AIMs: Define, compute, and interpret the convexity of a fixed income security given a change in yield and the resulting change in price. Contrast DV01 and effective duration as measures of price sensitivity.
Questions:
17.1. A $100 bond with 7.0 years to maturity has a 4.0% per annum coupon rate that is paid semi-annually. What is the effective convexity of the bond when the yield is 4.0% such that the bond's price is $100 (if coupon rate equals yield, bond prices at par)?
a. 42.60
b. 98.77
c. 214.30
d. 856.80
17.2. A 15-year zero-coupon bond has a price of $63.98 when the yield is 3.00%. At this 3.00% yield, the bond's dollar duration is -952.0; if the yield increases by 10 basis points to 3.10% the bond's dollar duration drops to -938.0. Recall that the dollar duration is the first derivative of the price-rate function, dP/dy (modified duration is -1/P multiplied by this dollar duration). What is the bond's convexity at 3.00%?
a. 28
b. 124
c. 219
d. 435
17.3. A 30-year 4.0% semi-annual coupon bond has a price of $100.00 at a yield of 4.00%. At this 4.00% yield the bond has a modified duration of 16.980 years. If the yield drops by one basis point, to 3.99%, the price increases to $100.17 and the duration increases to 17.030 years. What is the bond's convexity at a 4.0% yield? (significantly more difficult than an exam question)
a. 125
b. 790
c. 1,646
d. 4,333
Answers:
Questions:
17.1. A $100 bond with 7.0 years to maturity has a 4.0% per annum coupon rate that is paid semi-annually. What is the effective convexity of the bond when the yield is 4.0% such that the bond's price is $100 (if coupon rate equals yield, bond prices at par)?
a. 42.60
b. 98.77
c. 214.30
d. 856.80
17.2. A 15-year zero-coupon bond has a price of $63.98 when the yield is 3.00%. At this 3.00% yield, the bond's dollar duration is -952.0; if the yield increases by 10 basis points to 3.10% the bond's dollar duration drops to -938.0. Recall that the dollar duration is the first derivative of the price-rate function, dP/dy (modified duration is -1/P multiplied by this dollar duration). What is the bond's convexity at 3.00%?
a. 28
b. 124
c. 219
d. 435
17.3. A 30-year 4.0% semi-annual coupon bond has a price of $100.00 at a yield of 4.00%. At this 4.00% yield the bond has a modified duration of 16.980 years. If the yield drops by one basis point, to 3.99%, the price increases to $100.17 and the duration increases to 17.030 years. What is the bond's convexity at a 4.0% yield? (significantly more difficult than an exam question)
a. 125
b. 790
c. 1,646
d. 4,333
Answers:
