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Cooljas · 2024年04月18日

为什么第三个是错的?第五个是对的啊?

NO.PZ2023091701000056

问题如下:

Which of the following statements 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:

All else equal, convexity increase for longer maturities, lower coupons, and lower yields.

Bonds with embedded options (e.g., callable bonds) exhibit negative convexity over certain ranges of yields while straight bonds with no embedded options exhibit positive convexity over the entire range of yields.



1 个答案

pzqa39 · 2024年04月19日

嗨,从没放弃的小努力你好:


3 Convexity 和时间的平方成比例

5 当凸度为正值时,表示债券价格与收益率之间的关系呈现出一种向上弯曲的形状,即随着收益率的上升(或下降),债券价格的下降(或上升)速度逐渐减缓。对于不含期权的普通债券(通常称为“直”债券),其凸度总是正值. 对于固定息票债券,当市场利率上升时,不仅债券的市场价格下降,而且后续支付的利息现值也下降。然而,由于债券已经发行,其息票利率是固定的,这意味着尽管债券价格下降,但每期支付给债券持有者的利息金额是不变的。随着利率进一步上升,债券价格继续下降的速度会因利息支付相对增加而放缓,即价格曲线开始向上弯曲。相反,当市场利率下降时,债券价格上升,但由于固定息票,利息支付的现值相对增加不如价格上升快,价格曲线同样向上弯曲。这种现象确保了凸度始终为正

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