NO.PZ2016082402000014
问题如下:
Which of the following statements is/are true?
I. The convexity of a 10-year zero-coupon bond is higher than the convexity of a 10-year 6% bond.
II. The convexity of a 10-year zero-coupon bond is higher than the convexity of a 6% bond with a duration of 10 years.
III. Convexity grows proportionately with the maturity of the bond.
IV. Convexity is always positive for all types of bonds.
V. Convexity is always positive for straight bonds.
选项: I
only
I and II only
C.I and V only
D.II, III, and V only
解释:
ANSWER: C
Because convexity is proportional to the square of time to payment, the convexity of a bond is mainly driven by the cash flows far into the future. Answer I. is correct because the 10-year zero has only one cash flow, whereas the coupon bond has several others that reduce convexity. Answer II. is false because the 6% bond with 10-year duration must have cash flows much further into the future, say in 30 years, which will create greater convexity. Answer III. is false because convexity grows with the square of time. Answer IV. is false because some bonds, for example MBSs or callable bonds, can have negative convexity. Answer V. is correct because convexity must be positive for coupon-paying bonds.
请问为什么duration不同的时候,coupon越大 convexity越大?