Only do question 7. Use the uk gilt yields as reference. Below the workings explain how the working was done. Do everything in EXCEL.
Yield Curve and Immunization Strategies
Data:
The data required for the empirical analysis is provided in the spreadsheet “IC206_Project_Data_UK Gilt Yields.xlsx” and is available in the folder “Assignments” on Blackboard. The file contains the daily time-series of UK Treasury gilts with varying maturities from 1 month to 50 years. The data series represent the yield-to-maturity, expressed in percentage points. The sample period spans 10 years, from June 2006 to May 2016.
Task Description:
- Perform a preliminary analysis of the UK yields,, where Tdenotes the bond’s maturity ranging from 1M to 50Y: (a) provide summary statistics for each series and generate a correlation matrix for the yields; (b) generate a time-series plot of the yields for all maturities and a separate time-series plot that only includes the yields of bonds with maturities of 1Y, 5Y and 10Y. Describe and explain the evolution of yields over time on the backdrop of the macroeconomic environment and the monetary policy interventions. You are free to use verbal and visual illustrations.
- Transform the series of yields, into daily changes of yields: for all maturities. Compute summary statistics for the new series of . Plot the time-series of for the maturities of 1Y, 5Y and 10Y and produce a histogram for each of the three series. Compare your findings across the different maturities.
- Take the 5Y bond as your benchmark yield. Examine the unconditional co-movement between the daily changes in the 5Y benchmark bond () and the daily changes of the 1Y and 10Y bonds, respectively. To do this, (a) produce a scatterplot of the daily yield changes vis-à-vis [you can produce two separate plots for each pair or plot both in one graph]; (b) compute the correlations between the bonds; and (c) estimate an OLS regression with the 1Y (10Y) daily changes as the dependent variable and as the independent variable. This unconditional regression model can be written as:
where T is either 1Y or 10Y maturity.
Comment on your findings.
- Examine the conditional co-movement between the changes in the 5Y bond yields and the yield changes of the 1Y and 10Y bonds, respectively. Start by constructing two new dummy variables that indicate whether the 5Y bond yield increases or decreases. The first dummy variable,, is set equal to 1 if the daily change in the 5Y yield, , is positive, and 0 otherwise. The second dummy variable,, is set equal to 1 if the daily change in the 5Y yield, , is negative, and 0 otherwise. Estimate the conditional regression model:
where T is either 1Y or 10Y maturity.
Compare your findings from the conditional model to those derived from the unconditional model in (3). Comment on any potential differences depending on the degree and direction of co-movement.
- To examine whether the (unconditional) co-movement of the 1Y and 10Y yields with respect to the 5Y benchmark yields is stable or changes over time, compute the correlations and the regression slope over 6-month rolling window. To do this, you generate a time-series of correlation and regression estimates (in contrast to the single estimate of (3)) by moving the 6-month window forward as you add new observations to the sample. Use as your first 6-month estimation window the sample from 02/06/2006 – 30/11/2006 to calculate your first estimates. Then move the window forward to calculate your next estimates over the window 05/06/2006 – 01/12/2006. Continue this process until you reach the end of the entire sample period. Plot the time-series of the rolling correlation and regression slope estimates and comment on your findings.
- Plot the yield curve of the UK gilts at different points in time to reflect different yield curve environments (Hint: a look at the time-series plot of all maturities produced under (1) should help you select appropriate dates.) Comment on shifts in the yield curve over the sample period based on your knowledge of yield curve regimes and theories as well as the macroeconomic environment and the monetary policy interventions. Can you identify different yield curve regimes? Do they respond to different yield curve theories? Link your discussion to relevant academic literature.
- (a) As the Financial Risk Manager of a company you have been asked to hedge the interest rate risk for a liability of £1,000,000 that is due to be paid in exactly 4 years. Today is 29/05/2015, hence the payment is due on 29/05/2019. You have several options to hedge your liability by investing in different UK gilts with different maturities:
- You can perfectly hedge the payment by buying some quantity of a zero-coupon UK treasury bond with the same maturity as your liability.
- You can hedge the payment by buying some quantity of a zero-coupon UK treasury bond with a maturity of 2Y.
- You can hedge the payment by buying some quantity of a zero-coupon UK treasury bond with a maturity of 5Y.
- You can hedge the payment by buying a combination of the zero-coupon UK treasury bonds fromPart (2) and Part (3), such that the resulting portfolio has the same market value and the same duration as the liability at the time of the purchase.
[Hint: Portfolio (Bond A and Bond B) Duration = (% in A * Duration of A) + (% in B *
Duration of B)]
Start by calculating the current market value (present value) and determine the duration of the liability on 29/05/2015. Next, compute the current prices of the three zero-coupon bonds and determine their durations. Compute the number of bonds you need to purchase for each hedging strategy.
(b) One year later on 30/05/2016, you re-assess your hedging options. Re-calculate the market value of your liability and of each of the four bond positions on 30/05/2016. Which of the four hedging options has best tracked the liability’s market value, which has done the worst job? Discuss and explain your findings.