QuestionQuestion

Answer the following questions making sure to clearly explain the procedure you followed to determine your answers.
1. Plot the term structure of Treasury rates on February 15, 2011 for maturities up to 30 years.
2. Compute the monthly compounded 1-month Treasury rate on February 15, 2011.
3. Compute the price of the inverse floater.
4. Compute the duration and convexity of the inverse floater.
5. Compute the factor durations of the inverse floater with respect to the three factors in the Litterman-Scheinkman model (use the factor sensitivities in Figure 6 in Section V of the Notes and linear interpolation as needed).
6. Determine the portfolio of 1-month and 10-year Treasury STRIPS that: (i) has zero cost and (ii) matches the dollar duration of the company’s position in the inverse floater.
7. Determine the portfolio of 1-month, 1-year and 10-year Treasury STRIPS that: (i) has zero cost and (ii) matches the dollar duration and convexity of the company’s position in the inverse floater.
8. Determine the portfolio of 1-month, 1-year, 10-year and 20-year Treasury STRIPS that: (i) has zero cost and (ii) matches the dollar factor durations of the company’s position in the inverse floater.
9. Compute the change in the value of the company’s position in the inverse floater that would occur if the term structure suddenly shifted up by 50 basis points in a parallel fashion (assume that the shift occurs just after the rate for the first coupon payment has been set and thus does not a↵ect the amount of that payment).
10. Compute the changes in the value of the company’s position that would occur if the term structure suddenly shifted to the new level specified in part 9 assuming that the company has hedged using each of the three portfolios in parts 6-8.
11. Now suppose instead that the term structure suddenly shifts so as to correspond to the Svensson parameterization with β0 = 2.43883185, β1 = 2.16793102, 2 = 555.55896000, β3 = 557.34394358, T1 = 5.41413155 and T2 = 5.47016160.3 Produce a graph comparing the actual term structure on February 15, 2011 tothe new term structure, so as to confirm that this shift corresponds to a nonparallel shift of the term structure.
12. Compute the change in the value of the company’s position in the inverse floater that would occur if the term structure suddenly shifted to the new level specified in part 11 (again, assume that the shift occurs just after the first coupon has been set).
13. Compute the changes in the value of the company’s position that would occur if the term structure suddenly shifted to the new level specified in part 11 assuming that the company has hedged using each of the three portfolios in parts 6-8.

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