Yield Measures: Street Convention, True, and Government Equivalent Yields

John's new semi-annual coupon bond is scheduled to pay its USD 32 coupon on 31 March and 30 September of each year. Based on this promised payment every half-year, and the other necessary variables of the bond price and maturity, John can easily calculate his semi-annual bond yield of 6.1397%. This is the bond's __street convention yield__, calculated based on the assumption that these will be the actual payment dates. In practice, no two calendar dates will ever be valid payment dates over the course of many years, because they will sometimes fall on weekends or holidays. When this happens, the payments are made on the first business day following the scheduled payment date.

How do you suppose this affects the __true yield__, or the bond yield that John will actually get?

That's right! Since the payments will never come early, but sometimes will come late, this can only lower the actual, realized bond yield. So the true yield will never be larger than the street convention yield.

No, consider that any payment date which falls on a weekend or holiday is paid later. John will have to wait longer for his money.

No, consider that any bond payment which falls on a weekend or holiday is pushed back to a later date, but is never moved forward to an earlier date.

What would you estimate this difference in John's yield to be?

Absolutely. The difference of just a day or two for a few coupon payments will be really small. But John wants to know what it is, so he looks ahead in the calendar, finds the days which fall on weekends or holidays, adjusts his spreadsheet for that exact fraction of a period, and comes up with his true yield. It's 6.1345%. So that's just a difference of 0.0052 percentage points, or about half of a basis point. That's pretty typical for this adjustment, and it's never more than a basis point or so.

No, that's a bit generous. It's a fair guess without performing a calculation, but you'd have to think about the tiny inconvenience from waiting an extra day or two for a cash flow out of a calendar year.

No, that's far too large. Think about what the difference would really be to ask him to wait one or two extra days for a small coupon payment.

Do you think that is worth the extra effort to many analysts?

Incorrect, but you certainly place a high value on accuracy.

Correct, and most people agree with you.

There's also a __government equivalent yield__, which you might run into someday. This is a yield measure which converts from a simplified 30-day month and 360-day year to actual calendar days. So if you have a 4.9% yield quoted on a 30/360 basis, how do you think you would get to the government equivalent yield?

It's quite a bit of work for such a tiny difference, and this is why the true yield is often ignored. The street convention yield is by far more common.

No, the other way. You'll need to scale it by 365/360, like this:

You got it!

$$\displaystyle 4.90 \% \times \frac{365}{360} \approx 4.97 \% $$ So this adjustment does make a bit more of a noticeable difference, opposed to the street convention yield vs. the true yield. This is a 7 basis point difference, which is more notable to bond traders. It makes sense; adding 5 days of interest does a lot more than just moving a payment around a little. And for someone to deny an investor their full return would be so... unyielding!

To summarize: [[summary]]

It makes John's true yield smaller

It makes John's true yield larger

It makes John's true yield either smaller or larger, depending on the payment dates

About a 1.0% difference in yield

About a 0.1% difference in yield

Very small; perhaps just a basis point or less

Yes

No

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Scale it by 360/365

Scale it by 365/360

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