Bloomberg True Yield Uses the Bond’s Original Day-Count Convention
Summary
The document explains how Bloomberg’s bond “true yield” accounts for payment dates adjusted for weekends and holidays. Its central claim is that the yield calculation retains the bond’s original day-count convention, while shifting discount periods to reflect adjusted payment dates. The number of days in each coupon period remains based on the unadjusted schedule.
A worked Treasury example compares conventional yield with true yield using the same dirty price and cash flows. When payment dates move forward, the corresponding discount fractions increase by the number of extra calendar days, divided by the original coupon-period length. This produces a small yield difference. A second answer independently recalls an Actual/Actual treatment. The discussion is useful for replicating bond analytics, but rests on a particular example and respondent explanations rather than cited Bloomberg documentation; the example’s Actual/Actual convention should not be generalized to bonds with different conventions.
Key ideas
- Bloomberg true yield is described as using the bond’s original day-count convention.
- Adjusted payment dates change discount timing, while coupon amounts and original coupon-period day counts remain unchanged.
- The example adjusts discount fractions for extra calendar days caused by weekends or holidays.
- The reported yield difference is illustrated for one Treasury bond and may vary with the bond’s convention and schedule.
Tags
Full text
# What is the day-count basis of the "true yield" reported by Bloomberg for bonds?
# What is the day-count basis of the "true yield" reported by Bloomberg for bonds?
Plenty of sources the web, including Bloomberg's CFA pararation pages, state that the "true yield" reported by Bloomberg for bonds uses business adjusted payment dates for computation. However, I have found no information on the day-count basis of the "true yield" reported by Bloomberg for bonds?
Does anyone have access to Bloomberg documentation to answer my doubt? Or is there any international standard that Bloomberg follows?
Alternatively, if someone retrieves the following information of a bond from Bloomberg, I could figure out the day-count convention of the true yield on my own and provide an answer for the community:
- coupon rate
- price of the bond, preferably the dirty price (clean price plus convention is good enough)
- schedule of payments
- settlement date
- true yield reported
## Answer by Helin (score 3, accepted)
https://quant.stackexchange.com/a/77686
It follows the same day count convention as the original bond (e.g., Actual/Actual for US Treasuries).
Let's go through a concrete example. Consider the 4.75% maturing on February 28, 2009, for settlement on August 20, 2007 (I picked this example because the true yield spread is somewhat pronounced) at a dirty price of 102.9908288. Here are the cash flows:
| Coupon Date | Payment Date | Days in Coupon Period | Cash flow |
| 8/31/2007 | 8/31/2007 | 184 | 2.375 |
| 2/29/2008 | 2/29/2008 | 182 | 2.375 |
| 8/31/2008 | 9/1/2008 | 184 | 2.375 |
| 2/28/2009 | 3/2/2009 | 181 | 102.375 |
Column 1 is the unadjusted coupon dates, while column 2 reports the holiday/weekend-adjusted payment dates. Notice that this bond has two "bad days." Column 3 is the number of days in each coupon period (notadjusted for bad days).
The conventional price/yield formula would be:
$$ 102.9908288 = \frac{2.375}{(1 + y/2)^{11/184}} + \frac{2.375}{(1 + y/2)^{11/184+1}}+ \frac{2.375}{(1 + y/2)^{11/184+2}} + \frac{102.375}{(1 + y/2)^{11/184+3}}. $$ This gives us a yield to maturity of 4.2322761%.
To calculate the true yield, the price/yield formula would be modified as follows $$ 102.9908288 = \frac{2.375}{(1 + y/2)^{11/184}} + \frac{2.375}{(1 + y/2)^{11/184+1}}+ \frac{2.375}{(1 + y/2)^{11/184+2 + \color{red}{1/184}}} + \frac{102.375}{(1 + y/2)^{11/184 + 3 + \color{red}{2/181}}}. $$ The first two terms on the RHS are unchanged, because the coupon dates are already good days. For the third term, we add 1 more day to the discount fraction since the payment date is moved forward by one calendar day. By convention, the number of days in the coupon period is not adjusted. Likewise, for the fourth term, we add 2 more days to the discount fraction, but still use the 181 as the number of days in the coupon period. This gives us a yield to maturity of 4.2169103%.
The true yield spread is then 1.54 bps.
## Answer by DavidJN (score 0)
https://quant.stackexchange.com/a/85172
Given than the Bloomberg "true" yield adjusts the cash flow payment dates (but not the cash flow amounts) to good business dates, and then computes the "true" yield to those actual payment dates, I believe the answer to your question is that the inherent treatment in BBG true yield is actual/actual. That is how I remember replicating the BBG results.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.