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游游 · 2024年03月25日

计算器计算天数

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000070

问题如下：

Bond G, described in the exhibit below, is sold for settlement on 16 June 2014.

Annual Coupon 5%

Coupon Payment Frequency Semiannual

Interest Payment Dates 10 April and 10 October

Maturity Date 10 October 2016

Day Count Convention 30/360

Annual Yield-to-Maturity 4%

The accrued interest per 100 of par value for Bond G on the settlement date of 16 June 2014 is closest to:

选项：

A.

0.46.

B.

0.73.

C.

0.92.

解释：

C is correct.

The accrued interest per 100 of par value is closest to 0.92. The accrued interest is determined in the following manner: The accrued interest period is identified as66/180. The number of days between 10 April 2014 and 16 June 2014 is 66 days based on the 30/360 day count convention. (This is 20 days remaining in April + 30 days in May +16 days in June = 66 days total). The number of days between coupon periods is assumed to be 180 days using the 30/360 day convention.

Accrued interest = tT×PMT\text{Accrued interest = }\frac tT\times PMT

where:

t = number of days from the last coupon payment to the settlement date

T = number of days in the coupon period

t/T= fraction of the coupon period that has gone by since the last payment

PMT = coupon payment per period

Accrued interest = 66180×5.002=0.92\text{Accrued interest = }\frac{66}{180}\times\frac{5.00}2\text{=}0.92

考点：accrued interest

解析：accrued interest=coupon×t/T=(5/2)×(66/180)=0.92，故选项C正确。

由于债券半年付息，所以一期的coupon是2.5。t=66，代表的是trading day和上一个付息日之间的天数，4月10号到6月16号之间是66天。T代表的就是两个付息日之间的天数，由于我们现在是30/360，所以半年天数就是180天。将上述数据代入accrued interest的公式即可。

老师您好，请问用计算器计算天数是怎么操作的，已经用计算器按出了起始日期，不知道如何相减。

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3 个答案

吴昊_品职助教 · 2024年03月25日

嗨，爱思考的PZer你好：


计算器算出来的是实际的天数，会考虑大小月份，而30/360就是默认一年360天，一个月30天，忽略了大小月。

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努力的时光都是限量版，加油！

游游 · 2024年03月25日

这个计算器算出来是67，是因为把五月份取了31天吗，而按照30/360，是把每个月都按30天算？

吴昊_品职助教 · 2024年03月25日

嗨，从没放弃的小努力你好：


1、Day Count Convention 30/360，首先我们这道题是30/360的计算方式，所以用不到计算器DATE功能。2014年4月10日到2014年6月16日，之间一共是两个月多6天，一个月按照30天来计算，所以一共有：2×30+6=66 days，也就是我们这道题解析中表达的那样。

2、如果这道题的计算方式变成了actual/actual，我们才需要调用计算器DATE功能。

例如计算2014年4月10日到2014年6月16日实际一共有几天。

按“2nd”和数字键1，调用“DATE”功能。

①界面显示为出场设置：DT1=12-31-1990，按照英文的月/日/年习惯，将2014年4月10日输入为4.1014；注意输入完4后要按小数点，同时年份只输入后两位。输入后按ENTER，结果显示为DT1=4-10-2014

②按向下箭头，同理输入DT2=6-16-2014；

③按向下箭头，显示DBD后按CPT，得到两个日期之间间隔67天。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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