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Poppy · 2022年08月04日

请问算pv+和pv-能用计算器吗?

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000124

问题如下：

A bond with exactly nine years remaining until maturity offers a 3% coupon rate with annual coupons. The bond, with a yield-to-maturity of 5%, is priced at 85.784357 per 100 of par value. The estimated price value of a basis point for the bond is closest to:

选项：

A.

0.0086.

B.

0.0648.

C.

0.1295.

解释：

B is correct.

The PVBP is closest to 0.0648. The formula for the price value of a basis pointis:

PVBP=(PV−)−(PV+)2PVBP=\frac{(PV-)-(PV+)}2

where:

PVBP = price value of a basis point

PV– = full price calculated by lowering the yield-to-maturity by one basis point

PV+ = full price calculated by raising the yield-to-maturity by one basis point

Lowering the yield-to-maturity by one basis point to 4.99% results in a bond price of 85.849134:

PV−=3(1+0.0499)1+⋯+3+100(1+0.0499)9=85.849134PV-=\frac3{{(1+0.0499)}^1}+\cdots+\frac{3+100}{{(1+0.0499)}^9}=85.849134

Increasing the yield-to-maturity by one basis point to 5.01% results in a bond price of 85.719638:

PV+=3(1+0.0501)1+⋯+3+100(1+0.0501)9=85.719638PV+=\frac3{{(1+0.0501)}^1}+\cdots+\frac{3+100}{{(1+0.0501)}^9}=85.719638

PVBP=85.849134−85.7196382=0.06475PVBP=\frac{85.849134-85.719638}2=0.06475

Alternatively, the PVBP can be derived using modified duration:

ApproxModDur=(PV−)−(PV+)2×(ΔYield)×(PV0)ApproxModDur=\frac{(PV-)-(PV+)}{2\times(\Delta Yield)\times(PV0)}

ApproxModDur=85.849134−85.7196382×0.0001×85.784357=7.548ApproxModDur=\frac{85.849134-85.719638}{2\times0.0001\times85.784357}=7.548

PVBP = 7.548 × 85.784357 × 0.0001 = 0.06475

考点：PVBP

解析：PVBP衡量的是利率变化1bp，带来的债券价格变化。

分别算出利率下降1个bp的债券价格PV-(85.849134)和利率上升一个bp的债券价格PV+(85.719638)，两者相减再除以2，即可得PVBP=0.0648，故选项B正确。

注意：如果直接算出PV+（或PV-），它和原本的PV之间本身就是由于利率变化1bp造成的，所以两者直接相减即可，不需要除以2。 如果分别算出PV-和PV+，那么它俩之间是由于利率相差2bps造成的，所以相减之后需要除以2。

请问算pv+和pv-能用计算器吗?

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1 个答案

吴昊_品职助教 · 2022年08月04日

嗨，从没放弃的小努力你好：


可以的。

I/Y=4.99, N=9, PMT=3,FV=100,CPT→ PV- =85.849134

I/Y=5.01, N=9, PMT=3,FV=100,CPT→ PV+ =85.719638

----------------------------------------------
努力的时光都是限量版，加油！

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NO.PZ2016031001000124 问题如下 A bonwith exactly nine years remaining until maturity offers a 3% coupon rate with annucoupons. The bon with a yielto-maturity of 5%, is price85.784357 per 100 of pvalue. The estimateprivalue of a basis point for the bonis closest to: A.0.0086. B.0.0648. C.0.1295. B is correct.The PVis closest to 0.0648. The formula for the privalue of a basis pointis: PVBP=(PV−)−(PV+)2PVBP=\frac{(PV-)-(PV+)}2PVBP=2(PV−)−(PV+)​where:PV= privalue of a basis pointPV– = full pricalculatelowering the yielto-maturity one basis pointPV+ = full pricalculateraising the yielto-maturity one basis pointLowering the yielto-maturity one basis point to 4.99% results in a bonpriof 85.849134:PV−=3(1+0.0499)1+⋯+3+100(1+0.0499)9=85.849134PV-=\frac3{{(1+0.0499)}^1}+\cts+\frac{3+100}{{(1+0.0499)}^9}=85.849134PV−=(1+0.0499)13​+⋯+(1+0.0499)93+100​=85.849134Increasing the yielto-maturity one basis point to 5.01% results in a bonpriof 85.719638:PV+=3(1+0.0501)1+⋯+3+100(1+0.0501)9=85.719638PV+=\frac3{{(1+0.0501)}^1}+\cts+\frac{3+100}{{(1+0.0501)}^9}=85.719638PV+=(1+0.0501)13​+⋯+(1+0.0501)93+100​=85.719638PVBP=85.849134−85.7196382=0.06475PVBP=\frac{85.849134-85.719638}2=0.06475PVBP=285.849134−85.719638​=0.06475Alternatively, the PVcriveusing mofieration:ApproxMour=(PV−)−(PV+)2×(ΔYiel×(PV0)ApproxMour=\frac{(PV-)-(PV+)}{2\times(\lta Yiel\times(PV0)}ApproxMour=2×(ΔYiel×(PV0)(PV−)−(PV+)​ApproxMour=85.849134−85.7196382×0.0001×85.784357=7.548ApproxMour=\frac{85.849134-85.719638}{2\times0.0001\times85.784357}=7.548ApproxMour=2×0.0001×85.78435785.849134−85.719638​=7.548PV= 7.548 × 85.784357 × 0.0001 = 0.06475考点PVBP解析PVBP衡量的是利率变化1bp，带来的债券价格变化。分别算出利率下降1个bp的债券价格PV-(85.849134)和利率上升一个bp的债券价格PV+(85.719638)，两者相减再除以2，即可得PVBP=0.0648，故B正确。注意如果直接算出PV+（或PV-），它和原本的PV之间本身就是由于利率变化1bp造成的，所以两者直接相减即可，不需要除以2。 如果分别算出PV-和PV+，那么它俩之间是由于利率相差2bps造成的，所以相减之后需要除以2。 老师我想问下哈，这道题考的是PVBP的知识点，一般来说题目是不是会告诉你rate变动多少，是不是在没有说的情况下，我们就默认利率向上或向下变动1%，谢谢

2022-08-01 07:10 1 · 回答

NO.PZ2016031001000124 0.0648. 0.1295. B is correct. The PVis closest to 0.0648. The formula for the privalue of a basis pointis: PVBP=(PV−)−(PV+)2PVBP=\frac{(PV-)-(PV+)}2PVBP=2(PV−)−(PV+)​ where: PV= privalue of a basis point PV– = full pricalculatelowering the yielto-maturity one basis point PV+ = full pricalculateraising the yielto-maturity one basis point Lowering the yielto-maturity one basis point to 4.99% results in a bonpriof 85.849134: PV−=3(1+0.0499)1+⋯+3+100(1+0.0499)9=85.849134PV-=\frac3{{(1+0.0499)}^1}+\cts+\frac{3+100}{{(1+0.0499)}^9}=85.849134PV−=(1+0.0499)13​+⋯+(1+0.0499)93+100​=85.849134 Increasing the yielto-maturity one basis point to 5.01% results in a bonpriof 85.719638: PV+=3(1+0.0501)1+⋯+3+100(1+0.0501)9=85.719638PV+=\frac3{{(1+0.0501)}^1}+\cts+\frac{3+100}{{(1+0.0501)}^9}=85.719638PV+=(1+0.0501)13​+⋯+(1+0.0501)93+100​=85.719638 PVBP=85.849134−85.7196382=0.06475PVBP=\frac{85.849134-85.719638}2=0.06475PVBP=285.849134−85.719638​=0.06475 Alternatively, the PVcriveusing mofieration: ApproxMour=(PV−)−(PV+)2×(ΔYiel×(PV0)ApproxMour=\frac{(PV-)-(PV+)}{2\times(\lta Yiel\times(PV0)}ApproxMour=2×(ΔYiel×(PV0)(PV−)−(PV+)​ ApproxMour=85.849134−85.7196382×0.0001×85.784357=7.548ApproxMour=\frac{85.849134-85.719638}{2\times0.0001\times85.784357}=7.548ApproxMour=2×0.0001×85.78435785.849134−85.719638​=7.548 PV= 7.548 × 85.784357 × 0.0001 = 0.06475 考点PV解析PVBP衡量的是利率变化1bp，带来的债券价格变化。 分别算出利率下降1个bp的债券价格PV-(85.849134)和利率上升一个bp的债券价格PV+(85.719638)，两者相减再除以2，即可得PVBP=0.0648，故B正确。 注意如果直接算出PV+（或PV-），它和原本的PV之间本身就是由于利率变化1bp造成的，所以两者直接相减即可，不需要除以2。 如果分别算出PV-和PV+，那么它俩之间是由于利率相差2bps造成的，所以相减之后需要除以2。 如题。。。。。。。谢谢。

2022-01-14 17:52 1 · 回答

NO.PZ2016031001000124 0.0648. 0.1295. B is correct. The PVis closest to 0.0648. The formula for the privalue of a basis pointis: PVBP=(PV−)−(PV+)2PVBP=\frac{(PV-)-(PV+)}2PVBP=2(PV−)−(PV+)​ where: PV= privalue of a basis point PV– = full pricalculatelowering the yielto-maturity one basis point PV+ = full pricalculateraising the yielto-maturity one basis point Lowering the yielto-maturity one basis point to 4.99% results in a bonpriof 85.849134: PV−=3(1+0.0499)1+⋯+3+100(1+0.0499)9=85.849134PV-=\frac3{{(1+0.0499)}^1}+\cts+\frac{3+100}{{(1+0.0499)}^9}=85.849134PV−=(1+0.0499)13​+⋯+(1+0.0499)93+100​=85.849134 Increasing the yielto-maturity one basis point to 5.01% results in a bonpriof 85.719638: PV+=3(1+0.0501)1+⋯+3+100(1+0.0501)9=85.719638PV+=\frac3{{(1+0.0501)}^1}+\cts+\frac{3+100}{{(1+0.0501)}^9}=85.719638PV+=(1+0.0501)13​+⋯+(1+0.0501)93+100​=85.719638 PVBP=85.849134−85.7196382=0.06475PVBP=\frac{85.849134-85.719638}2=0.06475PVBP=285.849134−85.719638​=0.06475 Alternatively, the PVcriveusing mofieration: ApproxMour=(PV−)−(PV+)2×(ΔYiel×(PV0)ApproxMour=\frac{(PV-)-(PV+)}{2\times(\lta Yiel\times(PV0)}ApproxMour=2×(ΔYiel×(PV0)(PV−)−(PV+)​ ApproxMour=85.849134−85.7196382×0.0001×85.784357=7.548ApproxMour=\frac{85.849134-85.719638}{2\times0.0001\times85.784357}=7.548ApproxMour=2×0.0001×85.78435785.849134−85.719638​=7.548 PV= 7.548 × 85.784357 × 0.0001 = 0.06475把ytm5.01带入，直接v0减去v➕=pvbp可以吗

2021-05-07 15:01 1 · 回答

老师，想接着这道题请教一个知识点为什么说ration越大，interest rate risk越大呢？我之前理解的是大，所以期限长，所以利率风险越大。。想请教一下正确的思考。

2020-10-27 22:25 1 · 回答