Finance-QA297

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Overview
 
The project’s aim is to perform an analysis of yields derived from UK government bonds, and evaluate the ability of specific bonds to hedge a hypothetical liability.
 
Deliverables
 
Once you have completed your empirical analysis, you need to submit
• an Excel workbook containing all your calculations
• a short report (max 1,500 words) explaining and discussing your findings

The workbook needs to be submitted in .xlsx format. Please make sure that the workbook is as reader-friendly as possible. I would suggest that the calculations for each individual objective(see below) are presented in separate worksheets of the workbook.
 
The report should briefly discuss the findings that you present in the workbook. It should include tables and graphs where relevant, and should clearly indicate what you have done and what your results mean. You should focus on providing an intuitive discussion rather than reproducing chunks of theory or merely presenting statistics. The report should not exceed 1,500 words (plus tables and graphs). Any tables and graphs should be clearly labelled and referenced in the main text. The report should be divided into sections and sub-sections, including a short Introduction and a Conclusion.
 
Data
 
The data that will be required for the empirical analysis is in the spreadsheet “Coursework_01_UK_Yields.xlsx”. This file contains the daily time-series of UK yields.Maturities range from 1 month to 25 years, covering the entire term structure of UK interest
rates. The sample period spans 13 years, from January 2000 to December 2012
 

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Objectives 1-TO-1
 
[1] After selecting a specific maturity T, you should begin by providing a preliminary analysis of the chosen series of yields 𝑟𝑡
𝑇. Compute the main descriptive statistics for 𝑟𝑡
𝑇and compare them to those obtained for the benchmark 5-year yield. Plot the two seriesand compare the time evolution of your series to that of the benchmark 5-year yield.
[2] Compute the daily change of your series as

𝛥𝑟𝑡
𝑇 = 𝑟𝑡
𝑇 − 𝑟𝑡−1
𝑇
Compute descriptive statistics for the above series of changes in yields and produce the
respective histogram. Compare your results to those obtained for the changes in the
benchmark 5-year yield 𝛥𝑟𝑡
=[3] Examine the unconditional co-movement between your series 𝛥𝑟𝑡
𝑇and the benchmark series 𝛥𝑟𝑡
 
5. This can be done by producing a scatterplot, computing the correlation coefficient, and estimating an OLS regression with your series as the dependent variable and the benchmark as the independent variable. This unconditional regression model
can be written as
𝛥𝑟𝑡
𝑇 = 𝛼 + 𝛽𝛥𝑟𝑡
5 + 𝜀𝑡
 
[4] Examine the conditional co-movement between your series and the benchmark series. In order to do this, begin by constructing two new (dummy) variables that will signal whether the benchmark yield increases or decreases. The first (dummy) variable 𝐷𝑡
should take the value of 1 if the independent variable is positive and the value of 0 otherwise. The second (dummy) variable 𝐷𝑡 should take the value of 1 if the independent variable is negative or zero and the value of 0 otherwise.
Then, run the conditional regression model
 
𝛥𝑟𝑡
𝑇 = 𝛼 + 𝛽+𝐷𝑡
+𝛥𝑟𝑡
5 + 𝛽−𝐷𝑡
−𝛥𝑟𝑡
5 + 𝜀𝑡
and compare any potential differences between the degree of co-movement depending on the independent variable’s sign.
 
[5] Examine the time evolution of the (unconditional) co-movement between your series and the benchmark series. This can be done by computing rolling 6-month estimates of the correlation and the regression slope (in contrast to the single estimates in [3]).
 
[6] Suppose that you work for an insurance company, and that it is now the first trading day of December 2012. You are currently managing a liability which will call for a payment of £1,000,000 after exactly 4 years. You would like to evaluate the following ways in which you can fund/hedge this liability by investing in UK bonds
• `Perfectly funding the liability by purchasing some quantity of a zero-coupon bond
with the same maturity as the liability.
• Hedging the liability by purchasing some quantity of a zero-coupon bond with
maturity equal to the maturity T of your time-series.
 
• Hedging the liability by purchasing some quantity of a zero-coupon bond with
maturity equal to the benchmark maturity of 5 years.
• Hedging the liability by investing in both of the last two bonds. The resulting
portfolio should have the same market value and duration as the liability.
 
Begin by computing the current price (market value) and the Macaulay Duration of the liability and of the three bonds on the first trading day of December 2012. Then compute the required quantities of each bond that you will need to buy in order to fund/hedge the liability under each of the 4 options.
 
Suppose that now is the last trading day of December 2012. Re-calculate the market value of the liability and of the bond position under each of the 4 options [Note: When calculating prices and durations, if you need to use a discount rate with a maturity x
which is not readily available in the dataset, you should use the discount rate with a maturity immediately before the maturity x]. Rank the 4 options in terms of which one as best tracked the liability’s market value at the end of the month.
 
Product code: Finance-QA297
 
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