FINC6014 Fixed Income Securities- Assignment Problem

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Reference no: EM132390020

FINC6014 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. To minimise transaction costs you plan to hold a portfolio of only 9 securities. 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 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:

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, t₂ and t₃ terms).

a) Build the zero curve using this methodology using data on 2nd 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:

You decide the data provided to you by your assistant is accurate and use this datato 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.

Δprice = α+β₁Δlevel + ε (1.1)

Δprice = α + β₁Δlevel + β₂Δslope +β₃Δcurvature + ε (1.2)

c) Discuss if these models are appropriate at explaining returns.

d) Using the results from regression (1.1) plot the bonds β₁against its duration for each of the bonds. Explain why you have the relationship you see. Repeat the process for regression (1.2) for β₂and 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:

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.

a) What are the weights for these two portfolios

b) Track the performance of these portfolio fromfor 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?

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.

Reference no: EM132390020

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