问一道题：NO.PZ2016031001000115 [ CFA I ]

问题如下：

An investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. The bond’s Macaulay duration is closest to:

选项：

2.62.

2.78.

2.83.

解释：

C is correct.

The bond’s Macaulay duration is closest to 2.83. Macaulay duration (MacDur) is a weighted average of the times to the receipt of cash flow. The weights are the shares of the full price corresponding to each coupon and principal payment.

Thus, the bond’s Macaulay duration (MacDur) is 2.83.

Alternatively, Macaulay duration can be calculated using the following closed-form formula:

$MacDur={\{\frac{1+r}r-\frac{1+r+\lbrack N\times(c-r)\rbrack}{c\times\lbrack{(1+r)}^N-1\rbrack+r}\}}-(t/T)$

$MacDur={\{\frac{1.08}{0.08}-\frac{1.08+\lbrack3\times(0.06-0.08)\rbrack}{0.06\times\lbrack{(1.08)}^3-1\rbrack+0.08}\}}-0$

MacDur = 13.50 − 10.67 = 2.83

请问price at 94.8458和PV有什么关系呢？

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1 个答案

吴昊_品职助教 · 2020年09月03日

同学你好：

The bond is currently priced at 94.845806 per 100 of par. 指的就是债券当前的价格。解析中罗列的表格present value指的是每一期现金流的现值，比方说第一年的现金流6，往前折一年，得到的就是5.55556；第二年的现金流6，往前折两年，得到的就是5.144033，最后将三个现金流现值加总起来就是94.845806。

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NO.PZ2016031001000115 问题如下 investor buys a 6% annupayment bonwith three years to maturity. The bonha yielto-maturity of 8% anis currently price94.845806 per 100 of par. The bons Macaulration is closest to: A.2.62. B.2.78. C.2.83. C is correct.The bons Macaulration is closest to 2.83. Macaulration (Macr) is a weighteaverage of the times to the receipt of cash flow. The weights are the shares of the full pricorresponng to eacoupon anprincippayment.Thus, the bons Macaulration (Macr) is 2.83.考点Macaulration解析Macaculay久期就是平均还款期，权重就是现金流现值占总价格的比值。1、第二列CF就是每一期的现金流，分别是6、6和106；2、用折现率8%进行折现到零时刻，就可以得到各期的PV，分别是6/1.08=5.56; 6/(1.08)^2=5.144; 106/(1.08)^3=84.146。将这三个数据加总就是94.85（第三列）；3、权重就是每一个PV占94.85的比例，分别是5.56/94.85=0.0586；5.144/94.85=0.0542; 84.146/94.85=0.88714、最后一列就是第一列perio第四列权重相乘，最终得到M是2.83，故C正确。为什么要用portfolio 的思路呢？为什么要算每一期权重呢？

2023-05-01 05:08 1 · 回答

NO.PZ2016031001000115问题如下investor buys a 6% annupayment bonwith three years to maturity. The bonha yielto-maturity of 8% anis currently price94.845806 per 100 of par. The bons Macaulration is closest to: A.2.62. B.2.78. C.2.83. C is correct.The bons Macaulration is closest to 2.83. Macaulration (Macr) is a weighteaverage of the times to the receipt of cash flow. The weights are the shares of the full pricorresponng to eacoupon anprincippayment.Thus, the bons Macaulration (Macr) is 2.83.考点Macaulration解析Macaculay久期就是平均还款期，权重就是现金流现值占总价格的比值。1、第二列CF就是每一期的现金流，分别是6、6和106；2、用折现率8%进行折现到零时刻，就可以得到各期的PV，分别是6/1.08=5.56; 6/(1.08)^2=5.144; 106/(1.08)^3=84.146。将这三个数据加总就是94.85（第三列）；3、权重就是每一个PV占94.85的比例，分别是5.56/94.85=0.0586；5.144/94.85=0.0542; 84.146/94.85=0.88714、最后一列就是第一列perio第四列权重相乘，最终得到M是2.83，故C正确。用折现率8%进行折现，就可以得到各期的PV，第一期的折现 PMT =6，I/Y=8，N=1，FV=6，求出PV1=-11第二期的折现 PMT =6，I/Y=8，N=2，FV=6，求出PV2=-15第三期的折现 PMT =6，I/Y=8，N=3，FV=106，求出PV3=-99.6而实际上答案分别是6/1.08=5.56; 6/(1.08)^2=5.144; 106/(1.08)^3=84.146。将这三个数据加总就是94.85

2022-04-07 23:22 1 · 回答

NO.PZ2016031001000115 2.78. 2.83. C is correct. The bons Macaulration is closest to 2.83. Macaulration (Macr) is a weighteaverage of the times to the receipt of cash flow. The weights are the shares of the full pricorresponng to eacoupon anprincippayment. Thus, the bons Macaulration (Macr) is 2.83. Alternatively, Macaulration ccalculateusing the following closeform formulMacr={1+rr−1+r+[N×(c−r)]c×[(1+r)N−1]+r}−(t/T)Macr={\{\frac{1+r}r-\frac{1+r+\lbraN\times(c-r)\rbrack}{c\times\lbrack{(1+r)}^N-1\rbrack+r}\}}-(t/T)Macr={r1+r−c×[(1+r)N−1]+r1+r+[N×(c−r)]}−(t/T) Macr={1.080.08−1.08+[3×(0.06−0.08)]0.06×[(1.08)3−1]+0.08}−0Macr={\{\frac{1.08}{0.08}-\frac{1.08+\lbrack3\times(0.06-0.08)\rbrack}{0.06\times\lbrack{(1.08)}^3-1\rbrack+0.08}\}}-0Macr={0.081.08−0.06×[(1.08)3−1]+0.081.08+[3×(0.06−0.08)]}−0 Macr = 13.50 − 10.67 = 2.83麻烦老师说一下算这个表格里这些数据具体的计算步骤

2021-05-05 15:03 1 · 回答

2.78. 2.83. C is correct. The bons Macaulration is closest to 2.83. Macaulration (Macr) is a weighteaverage of the times to the receipt of cash flow. The weights are the shares of the full pricorresponng to eacoupon anprincippayment. Thus, the bons Macaulration (Macr) is 2.83. Alternatively, Macaulration ccalculateusing the following closeform formulMacr={1+rr−1+r+[N×(c−r)]c×[(1+r)N−1]+r}−(t/T)Macr={\{\frac{1+r}r-\frac{1+r+\lbraN\times(c-r)\rbrack}{c\times\lbrack{(1+r)}^N-1\rbrack+r}\}}-(t/T)Macr={r1+r−c×[(1+r)N−1]+r1+r+[N×(c−r)]}−(t/T) Macr={1.080.08−1.08+[3×(0.06−0.08)]0.06×[(1.08)3−1]+0.08}−0Macr={\{\frac{1.08}{0.08}-\frac{1.08+\lbrack3\times(0.06-0.08)\rbrack}{0.06\times\lbrack{(1.08)}^3-1\rbrack+0.08}\}}-0Macr={0.081.08−0.06×[(1.08)3−1]+0.081.08+[3×(0.06−0.08)]}−0 Macr = 13.50 − 10.67 = 2.83请问老师表格中perioweight是怎么算出来的

2020-10-21 18:15 1 · 回答

老师我是这样算的您看看对不对 [6/1.08+12/(1.08^2)+(106*3)/(1.08^3)]/94.845806

2020-10-20 17:21 2 · 回答

问一道题：NO.PZ2016031001000115 [ CFA I ]

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