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小熊猫 · 2025年03月05日

详细解释一下c选项?

NO.PZ2020042003000092

问题如下:

Which of the following statements is correct?

选项:

A.

Convexity refers to a nonlinear relationship between changes in an asset’s price and changes in market interest rates.

B.

An asset or portfolio bearing both a low duration and low convexity normally displays relatively large market risk

C.

Convexity decreases with the duration (maturity) of an asset.

D.

Price risk is smaller when interest rates are low than when they are high.

解释:

考点:对Risk Management for Changing Interest Rates: ALM and Duration Techniques-The Concept of Duration as a Risk-Management Tool的理解

答案:A

解析:

选项A的表述正确。

B选项错误,low duration and low convexity的债券具有较低的Market risk。关于B选项正确的表述为:

An asset or portfolio bearing both a low duration and low convexity normally displays relatively small market risk.

C选项错误,随着债券Maturity的增加,债券的Convexity数据会增加,C选项改成正确的表述为:

Convexity increases with the duration (maturity) of an asset.

D选项错误,当利率降低时,Price risk更大,因为债券有较高的DurationD选项改为正确的表述为:

Price risk is greater when interest rates are low than when they are high.

随着duration变大,convexity为什么也变大?

1 个答案

李坏_品职助教 · 2025年03月05日

嗨,从没放弃的小努力你好:


C.

Convexity decreases with the duration (maturity) of an asset.

C说的是,资产的凸性随着久期的增加而下降。


当其他条件不变的情况下,一个资产(比如债券)的凸性是和久期一起变大的。

这个需要看一下FRM一级 Financial Market的教材:

从教材案例16.6可以看出,凸性本质上就是Time的平方的加权平均值。随着Time变长,久期也是变大的,Time的平方也变大,所以凸性跟着一起变大了。




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