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🤨肖大YAN😊 · 2020年11月05日

问一道题:NO.PZ2016031001000076 [ CFA I ]

问题如下:

A 5-year, 5% semiannual coupon payment corporate bond is priced at 104.967 per 100 of par value. The bond’s yield-to-maturity, quoted on a semiannual bond basis, is 3.897%. An analyst has been asked to convert to a monthly periodicity. Under this conversion, the yield-to-maturity is closest to:

选项:

A.

3.87%.

B.

4.95%.

C.

7.67%.

解释:

A is correct.

The yield-to-maturity, stated for a periodicity of 12 (monthly periodicity), is 3.87%.The formula to convert an annual percentage rate (annual yield-to-maturity) from one periodicity to another is as follows:

(1+APRmm)m=(1+APRnn)n{(1+\frac{APRm}m)}^m={(1+\frac{APRn}n)}^n

(1+0.038972)2=(1+APR1212)12{(1+\frac{0.03897}2)}^2={(1+\frac{APR12}{12})}^{12}

(1.01949)2=(1+APR1212)12{(1.01949)}^2={(1+\frac{APR12}{12})}^{12}

1.03935=(1+APR1212)121.03935={(1+\frac{APR12}{12})}^{12}

(1.03935)1/12=[(1+APR1212)12]1/12{(1.03935)}^{1/12}={\lbrack{(1+\frac{APR12}{12})}^{12}\rbrack}^{1/12}

1.00322=(1+APR1212)1.00322={(1+\frac{APR12}{12})}

1.003221=(APR1212)1.00322-1={(\frac{APR12}{12})}

APR12 = 0.00322 × 12 = 0.03865, or approximately 3.87%.

计算机算出I/Y=1.948%,*2不等於3.896%(年化)吗? 为什么还要APR2,为什么不是(1+APR12/12)12次方=1+3.897%
1 个答案

吴昊_品职助教 · 2020年11月05日

同学你好:

你通过计算器算出来的I/Y再乘以2得到 3.897%,或者直接用题干给的已知信息3.897%,都是一年计息两次的年化收益率,即APR2。并不是你认为的APR1。如果要算APR1,需要额外列式:1+APR1=(1+APR2/2)^2。所以这道题直接通过APR2转换到APR12,按照题目解析中给出的公式计算即可。

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NO.PZ2016031001000076 问题如下 A 5-year, 5% semiannucoupon payment corporate bonis price104.967 per 100 of pvalue. The bons yielto-maturity, quoteon a semiannubonbasis, is 3.897%. analyst hbeen asketo convert to a monthly periocity. Unr this conversion, the yielto-maturity is closest to: A.3.87%. B.4.95%. C.7.67%. A is correct.The yielto-maturity, statefor a periocity of 12 (monthly periocity), is 3.87%.The formula to convert annupercentage rate (annuyielto-maturity) from one periocity to another is follows:(1+APRmm)m=(1+APRnn)n{(1+\frac{APRm}m)}^m={(1+\frac{APRn}n)}^n(1+mAPRm​)m=(1+nAPRn​)n(1+0.038972)2=(1+APR1212)12{(1+\frac{0.03897}2)}^2={(1+\frac{APR12}{12})}^{12}(1+20.03897​)2=(1+12APR12​)12(1.01949)2=(1+APR1212)12{(1.01949)}^2={(1+\frac{APR12}{12})}^{12}(1.01949)2=(1+12APR12​)121.03935=(1+APR1212)121.03935={(1+\frac{APR12}{12})}^{12}1.03935=(1+12APR12​)12(1.03935)1/12=[(1+APR1212)12]1/12{(1.03935)}^{1/12}={\lbrack{(1+\frac{APR12}{12})}^{12}\rbrack}^{1/12}(1.03935)1/12=[(1+12APR12​)12]1/121.00322=(1+APR1212)1.00322={(1+\frac{APR12}{12})}1.00322=(1+12APR12​)1.00322−1=(APR1212)1.00322-1={(\frac{APR12}{12})}1.00322−1=(12APR12​)APR12 = 0.00322 × 12 = 0.03865, or approximately 3.87%.考点APR的转换解析这里考查的是不同计息频率的收益率之间的转换。一年计息两次的年化收益率,即APR2 ,转换到一年计息12次的APR12 ,可以同时转换到一年计息一次(相当于一个过渡)。即(1+APR2 /2)2 =1+EAR=(1+APR12 /12)12 ,得到APR12 为3.87%。 请问APR是在哪里学过呢,怎么这一章我没有看到这个知识点呢?谢谢!

2023-04-27 05:08 1 · 回答

NO.PZ2016031001000076问题如下A 5-year, 5% semiannucoupon payment corporate bonis price104.967 per 100 of pvalue. The bons yielto-maturity, quoteon a semiannubonbasis, is 3.897%. analyst hbeen asketo convert to a monthly periocity. Unr this conversion, the yielto-maturity is closest to: A.3.87%.B.4.95%.C.7.67%. A is correct.The yielto-maturity, statefor a periocity of 12 (monthly periocity), is 3.87%.The formula to convert annupercentage rate (annuyielto-maturity) from one periocity to another is follows:(1+APRmm)m=(1+APRnn)n{(1+\frac{APRm}m)}^m={(1+\frac{APRn}n)}^n(1+mAPRm​)m=(1+nAPRn​)n(1+0.038972)2=(1+APR1212)12{(1+\frac{0.03897}2)}^2={(1+\frac{APR12}{12})}^{12}(1+20.03897​)2=(1+12APR12​)12(1.01949)2=(1+APR1212)12{(1.01949)}^2={(1+\frac{APR12}{12})}^{12}(1.01949)2=(1+12APR12​)121.03935=(1+APR1212)121.03935={(1+\frac{APR12}{12})}^{12}1.03935=(1+12APR12​)12(1.03935)1/12=[(1+APR1212)12]1/12{(1.03935)}^{1/12}={\lbrack{(1+\frac{APR12}{12})}^{12}\rbrack}^{1/12}(1.03935)1/12=[(1+12APR12​)12]1/121.00322=(1+APR1212)1.00322={(1+\frac{APR12}{12})}1.00322=(1+12APR12​)1.00322−1=(APR1212)1.00322-1={(\frac{APR12}{12})}1.00322−1=(12APR12​)APR12 = 0.00322 × 12 = 0.03865, or approximately 3.87%.考点APR的转换解析这里考查的是不同计息频率的收益率之间的转换。一年计息两次的年化收益率,即APR2 ,转换到一年计息12次的APR12 ,可以同时转换到一年计息一次(相当于一个过渡)。即(1+APR2 /2)2 =1+EAR=(1+APR12 /12)12 ,得到APR12 为3.87%。 这里求出或者看出一年计息两次的变化收益率是3.897%之后怎么按计算器求出最终答案?题目是要求按出计息12次的年化收益率吗?

2022-10-13 22:55 1 · 回答

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2022-07-28 08:19 1 · 回答

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2022-06-24 01:19 1 · 回答

我用计算器这么按的 N=5*12=60 PV= -104.967  PMT= 100*5%/12=0.4167 FV=100 算出来 IY=0.3254这个应该是月化,我再乘以 12 得到对应的年化是 3.9,为什么这样是不对的呢?

2020-11-06 22:33 1 · 回答