, for example, that at the start of each 4 week period,
the effective value of the hedge portfolio is
V¯tstart = α
4∑
i=1
Ai(tstart) · (1 +Ri(tstart) · 28/365)(1 +Ri(tstart) · di(tstart)/365) ,
where Ai(tstart), Ri(tstart), di(tstart) are the notional amount, BBSW1M rate, and the number
of days to maturity, respectively, for the deposit underlying the index that has i weeks to
maturity at tstart, and α is the scaling factor to ensure that Vtstart = 100, 000, 000. The value
of the hedge portfolio at the end of the 4 week period can be approximated as
V¯ ?tend ≈ α
4∑
i=1
Ai(tend) · (1 +Ri(tend) · 28/365)(1 +Ri(tend) · di(tend)/365)
+ α
4∑
i=1
Ai(tstart) ·m · 7i365 ·
(
1 + 0.015 · 7365
)4−i
+ α
4∑
i=1
Ai(tend) ·m · 7(4− i)365 .
Note that V¯tstart/α were computed in Question 1 for all tstart, and the first term in V¯ ?tend has
the same form as V¯tstart . Note also that the return on the hedge portfolio is independent of α,
and so we do not need to compute α for the purposes of this question. [18 marks]
(a) Provide a brief justification for the approximation of V¯ ?tend given above. [3 marks]
(b) Compute V¯ ?4 /α and V¯ ?199/α to 2 decimal places. [4 marks]
(c) For each of the 196 rolling 4 week historical periods, compute the profit/loss from main-
taining the strategy over the period. That is, paying the return on the index to the client
and computing the return on the hedge deposits using V¯tstart and V¯ ?tend for each period. Fill
in the following table with the profit/loss for the first and final 4 week periods, and the
mean and the standard deviation over the entire 196 historical periods. [8 marks]
PnL1 PnL190 mean std. deviation
– – – –
(d) Describe and explain the performance of the hedging strategy over continuation periods.
Is it consistent with what was expected? [3 marks]
4. Analyse the exit stage of the hedging strategy by following the steps outlined below. Note that
during the exit stage, the hedge deposits that mature must be reinvested at the official cash
rate on a weekly basis rather than being rolled over for another 4 week period since the deposit
amounts must be returned to the client. To be more specific, assume that the value V¯tstart at
the beginning of the exit stage is given by the expression in Question 3, but the terminal value
is now given by [15 marks]
V¯ ?tend = α
4∑
i=1
Ai(tstart) · (1 +Ri(tstart) · 28/365) ·
(
1 + 0.015 · 7365
)4−i
+ α
4∑
i=1
Ai(tstart) ·m · 7i365 ·
(
1 + 0.015 · 7365
)4−i
.
5(a) Compute V¯ ?4 /α and V¯ ?199/α to 2 decimal places. [4 marks]
(b) For each of the 196 rolling 4 week historical periods, compute the profit/loss from exiting
the strategy over the period. That is, paying the return on the index to the client and
computing the return on the hedge deposits using V¯tstart and V¯ ?tend for each period. Fill in
the following table with the profit/loss for the first and final 4 week periods, and the mean
and the standard deviation over the entire 196 historical periods. [8 marks]
PnL1 PnL196 mean std. deviation
– – – –
(c) By analysing the data, describe and explain the situations under which the exit stage of
the strategy leads to profit and to loss. [3 marks]
5. Based on your findings from the above analyses, and other issues that may not have been
considered, answer the following questions: [7 marks]
(a) It was observed that the entry and exit stages of the hedging strategy poses greatest risks.
What could be done to limit the impact of the potential losses that may be incurred over
these stages? [2 marks]
(b) Identify and explain a risk that was not considered in the above analysis. [2 marks]
(c) Suggest an alternative hedging strategy for the TRS, along with its advantages and/or
disadvantages over the proposed strategy. Please note that the alternative strategy just
needs to be “reasonable”, so do not spend too much time trying to come up with a perfect
alternative hedge. [3 marks]