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Dang.D · 2020年10月09日

问一道题：NO.PZ2016031001000126

  1. CFA I
  2. Fixed Income

问题如下：

A bond is currently trading for 98.722 per 100 of par value. If the bond’s yield-to-maturity (YTM) rises by 10 basis points, the bond’s full price is expected to fall to 98.669. If the bond’s YTM decreases by 10 basis points, the bond’s full price is expected to increase to 98.782. The bond’s approximate convexity is closest to:

选项：

A.

0.071.

B.

70.906.

C.

1,144.628.

解释：

B is correct.

The bond’s approximate convexity is closest to 70.906. Approximate convexity

(ApproxCon) is calculated using the following formula:

ApproxCon=[PV−+PV+−(2×PV0)]/(ΔYield2  ×  PV0)ApproxCon=\lbrack PV_-+PV_+-(2\times PV_0)\rbrack/(\Delta Yield^{2\;}\times\;PV_0)

where:

PV_ = new price when the yield-to-maturity is decreased

PV+ = new price when the yield-to-maturity is increased

PV0 = original price

ΔYield = change in yield-to-maturity

ApproxCon

 = [98.782 + 98.669−(2×98.722)]/(0.0012×98.722)\text{ }=\text{ }\lbrack98.782\text{ }+\text{ }98.669-(2\times98.722)\rbrack/(0.001^2\times98.722)

 = 70.906\text{ }=\text{ }70.906

ΔYield = change in yield-to-maturity，这个变化量就是指YTM上升或者下降的那个变化值么


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1 个答案

WallE_品职答疑助手 · 2020年10月09日

同学您好，

是的哈，就是那个变化的10 basis point

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NO.PZ2016031001000126 问题如下 A bonis currently trang for 98.722 per 100 of pvalue. If the bons yielto-maturity (YTM) rises 10 basis points, the bons full priis expecteto fall to 98.669. If the bons YTM creases 10 basis points, the bons full priis expecteto increase to 98.782. The bons approximate convexity is closest to: A.0.071. B.70.906. C.1,144.628. B is correct.The bons approximate convexity is closest to 70.906. Approximate convexity(ApproxCon) is calculateusing the following formula:ApproxCon=[PV−+PV+−(2×PV0)]/(ΔYiel  ×  PV0)ApproxCon=\lbraPV_-+PV_+-(2\times PV_0)\rbrack/(\lta Yiel{2\;}\times\;PV_0)ApproxCon=[PV−​+PV+​−(2×PV0​)]/(ΔYiel×PV0​)ApproxCon = [98.782 + 98.669−(2×98.722)]/(0.0012×98.722)\text{ }=\text{ }\lbrack98.782\text{ }+\text{ }98.669-(2\times98.722)\rbrack/(0.001^2\times98.722) = [98.782 + 98.669−(2×98.722)]/(0.0012×98.722) = 70.906\text{ }=\text{ }70.906 = 70.906考点convexity解析题干中98.669是利率上升10bps的债券价格PV+，98.782是利率下降10bps的债券价格PV-，代入上述公式即可得convexity为70.906，故B正确。 convexity 的公式原型是由变化值除Y的变化值得来，其中和的值用的是ΔYiel= 0.001我能理解，为什么分母中的ΔYiel也是 0.001呢，在这个两个ration的变化中，yiel是一共变化了两个0.001也就是0.002吗？

2022-04-22 22:59 1 · 回答