The Zero Data Curve

Group Assignment FINC6014
Semester 2, 2019
Fixed Income Portfolio Management

1. Introduction
You are the manager of a long only Australian passive fixed income fund. Your goal is to track
an index which is an equally weighted portfolio of ACGS (see “All tickers.csv” for a list). To
minimise transaction costs you plan to hold a portfolio of only 9 securities (see “Portfolio
Tickers.csv” for a list). You intend on using factor based replication. You believe the key factors
driving ACGS returns all come from the shape of the term structure. Accordingly, you will match
your portfolios sensitivity to changes in the slope, level and curvature of the term structure
(zero/spot curve) to that of the indexes. Your assistant provides you with recent daily historical
zero curve data (“zeroData.csv”) which they obtained from Bloomberg. However, your assistant
is unsure how Bloomberg actually computed the zero data. Your Assistant also downloaded
historical prices for all the bonds. However they were not sure if you needed dirty prices, clean
prices or both.
2. Requirements
a) Estimate the zero curve: (7 marks)
To test the zero curve data provided by your assistant is reasonable, you decide to build the zero
curve for one day. Robert Scott from Schroders has provided you with his paper “A real time
zero-coupon yield curve cubic spline in Excel” which you will use as a reference to build the zero
curve by estimating a McCullough polynomial (section 3 of the paper) using a third order
polynomial (ie. a t, t 2 and t 3 terms).
a) Build the zero curve using this methodology using data on 2 nd May 2019. What are the
coefficients obtained?
b) Obtain the zero curve provided to you in the “zeroData.csv” file on the same day
c) Plot your zero curve and the zeroData.csv zero curve on the same chart
d) Why might your zero curve look different to the zero curve in zeroData.csv
b) Estimate Bond loadings: (10 marks)
You decide the data provided to you by your assistant is accurate and use this data to determine
each bonds price sensitivity to changes in slope, level and curvature.
a) First calculate the slope, level and curvature of the zero curve for each day. (For curvature
use this distance between the 10 years spot and what it would be if the zero curve was a
straight line)
b) Next you estimate the following two regressions for each of the bonds. Determine if you
should use clean or dirty prices for the regressions.
1pricelevel

123pricelevelslopecurvature

c) Discuss if these models are appropriate at explaining returns.
d) Using the results from regression plot the bonds 1

against its duration for each of the
bonds. Explain why you have the relationship you see. Repeat the process for regression
(1.2) for 2

and duration.

e) Only 3 months of data was used for this estimation, explain why using a short window of
data is beneficial. What could be one limitation of using only 3 months of data?

c) Portfolio formation and tracking: (8 marks)
You now form two portfolios and decide to track their performance. The first portfolio is
optimised to match the duration of the index. The second portfolio is optimised to match your
portfolios loadings on slope, level and curvature of the yield curve to be as close as possible to
the loadings of the index (Hint – minimise the sum of the squared differences. Also use a starting
point for the optimisation of an equally weighted portfolio).
a) What are the weights for these two portfolios
b) Track the performance of these portfolio from for August 2019 and plot their
performances relative to the indexes.
c) Calculate the tracking error and explain why there is a difference. Which portfolio
would you expect to have a lower tracking error?

Assignments must be completed in groups of 4-5 people. Not following these instructions will
incur a 20% penalty. If an individual requires the course co-ordinator to help them form a
group as they are unable to do so themselves, the individual will lose 20% of their mark.
Assignments must be submitted electronically using Turnitin via Blackboard. Please attach a
cover page your names and student numbers. Should submission problems occur, students should
contact Business eLearning Support first on 9036 6433 or business.elearning@sydney.edu.au as
soon as possible, and if necessary the lecturer.
Due date: 4pm Monday 21st October
Maximum length of assignment: 12 pages excluding cover sheet, title page and appendix.
Formatting requirements: 1.5 line spacing 2 cm margins, 12 pt font.
Weight of Final Mark: 25%

 

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