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· 2022年03月20日

第一句不理解

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.

请问为什么duration不同的时候,coupon越大 convexity越大?

1 个答案

李坏_品职助教 · 2022年03月20日

嗨,努力学习的PZer你好:


第一个说的是10年期零息债券的凸性convexity大于10年期6% coupon的附息债券。


convexity主要受到债券未来的一系列现金流里面,距离现在最远的那些现金流。这俩债券期限都是10年,零息债券所有的现金流都是10年后才能收到,而6% coupon的债券会提前收到好几笔coupon,所以零息债券的 convexity大于6% coupon 债券。I是正确的。

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