Question
QUESTION 2 Assume the yield curve is flat at 7.5% pa nominal. A cash and $duration-neutral butterfly is to be constructed by selling one thousand
QUESTION 2
Assume the yield curve is flat at 7.5% pa nominal. A cash and $duration-neutral butterfly is to be constructed by selling one thousand 9-year zero coupon bonds and purchasing q_s and q_l zero coupon bonds with maturities 5 and 14 years' respectively. We assume that interest accrues semi-annually. We also assume each bond has a face value of $100.
(a) What is the price of the 5-year bond?
*36.33
*35.67
*69.66
*69.20
(b) What is the price of the 9-year bond?
*69.20
*35.67
*52.16
*51.55
(c) What is the price of the 14-year bond?
*51.55
*36.33
*69.20
*35.67
(d) What is the modified duration of the 5-year bond?
*4.651
*4.819
*5
*9.639
(e) What is the modified duration of the 9-year bond?
*8.372
*17.349
*8.675
*9
(f) What is the modified duration of the 14-year bond?
*14
*13.023
*26.988
*13.494
(g) What is the standardized convexity of the 5-year bond?
*25.960
*102.192
*25.548
*69.202
(h) What is the standardized convexity of the 9-year bond?
*77.88
*79.431
*51.548
*317.724
(i) What is the standardized convexity of the 14-year bond?
*35.672
*754.362
*210
*188
(j) What is the cash-neutral equation in the system of equations needed to find q_s and q_l?
*q_s*69.66+q_1*36.33=52,158.35
*q_s*35.67+q_1*69.20=51,548.27
*q_s*36.33+q_1*69.66=52,158.35
*q_s*69.20+q_1*35.67=51,548.27
(k) What is the $Duration-neutral equation in the system of equations needed to find q_s and q_l?
*q_s*346.01+q_1*499.41=463,934.44
*q_s*481.36+q_1*333.50=447,165.72
*q_s*499.41+q_1*346.50=463,934.44
*q_s*333.50+q_1*481.36=447,165.72
(l): It can be shown that the solution to the system of equations is: q_s = 413.83 and q_l= 642.24. The profit from this strategy if the yield curve shifts upwards by 1% at all maturities is closest to:
*30.27
*64363
*52.67
*43.58
(m): What is the modified duration of a portfolio comprising : q_s = 413.83 short-maturity bond and q_l= 642.24 long maturity bonds?
*8.675
*17.349
*9
*8.372
(n): What is the standardized convexity of a portfolio comprising : q_s = 413.83 short-maturity bond and q_l= 642.24 long maturity bonds?
*98.011
*112.493
*95.187
*116.127
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