What is the day-count basis of the "true yield" reported by Bloomberg for bonds?

Question

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:

1. coupon rate
2. price of the bond, preferably the dirty price (clean price plus convention is good enough)
3. schedule of payments
4. settlement date
5. true yield reported

Answer 1

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.