Group Assignment FINC3019 –
Investment Group 8
Underlying Expectation:
Our expectation for the 3rd of May was that the RBA would keep the cash rate steady at 4.75%.
However, we expected the RBA would flag future rates increases later in the year and probably by
the September quarter. Moreover, we predicted that the yield curve would flatten over the period
due to mean reversion, the underlying cause of recent interest rate changes.
Our expectations were based on the assumption that the Efficient Market Hypothesis holds, at least
in the semi-strong form. This would mean that the yield curve on the medium-to-long term yields
was expected to flatten as the market factors in the possibility of a interest rate hike in the
September quarter due to the economic indicators such as a high $AUD and imported Chinese
inflation reflecting this possibility.
These expectations formed the basis of our strategy and assumptions concerning the expected
performance of our bond portfolio.
Rationale for the Expectation:
The rationale behind the expectation of unchanging interest rates on the 3rd of May was based on
the circumstances occurring in Queensland with its downturn in macroeconomic indicators following
the natural disasters. Further as reported by the Australian Financial Review (2011) there has also
been an increase in the sensitivity of the Australian labour market with higher unemployment rates
than what was anticipated. The recent increase in the AUD to above USD 1.1 has acted to slow down
(non mineral) exports and increase consumption of imports which has reduced economic growth
overall.
Hence, it was expected that the RBA would not raise interest
rates due to the potential implications on the economy given
the present state, such as an increase in unemployment and the
stagnation of growth. According to the A.F.R. (2011) the RBA
was not expected to increase interest rates in response to the
small spike in inflation for the recent economic quarter – this
can also be justified through the fact that the RBA target for
inflation is within 2-3% as an average over the course of the
cycle, therefore allowing for small spikes and dips to occur in
the short run. This expectation can also be justified through the Phillips Curve, assuming that this
relationship holds, in order for the RBA to decrease unemployment it would have to allow some
inflation growth; thereby not increasing interest rates at the present point in time.
We expected the RBA would increase the cash rate in the September quarter due to a record
increase in terms of trade and imported inflation generated from both China and the US along with
the extra stimulate pumped in the economy with the Queensland flood reconstructions.
Based on these assumptions and analysis we expected the yield curve to flatten over the long run;
whilst the short run interest rates remain unchanged in the immediate term. Short run interest rate
changes are largely driven by temporary factors in the economy such as the mining boom and other
strong macroeconomic shocks (Shann 2011). Whilst such shocks have a large effect on short term
rates, they may be seen to be largely irrelevant in determining long term rates. Evidently, our
expectation that the yield curve will flatten over the medium and long term is formulated by the
expectancy that yield curve will revert to its mean.
Further, we assume frictionless markets in all our calculations and hence no fees for short selling or
purchasing.
The Strategy:
Faced with such circumstances and expectations our
strategy involved the creation of two bullets through
investment in TB123 and TB128 (effectively creating a
barbell strategy) as well as through the short sale of
TB119 and the creation of a ‘cash neutral butterfly’
with TB117 and TB128.
Bond
Weight
Dollar Value
TB117 7.0902% of $120 million
TB123 58.3333% of $120 million
TB128 34.5765% of 120 million
∑
100% of 120 million
$8,508,200
$70,000,000
$41,491,800
$120,000,000
Strategy Distribution 1
The two bullets were constructed by having $70 million invested in TB123 and $30
million into TB128.
The ‘cash neutral butterfly’ was made by short selling TB119 to the
value of $20 million thereby effectively increased our overall bond
portfolio value to $120,000,000. The $20 million was distributed
across the TB117 ($8,499,500) and TB128 ($11,500,500).
NB: Please refer to Appendix 1 for above
calculations
Rationale behind the chosen strategy:
Aim:
-
-
The $70 million bullet in TB123 was meant to lower the overall duration of the portfolio
through its large weighted impact on the overall duration.
The $30 million bullet in TB128 was aimed to increase the overall convexity of the
portfolio through its weighted impact.
o Together the two would work to create a barbell and offset each other’s risks by
increasing the degree of diversification within our portfolio.
The cash neutral butterfly created through the short selling of the TB119 for $20 million
was incorporated as a safety mechanism to lower overall risks of the portfolio if a
parallel movement of the yield curve occurred during the period.
The expected results were that:
-
We would hold the short term bond (TB117) until maturity. If held to maturity we would
roll it over at a higher rate and generate excess returns.
The investment in the long bond as bullet TB128 was a hedge against unfavourable and
unexpected interest rate fluctuations. As a long term and highly convex bond, TB128
would work to minimise the effect of extensive shifts in the yield curve.
-
-
-
The fact that the interest rates were expected to stay the same, the investment in TB123
was to make it a ‘safe’ asset in the portfolio as it is close to maturity, therefore having a
guaranteed capital value. Given that our expectations manifested this bond would be
used to ‘ride the yield curve’ and be sold just prior to the anticipated interest rate
increase, thereby extrapolating higher returns.
Further, the cash neutral butterfly would minimise losses in case our expectations were
incorrect and the yield curve experiences a parallel shift. However, if the expectations
were correct, the shorter wing of the butterfly composed of TB117 would act as a zero
coupon bond with safe capital value; thereby further lowering the overall risk exposure
of our portfolio.
Together these bonds made a portfolio and compared to the benchmark had a lower risk
level via lower duration and a higher degree of curvature. These features were meant to
allow us to extrapolate abnormal returns, whilst maintaining low risk through the
structure of the investment strategy and offsetting factors.
Following an analysis of the bonds, the respective bonds chosen and analysed as follows:
Bond
TB117
TB123
TB128
Coupon
5.75%
5.75%
5.75%
Gross Price
101.875
103.599
103.011
Chosen Bonds Summary Table 2
McCauley Duration
0.0012
0.9396
8.3115
Convexity
0.0711
0.5476
81.8938
Modified Duration
0.0012
0.9172
8.0898
$ Duration
0.1203
95.0184
833.3423
NB: Please refer to Appendix 2 for
above calculations
Please note that we have ruled out any possibility of ‘bond picking’ based on underpricing in the
market by making the assumption that the Efficient Market Hypothesis holds at least in its semistrong form.
Further, by accepting the view that the Australian government is a sovereign one with the ability to
‘print’ its own money (expand the balance sheet of the central bank) and is able to change taxation
policies – we have neutralised the argument of risk associated with the CGB’s. Essentially these
bonds, both in our portfolio and the benchmark, are denoted in $AUD and the government has the
ability to print new funds or increase taxes, thereby repaying its liabilities ceteris paribus.
Analysis of the chosen bonds:
The decision to invest in TB123 and TB128 for our two bullets was effectively to extrapolate the
relative advantage of combining their duration and convexities. The duration on the TB123 bond is
0.9389 while the duration of the TB128 bond is 8.22. Given that with longer duration comes greater
interest rate risk and an expectation that the market will factor in an increase in interest rates in the
near future a 70-30 split between these two bullets made justifiable sense. TB123 was chosen ahead
of the shorter TB117 because of its potential greater volatility being the shortest bond on offer.
Nevertheless, assuming that the Efficient Market Hypothesis holds we expected dynamic reactions
of the yield curve in the medium-to–long term parts.
Similarly, with the convexities of these bonds, a convexity of 1.295 for the TB123 bond as opposed to
the convexity of 81.5 for the TB128 bond highlights their vast disparities. The advantage of
combining these convexities is that we will be able to maximise our gains and minimise our losses to
some extent, something which could not be done by purely concentrating investment in one short
term bonds. By investing a portion of our funds in a bond with a higher convexity, it allowed us to
mitigate some of our capital losses in the event of yields increasing. TB128 was chosen ahead of its
nearby counterparts for this reason as it provided more of a cushion in the event of yields changing
with its relatively high convexity figure of 81.5.
The idea behind investing in TB117 and TB128 as our butterfly wings was to hedge ourselves across
the yield curve and to further work as a ‘security’ aspect of our strategy. In effect, although we were
aiming to make an active fund portfolio, we feel that this should be done with minimum potential
risk and volatility; therefore this justifies our strong focus on several smaller strategies coming
together in the aggregate under one to mitigate each other’s losses and potential exposures.
Analysis of the barbell:
A barbell was constructed through a long position in TB123 and TB128 with the strategic aim of
purchasing and holding. As argued by Mauro (2011) this strategy allowed a conservative method for
the management of interest rate volatility faced with uncertain potential upward movements. Even
though we expected that the RBA would not increase the cash rate on the 3rd of May, our
expectation was that the market would have factored in the expectations of increased interest rates
in the September quarter (assuming that Efficient Market Hypothesis holds in semi-strong form).
This in effect would have altered the curvature of the yield curve at the medium-to-long term
maturities.
The creation of the barbell also worked to provide our portfolio with greater diversification,
compared to holding a single bullet; thereby spreading the risk within the portfolio. Furthermore,
the barbell combination allowed us to benefit from yield enhancement as it effectively generated a
higher yield for arguably the same level of risk. The assumption of the same level of risk is that the
bonds, although different in maturities, were issued by the same sovereign government and
denoted in the same currency – this effectively allows us to assume equal probability of default on
the two securities ceteris paribus.
Furthermore, the barbell allowed us to undertake speculation on the shape of the curve in order to
profit from the changing in the shape of the curve that were expected with the market factoring in
the potential rate hike in June this year.
Another factor that went into the construction of our barbell was the ensuring of duration neutrality
and maximising convexity, thereby allowing parallel shifts in the curve to be profitable.
Analysis of the butterfly:
Through the use of TB117 and TB128 we have managed to create a ‘cash neutral’ butterfly by shortselling TB119 to the magnitude of $20 million. The allocation of the generated income between
TB117 and TB128 were 42.5421% in the former and 57.4579% in the latter.
Through such a strategy we have managed to protect our butterfly against small parallel shifts in the
yield curve. In the aggregate, the effect of such a precautionary aspect of the overall strategy was to
minimise any potential losses to our portfolio that may have occurred if our expectations turned out
to be incorrect.
Nevertheless, we expected the butterfly to also add value to our overall strategy – if our
expectations of the medium-to-longer part of the yield curve would factor in the expected interest
rate hike in June, then the butterfly would generate profit. Therefore, the higher concentration of
the overall investment was in the latter bond – thus tailored to the expected changes in the
curvature of this part of the yield curve (under the assumption of the Efficient Market Hypothesis).
It is important to note, that the rationale behind such a precautionary measure is based on the fact
that, although our main aim is to create an active fund whose performance would be greater than
that of the benchmark, we also aimed to do so with minimised potential risk levels.
Analysis of the overall portfolio:
By combining the two sets of strategies we managed to create a portfolio of $120 million. In effect
the characteristics of our portfolio were:
Portfolio Characteristics
Duration
Convexity
Portfolio Characteristics 3
3.440
28.686
NB: Please refer to Appendix 3 for the
calculations
Evidently, by combining these bonds in a portfolio we have counteracted the high Macaulay
Duration of TB128 using the relatively lower Macaulay Durations of TB117 and TB123. Therefore
having a lower Macaulay Duration overall it has reduced the amount of time needed to recover the
funds invested in the portfolio – if held to maturity. This is beneficial as we predict rates to increase
in the future, and a lower duration portfolio performs better under these conditions.
Furthermore, through the weighted incorporation of the given bonds we have increased the overall
convexity of our portfolio to 28.686 – evidently here we have managed to use the weighted impact
of TB128 to account for the low convexities of TB117 and TB123.
The portfolio was developed around the expectations that there would be a lack of movement to the
interest rates in the short run as well as the factorisation of yield curve curvature being changed at
the medium-to-long rates. Hence the relatively high convexity would enhance any upward gains and
minimise any downward losses.
Comparison between Portfolio and Benchmark Characteristics:
The Benchmark against our portfolio is
being measured is the equally weighted
average of all the bonds on issue:
-
-
Benchmark Characteristics
Macaulay Duration
4.083
Convexity
26.659
Given that the Macaulay duration of the benchmark is the equally weighted duration of all
the bonds which comprise it, the Benchmark (Macaulay Duration) = 4.083
Compared with our portfolio; Portfolio Macaulay Duration = 3.440
o Therefore our portfolio presents a shorter time needed
to recover
initial3 for above
NB: Please
refer to the
Appendix
investment – hence minimising the risk potential faced
by the investor over the
calculations
investment horizon
The Benchmark Convexity = 26.659
Our Portfolio Convexity = 28.686
o
-
Evidently our portfolio has a higher convexity and therefore more potential to gain
on upward movements in the prices of the bonds
Nevertheless for analytical purposes it needs to be noted that both the benchmark and our
portfolio face the same systematic risk because they are both composed of securities issued
by the same entity – the Australian government.
Discussion of Risks:
The main risk which was faced by our portfolio is ‘active risk’ – which represents the tracking error.
Given that our aim was to attempt to beat the benchmark, we expected a relatively high tracking
error. By assuming frictionless markets and hence no transaction costs, the potential differences
between our portfolio and benchmark were the implications of differing weights and inclusion of
different bonds.
TE = √𝜎^2(𝑅𝑝 − 𝑅𝑏) ; therefore our tracking error was 0.16% - this reflects the fact our final results
were not significantly different from that of the benchmark. Whilst this means that we did not
succeed in generating higher returns, it needs to be noted that our returns were generated at a
lower risk level (as discussed above). Nevertheless, a low TE does reflect the fact that portfolio
managed to follow the benchmarks developments closely.
Errors in information processing as part of the behavioural risks are also of significance and need to
be discussed. Due to the fact that we invested a large portion of our funds (70%) in one of the
shortest bonds (TB123) it can be postulated that we placed excessive weight on recent events in
economic expectations - referred to as ‘memory bias’ (Bodie, Kane & Marcus 2011). Consequently,
one can argue that our portfolio makeup was overly focused on these short term expectations.
Evaluation of Developments from 2nd May – 13th May 2011:
From the table below the difference in returns between the benchmark and the portfolio are visible.
NB: excluding
transaction
costs
Benchmark
Portfolio
Initial Capital Invested
$100,000,000
$100,000,000 (with short sell of
$20M)
Final Dollar
Value
$100,505,653
Percentage return with
leverage
0.5057%
$120,407,923
0.4079%
NB: Please refer to Appendix 4 for above
calculations
Pricing of the Bonds:
Daily bond yields were obtained from the Reserve Bank of Australia (RBA) website (Reserve Bank of
Australia 2011). These are the average prices reported by bond dealers at closing, so are a fair
representation of a CGB’s daily yield. We have used t+2 settlement rather than the convention of t+3
(AFMA 2008) to determine a settlement date of 27/04/2011. This is due to the Easter holiday period.
T+3 trading would require the bond purchases to occur on the 21/04/2011 and 6 days of interest
would accrue, greatly skewing the results - particularly considering we are only examining a two
week period. Given the unusual circumstances we believe this assumption is justified. It is assumed
that as we are purchasing AAA rated Government securities (AAP 2011a), they are risk free and so
no distress provisions need to be included . We further assume the bonds will be redeemed for the
full value of $100 on maturity. We assume biannual payments as this is the market convention
(AFMA 2008). Prices were calculated in Excel using the “Price” function with an actual/actual day
count. While the Australian convention is actual/365 (AFMA 2008), we have used actual/actual for
its greater accuracy and consistency. This is highly important as we are valuing these bonds over a
two week period only, so a missing day can have an extremely significant valuation impact. Excel’s
“Price” function only gives us the capital price without any accrued interest. To calculate this we
have calculated the days from the previous coupon and multiplied this by half the coupon payment.
Adding the accumulated interest to the capital price we determine the gross price of each CGB.
Prices have been recalculated daily for each tranche of bonds to reflect the increased amount of
accrued interest.
Exhibit 1 – the Yield Curve over Time
5.600
5.400
5.480 5.440 5.440
5.465
5.415
5.455 5.425 5.480
5.395 5.405
4.975
4.890 4.855 4.905 4.880
4.745 4.735 4.750 4.720 4.745
4.995
5.200
5.000
4.800
4.600
4.400
4.200
Exhibit 2 – CGB Yield Curve Shifts over the period
4.950 4.980
4.905 4.905
4.740 4.710 4.710
4.690 4.690
TB117
TB123
TB128
5.600
5.400
5.200
5.000
Yield Curve 27/04/2011
4.600
4.400
Exhibit 3 – Comparative Portfolio Analysis
Portfolio Value
600000
500000
Profit
400000
300000
200000
100000
0
Exhibit 4 – Relative Performance of CGB Securities:
Exhibit 5 – The Butterfly Performance over the period 27/04 to 13/05
Benchmark
01-Apr-22
01-Nov-21
01-Jan-21
01-Jun-21
01-Aug-20
01-Mar-20
01-May-19
01-Jul-18
01-Dec-18
01-Feb-18
01-Apr-17
01-Sep-17
01-Jun-16
01-Nov-16
01-Jan-16
01-Aug-15
01-Mar-15
01-Oct-14
01-May-14
01-Jul-13
01-Dec-13
01-Feb-13
01-Sep-12
01-Apr-12
01-Nov-11
Yield Curve 13/5/2011
01-Jun-11
4.200
01-Oct-19
Yield Curve
4.800
Profit/Loss $
Butterfly Performance
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
-5000
-10000
Exhibit 6: ASX Movements 27/04/2011-13/05/2011
Evaluation of Trading Strategy from 2nd May – 13th May 2011:
By investing a significant portion of our portfolio in the short-term bond TB123 we were expecting
rates to remain relatively stable during the two week period which would allow us to benefit the
structure of our strategy. The investment in the long-term bond TB128 was undertaken with the
purpose of hedging. If long term yields were to flatten or slightly fall we would profit by receiving a
capital gain due to the price appreciation.
A butterfly across the yield curve was also another hedging instrument used in our portfolio. As a
result we invested in both the shortest and longest bonds to hedge ourselves across the entire yield
curve. We expected to profit from a flattening of the yield curve in the long run and hence why a
cash-neutral butterfly was included. Therefore, once again this is reflective of the fact that although
we aimed to maximise returns, our strategy desired to lower our overall risk exposure through its
internal interactions.
Our portfolio succeeded in outperforming the index for 40% of the review period while exhibiting
lower risk (as measured by convexity). However, the final values paint a less flattering result, with a
20% underperformance over the period.
Arguably our first mistake was placing 58% of the portfolio in TB 123. While we were correct in our
prediction that cash rates would increase soon, we significantly misjudged the speed at which this
would occur. Exhibit 4 demonstrates that our first bullet of $70m was a “blank”, returning only
0.16% against an average return of 0.51%. Exhibit 2 shows the unusual movement in the yield curve,
a downward shift coupled with a general flattening. TB 123 behaved in a manner contrary to our
expectations. Indeed it was the only bond to exhibit an increased yield (overall we made a profit due
to accrued interest). Our mistake was playing in a crowded trade – consensus economic forecasts by
11 of 13 economists anticipated a rate rise in the September quarter (AAP 2011b). TB123 due 28th
April 2011 was the most suitable bond for investors to purchase and rollover to capitalise on this
expectation. However, a bullish RBA economic assessment has increased the probability of a June
rate rise to at least 50% (Bassanese 2011). At the short end of the yield spectrum, this has resulted in
bond traders swapping out of longer dated bonds (AAP 2011c) including TB 123 into cash (with zero
duration) and short term treasuries such as TB 117. Rather than trading at a premium to the other
medium term bonds, Exhibit 2 shows TB 123’s yield is now on par due to marginal investors
switching out of this bond.
However, our 30% weighting in TB 128 has significantly offset the negative performance of TB123.
Exhibit 4 reveals TB 128 was the best performing bond over the period, generating a return of
0.96%. TB128’s higher convexity of 81.89 means that increased interest rates will have a reduced
effect on price; lower rates will have a more significant price effect. Following a downwards
movement in the yield curve, the TB128 price increased very significantly. Constructing a barbell
across the yield curve has acted to reduce underperformance when the market behaves contrary to
our expectations, while allowing for outperformance should the market act in the manner expected.
The two most significant misjudgements in our trading strategy was the direction and timing of the
interest rates. Our expectation was that the RBA would take no action in May, which proved to be
correct. However, our view that rates would not increase until the September quarter was put into
question by a very high march inflation result and the wording of the monetary policy statement
(Mitchell 2011). Our second misjudgement was the direction of interest rates. Our expectation was
that the required yield would rise to compensate for an impending interest rate increase. Indeed,
given the RBA recently signalled higher short-term interest rates as soon as June (Bassanese 2011;
Rollins and McDuling 2011), it seems unusual that the yield curve would decrease and flatten. We
postulate this may have occurred due to recent market movements. Exhibit 6 shows that over the
review period the ASX declined from above 4900 to 4694, or almost 4.2%. This correction is largely a
result of the $AUD reaching record highs (AAP 2011) and the impact this will have on listed
companies, particularly those with substantial foreign assets. Across the investment horizon,
investors have moved from risky securities into safer assets including CGB’s. This has pushed down
yields across the curve. This has had a detrimental short-term effect on our portfolio’s valuation,
however it could be argued these are temporary factors that will quickly reverse when investors
regain confidence.
Our cash neutral butterfly has performed well in generating a profit of $10200 despite a net
investment of $0. This butterfly was designed to have a negative return for a steepening and a
positive return for a flattening yield curve, as the majority of the dollar duration is contained in the
right wing. However, our rationale for this strategy was to capitalise on medium-term
macroeconomic factors and a belief that the yield curve is mean reverting. If transaction costs were
present, this trading strategy may not have been profitable to hold over the medium term. However,
on a risk-weighted basis this strategy has added significant profits without a consummate increase in
risk. Furthermore, it has allowed us to profit from expected shifts in the interest rate curvature
without needing to invest any net capital.
We speculate that over the medium term the CBG yield curve will flatten yield curve is a form of
mean reversion (historically, Australia has always had quite flat bond yields in comparison to the
steep yield curve currently on offer .The RBA rate rise would push interest rates to their ‘normal’
level of approximately 5%. This would be a powerful signal that the economy is returning to typical
conditions, and therefore a ‘normal’ yield curve should prevail. However, the sudden downward
shift in absolute yields seems unusual given an imminent rate rise.
Performance Measures:
The performance measure that we have chosen in order to evaluate the overall performance of our
portfolio compared with the benchmark is the Sharpe’s Ratio as it conveys the active return above
that of the risk free rate and standardises it with the standard deviation.
S = [0.004079 – 0.005057]/0.0016
S = - 0.6113
Therefore this measure would reaffirm that we have underperformed the benchmark’s level of
returns. Nevertheless, given that we were dealing with debt securities, and not with equity, a more
accurate and more appropriate reflection of the overall performance of our portfolio compared to
the benchmark is given by the Tracking Error. This measure is specifically made as a reflection on the
performance in debt markets of portfolios compared to benchmarked targets.
Given that we are an active fund we wanted a relatively high tracking error. However, due to our risk
aversion the tracking error we ended up with was only 0.16%. This low tracking error reflects the
fact that our portfolio returns and performance have closely followed the benchmarks performance.
On the other hand, as discussed earlier, our portfolio had comparatively less risk than the
benchmark due to the relatively lower duration and higher convexity. Therefore, if one was to
undertake to draw parallels in analysis between our portfolio and the benchmark through
Markowtiz’s Efficient Portfolio Theory it can be argued that the lower return that we gained from
our portfolio came about as a result of the lower embedded risk, therefore justifying a lower level of
compensation.
Final Outcome of Portfolio and Market Performance:
Overall the strategy performed as following

Overall profit of $407,923


Nevertheless, Benchmark Profit $505,653
o The 70% short end of yield curve bullet underperformed
o But most of its losses were neutralised by the performance of the 30% longer
maturity bullet
o The ‘cash neutral’ butterfly further limited losses and worked to contribute to the
overall profit
Evidently, whilst we did not beat the benchmark performance, we can conclude that our
portfolio was exposed to less risk overall. This is reflected in the relatively lower average
duration and higher convexity. Therefore, whilst we may have underperformed the
benchmark by approximately 19.33%, our strategy involved less risk and in absolute terms
still made a positive return.
Potential Changes and Improvements that could be made:
With the performance of our portfolio, set in the background of actual changed in the market and
development of the yield curve; it becomes evident that the best strategy to have been
implemented during this period was a greater concentration of funds in the longer term maturities.
Even though our portfolio generated a positive return, this was not added by our large concentration
of $70 million in the short term bond TB117 – even though we expected that its low convexity
(0.1194) would have cushioned any negative movements against the portfolio set up. However, the
benefits of having such a bond in ones portfolio, that perhaps has a longer holder period than 1
week, is that the bond has a very low duration, therefore the investor would have been able to
recover their investment in the asset relatively fast – thus decreasing the overall risk faced in regards
to uncertainty of cash flows.
Other improvements that could have been undertaken in order to increase the overall success of the
portfolio include greater research into the performance of certain bonds and their behaviour over
time by the group. There also needed to be a greater incorporation of inflation expectations both
domestic and abroad in order to provide a more accurate reflection about the potential trajectory of
interest rates in the future. This could have been done through the study of differences in yields on
inflation-indexed bonds and conventional bonds in order to allow some basis for the formulation of
inflationary expectations. This way the breakeven inflation data could have provided some
information about the potential future movement in inflation as well interest rates.
Further, greater diversification within the portfolio itself would have benefited the overall
performance. This would have included, but not limited to, the inclusion of equity stocks, inflation
indexed bonds as well as the use of futures in order to hedge against possible interest rate
movements or even possibly the inclusion of some good quality (highly rates) RMBS or CDO’s. One
could argue that as the interest rates did not increase in the short-term there should have been no
increase in the default risks of the domestic RMBS.
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







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AAP (2011a). Moody's reaffirms triple-A rating Courier Mail. Brisbane, News Corp.
AAP (2011b). Aust bonds mixed ahead of rates decision. Australian Financial Review,
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AAP (2011c). RBA’s hint of rate rise weakens bonds. The Australian Financial Review,
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AFMA (2008). Debt Capital Market Conventions Australian Financial Markets Association.
Bassanese, D. (2011). Don’t ignore those RBA warning noises. Australian Financial Review,
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Bodie, Z, Kane, A & Marcus, A.J, (2011), Investments, McGraw Hill –Irwin, 9th edition,
pp.382-383
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
JP Morgan 2003, ‘ALM Advisory Global Offsite 2003’, JP Morgan, Sept. 3-4 2003.

Martellini, L., Priaulet, P., Priaulet, S., ‘Understanding the Butterfly Strategy’, R&I Notes,
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
Mauro, M (2011), Weighing the Risks, Bank of America Merrill Lynch – The Fixed Income
Digest
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Mitchell, A. (2011). Two RBA rate rises in offing as inflation fears climb. Australian
Financial Review, Fairfax.
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Government Securities." Retrieved 18/05/2011, from
www.rba.gov.au/statistics/tables/xls/f16.xls.
Rollins, A. and J. McDuling (2011). Rates on the way up despite contraction. Australian
Financial Review, Fairfax
Rosenberg, J. A., et al., ‘Derivatives Reform and Corporate Bonds’, Credit Market
Strategist, Bank of America Merrill Lynch, 2011.

Shann, E. (2011), Miners hold the key to your house rates, The Daily Telegraph, Retrieved
10/05/2011 from http://www.news.com.au/money/interest-rates/miners-hold-the-key-to-yourhouse-rates/story-e6frfmn0-1226039523405#ixzz1KbIYX22T
Appendices:
Appendix 1:
Weight in TB117 = $8,508,200/$120,000,000 = 7.0902% of $120m
Weight in TB123 = $70,000,000/$120,000,000 = 58.3333% of $120m
Weight in TB128 = $41,491,800/$120,000,000 = 34.5765% of $120m
-
With our strategy, following the short sale of TB119 of $20 million the overall portfolio value
increased to $120 million
The weights for the bullets were chosen by prioritisation and arbitrage
The weights for the cash neutral butterfly were calculated as
XS = MD(L) – MD(M)/MD(L)-MD(S) XL = MD(M) – MD(S)/MD(L)-MD(S)
Appendix 2:
The Macualey duration was calculated through an excel function “DURATION” and was determined
by settlement, maturity, coupon yield, frequency and basis. Alternatively, the Macauley duration can
be calculated through the formula
N
D=(∑
t=1
tC
N100
+
)÷P
(1 + y)t (1 t y)N
The Modified duration was simply calculated through the formula:
MD =
D
1+y
The equation for MD was then manipulated to find $duration.
MD =
$duration
P
$duration = MD x P
$D =
dP
1
C
2C
3C
NC
NM
= [
+
+
+ ⋯+
+
]
2
3
N
(1 + y)
(1 + y)
(1 + y)N
dY
1 + y 1 + y (1 + y)
The Capital Price was calculate using the “PRICE” function in excel and was determined by
settlement, maturity, rate, yield, redemption, frequency and basis.
The accrued interest was then calculated using the formula:
AI =
Days from Payment
100
x Rate x
Days in period
2
From this, the Gross price was determined as the Capital Price plus the Accrued Interest.
NB: Gross price was used in our calculations to take into account the accrued interest
Convexity Calculator
Price, coupon, life and yield are obtained directly from the bond prices derived earlier. Life is
determined using the “YEARFRAC’ function to express the number of days between the settlement
and maturity as a fraction. The basis is actual/actual to minimise any computational errors due to
missing days. The “TRUNC” function has been used to determine the number of whole years. Yield
and Face value are notionally set at 100 and 2 respectively, although these can be changed without
causing any errors. Using the “If” function and the “Trunc” function we determine if any part of the
bond needs to be treated as a zero coupon bond. If so, we adjust the PV of this first period and each
subsequent period cash flow accordingly. As Excel does not have an inbuilt derivative function we do
this manually in two steps by calculating 1+y^(t+2) and t(t+1)*CF. We then divide through to
calculate t(t+1)*CF/ 1+y^(t+2). But summing these together and dividing by 4 (as this is the second
derivative) and the bond price we can determine the overall convexity.
To use the convexity calculator, either enter the desired values or use the scenario analysis with
values already included for significant bonds.
Convexity formulae:
N
d2 P
t(t + 1)C
N(N + 1)100
= ∑
+
2
t+2
(1
(1 + y)N+2
dy
+ y)
t=1
Convexity in years =
convexity in m periods per year
m2
Appendix 3:
-
To calculate our portfolio characteristics – it was the same approach as for the benchmark –
an equally weighted average of the bonds we used and their respective weights within the
overall portfolio; therefore as percentage of weight over the $120 million value of the
portfolio
Weighted Average Duration
j
Dp = ∑ x(i)D(i)
i=1
= TB117 Dur. x Weight + TB123 Dur. x Weight + TB128 Dur. x Weight
Weighted Average Duration
= (0.070902*0.0012) + (0.9396*. 583333) + (8.3115*. 345765) = 3.440
Weighted Average Convexity
= TB117 Conv. x Weight + TB123 Conv. x Weight + TB128 Conv. x Weight
Weighted Average Convexity
= (0.070902*0.0711) + (0.5476*. 583333) + (81.8938*. 345765) = 28.686
Calculations for the Benchmark’s Characteristics:
-
Equally weighted average MacAulay Duration
Equally weighted average of Convexity
Weight of Each Bond in Benchmark
=
100%
Number of Bonds
=
100%
= 6.6667%
15
Benchmark Duration
= (0.067*1.467) + (0.067*1.887) + (0.067*2.427) + (0.067*2.824) + (0.067*3.244)
+ (0.067*3.563) + (0.067*4.515) + (0.067*4.930) + (0.067*5.627)
+ (0.067*6.495) + (0.067*7.388) + (0.067*7.591)
= 4.083
Benchmark Convexity
= (0.067*2.824) + (0.067*4.484) + (0.067*7.067) + (0.067*9.463) + (0.067*11.970)
+ (0.067*14.560) + (0.067*23.210) + (0.067*27.900) + (0.067*36.360)
+ (0.067*48.23) + (0.067*61.880) + (0.067*69.05)
= 26.659
Appendix 4:
Calculation of Returns between the benchmark and the portfolio
To find the percentage return of the benchmark we simply subtract the initial capital invested from
the final dollar value and divide this figure by the initial capital invested.
Percentage Return of the Benchmark
= (Final dollar value-Initial Capital Invested) ÷ Initial Capital Invested
= (100,505,653-100,000,000) ÷ 100,000,000
= 0.5057%
Similarly, the percentage return of the portfolio was calculated:
Percentage Return of the Portfolio
=(Final dollar value-Initial Capital Invested with 20mill shortsell) ÷ Initial Capital Invested
= (120,407,923-120,000,000) ÷ 120,000,000
= 0.4079%
Appendix 5:
Derivation of Cash and Dollar Duration Neutral Butterfly
The basic formula used is
Q* 13.1372967+w*820.3761448=20000000* 353.5569318,
Q*102.222057+w*103.980862=20000000*102.104798
In words, these two constraints represent values where the cash cost and the dollar duration of the
butterfly equals zero (hence why it is called a cash and dollar duration neutral butterfly).
Annoyingly, Excel can’t solve simultaneous equations. So, we have presented this simultaneous
equation in Matrix form. We have found the inverse of the matrix using the “MINVERSE” function
and multiplied both sides by this figure. On the left side, the inverse matrix cancels out the first
matrix to form the identity matrix. We are left with only x and y. However, multiplying the right side
by the inverse matrix using the “MMULT” function produces the percentage split between both
bonds. We have substituted this figure into our portfolio analysis.