Assume the yield curve is flat at 7

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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