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.
解析：
下面哪句陈述是正确的？
I. 10年期零息债券的凸度高于10年期6%债券的凸度。
正确，久期不同的时候，coupon越少，convexity越大。
II. 10 年期零息债券的凸度高于期限为 10 年的 6% 债券的凸度。
错误，久期相同的时候，coupon 越大，convexity越大。
III. 凸度与债券的到期日成正比。
错误，Convexity 和时间的平方成比例。
IV. 对于所有类型的债券，凸性总是正的。
错误，callable bond会有负的convexity。
V. 对于不含权的债券凸性总是正的。
正确。
选C。
II. 10 年期零息债券的凸度高于期限为 10 年的 6% 债券的凸度。
错误，久期相同的时候，coupon 越大（现金流越分散），convexity越大。这个没问题
I. 10年期零息债券的凸度高于10年期6%债券的凸度。
正确，久期不同的时候，coupon越少，convexity越大。这是为什么？从哪个角度看出来的？
