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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
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  • $\begingroup$ have you tried F1 F1? $\endgroup$ Dec 11, 2023 at 19:47

1 Answer 1

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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.

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  • $\begingroup$ Nice! Where did you find the supporting information? Is this methodology used only by Bloomberg or is it more widespread? If you found my question relevant, please upvote it. $\endgroup$ Dec 12, 2023 at 2:20
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    $\begingroup$ Hi @RodolfoOviedo I'd characterize this as industry standard calculation. $\endgroup$
    – Helin
    Dec 12, 2023 at 5:10

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