问题如下图：
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NO.PZ2016082402000014 问题如下 Whiof the following statements is/are true? I. The convexity of a 10-year zero-coupon bonis higher ththe convexity of a 10-ye6% bon II. The convexity of a 10-year zero-coupon bonis higher ththe convexity of a 6% bonwith a ration of 10 years. III. Convexity grows proportionately with the maturity of the bon IV. Convexity is always positive for all types of bon. V. Convexity is always positive for straight bon. I only I anII only I anV only II, III, anV only ANSWER: Because convexity is proportionto the square of time to payment, the convexity of a bonis mainly iven the cash flows finto the future. Answer I. is correbecause the 10-yezero honly one cash flow, wherethe coupon bonhseverothers threconvexity. Answer II. is false because the 6% bonwith 10-yeration must have cash flows mufurther into the future, sin 30 years, whiwill create greater convexity. Answer III. is false because convexity grows with the square of time. Answer IV. is false because some bon, for example MBSs or callable bon, chave negative convexity. Answer V. is correbecause convexity must positive for coupon-paying bon.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 bon有负的convexity。V. 对于不含权的债券凸性总是正的。正确。选 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？
NO.PZ2016082402000014问题如下 Whiof the following statements is/are true? I. The convexity of a 10-year zero-coupon bonis higher ththe convexity of a 10-ye6% bon II. The convexity of a 10-year zero-coupon bonis higher ththe convexity of a 6% bonwith a ration of 10 years. III. Convexity grows proportionately with the maturity of the bon IV. Convexity is always positive for all types of bon. V. Convexity is always positive for straight bon. I only I anII only I anV only II, III, anV only ANSWER: Because convexity is proportionto the square of time to payment, the convexity of a bonis mainly iven the cash flows finto the future. Answer I. is correbecause the 10-yezero honly one cash flow, wherethe coupon bonhseverothers threconvexity. Answer II. is false because the 6% bonwith 10-yeration must have cash flows mufurther into the future, sin 30 years, whiwill create greater convexity. Answer III. is false because convexity grows with the square of time. Answer IV. is false because some bon, for example MBSs or callable bon, chave negative convexity. Answer V. is correbecause convexity must positive for coupon-paying bon.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 bon有负的convexity。V. 对于不含权的债券凸性总是正的。正确。选 可以一下I和II的结论吗
NO.PZ2016082402000014 问题如下 Whiof the following statements is/are true? I. The convexity of a 10-year zero-coupon bonis higher ththe convexity of a 10-ye6% bon II. The convexity of a 10-year zero-coupon bonis higher ththe convexity of a 6% bonwith a ration of 10 years. III. Convexity grows proportionately with the maturity of the bon IV. Convexity is always positive for all types of bon. V. Convexity is always positive for straight bon. I only I anII only I anV only II, III, anV only ANSWER: C Because convexity is proportionto the square of time to payment, the convexity of a bonis mainly iven the cash flows finto the future. Answer I. is correct because the 10-yezero honly one cash flow, wherethe coupon bonhas severothers threconvexity. Answer II. is false because the 6% bond with 10-yeration must have cash flows mufurther into the future, sin 30 years, whiwill create greater convexity. Answer III. is false because convexity grows with the square of time. Answer IV. is false because some bon, for example MBSs or callable bon, chave negative convexity. Answer V. is correbecause convexity must positive for coupon-paying bon. Answer II. is false because the 6% bonwith 10-yeration must have cash flows mufurther into the future, sin 30 years, whiwill create greater convexity. 为什么有coupon的bonconvexity更大
NO.PZ2016082402000014 Whiof the following statements is/are true? I. The convexity of a 10-yezero-coupon bonis higher ththe convexity of a 10-ye6% bon II. The convexity of a 10-yezero-coupon bonis higher ththe convexity of a 6% bonwith a ration of 10 years. III. Convexity grows proportionately with the maturity of the bon IV. Convexity is always positive for all types of bon. V. Convexity is always positive for straight bon. I only I anII only I anV only II, III, anV only ANSWER: C Because convexity is proportionto the square of time to payment, the convexity of a bonis mainly iven the cash flows finto the future. Answer I. is correbecause the 10-yezero honly one cash flow, wherethe coupon bonhseverothers threconvexity. Answer II. is false because the 6% bonwith 10-yeration must have cash flows mufurther into the future, sin 30 years, whiwill create greater convexity. Answer III. is false because convexity grows with the square of time. Answer IV. is false because some bon, for example MBSs or callable bon, chave negative convexity. Answer V. is correbecause convexity must positive for coupon-paying bon. 请问为什么ration不同的时候，coupon越大 convexity越大？
NO.PZ2016082402000014 I anII only I anV only II, III, anV only ANSWER: C Because convexity is proportionto the square of time to payment, the convexity of a bonis mainly iven the cash flows finto the future. Answer I. is correbecause the 10-yezero honly one cash flow, wherethe coupon bonhseverothers threconvexity. Answer II. is false because the 6% bonwith 10-yeration must have cash flows mufurther into the future, sin 30 years, whiwill create greater convexity. Answer III. is false because convexity grows with the square of time. Answer IV. is false because some bon, for example MBSs or callable bon, chave negative convexity. Answer V. is correbecause convexity must positive for coupon-paying bon. 老师能详细一下这道题吗
这个可以看作结论来记一下：convexity可以衡量现金流的离散程度，其他条件相同的情况下，coupon越大，也就是现金流越分散，convexity则越大。所以第二个选项是错的。