[Wiki] Taxable Equivalent Yield (TEY)

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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

daw007 wrote: Fri Feb 03, 2023 2:01 am Thanks for your input! I made the changes recommended and tried to sort it logically. Let me know what you think! I don't understand the below sentence exactly though. Where would you suggest using ATY instead of (1-f-s)?
I would emphasize that the term used to compute ATY, (1-f-s), is always the denominator in a TEY formula. Then, you can just use ATY instead of (1-f-s) in the denominator of the formula in its final form.
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That was inaccurate. I rewrote it, but apparently you copied my reply before the edit. Here is the edited section:
I would emphasize that the term used to compute ATY for fully taxable fixed income, (1-f-s), is always the denominator in a TEY formula. The numerator always is the ATY for the type of fixed income of interest. For example, for a Treasury:

ATY = Y * (1-f) (for Treasuries)

TEY = ATY/(1-f-s) = Y * (1-f)/(1-f-s)

No TEY formula is required for fully taxable fixed income (e.g., HYSA, fully-taxable MM fund), since the TEY is just the stated yield; i.e.,

TEY = Y (for fully taxable fixed income).
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

Good work on the latest version. Here are some comments.

This statement currently is incorrect;
For example, US treasuries have lower rates than high yield savings account but are not subject to state and local income tax.
As of yesterday, the 1m CMT yield was 4.62%, which is higher than most HYSAs.

You could make the statement correct by adding the word "sometimes" before "US treasuries". Also, "Treasuries" usually is capitalized. I would insert "short-term", since those are the Treasuries you might compare to a HYSA.

You might also want to add something like, "So, if you pay state income tax, the TEY of a short-term Treasury could be higher than the TEY of the HYSA, even though the HYSA interest rate is higher than the Treasury yield.".

Overall, the new version is much better. Personally, I would include the derivations in the main article, perhaps at the end, but it's not that big of a deal I guess.

The use of ATY needs to be cleaned up based on my edited reply. For each derivation, I would add an equation that defines ATY for the type of fixed income. It always is the numerator, not just for in state munis. It's just that for in state munis. Examples:

State munis:

ATY = Ym
TEY = ATY/(1-f-s) = Ym/(1-f-s)

Treasuries:

ATY = Yt * (1-f)
TEY = ATY/(1-f-s) = Yt * (1-f) / (1-f-s)

I think this approach makes it easier to remember the formulas. Most people have an easier time understanding ATY, and can probably understand and remember the ATY formulas. Then, one just needs to remember the denominator, which is always the same.

I haven't reviewed everything in detail yet.

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by LadyGeek »

daw007 wrote: Fri Feb 03, 2023 11:06 am
LadyGeek wrote: Fri Feb 03, 2023 6:30 am Also please note that a wiki editor has commented in the Talk page. (It's how editors communicate within the wiki.)

The suggestion is to move the equation derivations to a separate page. Two examples are provided.

I would agree. Leave the underlying math for those interested in the details.
thanks for letting me know! I moved the derivations as suggested and responded to the talk page.
You're welcome. The new draft page is here: User:Daw007/Tax equivalent yield (math)
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

If I were to write the OP today, I would do it differently. Instead of modifying the OP now, here is a draft of the way I'd write it the first part of it now.

-----------------------

When buying fixed-income securities (Treasuries, in-state municipal bonds, out-of-state munis, corporate bonds, CDs, etc) or bond or money market funds in taxable accounts, you want to compare yields on an taxable-equivalent basis, since each of these may be taxed differently. What matters is the yield you have left to spend after you pay income taxes. Of course inflation is a factor too, but here I'll just discuss the tax equivalence aspect.

You can compare either after tax yield (ATY), or equivalent before tax yield, which is called taxable-equivalent yield (TEY). The convention seems to be to do the latter, probably because most yields we see quoted are taxable yields.

We can derive the TEY of a particular type of fixed income starting with the following equation:

ATY = TEY * tt

where tt is the total marginal income tax rate applicable to fully taxable fixed income. For the non-itemizing case, which probably will be vast majority under the tax laws as of 2023, tt is the same for all types of fixed income:

tt = (1-f-s)

where f = federal marginal tax rate and s = state marginal tax rate. These marginal tax rates are not the same as the top tax bracket; they include anything that affects the true marginal tax rate; e.g., f includes NIIT and AMT if applicable. If you pay local income tax, you'd include that in s, or add another term for it.

Solving for TEY,

TEY = ATY/tt
TEY = ATY/(1-f-s)

For a fully taxable fixed income, TEY is simply the yield:

TEY = Y

ATY = TEY * (1-tt)
ATY = Y*(1-tt)
ATY = Y*(1-f-s)

where Y = yield to maturity. Note that for bank accounts, using APY for yield gives results that generally are close enough for comparisons.

For in-state muni income, which is exempt from federal and state tax, ATY is simply the yield, so:

ATY = Y

TEY = ATY/tt

TEY = Y/(1-f-s)

For out of state muni income, which is exempt from federal income tax but not from state income tax:

ATY = Y*(1-s)

TEY = ATY/tt

TEY = Y*(1-s)/(1-f-s)

For Treasury income, which is exempt from state and local income tax:

ATY = Y*(1-f)

TEY = ATY/tt

TEY = Y*(1-f)/(1-f-s)

-----------------------

I would make similar changes for the itemizing case and for the partially tax-exempt cases.

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by daw007 »

Kevin M wrote: Fri Feb 03, 2023 11:51 am Good work on the latest version. Here are some comments.

This statement currently is incorrect;
For example, US treasuries have lower rates than high yield savings account but are not subject to state and local income tax.
As of yesterday, the 1m CMT yield was 4.62%, which is higher than most HYSAs.

You could make the statement correct by adding the word "sometimes" before "US treasuries". Also, "Treasuries" usually is capitalized. I would insert "short-term", since those are the Treasuries you might compare to a HYSA.

You might also want to add something like, "So, if you pay state income tax, the TEY of a short-term Treasury could be higher than the TEY of the HYSA, even though the HYSA interest rate is higher than the Treasury yield.".

Overall, the new version is much better. Personally, I would include the derivations in the main article, perhaps at the end, but it's not that big of a deal I guess.

The use of ATY needs to be cleaned up based on my edited reply. For each derivation, I would add an equation that defines ATY for the type of fixed income. It always is the numerator, not just for in state munis. It's just that for in state munis. Examples:

State munis:

ATY = Ym
TEY = ATY/(1-f-s) = Ym/(1-f-s)

Treasuries:

ATY = Yt * (1-f)
TEY = ATY/(1-f-s) = Yt * (1-f) / (1-f-s)

I think this approach makes it easier to remember the formulas. Most people have an easier time understanding ATY, and can probably understand and remember the ATY formulas. Then, one just needs to remember the denominator, which is always the same.

I haven't reviewed everything in detail yet.

Kevin
thanks for the kind words! i made changes as recommended in this post. then, i saw you had graciously took time to rewrite your formula derivations in another post. i will tackle that in the next 2-3 days.
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

After thinking about it some more, I think it would be more effective to just leave "tt" (total marginal tax rate) as the denominator in the TEY formulas. This might help eliminate confusion about handling NIIT, AMT and other things that cause the marginal tax rates to change. So, the TEY formula always is just:

TEY = ATY/tt

The main job is to determine ATY and what to include in tt.

I don't' have time to rewrite it with this simplification now, but I'll get back to it soon.

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

Next draft

-----------------------

When buying fixed-income securities (Treasuries, in-state municipal bonds, out-of-state munis, corporate bonds, CDs, etc) or bond or money market funds in taxable accounts, you want to compare yields on an taxable-equivalent basis, since each of these may be taxed differently. What matters is the yield you have left to spend after you pay income taxes. Of course inflation is a factor too, but here I'll just discuss the tax equivalence aspect.

You can compare either after tax yield (ATY), or equivalent before tax yield, which is called taxable-equivalent yield (TEY). The convention seems to be to do the latter, probably because most yields we see quoted are taxable yields.

Due to the current $10K limitation on SALT deductions, and the relatively high standard deductions, most people will not derive any income tax benefit with respect to investment income by itemizing deductions, and the derivations in this section are based on this assumption.

Let's start by considering fully taxable income, for which

ATY = Y * (1-tt),

where Y is the yield and tt is the total marginal income tax rate. For example, for marginal income tax rates of 22% federal and 9.3% state, with no NIIT, AMT or other credit phase-ins or phase-outs,

tt = (22% + 9.3%) = 31.3%.

These marginal tax rates are not the same as the top tax brackets; they include anything that affects the true marginal tax rate; e.g., NIIT and AMT, and local income tax. For example, for marginal income tax rates of 35% federal, 3.8% NIIT, and 5% state,

tt = (35% + 3.8% + 5%) = 43.8%.

We can rewrite the first equation as

Y = ATY/(1-tt).

This equation only applies to fully taxable income (for bank accounts, using APY for Y gives results that generally are close enough for comparisons). To extend it to other types of income, we can replace Y with TEY, which stands for taxable equivalent yield. For fully taxable income, TEY = Y, and we can rewrite the equation as:

TEY = ATY/(1-tt)

Next, we determine ATY for different types of income, and use that to compute TEY.

For in-state muni income, which is exempt from federal and state tax, ATY is simply the yield, so:

TEY = ATY/(1-tt)

ATY = Y

TEY = Y/(1-tt).

Note that tt is the same in all TEY equations, so we would use the same tt as in the previous examples; e.g., 31.3% or 43.8%.

For out of state muni income, which is exempt from federal income tax but not from state income tax, so

tt = s,

where s = marginal state income tax rate, so,

TEY = ATY/ (1-tt)

ATY = Y*(1-s)

TEY = Y*(1-s)/ (1-tt)

For Treasury income, which is exempt from state and local income tax, so tt is the marginal federal income tax rate, f (including NIIT, AMT, etc.), and,

TEY = ATY/ (1-tt)

tt = f

ATY = Y*(1-f)

TEY = Y*(1-f)/(1-tt)

-----------------------

I would make similar changes for the itemizing case and for the partially tax-exempt cases.

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

Here is my dialogue with GPT playground about terminology:
Me: Which term is more common: "tax equivalent yield" or "taxable equivalent yield"?

GPT: "Taxable equivalent yield" is the more common term.

Me: How did you determine that?

GPT: I determined this by looking at the relative frequency of use of the two terms in online searches and on financial websites.

Me: What is the relative frequency of each term?

GPT: The relative frequency of "tax equivalent yield" and "taxable equivalent yield" is roughly 3:1.

Me: This seems to imply that "tax equivalent yield" is more common, doesn't it?

GPT: No, it implies that "taxable equivalent yield" is more common. The relative frequency of 3:1 indicates that "taxable equivalent yield" is used three times more often than "tax equivalent yield".

Me: Which is more common: "taxable-equivalent yield" or "taxable equivalent yield"; i.e., with or without the hyphen?

GPT: "Taxable equivalent yield" is more common, without the hyphen.
Here is a similar dialogue with Chat GPT:
Me: Which term is more common: "tax equivalent yield" or "taxable equivalent yield"?

GPT: "Taxable equivalent yield" is more commonly used.

Me: How much more common is it?

GPT: As a language model, I do not have data on the exact usage frequency of these terms. However, "taxable equivalent yield" is generally considered to be the standard terminology used in finance and is more widely recognized and understood.

Me: How did you determine that?

GPT: As a language model, I have been trained on a diverse range of text from the internet, including articles, websites, and financial reports. This training data allows me to recognize patterns and commonly used terminology in different fields, including finance. Based on this training, "taxable equivalent yield" is the term that is most frequently used and recognized in finance, which is why I concluded that it is the more commonly used term.

Me: Which is more common: "taxable-equivalent yield" or "taxable equivalent yield"; i.e., with or without the hyphen?

GPT: "Taxable equivalent yield" without the hyphen is more commonly used.
Based on this, I'd recommend using "taxable equivalent yield" consistently throughout, including the title.

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by daw007 »

okay, I think I'm as close to done as I can be. I encompassed the suggested revision by Kevin M posted Sun Feb 05, 2023 9:02 pm. I also changed to Taxable equivalent yield.

I did not rewrite the derivations under "For funds partially exempt from state income tax" as that is a little over my head.

let me know what you think before I ask the mods to move it to be live.

thanks for all your help everyone!
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by LadyGeek »

FYI - Any wiki editor can move the page "live", but you should be comfortable doing so (move the page to the "Article" namespace and remove the User: prefix). There are also a few administrative details to take care of like adding categories and updating the navigation menu.

You can make the request in this thread or in the "Talk" page of the article. It makes sense to have both draft pages ready and moved together.
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

Looks really good! I would probably tweak a few things, and can provide some additional suggestions, but I think it's good enough to go live unless others object. It can still be tweaked after it's live.

One example is the use of the USGO percentage for 2018, and the mention that "we don't know what it will be for 2019". It's fine to use 2018 in the example, but we can mention that for 2022 VMFX did not meet the 50% requirement for CA, NY and CT, so fund holders in these states receive no state tax exemption for 2022. This highlights the risk in assuming the state tax exemption percentage for the current year.

Thanks a lot for doing this. I think this fills a big gap in the BH Wiki.

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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by daw007 »

moved to live.

no worries, I have gained so much knowledge from bogleheads and just wanted to donate back something to the best place for financial advice I know!
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

I think you need to change the link in the Example and usage section in the main page from User:Daw007/Taxable equivalent yield (math) to Taxable equivalent yield (math) - Bogleheads.

I'll add links to these Wiki pages in the OP.

Thanks,

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by daw007 »

Kevin M wrote: Tue Feb 07, 2023 4:36 pm I think you need to change the link in the Example and usage section in the main page from User:Daw007/Taxable equivalent yield (math) to Taxable equivalent yield (math) - Bogleheads.
whoops. fixed.
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by LadyGeek »

Looks good. The wiki editors made a few administrative updates. Here are the wiki pages:

- Taxable equivalent yield
- Taxable equivalent yield (math)

They're ready for the proposed additional tweaks.
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by exodusing »

The wiki has the defined term ATY, but does not use it.

The wiki acknowledges that "AFTER tax yield is most important as each individual's marginal tax rate is different", but nonetheless says "You can compare either after tax yield (ATY), or equivalent before tax yield, which is called taxable equivalent yield (TEY). The convention seems to be to do the latter, probably because most quoted yields are taxable yields." No formula is provided for ATY.

Given that ATY is easier to compute and, as noted, most important, you might consider saying more about it or linking to a page which covers it. Also, another reason for the TEY convention is that TEY is a higher number than ATY and fund companies prefer higher numbers in this context.
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by grabiner »

exodusing wrote: Thu Feb 16, 2023 4:55 pm The wiki has the defined term ATY, but does not use it.

The wiki acknowledges that "AFTER tax yield is most important as each individual's marginal tax rate is different", but nonetheless says "You can compare either after tax yield (ATY), or equivalent before tax yield, which is called taxable equivalent yield (TEY). The convention seems to be to do the latter, probably because most quoted yields are taxable yields." No formula is provided for ATY.
I added an example to the wiki page, showing the equivalence (two bonds with the same TEY and ATY).
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

exodusing wrote: Thu Feb 16, 2023 4:55 pm The wiki has the defined term ATY, but does not use it.

The wiki acknowledges that "AFTER tax yield is most important as each individual's marginal tax rate is different", but nonetheless says "You can compare either after tax yield (ATY), or equivalent before tax yield, which is called taxable equivalent yield (TEY). The convention seems to be to do the latter, probably because most quoted yields are taxable yields." No formula is provided for ATY.

Given that ATY is easier to compute and, as noted, most important, you might consider saying more about it or linking to a page which covers it. Also, another reason for the TEY convention is that TEY is a higher number than ATY and fund companies prefer higher numbers in this context.
I agree that ATY should be better explained in the main page. I would say something like:

All TEY formulas take the form ATY/(1-tt), where ATY is after tax yield, and tt is total marginal tax rate (including federal, state, NIIT, AMT, etc.); tt is the same in all of the formulas for not itemizing. Then, in each section, define ATY for that type of income; e.g.,

For an in state muni, ATY = Y, so TEY = Y/(1-tt).

Out of state muni: ATY = Y*(1-s)
US Treasury: ATY = Y*(1-f)

There is a link to the math page which defines ATY.

I disagree with the last sentence. The main reason to use TEY is that it's easier to compare to fully taxable yields, since no additional calculations are required for the latter. People know what the APY at their bank is, and TEY is a better number to compare to APY (not exactly the same, but close enough for most comparisons). People know what the yield of their full taxable money market fund is, etc.

At any rate, you are free to use ATY, but TEY is used so often in posts on the forum (including by me), that it's good to have a place where it's defined.

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by daw007 »

Revised wiki entry to add in Kevin M's suggestion: "All TEY formulas take the form ATY/(1-tt)" and added in ATY formulas for in stat muni, out of state muni, and US treasury.

Did not put in the part explaining ATY, tt b/c it's stated in the section immediately below.

Kevin M wrote: Thu Feb 16, 2023 8:24 pm I agree that ATY should be better explained in the main page. I would say something like:

All TEY formulas take the form ATY/(1-tt), where ATY is after tax yield, and tt is total marginal tax rate (including federal, state, NIIT, AMT, etc.); tt is the same in all of the formulas for not itemizing. Then, in each section, define ATY for that type of income; e.g.,

For an in state muni, ATY = Y, so TEY = Y/(1-tt).

Out of state muni: ATY = Y*(1-s)
US Treasury: ATY = Y*(1-f)

There is a link to the math page which defines ATY.

I disagree with the last sentence. The main reason to use TEY is that it's easier to compare to fully taxable yields, since no additional calculations are required for the latter. People know what the APY at their bank is, and TEY is a better number to compare to APY (not exactly the same, but close enough for most comparisons). People know what the yield of their full taxable money market fund is, etc.

At any rate, you are free to use ATY, but TEY is used so often in posts on the forum (including by me), that it's good to have a place where it's defined.

Kevin
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

I am in awe of how responsive you are in incorporating feedback! I encouraged a forum member who had commented on it in another thread to post here, and that forum member did! And then you responded!

I had to read grabiner's example addition twice to get it (it is late, and I am old), but it does make sense. Others should comment on if this helps them understand it.

Such a wonderful community. :D :D :D

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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by daw007 »

just happy to help!
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Deskandchairs »

For a topic of this magnitude, it would be helpful to start with important definitions.
Do we all understand what is meant by "yield"?
In the bond world, bonds are conventionally compared based on "yield to maturity." This information is prominently displayed on many/most broker websites.

I believe that is the incorrect "yield" to be using in these TEY formulas and comparisons.
Rather the "simple" yield (or as Vanguard calls it, the "current yield") is, I believe, what should be used. That is the annual distribution (interest amount) divided by the price paid.

This distinction is particularly import in the current financial setting, where many bonds have low coupons and are selling at a steep discount. The accretion of the discount is not tax free, unlike the coupon. The yield to maturity encompasses the discount in the yield calculation, hence, mixing tax attributes.

Am I correct?
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Re: [Wiki] Taxable Equivalent Yield (TEY)

Post by Kevin M »

Deskandchairs wrote: Wed Sep 27, 2023 11:17 pm For a topic of this magnitude, it would be helpful to start with important definitions.
Do we all understand what is meant by "yield"?
In the bond world, bonds are conventionally compared based on "yield to maturity." This information is prominently displayed on many/most broker websites.

I believe that is the incorrect "yield" to be using in these TEY formulas and comparisons.
Rather the "simple" yield (or as Vanguard calls it, the "current yield") is, I believe, what should be used. That is the annual distribution (interest amount) divided by the price paid.

This distinction is particularly import in the current financial setting, where many bonds have low coupons and are selling at a steep discount. The accretion of the discount is not tax free, unlike the coupon. The yield to maturity encompasses the discount in the yield calculation, hence, mixing tax attributes.

Am I correct?
You can use any type of yield you want. I think industry standard is to use YTM.

Here we just provide the math to do the calculation--it's up to you to factor in any additional considerations you might have.

It seems like you're thinking about munis. The TEY formulas can be applied to other types of bonds, such as Treasuries, which are exempt from state income tax. It's not a topic for this thread, but in most states, Treasury accrued market discount is exempt from state tax, and in all states accrued acquisition discount is exempt.
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