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claireteng · 2022年07月01日

能否解释下

  1. FRM I
  2. Valuation And Risk Models

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：

A.

I only

B.

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.

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. 为什么有coupon的bond convexity更大

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品职答疑小助手雍 · 2022年07月02日

同学你好，我看你也考了CFA了，和barbell的凸性比bullet大同理，你就把coupon想成小的债券就可以了。

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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？

2024-04-21 11:15 1 · 回答

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

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