Bond Yield Discounting: Scheduled Dates Versus Payment Dates
Summary
The document asks which date convention to use when discounting bond cash flows whose interest accrual date and payment date differ, such as when a scheduled date falls on a holiday or payment is contractually delayed. It contrasts the date when an amount is earned and legally due with the later date when the holder receives funds and can reinvest them.
The answer distinguishes street-convention yield calculations, which traditionally use unadjusted scheduled dates, from true-yield calculations, which use actual business-day payment dates. It also reports that actual cash flow dates are commonly used for calculations such as Z-spreads and asset-swap spreads. These are convention-based distinctions rather than a universal rule for every valuation; the appropriate date depends on the yield or spread measure being calculated.
Key ideas
- Bond accrual dates and cash receipt dates can differ because of business-day conventions or payment delays.
- Street-convention yield calculations traditionally use unadjusted scheduled dates.
- True-yield calculations use the actual business-day cash flow dates.
- Z-spread and asset-swap spread calculations commonly use actual payment dates.
Tags
Full text
# Should Earned or Received date be used in bond valuation discount factor
# Should Earned or Received date be used in bond valuation discount factor
Is there a market convention for which date should be used when calculating time to cash flow in a discount function?
In practice bond cash flow dates often differ between earned and received dates. Such as Roll conventions on weekends and holidays when interest is calculated up until the scheduled date but payment rolls to the next business day. Or contractual payment delays where interest is not distributed until n days after it is earned.
e.g. Take the basic yield equation below where $t_i$ is the time to each cash flow $i$ represented as time in years from evaluation date $t_i = T_i - T_0$
$ p = \sum_{i=1}^n\frac{C_i}{(1+y)^{t_i}}$
I can justify either one in the following ways:
- Earned date represents the time when the cash flow is known and legally obligated to the bond holder
- Received Date is when the cash provides economic value. i.e. Can be reinvested
## Answer by Dimitri Vulis (score 2, accepted)
https://quant.stackexchange.com/a/84062
Traditionally, in "street convention" bond yield calculations, we use dates that are not adjusted for non-business days. But for "true yield", we use actual cash flow dates, which are business days. See, for example, https://ift.world/booklets/fixed-income-introduction-to-fixed-income-valuation-part4 Section 3.4
In other calculations where this distinction matters a little, such as Z-spreads or asset swap spreads, I believe almost everyone uses actual cash flow dates, same as for true 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.