What is going on with short-term taxable bonds?

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
Post Reply
User avatar
Topic Author
grabiner
Advisory Board
Posts: 27458
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

What is going on with short-term taxable bonds?

Post by grabiner » Sat Aug 01, 2020 11:42 am

Normally, bond yields on funds of comparable duration should reflect the risk of the bonds, but the current yields on Vanguard's short-term funds don't reflect this.

All yields are on Admiral shares, which have expenses between 0.07% and 0.10%. In increasing order of risk:

Short-Term Treasury: 0.01%
Short-Term Treasury Index: 0.10% (slightly more risk for longer duration than Short-Term Treasury)
Short-Term Federal: 1.09% (some call risk on mortgage bonds, and mostly not backed by full faith and credit)
Short-Term Bond Index: 0.39% (66% Treasuries, 34% corporates)
Short-Term Investment-Grade: 1.33% (36% rated A, 31% rated BBB, 3% junk or not rated)
Short-Term Corporate Bond Index: 0.98% (45% rated A, 46% rated BBB)

Treasury yields may be artificially depressed, which accounts for the low yield on Short-Term Bond Index. Still, it doesn't make sense that Short-Term Federal, which holds mostly bonds with implicit government guarantees (such as FNMA and FHLMC), has a higher SEC yield than Short-Term Corporate Bond Index, which holds almost half its bonds in BBB corporates. In addition, I don't see why Short-Term Investment-Grade has a higher yield than Short-Term Corporate Bond Index; the index has a slightly longer duration and lower quality.

For intermediate-term bonds, the yields are in the right order. Corporate bonds yield more than GNMAs, and Intermediate-Term Corporate Bond Index, with slightly lower quality and a slightly longer duration, has a higher yield than Intermediate-Term Investment-Grade (1.73% versus 1.59%).
Wiki David Grabiner

User avatar
Doc
Posts: 9688
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: What is going on with short-term taxable bonds?

Post by Doc » Sat Aug 01, 2020 12:57 pm

grabiner wrote:
Sat Aug 01, 2020 11:42 am
Still, it doesn't make sense that Short-Term Federal, which holds mostly bonds with implicit government guarantees (such as FNMA and FHLMC), has a higher SEC yield than Short-Term Corporate Bond Index, which holds almost half its bonds in BBB corporates.
I'm missing something.

Name, Ticker, Asset class, SEC yield, 2nd quarter 2020
Short-Term Federal, VSGBX Bond - Short-term Government, 0.99% A 30 day 7/29/2020, 1.01%
Short-Term Corporate Bond Index Admiral Shares, VSCSX, Bond - Short-term Investment, 0.98% A 30 day 7/29/2020, 5.55%

I think that because of the recovery from the March kerfuffle that short term metrics are distorted by the bottoms of different assets not occuring at the same time. A lot of 30 day SEC or even 90 day returns look weird because of different bottoms. I currently use year to date periods to get around this distortion.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
Topic Author
grabiner
Advisory Board
Posts: 27458
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

Re: What is going on with short-term taxable bonds?

Post by grabiner » Sat Aug 01, 2020 1:05 pm

Doc wrote:
Sat Aug 01, 2020 12:57 pm
grabiner wrote:
Sat Aug 01, 2020 11:42 am
Still, it doesn't make sense that Short-Term Federal, which holds mostly bonds with implicit government guarantees (such as FNMA and FHLMC), has a higher SEC yield than Short-Term Corporate Bond Index, which holds almost half its bonds in BBB corporates.
I'm missing something.

Name, Ticker, Asset class, SEC yield, 2nd quarter 2020
Short-Term Federal, VSGBX Bond - Short-term Government, 0.99% A 30 day 7/29/2020, 1.01%
Short-Term Corporate Bond Index Admiral Shares, VSCSX, Bond - Short-term Investment, 0.98% A 30 day 7/29/2020, 5.55%
I used Admiral shares of Short-Term Federal for comparison, so that the expenses are closer; this is where I get the 1.09% yield.
I think that because of the recovery from the March kerfuffle that short term metrics are distorted by the bottoms of different assets not occuring at the same time. A lot of 30 day SEC or even 90 day returns look weird because of different bottoms. I currently use year to date periods to get around this distortion.
That would explain the returns, but not the yields; the 30-day SEC yields should be based on bond prices (and yields) from July.

I did check a chart; Short-Term Federal didn't lose anything in March, while Short-Term Corporate Bond Index lost 8% top to bottom but made it up from the end of March through July. The two funds have essentially the same return since March 5, which was the day the corporate collapse begin.
Wiki David Grabiner

User avatar
Doc
Posts: 9688
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: What is going on with short-term taxable bonds?

Post by Doc » Sat Aug 01, 2020 1:26 pm

grabiner wrote:
Sat Aug 01, 2020 1:05 pm
I think that because of the recovery from the March kerfuffle that short term metrics are distorted by the bottoms of different assets not occuring at the same time. A lot of 30 day SEC or even 90 day returns look weird because of different bottoms. I currently use year to date periods to get around this distortion.
That would explain the returns, but not the yields; the 30-day SEC yields should be based on bond prices (and yields) from July.
If 30 days ago one had recovered more than another (different bottoms) the 30 day SEC yields would not really be measuring the same thing.

Eg, Week ending price:

20, 20, 25, 25, 30

vs

20, 25, 25, 25, 30

I haven't really pursued this idea but in general the 30 Day SEC yields seem distorted lately while the YTD yields seem OK.

(Caveat, I may not be interpreting the SEC yield formula correctly.)
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Sat Aug 01, 2020 3:27 pm

I think SEC yield may sometimes give odd, flawed results. I do not know why, but I think that is what is happening here.

On Vanguard's portfolio tab, there is a YTM reported, for short term federal (VSGDX) this is 0.8%. Unfortunately, this has not been updated, so that 0.8% is as of 6/30. However, when you do a search of past price on the "Price and Performance" tab, it will also show the historical SEC yield. So as of 6/30, this shows SEC yield for short term federal (VSGDX) was 1.4%, which is 0.6% higher than the YTM.

For short term corp, the YTM and SEC yields match. As of 6/30 SEC was 1.21% and YTM was 1.2%.

OTOH, there was no net change in price for VSGDX in July and total return over the past month was 0.11%, so that would be about 1.3% annualized and so is in line with the SEC yield rather than the YTM from 6/30. :confused
Time is your friend; impulse is your enemy. - John C. Bogle

Northern Flicker
Posts: 6045
Joined: Fri Apr 10, 2015 12:29 am

Re: What is going on with short-term taxable bonds?

Post by Northern Flicker » Sat Aug 01, 2020 5:05 pm

I think three things are in play.

1. SEC yield is a 30-day moving average, leading to some distortions in the comparison (as mentioned above).

2. There may be (being generous with the verb) some market distortions being caused by the Federal Reserve, especially for corporate credit, but also for treasuries.

3. Call risk for mortgages is high right now. You may be getting a wide spread as a premium for that because the market may think you will not get the premium for very long.
Last edited by Northern Flicker on Sat Aug 01, 2020 11:49 pm, edited 1 time in total.
Risk is not a guarantor of return.

livesoft
Posts: 72619
Joined: Thu Mar 01, 2007 8:00 pm

Re: What is going on with short-term taxable bonds?

Post by livesoft » Sat Aug 01, 2020 5:09 pm

I think the numbers are probably updated on different days by different people within Vanguard, so that they are stale and meaningless at this level of lack of detail.
Wiki This signature message sponsored by sscritic: Learn to fish.

Northern Flicker
Posts: 6045
Joined: Fri Apr 10, 2015 12:29 am

Re: What is going on with short-term taxable bonds?

Post by Northern Flicker » Sat Aug 01, 2020 11:50 pm

livesoft wrote:
Sat Aug 01, 2020 5:09 pm
I think the numbers are probably updated on different days by different people within Vanguard, so that they are stale and meaningless at this level of lack of detail.
That would have a very small impact on 30-day moving averages.
Risk is not a guarantor of return.

xenial
Posts: 2690
Joined: Tue Feb 27, 2007 1:36 am
Location: USA

Re: What is going on with short-term taxable bonds?

Post by xenial » Sun Aug 02, 2020 12:40 am

Vanguard's reported SEC yields are suspect. The corporate ETFs are especially funky. As of 7/29, Short Corporate (VCSH) yields 1.00%, Intermediate Corporate (VCIT) yields 1.75%, Long Corporate (VCLT) yields 2.83%, and Total Corporate (VTC) yields 3.05%. The problem is that Total Corporate invests exclusively in the other three ETFs. It's a miracle!

User avatar
Steve Reading
Posts: 2120
Joined: Fri Nov 16, 2018 10:20 pm

Re: What is going on with short-term taxable bonds?

Post by Steve Reading » Sun Aug 02, 2020 12:51 am

xenial wrote:
Sun Aug 02, 2020 12:40 am
Vanguard's reported SEC yields are suspect. The corporate ETFs are especially funky. As of 7/29, Short Corporate (VCSH) yields 1.00%, Intermediate Corporate (VCIT) yields 1.75%, Long Corporate (VCLT) yields 2.83%, and Total Corporate (VTC) yields 3.05%. The problem is that Total Corporate invests exclusively in the other three ETFs. It's a miracle!
Lmao
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson

User avatar
Topic Author
grabiner
Advisory Board
Posts: 27458
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

Re: What is going on with short-term taxable bonds?

Post by grabiner » Sun Aug 02, 2020 9:19 am

xenial wrote:
Sun Aug 02, 2020 12:40 am
Vanguard's reported SEC yields are suspect. The corporate ETFs are especially funky. As of 7/29, Short Corporate (VCSH) yields 1.00%, Intermediate Corporate (VCIT) yields 1.75%, Long Corporate (VCLT) yields 2.83%, and Total Corporate (VTC) yields 3.05%. The problem is that Total Corporate invests exclusively in the other three ETFs. It's a miracle!
Vanguard explains this anomaly with the notes on the fund page. VTC reports an SEC yield under definition B (based on the yields of the underlying holdings), as if it were a stock fund, rather than definition A (based on past 30 days' yield to maturity). Since the ETFs have a higher dividend payout than their SEC yield, VTC uses that dividend payout to report a higher SEC yield.

The reported yields to maturity (select "Bond Attributes" from the fund list) make sense: 1.2% for Short-Term Corporate, 2.0% for Intermediate-Term Corporate, 3.2% for Long-Term Corporate, and 2.2% for Total Corporate. These are all as of June 30, and except for VTC, they are slightly higher than the July 31 SEC yield, reflecting a decline in rates over the last month.

The yields to maturity for the short-term fund make a little more sense, but still don't resolve the anomaly:

Short-Term Treasury: 0.2%
Short-Term Treasury Index: 0.2%
Short-Term Federal: 0.8% (lower than reported SEC yield)
Short-Term Bond Index: 0.5%
Short-Term Investment Grade: 1.3% (about equal to reported SEC yield)
Short-Term Corporate Index: 1.2%

Short-Term Investment-Grade and Short-Term Corporate Index have essentially the same July returns, so the difference between their yields shouldn't increase in July unless there was substantial turnover in which bonds were sold and replaced by other bonds with different yields. (This could happen in theory; Short-Term Corporate Index must sell bonds when they are downgraded to BB, and replace them with lower-yielding bonds, while Short-Term Investment-Grade can keep a small amount in BB-rated bonds.)
Wiki David Grabiner

Northern Flicker
Posts: 6045
Joined: Fri Apr 10, 2015 12:29 am

Re: What is going on with short-term taxable bonds?

Post by Northern Flicker » Sun Aug 02, 2020 1:34 pm

I assume the yield-to-maturity of Short-term-federal is lower than SEC yield because the SEC yield is a 30-day moving average and the yields of what it holds have fallen in the last week.

I'm currently unclear if the topic in the thread is about anomalies in reported data, surprising variations in the yields of different assets, or both.
Risk is not a guarantor of return.

User avatar
Doc
Posts: 9688
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: What is going on with short-term taxable bonds?

Post by Doc » Sun Aug 02, 2020 3:50 pm

Northern Flicker wrote:
Sun Aug 02, 2020 1:34 pm
I assume the yield-to-maturity of Short-term-federal is lower than SEC yield because the SEC yield is a 30-day moving average and the yields of what it holds have fallen in the last week.
The SEC yield takes the dividends and interest received over the past 30 days net of the accrued expenses divided by the funds assets (sort of) at the end of the period and annualizes it. (The annualization calc is kind of weird is kind of weird. It uses the 30 day rate raised to the sixth power and multiplies by 2.)

I speculate that weirdness might be due to using the highest price on the last day times the average daily number of shares as the funds assets. If the price was out of whack on the last day of the period the SEC yield would be out of whack proportionately.

The formula for SEC 30-day yield is

Image

Where:

a = dividends and interest collected during the past 30 days
b = accrued expenses of the past 30 days
c = average daily number of outstanding shares that were entitled to distributions
d = the maximum public offering price per share on the last day of the period

https://en.wikipedia.org/wiki/30-day_yield

David Grabiner should be able to tell us. He's the math guy. Oh gee whiz it's his thread and his question. :D
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Sun Aug 02, 2020 4:38 pm

Doc wrote:
Sun Aug 02, 2020 3:50 pm
Northern Flicker wrote:
Sun Aug 02, 2020 1:34 pm
I assume the yield-to-maturity of Short-term-federal is lower than SEC yield because the SEC yield is a 30-day moving average and the yields of what it holds have fallen in the last week.
The SEC yield takes the dividends and interest received over the past 30 days net of the accrued expenses divided by the funds assets (sort of) at the end of the period and annualizes it. (The annualization calc is kind of weird is kind of weird. It uses the 30 day rate raised to the sixth power and multiplies by 2.)

I speculate that weirdness might be due to using the highest price on the last day times the average daily number of shares as the funds assets. If the price was out of whack on the last day of the period the SEC yield would be out of whack proportionately.

The formula for SEC 30-day yield is

Image

Where:

a = dividends and interest collected during the past 30 days
b = accrued expenses of the past 30 days
c = average daily number of outstanding shares that were entitled to distributions
d = the maximum public offering price per share on the last day of the period

https://en.wikipedia.org/wiki/30-day_yield

David Grabiner should be able to tell us. He's the math guy. Oh gee whiz it's his thread and his question. :D
But the wording used to define the term "a" is not the best. As noted here: https://www.bogleheads.org/wiki/SEC_Yield
The SEC also includes clarifications of the definition. In particular, "Dividends and interest" for a bond is computed from yield to maturity, or yield to call if the bond is likely to be called, not the coupon payments on the bond.

Or as stated here: https://www.calamos.com/globalassets/me ... _final.pdf
The calculation uses the current yields to worst of all fixed income portfolio holdings

Or from the horses mouth:
Image
https://www.sec.gov/files/formn-1a.pdf
Time is your friend; impulse is your enemy. - John C. Bogle

User avatar
Doc
Posts: 9688
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: What is going on with short-term taxable bonds?

Post by Doc » Sun Aug 02, 2020 4:59 pm

jeffyscott wrote:
Sun Aug 02, 2020 4:38 pm
Or from the horses mouth: ...
OMG
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

Northern Flicker
Posts: 6045
Joined: Fri Apr 10, 2015 12:29 am

Re: What is going on with short-term taxable bonds?

Post by Northern Flicker » Sun Aug 02, 2020 5:24 pm

The formula says the following:

1. Use 30 days of net income divided by total fund balance/principal at end of the period as an estimate of internal rate of return over the period. A precise number would require calculating IRR using the fund balance at the time of each cash flow.

2. Compound that monthly rate for 6 months.

3. Double the result of step 2 to reach an annualized rate that will be a little bit lower than if the 30-day rate were compounded for 12 months. This may be done to account for the loss of compounding when dividends are distributed. Of course you can reinvest the distribution to continue compounding your personal return, but that does not change the compound yield of the fund itself.

The only area where there is any real discrepancy introduced by the formula is using the fund balance at the end of the 30-day period as an estimate for the fund balance at the time of each cash flow, and compounding the rate associated with each cash flow. This effect is lower when rates are lower, so should be neglible compared to the delay in incorporating rate changes into the 30-day average when rates are moving duribg the 30 days.

Intermediate-term mortgage option-adjusted spreads (spreads that price credit risk and the premium received for prepayment options) seem to be around 100 bp right now, so a 50-60 bp spread for shorter duration instruments does not seem outrageously high in comparison-- maybe a little higher than I would expect.

If you look at VFIUX it only needs to hold 80% of its portfolio in treasuries. It has about 16% of its assets in MBS and ABS, which is reflected in its higher yield than VSIGX which is a treasury index fund.
Risk is not a guarantor of return.

User avatar
Topic Author
grabiner
Advisory Board
Posts: 27458
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

Re: What is going on with short-term taxable bonds?

Post by grabiner » Sun Aug 02, 2020 5:47 pm

Northern Flicker wrote:
Sun Aug 02, 2020 5:24 pm
The formula says the following:

1. Use 30 days of net income divided by total fund balance/principal at end of the period as an estimate of internal rate of return over the period. A precise number would require calculating IRR using the fund balance at the time of each cash flow.

2. Compound that monthly rate for 6 months.

3. Double the result of step 2 to reach an annualized rate that will be a little bit lower than if the 30-day rate were compounded for 12 months. This may be done to account for the loss of compounding when dividends are distributed. Of course you can reinvest the distribution to continue compounding your personal return, but that does not change the compound yield of the fund itself.
The reason for #3 is to match the way bonds usually work. A $1000 bond with a 6% coupon pays a $30 coupon every six months, which is treated by rules #1 and #2 as accruing at a 0.494% monthly rate. If the bond is trading at par, it is quoted as having a 3% semiannual yield, which is reported as a 6% SEC yield, even though your annual return would be 6.09% if you reinvested the coupon at 6% interest.
If you look at VFIUX it only needs to hold 80% of its portfolio in treasuries. It has about 16% of its assets in MBS and ABS, which is reflected in its higher yield than VSIGX which is a treasury index fund.
The same thing applies to the short-term funds; Vanguard Short-Term Treasury is only 89% Treasury bonds. This helps to explain why it has a higher yield than the index.
Wiki David Grabiner

User avatar
Kevin M
Posts: 11578
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: What is going on with short-term taxable bonds?

Post by Kevin M » Sun Aug 02, 2020 5:59 pm

jeffyscott wrote:
Sun Aug 02, 2020 4:38 pm
Doc wrote:
Sun Aug 02, 2020 3:50 pm
The SEC yield takes the dividends and interest received over the past 30 days net of the accrued expenses divided by the funds assets (sort of) at the end of the period and annualizes it.
<snip>
The formula for SEC 30-day yield is

Image

Where:

a = dividends and interest collected during the past 30 days

<snip>

https://en.wikipedia.org/wiki/30-day_yield
<snip>
But the wording used to define the term "a" is not the best.
<snip>
It's worse than that--the Wikipedia article leaves out the most important part of how "a" is calculated for a bond fund.

I think the Wikipedia article is flat out wrong in this statement:
Wikipedia wrote:It is not the same as the yield to maturity for the bonds in the portfolio, as it does not take into account the amortization of the premiums or discounts at which the bonds are trading.
To highlight the relevant part of the SEC 30-day yield calculation, as shown in the graphic above shared by jeffyscott:
SEC wrote:To calculate interest earned on debt obligations for purposes of “a” above:

(a) Calculate the yield to maturity of each obligation held by the Fund based on the market value of the obligation
Yield to maturity most certainly does "take into account the amortization of the premiums or discounts at which the bonds are trading". It appears to me that whoever wrote that part of the Wikipedia article doesn't really understand the 30-day yield calculation.

SEC yield for bond funds most certainly is a form of yield to maturity--it's basically a 30-day lagging average YTM minus expenses.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Sun Aug 02, 2020 9:49 pm

Kevin M wrote:
Sun Aug 02, 2020 5:59 pm
SEC yield for bond funds most certainly is a form of yield to maturity--it's basically a 30-day lagging average YTM minus expenses.

Kevin
If I understand correctly, though, it's not an average of each day's YTM, where each day's YTM would be based on that day's NAV.

Taking a single bond on the last day of the month, let's say it's YTM is 1% and market value is $1100, that's step 1.(a) from the SEC instructions. Then 1.(b) calculates the daily interest earned, based on that YTM, which would be ($1100)(0.01)/360 = $0.030556 or $0.91667 for 30 days.

That $0.91667 would be the interest earned by that bond, the "a" in the SEC formula (assuming it's one that is not affected by any of the other instructions that go with the SEC formula).

One thing that seems odd is that it says to use the purchase price, not the market value "with respect to obligations purchased during the month". So it seems that if the bond with a value of $1100 in my example had been purchased for, say $1050 sometime during the month, that $1050 purchase price rather than the $1100 end of month market value would be used to calculate the YTM.
Time is your friend; impulse is your enemy. - John C. Bogle

Northern Flicker
Posts: 6045
Joined: Fri Apr 10, 2015 12:29 am

Re: What is going on with short-term taxable bonds?

Post by Northern Flicker » Mon Aug 03, 2020 12:21 pm

jeffyscott wrote: If I understand correctly, though, it's not an average of each day's YTM, where each day's YTM would be based on that day's NAV.
Correct. Suppose large net inflows to the fund occur at the end of the 30-day period. It will then underestimate the contribution to yield of cash flows that occurred in the 30-day window before the inflows. Large net outflows would have the opposite effect.
Risk is not a guarantor of return.

User avatar
Doc
Posts: 9688
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: What is going on with short-term taxable bonds?

Post by Doc » Tue Aug 04, 2020 11:30 am

Northern Flicker wrote:
Mon Aug 03, 2020 12:21 pm
jeffyscott wrote: If I understand correctly, though, it's not an average of each day's YTM, where each day's YTM would be based on that day's NAV.
Correct. Suppose large net inflows to the fund occur at the end of the 30-day period. It will then underestimate the contribution to yield of cash flows that occurred in the 30-day window before the inflows. Large net outflows would have the opposite effect.
??? The "a" in the formula is "dividends and interest collected during the past 30 days". I think one of us has this bass ackward. I think there is no effect on the 30-day SEC no matter when during the month that large amount occured.

Recently the "weirdness" I have noticed in the SEC 30 may be due to a price jump or drop near the end of the period. :idea:
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Tue Aug 04, 2020 12:37 pm

Doc wrote:
Tue Aug 04, 2020 11:30 am
Northern Flicker wrote:
Mon Aug 03, 2020 12:21 pm
jeffyscott wrote: If I understand correctly, though, it's not an average of each day's YTM, where each day's YTM would be based on that day's NAV.
Correct. Suppose large net inflows to the fund occur at the end of the 30-day period. It will then underestimate the contribution to yield of cash flows that occurred in the 30-day window before the inflows. Large net outflows would have the opposite effect.
??? The "a" in the formula is "dividends and interest collected during the past 30 days". I think one of us has this bass ackward. I think there is no effect on the 30-day SEC no matter when during the month that large amount occured.

Recently the "weirdness" I have noticed in the SEC 30 may be due to a price jump or drop near the end of the period. :idea:
No it's actually "dividends and interest earned", and they are "earned" as this defined in the instructions following the formula. Read the SEC document instead of relying on wikepedia, I already posted an image of the pertinent section in this discussion right here: viewtopic.php?p=5412766&sid=fc7c873a29d ... f#p5409443

see item 1(a)...yield to maturity...
Time is your friend; impulse is your enemy. - John C. Bogle

User avatar
Doc
Posts: 9688
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: What is going on with short-term taxable bonds?

Post by Doc » Tue Aug 04, 2020 3:49 pm

jeffyscott wrote:
Tue Aug 04, 2020 12:37 pm
No it's actually "dividends and interest earned", and they are "earned" as this defined in the instructions following the formula. Read the SEC document instead of relying on wikepedia, I already posted an image of the pertinent section in this discussion right here: viewtopic.php?p=5412766&sid=fc7c873a29d ... f#p5409443
I don't understand the nuances but I don't really care. I have very little need to look at 30 Day SEC yields so I am bowing out of this discussion. :beer
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
Kevin M
Posts: 11578
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: What is going on with short-term taxable bonds?

Post by Kevin M » Tue Aug 04, 2020 5:38 pm

jeffyscott wrote:
Sun Aug 02, 2020 9:49 pm
Kevin M wrote:
Sun Aug 02, 2020 5:59 pm
SEC yield for bond funds most certainly is a form of yield to maturity--it's basically a 30-day lagging average YTM minus expenses.

Kevin
If I understand correctly, though, it's not an average of each day's YTM, where each day's YTM would be based on that day's NAV.

Taking a single bond on the last day of the month, let's say it's YTM is 1% and market value is $1100, that's step 1.(a) from the SEC instructions. Then 1.(b) calculates the daily interest earned, based on that YTM, which would be ($1100)(0.01)/360 = $0.030556 or $0.91667 for 30 days.

That $0.91667 would be the interest earned by that bond, the "a" in the SEC formula (assuming it's one that is not affected by any of the other instructions that go with the SEC formula).
You make a good point here. I've never really worked through the details of the SEC 30-day yield formula, but I'm starting to work on that now. Let's look at it bit by bit.

EDIT: I originally quoted the SEC yield quotation instructions for Form N-3, but Form N-1A is what's used for mutual funds. There are essentially no differences that effect any of my comments, but some of the wording is slightly different, and Form N-1A has an additional instruction for tax-exempt bonds. I edited the quotes to be consistent with Form N-1A, and hopefully got them all corrected.
SEC wrote:(2)Yield Quotation. Based on a 30-day (or one month) period ended on the date of the most recent balance sheet of the Registrant included in the registration statement, calculate the Fund’s yield by dividing the net investment income per share earned during the period by the maximum offering price per share on the last day of the period, according to the following formula:

YIELD = 2[((a - b)/cd + 1)^6- 1]
Note: I reformatted the formula slightly, so I don't have to use an image or sub/super-scripts

Looking at the underlined portion of the quote immediately above, we are looking at a 30-day period ending on a particular date. Looking at nothing but this, it would seem that we're looking at some sort of lagging 30-day yield.
Where:
a = dividends and interest earned during the period.
b = expenses accrued for the period (net of reimbursements).
c = the average daily number of shares outstanding during the period that were entitled to receive dividends.
d = the maximum offering price per share on the last day of the period.
I'm focusing here only on "a", which for a bond fund is the "interest earned during the period".
SEC wrote:1.To calculate interest earned on debt obligations for the purpose of “a” above:
A bond is a debt obligation, so it's only the interest part that we're interested in for bond funds. Dividends would apply to a stock fund.
SEC wrote:(a)Compute the yield to maturity of each obligation held by the Fund <snip>
Note: I am underlining the bits I want to emphasize.

As some of us understand, but some seem to still not be getting, interest ("a" in the formula) for a bond fund is based on the yield to maturity of the bonds held by the fund. It is not based on the interest payments the fund has received over a 30-day period.
SEC wrote:<snip> based on the market value of the obligation (including actual accrued interest) <snip>
Note that the YTM is to be calculated on the dirty price (including accrued interest), whereas the YTM quotes we see at brokers are calculated on the clean price (not including accrued interest). This can make a big difference. Just looking at one bond I pulled a quote for today, the clean price is 108.338 and the corresponding YTM is 0.009%. But there is $3.839 of accrued interest per $100, so the dirty price is 112.177, and the yield calculated from that price is -3.416% (there's a minus sign in front of this number)!

I've never considered this before, but it seems that including accrued interest in calculating YTM not only lowers SEC yield relative to YTM, but also could cause some of the weird discrepancies that are sometimes seen in daily changes in SEC yield vs. price. On the day the interest is paid, the contribution to SEC yield of the bond will increase, perhaps dramatically (since the yield on that day will then be calculated on the lower, clean price).
SEC wrote:<snip> at the close of business on the last business day of each month, <snip>
So does "last business day of each month" refer to the last business day of the month (or 30-day period) for which we are calculating 30-day yield, or for the last business day of the month (or 30-day period) before that? If the former, which is what it sounds like to me, then the "subsequent month" referred to in step (b), below, would be the future 30 days, which would not be consistent with period referred to in the first paragraph of the instructions.
SEC wrote:<snip> or, with respect to obligations purchased during the month, the purchase price (plus actual accrued interest).
Agree with jeffyscott that this is weird, and will have definite distortions relative to YTM calculated based on the price at the end of the month or 30-day period.
SEC wrote:The maturity of an obligation with a call provision(s) is the next call date on which the obligation reasonably may be expected to be called, or if none, the maturity date.
No comment.
SEC wrote:(b)Divide the yield to maturity by 360 and multiply the quotient by the market value of the obligation (including actual accrued interest) to determine the interest income on the obligation for each day of the subsequent month that the obligation is in the portfolio. Assume that each month has thirty days.
Again, if we use the YTM at the end of the 30-day period for which we are calculating the 30-day yield, the "subsequent month" would refer to the following month, which does not seem consistent with the first paragraph of the yield calculation instructions. The YTM at the end of the previous month (or 30-day period) would be relevant to the theoretical income earned for "a 30-day (or one month) period ended on the date" for which we are calculating the 30-day yield.

Which is it? If it's the YTM at the end of the period for which we're calculating the yield, then this part is not a lagging 30-day yield at all, but a completely forward-looking yield. But then that doesn't represent the theoretical income earned during the previous 30-day period we're calculating it for.
SEC wrote:(c)Total the interest earned on all debt obligation and all dividends accrued on all equity securities during the thirty-day (or one month) period. Although the period for computing interest earned is based on calendar months, a 30-day yield may be calculated by aggregating the daily interest on the portfolio from portions of 2 months. In addition, a Fund may recalculate daily interest income on the portfolio more than once a month.
Only comment here is that this clarifies that funds that report SEC yields daily, such as Vanguard funds, are being consistent with the SEC instructions.
(d)For a tax-exempt obligation issued without original issue discount and having a current market discount, use the coupon rate of interest in lieu of the yield to maturity. For a tax-exempt obligation with original issue discount in which the discount is based on the current market value and exceeds the then-remaining portion of original issue discount (market discount), base the yield to maturity on the imputed rate of the original issue discount calculation. For a tax-exempt obligation with original issue discount, where the discount based on the current market value is less than the then-remaining portion of original issue discount (market premium), base the yield to maturity on the market value.
Definitely different for tax-exempt bonds!

I'll just add that I took a very simple case, assuming a fund with one bond, a yield of 1.000%, a price of 100, and no expenses, and the SEC yield formula implemented in my spreadsheet returned a yield of 1.002%, so it seems that ignoring all of the complications, like including accrued interest in the price in calculating YTM, the SEC yield formula results in something that is very close to a standard YTM calculation.

Here's the formula I used in my spreadsheet:

Code: Select all

=2*(((a-b)/(c_*d) + 1)^6 - 1)
Note: I replaced "c" with "c_" because "c" is not a valid range name in Google Sheets, and I'm using range names to implement the formula in my spreadsheet.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Tue Aug 04, 2020 10:08 pm

Kevin M wrote:
Tue Aug 04, 2020 5:38 pm
jeffyscott wrote:
Sun Aug 02, 2020 9:49 pm
Kevin M wrote:
Sun Aug 02, 2020 5:59 pm
SEC yield for bond funds most certainly is a form of yield to maturity--it's basically a 30-day lagging average YTM minus expenses.

Kevin
If I understand correctly, though, it's not an average of each day's YTM, where each day's YTM would be based on that day's NAV.

Taking a single bond on the last day of the month, let's say it's YTM is 1% and market value is $1100, that's step 1.(a) from the SEC instructions. Then 1.(b) calculates the daily interest earned, based on that YTM, which would be ($1100)(0.01)/360 = $0.030556 or $0.91667 for 30 days.

That $0.91667 would be the interest earned by that bond, the "a" in the SEC formula (assuming it's one that is not affected by any of the other instructions that go with the SEC formula).
You make a good point here. I've never really worked through the details of the SEC 30-day yield formula, but I'm starting to work on that now. Let's look at it bit by bit.

EDIT: I originally quoted the SEC yield quotation instructions for Form N-3, but Form N-1A is what's used for mutual funds. There are essentially no differences that effect any of my comments, but some of the wording is slightly different, and Form N-1A has an additional instruction for tax-exempt bonds. I edited the quotes to be consistent with Form N-1A, and hopefully got them all corrected.
SEC wrote:(2)Yield Quotation. Based on a 30-day (or one month) period ended on the date of the most recent balance sheet of the Registrant included in the registration statement, calculate the Fund’s yield by dividing the net investment income per share earned during the period by the maximum offering price per share on the last day of the period, according to the following formula:

YIELD = 2[((a - b)/cd + 1)^6- 1]
Note: I reformatted the formula slightly, so I don't have to use an image or sub/super-scripts

Looking at the underlined portion of the quote immediately above, we are looking at a 30-day period ending on a particular date. Looking at nothing but this, it would seem that we're looking at some sort of lagging 30-day yield.
To use a particular month as an example, that seems to say that on June 30 you would take the "net investment income earned", which would be whatever was earned for the period June 1-30 and in the denominator you're using the share price on June 30 for the calculation. (and, again, net investment income here is based on the YTM-based calculations, as you know)
SEC wrote:<snip> based on the market value of the obligation (including actual accrued interest) <snip>
SEC wrote:<snip> at the close of business on the last business day of each month, <snip>
Kevin wrote:So does "last business day of each month" refer to the last business day of the month (or 30-day period) for which we are calculating 30-day yield, or for the last business day of the month (or 30-day period) before that? If the former, which is what it sounds like to me, then the "subsequent month" referred to in step (b), below, would be the future 30 days, which would not be consistent with period referred to in the first paragraph of the instructions.
SEC wrote:(b)Divide the yield to maturity by 360 and multiply the quotient by the market value of the obligation (including actual accrued interest) to determine the interest income on the obligation for each day of the subsequent month that the obligation is in the portfolio. Assume that each month has thirty days.
Kevin wrote:Again, if we use the YTM at the end of the 30-day period for which we are calculating the 30-day yield, the "subsequent month" would refer to the following month, which does not seem consistent with the first paragraph of the yield calculation instructions. The YTM at the end of the previous month (or 30-day period) would be relevant to the theoretical income earned for "a 30-day (or one month) period ended on the date" for which we are calculating the 30-day yield.

Which is it? If it's the YTM at the end of the period for which we're calculating the yield, then this part is not a lagging 30-day yield at all, but a completely forward-looking yield. But then that doesn't represent the theoretical income earned during the previous 30-day period we're calculating it for.
Yeah, that part confused me. I was hoping maybe you were gonna explain it. :)

These instructions refer to "a", which is "dividends and interest earned during the period" and it seems clear that "the period" would be June 1-30 on June 30 (let's just assume it's a business day). But from the way it is worded it is not really clear to me if are we to calculate the YTM on May 31 or June 30, when doing this calculation for the June 1-30 period. My initial inclination was that it's the YTM on June 30 because it's reported as SEC yield as of June 30. But then, since it says "subsequent month" in the next part, it seems like that subsequent month should be June 1-30 and so the YTM calculation must be done for May 31 :?: .

Would it make sense if we are meant to take the YTM on May 31 and then divide that May 31 YTM by 360, so then it is a daily YTM. Then that daily YTM is multiplied by the market value of the obligation on each day June 1, 2, 3, 4, ..., 30 and then you add those up to get the "a" in the formula, the "interest earned during the period"? That would seem to make the "a" in the formula a 30 day something (call it a 30 day YTM-based income, perhaps :?: ).
Time is your friend; impulse is your enemy. - John C. Bogle

User avatar
Kevin M
Posts: 11578
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: What is going on with short-term taxable bonds?

Post by Kevin M » Wed Aug 05, 2020 4:57 pm

jeffyscott, you have accurately elaborated on my confusion about the date to be used for calculating the YTM that is used in calculating "a" in the formula.

I also find it confusing that they use the term "each month", in "at the close of business on the last business day of each month". "Each" implies that we are looking at more than one month, but everything else in the language seems to pertain to a single month or 30-day period. Why don't they say something like "Calculate the yield to maturity ... at the close of business on the last business day of the 30-day (or one month) period referred to above", or "... at the close of business on the last business day preceding the 30-day (or one month) period referred to above"?

If we assume that the instruction means to use the last business day preceding the 30-day period, then does the instruction, "with respect to obligations purchased during the month, the purchase price (plus actual accrued interest)" makes more sense, since that bond would not have been owned by the fund at the beginning of the period?

Oh, and what about bonds that are sold "during the month"?

I find it frustrating that in searching for an actual example of calculating this yield, all I find are examples where the interest and dividends are are specified as dollar amounts--nothing about how to calculate the interest for a bond using YTM as specified in the instructions.

Even more confusing, I found an SEC document in which they added the instruction, "Yield will be calculated based upon a rolling 30-day average.":
To calculate interest earned on debt obligations for purposes of “a” above:

(a) Calculate the yield to maturity of each obligation held by the Fund based on the market value of the obligation (including actual accrued interest) at the close of business on the last business day of each month or, with respect to obligations purchased during the month, the purchase price (plus actual accrued interest). The maturity of an obligation with a call provision(s) is the next call date on which the obligation reasonably may be expected to be called, or if none, the maturity date.

(b) Divide the yield to maturity by 360 and multiply the quotient by the market value of the obligation (including actual accrued interest) to determine the interest income on the obligation for each day of the subsequent month that the obligation is in the portfolio. Assume that each month has 30 days. Yield will be calculated based upon a rolling 30-day average.

(c) Total the interest earned on all debt obligations and all dividends accrued on all equity securities during the 30-day (or one month) period. Although the period for calculating interest earned is based on calendar months, a 30-day yield may be calculated by aggregating the daily interest on the portfolio from portions of 2 months. In addition, a Fund may recalculate daily interest income on the portfolio more than once a month. Yield will be calculated based upon a rolling 30-day average.
How are we to interpret this addition?

Also, any thoughts on my interpretation that they are saying to use the dirty price in the YTM calculation ("based on the market value of the obligation (including actual accrued interest)"). Not sure what the word "actual" means here either. Either interest is accrued or not.

I calculated the YTM and SEC yield based on clean and dirty prices for all Treasuries maturing in 1 year or more, and for clean the average YTM is 0.362% and for dirty price it's 0.171%, and the average SEC yields are 0.363% and 0.172% respectively.

Just a data point for the record, for VSIGX (Int-term Treasury index Admiral), the YTM was 0.4% on 6/30/2020, and the SEC yield was 0.35% on that date. The ER is 0.07%, so the SEC yield is more than the YTM minus the ER. This is not consistent with what I'm seeing if SEC yield is calculated based on dirty price--we'd expect it to be lower. Also, the 5y Treasury yield was almost the same on May 29 at 0.30% and June 30 at 0.29%. Ditto for 10y, at 0.65% and 0.66% respectively. So for this period, these yields don't give us a clue as to which are used (beginning or end of period).

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Wed Aug 05, 2020 10:41 pm

Kevin M wrote:
Wed Aug 05, 2020 4:57 pm
If we assume that the instruction means to use the last business day preceding the 30-day period, then does the instruction, "with respect to obligations purchased during the month, the purchase price (plus actual accrued interest)" makes more sense, since that bond would not have been owned by the fund at the beginning of the period?
Yes, I had the same thought about that and I think that adds to the evidence that that it's the YTM from the last day of the previous month that's to be used.
Oh, and what about bonds that are sold "during the month"?
Using the YTM on the last day of the prior month would work for those, until the day sold and then after that they would contribute $0 to "a" in the formula.
I find it frustrating that in searching for an actual example of calculating this yield, all I find are examples where the interest and dividends are are specified as dollar amounts--nothing about how to calculate the interest for a bond using YTM as specified in the instructions.
It is strange that it seems to be impossible to find either that or a description in plain language of how it's to be calculated. Menawhile, misinformation on how it's calculated seems to be common.
Even more confusing, I found an SEC document in which they added the instruction, "Yield will be calculated based upon a rolling 30-day average.":
...
How are we to interpret this addition?
Maybe that's was just added to that agreement between the two because the Russell Investment Company wanted the SEC yield to be updated every day by State Street Bank?
Also, any thoughts on my interpretation that they are saying to use the dirty price in the YTM calculation ("based on the market value of the obligation (including actual accrued interest)"). Not sure what the word "actual" means here either. Either interest is accrued or not.
I don't really understand that part very well, but the price including accrued interest is total that you would actually pay to buy the bond on the last day of the prior month, say on May 31 if we are looking at the SEC yield as of June 30 (I'm going with that prior month interpretation, now). Were I to buy a bond on May 31, the total dollar amount that I paid for the investment would include accrued interest, so it makes sense to me that it would be included. Anyone buying a share of a bond fund on May 31 would pay a price that includes the value of all accrued interest. I don't know why the "actual" is there. The only distinction that I can think of is that things like T-bills accrue interest continuously, because they have no coupons, bonds that do have coupons accrue interest only between the coupon payments, but it's still actually accrued until it is paid.
I calculated the YTM and SEC yield based on clean and dirty prices for all Treasuries maturing in 1 year or more, and for clean the average YTM is 0.362% and for dirty price it's 0.171%, and the average SEC yields are 0.363% and 0.172% respectively.
Ah, and is there an index fund that includes all those that reports it's current SEC yield? Hmm, there is and it reports SEC yield at 0.33% as of Aug 4 and the ER is 0.15%, which would mean without expenses it'd be 0.45% (neglecting the 0.09% premium). :confused
https://www.ishares.com/us/products/239 ... y-bond-etf

Edit: After posting, I realized that a problem with comparing your average to that ETF could be that yours is probably an equal weighted average while the fund would be weighted by the market values.
Time is your friend; impulse is your enemy. - John C. Bogle

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Fri Aug 07, 2020 10:04 am

While I don't know if it is 100% correct, I finally found something which might be an accurate, understandable, description of what the results of a 30 day SEC yield calculation represent:

The 30-day SEC yield is hypothetical in the sense that it does not represent the actual earnings of a bond fund. Rather, a bond fund calculates what its current portfolio would earn in daily interest based on the current yield to maturity (YTM) of each of the bonds in the portfolio, regardless of whether the fund actually held all the bonds over the preceding 30 days. The YTM of an individual bond is a forward-looking estimate of how much an investor will earn from the bond assuming it is held to maturity and assuming all cash flows from the bond are reinvested at the YTM rate. In other words, the 30-day SEC yield employs a forward-looking estimate of income based on current market prices to calculate how much hypothetical income a bond fund would have earned over the prior 30 days had the fund held its current portfolio for the entire period.
https://www.forbes.com/sites/johnjacobs ... 4169e82807

One other find, though it's from 1993 and so rules may have changed:
(For MBS :?: ) the SEC has given them a choice: to amortize premiums and discounts or not to amortize them. Thus, two funds hypothetically could have identical portfolios and costs but different yields because of different policies for adjusting investment income.
https://www.chicagotribune.com/news/ct- ... story.html
Time is your friend; impulse is your enemy. - John C. Bogle

User avatar
Kevin M
Posts: 11578
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

SEC yield: accrued interest

Post by Kevin M » Fri Aug 07, 2020 7:28 pm

I think I cracked the nut on my confusion about the impact of accrued interest in calculating YTM, per this instruction:
SEC wrote:Calculate the yield to maturity of each obligation held by the Fund based on the market value of the obligation (including actual accrued interest) <snip>
The bottom line is that it doesn't work to just plug the dirty price (=clean price plus accrued interest per $100) into the YIELD function. To understand this, I had to think about how YTM relates to cash flows.

YTM is a discount rate that equalizes the present value of cash flows to bond price. The cash flows are very different if there's a large amount of accrued interest on the settlement (or calculation) date compared to if there is little or no accrued interest. Consider the extreme case for cash flows the day before the interest is paid compared to cash flows the day it's paid. In the former case, your first (negative) cash flow will be larger since it includes almost six months of accrued interest, but you'll get a positive cash flow the next day. In the latter case, your first negative cash flow will be smaller, since there is no accrued interest, but you won't get your first positive cash flow for six months.

I used the XIRR function for the two scenarios to demonstrate this to myself, which showed that the XIRR for the two scenarios is essentially identical. However, if I naively plug in the dirty price (with almost six months of accrued interest) into the YIELD function, the yield is one half of using the clean price. Glad to share details if anyone is interested.

The bottom line is that I think it's probably good enough for our purposes in trying to figure all of this out to just calculate YTM of each bond using the clean price.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: SEC yield: accrued interest

Post by jeffyscott » Fri Aug 07, 2020 10:04 pm

Kevin M wrote:
Fri Aug 07, 2020 7:28 pm
I think I cracked the nut on my confusion about the impact of accrued interest in calculating YTM, per this instruction:
SEC wrote:Calculate the yield to maturity of each obligation held by the Fund based on the market value of the obligation (including actual accrued interest) <snip>
The bottom line is that it doesn't work to just plug the dirty price (=clean price plus accrued interest per $100) into the YIELD function. To understand this, I had to think about how YTM relates to cash flows.

YTM is a discount rate that equalizes the present value of cash flows to bond price. The cash flows are very different if there's a large amount of accrued interest on the settlement (or calculation) date compared to if there is little or no accrued interest. Consider the extreme case for cash flows the day before the interest is paid compared to cash flows the day it's paid. In the former case, your first (negative) cash flow will be larger since it includes almost six months of accrued interest, but you'll get a positive cash flow the next day. In the latter case, your first negative cash flow will be smaller, since there is no accrued interest, but you won't get your first positive cash flow for six months.

I used the XIRR function for the two scenarios to demonstrate this to myself, which showed that the XIRR for the two scenarios is essentially identical. However, if I naively plug in the dirty price (with almost six months of accrued interest) into the YIELD function, the yield is one half of using the clean price. Glad to share details if anyone is interested.

The bottom line is that I think it's probably good enough for our purposes in trying to figure all of this out to just calculate YTM of each bond using the clean price.

Kevin
Thanks for clearing that up. Higher price due to more accrued interest is offset by the fact that you get that extra amount back sooner. But the yield function was assuming you did not get a coupon payment for 6 months in both cases.
Time is your friend; impulse is your enemy. - John C. Bogle

User avatar
Kevin M
Posts: 11578
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: What is going on with short-term taxable bonds?

Post by Kevin M » Sat Aug 08, 2020 3:10 pm

Kevin M wrote:
Wed Aug 05, 2020 4:57 pm
I calculated the YTM and SEC yield based on clean and dirty prices for all Treasuries maturing in 1 year or more, and for clean the average YTM is 0.362% and for dirty price it's 0.171%, and the average SEC yields are 0.363% and 0.172% respectively.
This was a very quick and dirty first shot at just verifying that the the SEC yield formula generates a number close to the YTM for each individual bond (it does). The numbers quoted above were just averages of the results of YTM or the SEC yield formula applied to each bond, but that's not how SEC yield is calculated. And of course we can ignore yields calculated on dirty price, per my previous reply.

For my next pass, I calculated the SEC yield as follows.

I assume the fund holds 1 of each bond (all nominal Treasuries with maturity of one year or more), and that each bond has a face value of 100 (just so I can use prices directly in the formulas). So the "market value of the obligation (including actual accrued interest)" is the dirty price, which we need for this step:
Divide the yield to maturity by 360 and multiply the quotient by the market value of the obligation (including actual accrued interest) to determine the interest income on the obligation for each day of the subsequent month that the obligation is in the portfolio. Assume that each month has 30 days.
I also assume that the fund composition is constant for the 30-day period, so c*d in the formula (average number of shares times price per share on the last day of the period) is the sum of the dirty prices; i.e., the market value of the fund.

I assume no expenses ("b"=0), so "a - b: in the formula just equals "a".
  1. Use YIELD with the clean price to calculate YTM for each bond. Alternately could just use yield from the downloaded quotes.
  2. Per the instructions, divide the YTM for each by 360, multiply by the dirty price (market value including accrued interest) to get the "interest income on the obligation for each day of the subsequent month", and multiply by 30 to get the interest for each bond for the 30-day period.
  3. Calculate the sum of the results from step 2. This is "a" = total interest earned on all debt obligations during the 30-day (or one month) period. This value is 10.264.
  4. Calculate the sum of the dirty prices, which is c*d, the market value of the fund on the last day of the period. This value is 30,278. Incidentally, the sum of the clean prices is 30,073, so it doesn't make much difference whether or not accrued interest is included.
  5. Divide the result from step 3 by the result from step 4. This gives us the "(a-b) / (c*d)" part of the formula.
  6. Use the result from step 5 in the yield quotation formula. The result is an SEC yield of 0.407%. As mentioned above, it doesn't make much difference if I use clean price or dirty price for market value; the result (SEC yield) using clean prices for market values is the same to 3 decimal places in percentage terms (i.e., 0.407%).
This still doesn't address the confusion about whether to use the "current YTM", which what is stated in the quote in jeffyscott's most recent reply, and also is what Vanguard says, or the YTM at the start of the "prior 30 days". Here's what Vanguard says:
A security's income, for the purposes of this calculation, is based on the current market yield to maturity (for bonds) or projected dividend yield (for stocks) of the fund's holdings over a trailing 30-day period.
I interpret "current" as it is defined, "occurring in or existing at the present time", and I take "present time" to mean now, not 30 days ago. But how does this relate to "the fund's holdings over a trailing 30-day period"?

Also, I should note that I used ask yields and prices in doing the calculations, but it may be that bid prices are used. I know that treasury.gov yields are based on bid prices. Using bid prices would result in a higher SEC yield (bid price is lower, so bid yield is higher).

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
jeffyscott
Posts: 9002
Joined: Tue Feb 27, 2007 9:12 am
Location: Wisconsin

Re: What is going on with short-term taxable bonds?

Post by jeffyscott » Sat Aug 08, 2020 3:57 pm

I missed that current YTM part in the quoted description. It was the last part that seemed to make sense of it all to me. I read that as it's using what the YTM (less expenses) would have been had it held the current portfolio over the past 30 days, but adjusted to the current market prices. If that makes sense?

In other words, the 30-day SEC yield employs a forward-looking estimate of income based on current market prices to calculate how much hypothetical income a bond fund would have earned over the prior 30 days had the fund held its current portfolio for the entire period.
Time is your friend; impulse is your enemy. - John C. Bogle

Post Reply