Bond Yield Compounding Conventions and Frequency Conversion
Summary
Bond yields are generally quoted using a compounding frequency that matches the coupon payment schedule. Some markets instead standardize yields to the frequency used for local government bonds, which makes comparisons with benchmarks and across issuers easier. The document gives examples involving Eurozone corporate bonds and U.S. Treasury and U.K. gilt conventions, and notes that some zero-coupon bonds are still quoted with periodic compounding.
Yields quoted at different frequencies can be converted by equating their effective annual growth factors. The document provides a conversion relationship and cautions that its rearranged expression should be checked before use. It also says continuous compounding is not a usual market convention for bond yields. These are convention-based guidelines, not a universal rule: the applicable quote frequency depends on the bond market, and the examples do not cover every jurisdiction or instrument.
Key ideas
- Bond yield compounding usually follows the coupon payment frequency.
- Some markets quote yields using the local government bond frequency to support comparisons.
- Certain zero-coupon bonds use periodic compounding even though they do not pay coupons.
- Yields at different frequencies can be converted by equating their effective annual growth factors.
- The appropriate convention varies by market, and the document advises checking the algebra of its conversion expression.
Tags
Full text
# Yield of a Bond
# Yield of a Bond
If we have a `coupon bearing Bond` and want to calculate it's `Yield` then what is the standard practice to determine the Compounding frequency of Yield?
Is it always considered as `Continuously compounded`? or the compounding frequency matches with the Interest payment's frequency?
Appreciate for any pointer.
## Answer by Dimitri Vulis (score 6, accepted)
https://quant.stackexchange.com/a/57766
Almost always, the market convention is to use for yield the same frequency as the coupon payment frequency.
However in a few markets, the market convention is to convert this yield to the frequency of the local government bond. For example, if the local government bonds usually pay annually, as they do in Eurozone, and some corporate bond pays quarterly or semi-annually, then you annualize the latter bond's yield, so it is easier to compare with the rest of the universe. Conversely, U.S. treasury debt (notes and bonds) and U.K. gilts pay semi-annual coupons, so the yield of GBP bonds having other frequencies are often quoted as semi-annual, so that, e.g., spread over benchmark is more meaningful.
If you have access to Bloomberg terminal, look for the field 'conventional yield frequency', which contains this frequency (periodicity) conventionally used to quote this bond's yield.
However I have never seen any bond for which the convention would be convert the yield to continuous compounding.
I suggest you read this paper on gilts to get a good feeling for price-yield conventions.
Edit: Also in a few markets, the market conventions even for a yield of bonds that don't pay coupons is to use compounding anyway. For example, LTNs in Brazil have no coupons, have had maturities up to 5 years, their yield are conventionally quoted using annual compounding. There are non-coupon-paying bonds in Eurozone (example) whose yield is likewise quoted using annual compounding.
If $f_1$ and $f_2$ are frequencies (1 - annual, 2 - semiannual, 4 - quarterly, 12 - monthly...), and $y_{f_1}$ and $y_{f_2}$ denote the yields corresponding to these frequencies, then ${\left(1+\frac{y_{f_1}}{f_1}\right)}^{f_1}={\left(1+\frac{y_{f_2}}{f_2}\right)}^{f_2}$, so I think $y_{f_2} = \left(\left(1+\frac{y_{f_1}}{f_1} \right)^{\frac{f_1}{f_2}} -1 \right)\times {f_2} $ (check my algebra before using) - higher frequency quotes lower yield.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.