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runruncat · 2023年06月10日

Day Count Convention 30/360

  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 June2014 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。

老师上课举例6月15日-8月21日，6月15日-8月15日算2个月，在Day Count Convention 30/360下就是2*30=60天，然后8月15日-8月21日，就是21-15=6天，也不管什么算头不算尾，这样一共是60+6=66天。

本题是4月10日-6月16日，那就是4月10日-6月10日算2个月，在Day Count Convention 30/360下就是2*30=60天，然后6月10日-6月16日，也是16-10=6天，也一共是66天。

请问是这样算吗？总对要不要算头不算尾这类比较迷惑，像我这么算，也不用管大月小月闰月了，请问是我这种计算的思路吗？

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吴昊_品职助教 · 2023年06月10日

嗨，从没放弃的小努力你好：


1、Day Count Convention 30/360，只要题干中出现了这个字样，那就按照一个月30天来算，不用管大小月或者闰月。

2、“本题是4月10日-6月16日，那就是4月10日-6月10日算2个月，在Day Count Convention 30/360下就是2*30=60天，然后6月10日-6月16日，也是16-10=6天，也一共是66天。”这个思路是完全正确的。

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努力的时光都是限量版，加油！

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