Initial SEC yield and subsequent 5yr and 10yr returns

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dkturner
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by dkturner »

Doc wrote:
dkturner wrote:Correct me if I'm wrong, but premiums on bonds are amortized over the remaining life of the bonds held by a mutual fund aren't they? If that's the case how does the amortized yield result in a higher distribution yield than for a par bond? Doesn't the process of amortizing a premium put the distribution yield on a level playing field with bonds purchased at par?
When individuals amortize a bond premium they reduce the amount of interest received for tax purposes and also reduce their cost basis by an equal amount - say that's 1%. There is no cash flow that results from the amortization. The only cash is the amount of the coupon - say that's 3%.

A fund is required to pay out the coupon adjusted for the amount of any amortization or accretion so that the actual cash we receive is also the amount that we pay taxes on. In the case above that is only 2%. So the bond fund pays out less of a distribution in cash than the par bond. But the amortization also reduces the basis and the distribution yield is not effected to the same extent because of the arithmetic.

Say the price of the bond is 105.



Distribution yield of premium bond is 3/105 = 0.0283

Distribution yield of bond fund is 2/104=0.0192

Distribution yield of par bond 2/100=0.0200

So the opposite is true. The amortization makes the distribution yield lower not higher. :?:
Doc,

I understand the concepts of amortization and accretion. I know that amortizing a premium reduces the distributable income from a fixed income instrument. My comments were directed to an academic type who has little understanding of mutual fund accounting and, apparently, believes that a 4% coupon bond bought in a 2% interest rate enviornment produces twice as much distributable monthly income as a 2% coupon bond.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

dkturner wrote:Doc,

I understand the concepts of amortization and accretion. I know that amortizing a premium reduces the distributable income from a fixed income instrument. My comments were directed to an academic type who has little understanding of mutual fund accounting and, apparently, believes that a 4% coupon bond bought in a 2% interest rate enviornment produces twice as much distributable monthly income as a 2% coupon bond.
And my illustration was an attempt to provide an example.

Nuance: "... reduces the distributable income from a fixed income instrument fund." :D

Many of us that depend on distributions from their portfolio to fund living expenses it is important to distinguish between cash distributions and taxable distributions. In regard to the OP it seems to me that the SEC yield is a measure of the latter while future "returns" may have more of the "cash" aspects. But I really haven't thought through this idea.

As an aside I think it is better for retirees to consider their income coming from total return and not just dividends & interest but that is getting too far off subject.
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dkturner
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by dkturner »

Doc wrote:
As an aside I think it is better for retirees to consider their income coming from total return and not just dividends & interest but that is getting too far off subject.
I'm an old fashioned person and take the other side on the issue of income vs. total return. During trying times dividend income has held up better than equity total return. Additionally, Ken Fench's data cache demonstrates that equities with higher dividends generally produce higher total returns - although one has to be careful with the highest dividend payers. French's dividend data may simply be the other side of the value premium coin - it is what it is.

Interest income is another kettle of fish. Higher interest income hasn't been a winning strategy during trying times, when the highest quality, and lowest yielding, fixed income instruments really shine. 2008 was a classic demonstration of what happens to fixed income returns when the ship hits the sand. I'm in Jack Bogle's camp with respect to fixed income. When spreads between Treasuries and corporates are low, emphasize Treasuries. When spreads are wide (2009-?) emphasize investment grade corporates.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by richard »

Assume you hold $1,000 market value of Vanguard's Long-Term Tax-Exempt. It currently has a distribution yield of 3.76% and an SEC yield of 2.19%. You are receiving cash dividends at the rate of $37.60 per year. Assume interest rates don't change, the fund continues to operate as it has and you spend the dividends, neither buying nor selling any fund shares. Do you expect to continue receiving $37.60 per year? If not, approximately how much do you expect to receive in cash each year?
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Electron
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Electron »

richard wrote:Do you expect to continue receiving $37.60 per year? If not, approximately how much do you expect to receive in cash each year?
I would review the actual dividend payout in dollars per share and notice that it varies over time. It also varies with the number of days in the month. Also keep in mind that the portfolio can change in an actively managed bond fund. Bond indexes can also change over time.

https://personal.vanguard.com/us/funds/ ... =INT#tab=4

However, the good news is that the dividend tends to be more durable in the longer term funds. In recent years bond fund payouts have declined as rates came down. The rate of change was largely a function of the average maturity of the fund.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by richard »

Electron wrote:
richard wrote:Do you expect to continue receiving $37.60 per year? If not, approximately how much do you expect to receive in cash each year?
I would review the actual dividend payout in dollars per share and notice that it varies over time. It also varies with the number of days in the month. Also keep in mind that the portfolio can change in an actively managed bond fund. Bond indexes can also change over time.

https://personal.vanguard.com/us/funds/ ... =INT#tab=4

However, the good news is that the dividend tends to be more durable in the longer term funds. In recent years bond fund payouts have declined as rates came down. The rate of change was largely a function of the average maturity of the fund.
One reason the dividend has changed is that interest rates change. The question explicitly assumes rates don't change. Looking at annual distribution amounts should smooth out fluctuations due to the number of days in the month. I tried to assume away changes in bond indexes, but please pick a stronger assumption in order to neutralize that issue. This fund isn't very actively managed.

Anyway, I believe I've assumed away everything you list as a source of fluctuation.

Based on that, do you expect to continue to receive $37.60/year? If not, would you expect to receive more or less than $37.60 (no need to quantify)?

Prior posts mention the amortization of bond premium and the "mechanics of bond funds". Presumably, if rates stay the same, premium bonds would get replaced with par bonds over time. Would that affect your answer?

A major advantage of a longer term fund is more stability of income. A major disadvantage is the possibility of less stability of principal.
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Electron
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Electron »

richard wrote:Based on that, do you expect to continue to receive $37.60/year? If not, would you expect to receive more or less than $37.60 (no need to quantify)?
The $37.60 figure was based on only the December dividend so I would not necessarily expect that to continue. You may want to address two cases.

1. Interest rates all across the yield curve remain unchanged starting today. The fund has a third of the portfolio in bonds maturing in 20-30 years. As higher coupon bonds mature and are replaced with newly purchased bonds, the fund's dividend payout would be expected to decline. This is because rates have been coming down for many years. The fund holds a lot of bonds purchased when rates were higher than today.

2. Interest rates all across the yield curve have been unchanged for the last 30 years and will continue to remain unchanged. In this scenario, the dividend payout should be very stable. However, that would also assume that the types of bonds and credit quality remain essentially the same. Older bonds will continue to be replaced with newer bonds.

It is interesting to review the dividend history of the fund you are considering. Here is the dividend history for the Investor shares of the same fund going back to 1980. Notice that the monthly dividend has declined from $0.072 in 1980 to $0.037 today. You can get a similar history for Admiral shares VWLUX but the data starts in 2001.

http://finance.yahoo.com/q/hp?s=VWLTX&a ... f=2015&g=v

To answer your question from a practical standpoint assuming the existing portfolio, I would expect the monthly dividend to continue to decline by a small amount until some time after longer term rates have reversed their decline. You can download the Yahoo Finance data and actually plot the dividend trend over time. It is an interesting chart to view. However, you do have to remove the capital gains distributions to view only the monthly income.
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Kevin M
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Electron wrote: It is interesting to review the dividend history of the fund you are considering. <snip>

You can download the Yahoo Finance data and actually plot the dividend trend over time. It is an interesting chart to view. However, you do have to remove the capital gains distributions to view only the monthly income.
Yes, this is the way I got the dividend data to do the analysis of initial distribution yield vs. subsequent 5-year returns for VBMFX, which I posted about earlier in this thread. As I said, I didn't show the chart because it looks very similar to the SEC-yield/returns chart.

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grayfox
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by grayfox »

I looked at this same issue last year. Actually, I looked at various forecasting models for both stock funds and bond funds. For stock funds I looked at DDM, CAPE and FCF models. For bond funds, the SEC-YIeld model. I wanted to evaluate the accuracy of these various forecasting models. In other words, if a model predicts 4% return over some period, how accurate is that prediction? What should I expect to get? 0.04 +/- .001? +/-.01 +/- .02?

Vanguard has daily SEC yield going back to January 1994. I mostly looked at monthly data. Each end-of-month SEC-Yield was used as a prediction for the return over the next N-years. Yahoo has daily Adjusted-Close prices. With some programming and data scraping, it is a fairly straightforward to compare actual and predicted returns for Vanguard funds.

According to ISO 5725-1:1994 Accuracy = (trueness, precision). If you think if a bullseye as the actual value, each prediction is a shot that misses the target by some amount. the prediction error. Good trueness means that there is little or no bias in the prediction. Good precision means that the prediction form a tight circle.

Image
Poor Trueness, good precision

Image
Good Trueness, poor precision

The first bond fund I looked at was Vanguard Intermediate-Term Treasury Fund Investor Shares (VFITX). I chose the IT Treasury fund because it doesn't have the default risk and credit spreads changing.

This chart is for N = 5 years. The prediction model I wanted to test was the often repeated mantra that a bond fund will return the SEC-Yield when held for duration. The current duration of VFITX is 5.2 years. There is no historical duration data, so I chose a 5-year holding period. I also looked at other holding periods like 1, 2, 7, 10 years, but those are not the official SEC-Yield model.

The black line is SEC Yield, which is the predicted 5-year returns. The blue circles are the actual 5-year returns. The red and green lines represent a prediction interval using 2x the measured precision.

Image

The first observation is that, from 1994-2013, the prediction was biased low by 151 bps. This means that, on average, a monthly investment returned 150 bps more than the SEC-Yield prediction.

The precision was about 100 bps. With a 400 bps wide prediction interval, 68% of the monthly predictions fell within the interval. The rest were above. Some were more than 200 bps above the prediction. None were below the prediction interval. Very few even fell below the SEC-Yield prediction.

I'm not going to analyze the whys and wherefores of these results. My main takeaway is that, for VFITX, there is a distribution of outcomes. 2/3 of the time the 5-year return was within about 200 bps of SEC-Yield. 1994-2013 the return was almost always higher than the SEC Yield.
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Kevin M
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

grayfox, thanks for contributing! I may run my analysis on VFITX to see if I get the same results as you. Your results are even more surprising than the results for VBMFX.
grayfox wrote: Vanguard has daily SEC yield going back to January 1994.
Actually it's January 1993.
grayfox wrote: Yahoo has daily Adjusted-Close prices. With some programming and data scraping, it is a fairly straightforward to compare actual and predicted returns for Vanguard funds.
I may have already mentioned that I found returns calculated from the Yahoo adjusted close prices generally pretty close to return data obtained directly from Vanguard, but I found a few huge outliers for VBMFX. For most Vanguard funds, a better source is the set of Vanguard fund statistics spreadsheets on the BH Wiki, which have returns going back much further than on the Vanguard web site (1999) for funds that have existed longer.

Thanks for a great addition to the conversation!

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grayfox
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by grayfox »

We all know that if you hold a bond to maturity, the return is the Yield-to-Maturity YTM. For a bond fund, SEC Yield is analogous to YTM. So I had always thought that, on average, you would get the SEC Yield from a bond fund if the holding period was duration years. In other words, expected return of VFITX would be SEC Yield. Certainly there could be a distribution of outcomes. Some investments would return more and some less, but the center would be SEC Yield. Yet over the past 20 years, VFITX investments have consistently returned more than SEC YIELD. How can this be?

If you look at the holdings of VFITX, all the bonds are between 3 and 10 years. There are no bonds more than 10 years or less than 3 years.

Code: Select all

Under 1 Year	–4.6%
1 - 3 Years	0.0%
3 - 5 Years	49.9%
5 - 7 Years	31.0%
7 - 10 Years	23.7%
10 - 20 Years	0.0%
20 - 30 Years	0.0%
Over 30 Years	0.0%
Total	100.0%
Some Bogleheads like to describe a bond fund as analogous to a CD ladder. If it was like CD ladder, VFITX would hold bonds in about equal percentages from 10 down to 0 years. And the expected return might be the YTM or SEC Yield. So the CD ladder is a poor model for VFITX. The bond fund managers are probably doing some more complicated stuff than simply laddering Treasury bonds.

A better, but still simple, bond fund model might be buying 10-year bonds every year and selling them 7 years later when they are 3-year bonds. To keep things simple, suppose the fund buys a 10-year 5% bond at par. Let's say the yield curve has positive slope and the 3-year yields 3%. If interest rates don't change, when they sell it as a 3-year bond, the 5% bond will be selling at a premium and the fund will realize a capital gain. If the yield curve falls or steepens, and the 3-year is yielding 2%, the capital gain will be even greater. If you look at historical returns for VFITX, it breaks out capital return and income return. Some years are positive capital return and some years are negative. But since 1999 there are more positive years than negative years.

Code: Select all

Year Ended Capital Return	Income Return***	Total Return
2014	2.61%	1.71%	4.32%
2013	–4.50%	1.42%	–3.09%
2012	1.31%	1.36%	2.67%
2011	7.61%	2.18%	9.80%
2010	4.56%	2.79%	7.35%
2009	–4.66%	2.97%	–1.69%
2008	9.13%	4.20%	13.32%
2007	5.11%	4.87%	9.98%
2006	–1.56%	4.69%	3.14%
2005	–2.26%	4.57%	2.32%
2004	–1.09%	4.49%	3.40%
2003	–1.78%	4.15%	2.37%
2002	8.50%	5.64%	14.15%
2001	1.66%	5.89%	7.55%
2000	7.11%	6.92%	14.03%
1999	–9.07%	5.54%	–3.52%
We all know that rates have generally been falling during the period of the table 1999-2014. And also for the period of the chart 1994-2013. In fact, they've generally have fallen since 1982. I would guess that If there was SEC Yield data for 1982-1994, it would also show that the return was consistently greater than the SEC Yield. When VFITX was selling 3-year bonds, they would most likely have been priced higher than when bought as 10-year bonds, providing a capital return which added to the income return.

Image

I think that explains how VFITX consistently returned more than SEC Yield over about the 20 year period 1994-2013. Steepness of yield curve and falling yield curve provided positive capital return.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by grayfox »

BTW, as of today VFITX has SEC Yield = 1.30% and Duration = 5.2 years.
The 5 year Treasury has yield 1.61%
Penfed has a 5-year CD with APY = 1.61%
Bankrate.com shows a 2.32% 5-year Jumbo CD at CIT Bank.

For a 5-year holding period, which would you choose?
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

grayfox wrote:BTW, as of today VFITX has SEC Yield = 1.30% and Duration = 5.2 years.
The 5 year Treasury has yield 1.61%
Penfed has a 5-year CD with APY = 1.61%
Bankrate.com shows a 2.32% 5-year Jumbo CD at CIT Bank.

For a 5-year holding period, which would you choose?
Now have VFITX (actually admiral class) SEC 1.4%.

Will sell some to buy 5 yr TIPS in April.

Fixed income are part of a total portfolio which includes equities of course. CD's don't give the same portfolio risk reduction as Treasuries. I would not buy a $100k jumbo from CIT and 0.2% yield difference for the Penfed is not enough to give up the risk reduction from the Treasuries. Besides as has been pointed out throughout this thread the Treasuries have been out performing the SEC yield in the past. Whether that persists in a rising rate environment is yet to be known.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by longinvest »

grayfox wrote:Some Bogleheads like to describe a bond fund as analogous to a CD ladder. If it was like CD ladder, VFITX would hold bonds in about equal percentages from 10 down to 0 years. And the expected return might be the YTM or SEC Yield. So the CD ladder is a poor model for VFITX. The bond fund managers are probably doing some more complicated stuff than simply laddering Treasury bonds.
Grayfox,

I think that your conclusion is wrong. It is a good exercise to try to understand return on a CD ladder and realize that the YTM of the ladder is not its expected return. See: viewtopic.php?f=10&t=153753#p2306215 and the posts that follow.
Variable Percentage Withdrawal (bogleheads.org/wiki/VPW) | One-Fund Portfolio (bogleheads.org/forum/viewtopic.php?t=287967)
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Kevin M
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

grayfox, lots of good observations in your post. Much of this has been covered in other threads, but your post summarizes many of the points nicely.
grayfox wrote:We all know that if you hold a bond to maturity, the return is the Yield-to-Maturity YTM.
Not exactly. This is only true for a zero-coupon bond. For coupon bonds, the realized return will depend on coupon reinvestment rate as well.
grayfox wrote:Some Bogleheads like to describe a bond fund as analogous to a CD ladder. If it was like CD ladder, VFITX would hold bonds in about equal percentages from 10 down to 0 years. And the expected return might be the YTM or SEC Yield.
It depends on your assumptions. You came to the conclusion that yield curve shape and movement over time can have a big impact on returns for VFITX, but the surprising thing is the same is true for a simple bond ladder, even if bonds are held to maturity! The thread longinvest links to is one thread in which this is discussed. I think to believe it you may have to do the calculations yourself--that's what it took for me to believe it.
grayfox wrote:So the CD ladder is a poor model for VFITX. The bond fund managers are probably doing some more complicated stuff than simply laddering Treasury bonds.
This definitely is true. In another post, I showed the change in distribution of holdings by maturity between two reporting periods, and they were significant. There can be relatively large concentrations around certain maturities, and these can change over time. In the Vanguard reports, this is referred to as "yield curve management". They are making bets on the future shape and level of the yield curve; sometimes the bets pay off, sometimes they don't.
grayfox wrote:Let's say the yield curve has positive slope and the 3-year yields 3%. If interest rates don't change, when they sell it as a 3-year bond, the 5% bond will be selling at a premium and the fund will realize a capital gain.
Yes, this has been discussed extensively. Some posters use the term "roll yield" to describe this phenomenon.
grayfox wrote:If the yield curve falls or steepens, and the 3-year is yielding 2%, the capital gain will be even greater.
And the opposite is true as well, which is the reason I'm a bit reluctant to use the term roll yield. I think the term conjures an image of a bond dependably rolling down a static yield curve, which is not at all what happens in reality.

For any bond, all that determines the capital return component (to use Vanguard's phrase) are the prices at the beginning and end of the "holding period" (whatever period you are using to calculate your return). The yield curve steepness at the beginning of the holding period does not tell you that.

For a 5-year bond held for one year, all that matters is the price of a 5-year bond at the beginning of the holding period and the price of a 4-year bond at the end of the holding period. So the yield curve that matters is the line drawn between the corresponding yield-to-maturities at those to points (which are at two different times). This is not the way yield curves typically are drawn.

As long as one understands all of this, I guess the term "roll yield" is as good as any to describe how the price-change component adds to the realized yield.
grayfox wrote:If you look at historical returns for VFITX, it breaks out capital return and income return.
Ironic--I just spent some time last night copying these values for various funds into a spreadsheet, to be able to do analysis like you're doing here. First I spent some time trying to write a JavaScript function to do it, but couldn't figure out how to "see" the actual values from the script, as I've been able to do to pull other Vanguard data, like SEC yield and price history and fund holdings. I can see the values using "Inspect element", but not with "View page source", and apparently all I can pull with script is the latter.

I also calculated the arithmetic and geometric averages for each type of return for the entire 16-year period, and the geometric average for the last five years. Here are the values for VFITX:

Code: Select all

        Capital  Income   Total
        -------  ------   -----
Average 1.42%    3.96%    5.38%
GeoAvg  1.29%    3.95%    5.23%
5-year  2.24%    1.89%    4.12%
So we can see that for the entire period, the capital return component was significant, and for the last five years it has been the larger component of total return.

Another thing you will see by looking at distribution yield vs. SEC yield is that distribution yields have generally been higher in recent years, and income return is determined by distribution yield, not SEC yield. So in recent years, the income return component also has been higher than you would predict based on SEC yield, causing even more upward bias in the total return vs. initial SEC yield.

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

Kevin M wrote:grayfox wrote:
We all know that if you hold a bond to maturity, the return is the Yield-to-Maturity YTM.

Not exactly. This is only true for a zero-coupon bond. For coupon bonds, the realized return will depend on coupon reinvestment rate as well.
Kevin, you are being very loose with your definition of "realized return". You are thinking of "total return" not "reaized return". The realized return is considered as the Internal Rate of Return (IRR) based on the discounted cash flows of the investment and it does not matter whether you use the present value formulation (no reinvestment) or the future value formulation (reinvestment). You get exactly the same number. Didn't you just do a short XIRR example demonstrating this. Now if you decide that you should define "realized return" as the amount of money you have after some number of years i.e Total Return, you may have a point about reinvestment of cash flows. But that is not the standard definition of realized return.
Morningstar wrote:IRR vs. Total Return

Note: Realized return is also referred to as internal rate of return or IRR.

IRR is essentially a money-weighted return since cash contributions to the portfolio determine the return of the portfolio. Total return, on the other hand, is a time-weighted return, in that the timing of cash contributions to the portfolio is irrelevant since the portfolio is re-evaluated whenever there are cash inflows or outflows. It is time-weighted because only the time period over which the return is calculated matters. Think of time-weighted return as the return on the prices of the securities in the portfolio and money-weighted return as the return you receive on your money, based on when you invested it during the time period.
http://awgmain.morningstar.com/webhelp/ ... Return.htm
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Doc wrote:
Kevin M wrote:For coupon bonds, the realized return will depend on coupon reinvestment rate as well.
Kevin, you are being very loose with your definition of "realized return".
Perhaps, but you may have to take this discussion up with professors Bodie, Marcus and Kane, since I must have adopted this term from their widely-used textbook, "Investments" (or some other similar source). To be more precise, they use the phrases "rate of return realized over the life of the bond" and "realized compound yield" to describe what I meant by the abbreviated phrase "realized return".
Doc wrote:You are thinking of "total return" not "reaized return".
Yes and no. I am thinking of the annually compounded rate of return related to the total return, and I'm using the term "realized return" to describe that. Different sources may define the term differently, but I tend to fall back on textbooks for my definitions.

Let me explain it in a way that folks who do not live and breath discounted cash flow analysis should understand. We start with three numbers: initial value, final value and number of years between the two. The realized, annually-compounded rate of return is the rate of the return that results in the final value given the initial value and number of years.

Of course it's more precise to use math than words. We can start with either the simple present value or future value formula, and solve for the rate.

FV = PV * (1+r)^n
or
PV = FV / (1+r)^n

Solving for r:

r = (FV/PV)^(1/n) - 1

I'm talking about r, where PV is the amount we originally invested and FV is the amount we end up with at the end of n years (assuming we don't spend any of the cash flows).

Again, not for you, but for others that may appreciate a practical example, if I buy a "regular" 5-year Treasury with a YTM of 1.3%, I don't know that r in the above equation will be 1.3%. It probably won't be, since it will depend on the rate at which I can reinvest the coupons.

I personally probably would prefer a brokered CD with a YTM of 2% , but the principal is the same. Since I cannot reinvest the interest payments from the brokered CD in the brokered CD at the 2% rate, I don't know what r will be for this investment.

By contrast, for CD purchased directly from a bank or credit union, which in every case in my experience does allow me to reinvest in the CD at the stated rate, I do know that r = the stated CD rate (assuming of course no default, which is a different topic).

I'm not exactly sure what grayfox meant when he used the word "return", but given the potential confusion about this, I thought it was worth clarifying. Perhaps your post (and hopefully this one) have clarified it even better.

Kevin
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by grayfox »

longinvest wrote:
grayfox wrote:Some Bogleheads like to describe a bond fund as analogous to a CD ladder. If it was like CD ladder, VFITX would hold bonds in about equal percentages from 10 down to 0 years. And the expected return might be the YTM or SEC Yield. So the CD ladder is a poor model for VFITX. The bond fund managers are probably doing some more complicated stuff than simply laddering Treasury bonds.
Grayfox,

I think that your conclusion is wrong. It is a good exercise to try to understand return on a CD ladder and realize that the YTM of the ladder is not its expected return. See: viewtopic.php?f=10&t=153753#p2306215 and the posts that follow.
I will have to take your word for it that the expected return of a 5-year CD ladder is greater than the YTM. I can understand that if you run a 5-year ladder, then after 5 years all the CDs will be paying the higher 5-year interest rate. I knew that was one of the benefits of a CD ladder: once the ladder is set up, you only buy the longer 5-year CD which typically has higher yield.

Now as far as this investigation, what you are saying seems to provide additional explanation why the actual return of VFITX has been greater than SEC Yield, which only shoots bigger holes in the model which says that you should expect to get only the SEC Yield from VFITX.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by longinvest »

Grayfox, I did not say that the return will be greater than YTM; all I said is that YTM is not its expected return.

There are two components to the yearly return of the ladder. There's a speculative return; the difference in the marked-to-market value of the ladder due changes in the yield curve. There's a fundamental return; the interest payments which amount to the average of 5-year interest rates of the last 5 years. The sum of both returns is as unpredicable as changes in the yield curve.

So, even with such a simplified model, it is impossible to predict future returns with good precision over a specific time period, unless you make unrealistic assumptions such as fix the yield curve (and thus remove any uncertainty about reinvestment interest rates and future ladder valuations).
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

Kevin M wrote:Yes and no. I am thinking of the annually compounded rate of return related to the total return, and I'm using the term "realized return" to describe that. Different sources may define the term differently, but I tend to fall back on textbooks for my definitions.
And I tend to fall back on the industry standards.

Vanguard: Total returns
Short-term total return information is provided only as a service. Historical performance, particularly short-term performance, is no guarantee of future returns. Share price, yield, and return on an actual investment will fluctuate, and you may have a gain or loss when you sell your shares. Average annual returns include changes in share price and reinvestment of dividends and capital gains.

Fidelity: Total returns are historical and include change in share value and reinvestment of dividends and capital gains, if any.

Schwab: Refers to Morningstar which I already referenced.

The reason I prefer industry standards is that the financial industry is highly regulated and has required reporting standards as in the SEC yield. Academics on the other hand are self regulated by the professor himself other than in peer review process which is unlikely to call out any but egregious errors since the "worm turns" sometimes. Been there, done that.

I no longer know what all your charts are supposed to be measuring. If it's total return or the average annualized return which derives from the total return it is the same IRR calculation that is used to calculate that rate. And then it doesn't matter whether you use the present value or future value formulations. But since you are insisting that you must include reinvestment of cash flow you must be measuring something else. Hence you charts while not being an oranges to apples comparison they may be an oranges to grapefruits comparison. I'm don't think that is your intent and I think that the charts are actually doing this but your insistence on using the dividend reinvestment requirement is a concern.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by ogd »

grayfox wrote:I will have to take your word for it that the expected return of a 5-year CD ladder is greater than the YTM. I can understand that if you run a 5-year ladder, then after 5 years all the CDs will be paying the higher 5-year interest rate. I knew that was one of the benefits of a CD ladder: once the ladder is set up, you only buy the longer 5-year CD which typically has higher yield.
The simplified version is that as the bonds or CDs marked to market descend down the yield curve, their value increases and YtM decline. Even without trading them, if you take a snapshot of the YtM's you will get less than the starting (say) 3%, whereas the ladder as a whole will continue making 3%. This discrepancy stays the same as long as the yield curve stays static (which is a big assumption, more on that later).

This does not mean that the YtM is a flawed measure. Indeed, if you buy a 2 year bond at YtM 0.5% there's no way in heck you are making more than 0.5%/year for the remainder of the term; you could make at most 1% next year if the yields decline to zero and you promptly sell it, but still this is a far cry from the 3%-ish "distribution yield". Instead, the real action and reason for the return discrepancy occurs higher up the ladder, where bonds are making much more than 3% in some years.

This also doesn't mean you will do just as well with a ladder (holding to maturity) as you would with a fund. The simple artifice of selling bonds 2-3 years before maturity and holding them in a savings account is a big money maker presently. The slope is not the same along the curve and at the bottom end you have bank products biting into the desirability of the ladder.

The big gotcha in all of the above is that it assumes the yield curve will remain static; that is, the bond market will tolerate for long periods the clear discrepancy between a 10 year bond and two successive 5 year bonds because it's worried about risk or whatever. I don't think this is a good assumption; risk does eventually manifest or the premium goes away. In fact, we've seen a great amount of flattening over the last year or so, although to everyone's surprise including mine it occured much more on the higher end (e.g. 10 year yield going down) than the short end. The flatter the yield curve, the less we can expect from it.
grayfox wrote:Now as far as this investigation, what you are saying seems to provide additional explanation why the actual return of VFITX has been greater than SEC Yield, which only shoots bigger holes in the model which says that you should expect to get only the SEC Yield from VFITX.
I sort of miss 2013 when I was the one defending bond funds rather than trying to temper expectations. I think I was much better at it :?
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Doc wrote: I no longer know what all your charts are supposed to be measuring.
Doc, the rest of your post would be fun to reply to in detail, but I think we're getting too far off topic for this thread, so I'll just reply to the quoted comment, since that's on topic.

The term used in the charts is "5yr and 10yr annualized returns". These are the same returns that Vanguard refers to as "average annual returns", and the numbers are the same you'd see in the 5-year and 10-year columns. You can verify by looking at the chart in the OP, noting that the 5-year subsequent return for 2010 (12/31/2009 through 12/31/2014) is a little over 5.2%, and seeing that the 5-year return reported by Vanguard for VCAIX is 5.24%. Indeed, these numbers had better match, since I pulled the return data for 1999 on from Vanguard.

A note on terminology. I prefer "annualized return" to "average annual return", since the latter lends itself to confusion between arithmetic and geometric average return; this has come up more than once in the forum. As we know, it is the geometric mean, not the arithmetic mean. Another common term in use for this is Compound Annual Growth Rate, or CAGR. Whatever we call it, mathematically is the geometric mean, and that's what's shown in the charts.

As you know, there are different ways to compute the geometric mean. One is to use the formula I derived earlier, which would be convenient if you were working with cumulative return, e.g., as shown on an M* growth chart. Another way is to calculate it from the individual annual returns, either with a formula or using the spreadsheet GEOMEAN function. The latter is convenient in conjunction with the spreadsheet ARRAYFORMULA (at least Google's implementation of it), and that is what I use.

Specifically, if annual returns are in cells C19-C23, 5-year annualized return is calculated as:

Code: Select all

=ArrayFormula(GEOMEAN(1+$C19:$C23))-1


Hope this is helpful to someone,

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

Kevin M wrote:A note on terminology. I prefer "annualized return" to "average annual return", since the latter lends itself to confusion between arithmetic and geometric average return; this has come up more than once in the forum. As we know, it is the geometric mean, not the arithmetic mean. Another common term in use for this is Compound Annual Growth Rate, or CAGR. Whatever we call it, mathematically is the geometric mean, and that's what's shown in the charts.
Quicken wrote:Average annual return (IRR)

Definition

Often called the internal rate of return (IRR), the average annual return is usually defined as a percentage equal to the interest rate on a bank account that would give you the same total return on your investment. It takes into account money earned by the investment (interest, dividends, capital gains distributions) as well as changes in share price
http://quicken.intuit.com/support/help/ ... 82161.html

Two points:

1) The IRR or average annual return does not assume reinvestment of dividends. It is calculated from the sum of the discounted cash flows or if you prefer the sum of the future value of the cash flows. If you reinvest the distributions the cash flow for that period is zero.

2) You can call it what you want but if you choose to use terms not used by Morningstar, Fidelity, Vanguard or Quicken you are apt to add confusion to the discussion. And if you keep insisting that you must reinvest dividends you are adding to the confusion.

From your latest response your charts appear to be what was implied. It is your choice of words and "required" assumptions that made me question what you were showing.

It is this kind of confused wording and its consequences that was behind the need for SEC yield in the first place.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Abe »

As my Korean friend Mr. Lee used to say, "I'm con-foosed".
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Doc wrote:And if you keep insisting that you must reinvest dividends you are adding to the confusion.
I'm confused. I'm simply using the same calculations that everyone else does, including Vanguard. I'm not insisting on doing anything other than calculating geometric mean return (or whatever you want to call it) the way everyone else does.

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by richard »

Assume annual returns of 5%, 4%, 6%, -2%, 3%. Kevin's formula gives a result of 3.16%, as does a normal CAGR formula.

Doc, what do you get as average annual returns? EDIT: average annualized returns.

Kevin, how are you getting annual returns? That is, how are you computing annual returns from price change and distributions?
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

Kevin M wrote:
Doc wrote:And if you keep insisting that you must reinvest dividends you are adding to the confusion.
I'm confused.UI''m simply using the same calculations that everyone else does, including Vanguard. I'm not insisting on doing anything other than calculating geometric mean return (or whatever you want to call it) the way everyone else does.
Kevin
Kevin M wrote:grayfox, lots of good observations in your post. Much of this has been covered in other threads, but your post summarizes many of the points nicely.
grayfox wrote: wrote:
We all know that if you hold a bond to maturity, the return is the Yield-to-Maturity YTM.
Not exactly. This is only true for a zero-coupon bond. For coupon bonds, the realized return will depend on coupon reinvestment rate as well.
I's not your calculation it's the words you are using. Because you use non-industry standard words I'm not sure what your charts mean.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

richard wrote:Assume annual returns of 5%, 4%, 6%, -2%, 3%. Kevin's formula gives a result of 3.16%, as does a normal CAGR formula.

Doc, what do you get as average annual returns?

Kevin, how are you getting annual returns? That is, how are you computing annual returns from price change and distributions?
Now I'm the one that's confused.

The "average annual return" is 3.20% I think but I am making the assumption that "average annual returns" is the average of the individual annual returns but that's part of the language issue.

What we want to know is the average annualized returns or CAGR. But I am getting different answers depending on whether I use reinvestment or not and I don't believe that is right. I get 3.26% for the cash distributions and 3.16% for reinvestment of distributions. I'm using both XIRR and IRR in Excel. I also get the 3.16% by brute force multiplication and then taking the 5th root. But then I'm also getting 3.20% using the VFSCHEDULE function which is the average annual return number. I'm not an Excel expert. The negative return in the fourth year may be causing the problem.

I need to go out. I'll try to resolve these differences later if I can. But in any case the differences are all well within Kevin's error bands anyway.

I was never challenging Kevin's numbers only the words he used to describe what they were.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by richard »

I should have written average annualized returns. Sorry about that.

I'm just trying to figure out if the issue is purely wording or not.

Here is my calculation of the annual return on Vanguard's 500 index fund admiral:

Code: Select all

12/31/2013   -170.36
 3/20/2014      0.785
 6/19/2014      0.815
 9/18/2014      0.883
12/16/2014      1.034
12/31/2014    189.89
Vanguard reported 13.64%. I get 13.633% using Excel's xirr formula. 12/31 numbers are prices, the other numbers are dividends and their record dates.

Is this how Kevin and Doc would calculate annual returns?
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

richard wrote: Kevin, how are you getting annual returns? That is, how are you computing annual returns from price change and distributions?
I just use the annual total returns directly from Vanguard's website, or for returns before 1999, from the Vanguard fund statistics spreadsheets on the BH Wiki (put together by Barry Barnitz).

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Yesterday I was kind of burned out on the dialogue with Doc, and thought it was taking us too far off topic, so kept my last reply short. Now I've got my mojo back, and have realized that this probably is an important topic to clarify; i.e., what do we mean by "return" or "returns" in the context of this thread, and how is it calculated?

Doc seems to have two issues. One is related to terminology, and one is related to the subject of whether or not a particular return calculation "assumes" reinvestment of dividends.

Regarding terminology, as I pointed out before, I use the term "annualized returns" on the charts, e.g., in the OP. A quick Google search shows that this is a widely used and well understood term. If we want to hold up Vanguard as representative of "the industry", you can do this search to see if Vanguard uses the term:

Code: Select all

"annualized return" site:Vanguard.com
This returns many links, primarily to research papers they've done. Take a look at any of them, and you'll find the term used. I selected their most recent "Vanguard's economic and investment outlook" (December 2014), and found the term used nine times. So I think we can safely say that this is an "industry standard" term.

I'm using the term exactly the way Vanguard uses it.

On the performance pages/tabs on their website, they use the term "Average annual returns" instead, but it means exactly the same thing. They use this term because the SEC requires it. I happen to think "annualized returns" is better, since as I said before, it leads to less confusion as to whether it's an arithmetic mean or geometric mean being shown. If you read academic papers or finance textbooks, or even many investment articles on the web, you'll see that arithmetic mean and geometric mean are both widely used, so it's important to distinguish between them.

As far as I can tell, "annualized return" is used exclusively to indicate the geometric mean of annual returns when discussing multi-year periods (it's also used to indicate annualized returns for periods shorter than one year). In my opinion, the SEC made a mistake in using "annual" instead of "annualized".

Speaking of the SEC, that's a good segue into the topic of reinvested dividends that Doc seems so concerned about. He mentioned that I insist on including them in my calculations. Well I don't insist on it, but the SEC does insist on it, specifically with respect to calculating "average annual total return". Everyone can read it for themselves here: Final Rule: Disclosure of Mutual Fund After-Tax Returns (S7-09-00), in the section titled "Item 21. Calculation of Performance Data".

After showing the formula that must be used, which is exactly the simple version of the future value formula I showed in an earlier reply, but using different symbols, they provide this instruction:
SEC wrote:2. Assume all distributions by the Fund are reinvested at the price stated in the prospectus (including any sales load imposed upon reinvestment of dividends) on the reinvestment dates during the period.
So yes, reinvestment of distributions is assumed in the average annual total return values provided by Vanguard, which are the values I use to calculate 5-year and 10-year (or any subsequent N-year) returns.

Further, the geometric mean of annual returns, which is the mathematical term for the calculation of annual[ized] average [total] return, "assumes" that the entire cumulative return from previous years is invested in the subsequent year; i.e., no distributions are taken from the fund--they are all reinvested. So if we have annual total returns r1, r2, and r3, the geometric mean cumulative total return, expressed as a percentage, is calculated as:

Code: Select all

Cumulative Total Return % = (1+r1) * (1+r2) * (1+r3) - 1
EDIT: And the geometric mean is calculated as:

Code: Select all

GeoMean = [ (1+r1) * (1+r2) * (1+r3) ] ^ (1/3) - 1
Another common term used for this, Compound Annual Growth Rate, or CAGR, makes it explicit that this is a compound return. Compounding implies reinvestment of the previous returns, whether they came from capital appreciation or dividends. Since I use Vanguard's "total return" values, which incorporates both capital return and income return, I don't have to worry about what part of the return comes from dividends and what comes from capital appreciation. And I don't have to worry about cash flows, because there are no cash flows in the calculation--just annual returns.

If I wanted to do a calculation based on cash flows, instead of looking at annual returns, I'd look at cumulative total return over the period of interest, in which case there would be two cash flows: the original investment, and the final value (SEC uses the terms "initial payment" and "ending redeemable value", or "ERV"). I guess I could make it more complicated, and break out the distributions from the capital appreciation, and use an IRR calculation with more cash flows, but why would I go to the trouble of doing that when I can get the same value with a much simpler calculation?

Now, I think I know where Doc is coming from with the whole "you don't have to assume reinvestment of dividends" thing. He's probably read the same paper that I've read that explains that a common misconception is that a present value calculation or internal rate of return calculation assumes that the cash flows (e.g., dividends) are reinvested. These calculations don't assume anything about what happens with the cash flows, but just describe the relationship between the present value of cash flows and a constant discount rate.

I think the misunderstanding arises because a common statement is something like this (from "Investments", by Bodie, Kane and Marcus"):
The yield to maturity can be interpreted as the compound rate of return over the life of the bond under the assumption that all bond coupons can be reinvested at an interest rate equal to the bond's yield to maturity. Yield to maturity is widely accepted as a proxy for average return.
(Highlights mine)

I highlighted the first phrase because it's import to note that "can be interpreted as" does not say that the formula for yield to maturity assumes anything. It's just a way to think about it--it's a mental model that helps people understand the concept. Doc may feel that it's misleading, but I don't. I highlighted "proxy" to emphasize that YTM is not the same thing as average [annual[ized]] return.

As I've shown before, an IRR calculation will give you the same result whether you assume reinvested dividends or not, but as I also showed, this does not mean that they both necessarily result in the same "ending redeemable value". As an investor, I'm more interested in the ERV than the IRR.

Kevin
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

richard wrote:I should have written average annualized returns. Sorry about that.

I'm just trying to figure out if the issue is purely wording or not.

Here is my calculation of the annual return on Vanguard's 500 index fund admiral:

Code: Select all

12/31/2013   -170.36
 3/20/2014      0.785
 6/19/2014      0.815
 9/18/2014      0.883
12/16/2014      1.034
12/31/2014    189.89
Vanguard reported 13.64%. I get 13.633% using Excel's xirr formula. 12/31 numbers are prices, the other numbers are dividends and their record dates.



Is this how Kevin and Doc would calculate annual returns?
Yes and no. The way you are using XIRR is the present value formulation of the discounted cash flow equations. Kevin is insisting that you must reinvest dividends to get the "right" answer. Yet Vanguard by using the "growth" or future value formulation gets exactly the same answer. Reinvesting dividends is not a requirement. The answer is the same both ways. Since I use Quicken to do the calculation and am most familiar with the present value formulation (in an industrial setting using a hurdle rate to calculate the net present value instead of the reverse) I prefer the present value formulation. But people like Kevin and Nisiprius (presumably) may prefer the future value formulations since the data is often provided more easily as in growth charts or in Yahoo adjusted price data for example. Both methods are right and should give the same answer. (I still haven't figured why my previous attempt with the negative cash flow is screwed up.)

And don't be sorry about using annual instead of annualized. It seems Vanguard, Fidelity and Schwab all use "average annual returns". I was just trying to make a point by misinterpreting the term which is the word problem that Kevin was addressing some time back when he said he prefers "average annualized returns". While there may be some confusion about arithmetic and geometric average I think we should stick with the common industry terminology.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

Richard's "written" test and my failure to get the right answers brought some clarity to this subject.

Our confusion lies in two related but actually separate "problems". One is math and the other is definitions.

Words: Kevin points out the confusion of arithmetic and geometric means and chooses to average "annualized" instead of average "annual" returns. I suggest we use "Compound Annual Growth Rate - CAGR" which I believe is the actual number that the various fund sites use with varying names. Kevin I believe is using this value in his charts. Another word problem is using "reinvestment of dividends" and future value as the same concept. I fell into this trap and Kevin was not able to pull me out. Bias of the familiar on both our parts.

Math: YTM is bond speak for Internal Rate of Return (IRR). The IRR calculation is the "rate" that causes the time weighted value of all the cash flows to equal zero. Traditionally the weighting factor is the discount rate 1/(1+i)^n but it can also be used with the future value as the weighting factor (1+i)^(N-n). Same result. The CAGR also calculates a value based on the cash flows (but only 2) and it is not time weighted. The result is that if the returns are not constant from period to period one obtains different results from the two methods. The IRR gives greater weight to early cash flows and the CAGR effective weights all the same.

Problem for the class: It is often stated that the SEC yield is the YTM for a fund. Is it actually the CAGR for the fund not the YTM (IRR)?
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Doc wrote: Problem for the class: It is often stated that the SEC yield is the YTM for a fund. Is it actually the CAGR for the fund not the YTM (IRR)?
Perhaps this is best answered by looking at the SEC yield formula and the accompanying instructions provided by the SEC. This can be viewed in www.sec.gov/about/forms/formn-1a.pdf in section "Item 26. Calculation of Performance Data".

Here is the SEC yield formula:

Image

And here is the relevant instruction:
1. 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.

(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.

(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 taxexempt
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.
Note that instruction 1(a) requires calculating "yield to maturity of each obligation held by the Fund". This is why I think SEC yield commonly is thought of as a type of yield to maturity, although clearly the calculation has some other components.

The linked SEC document also includes the required formula for calculating "average annual total returns", which is based on the simple (two cash flows) version of the future value formula). Since I have the document handy, here is the formula for calculating "average annual total return":
(1) Average Annual Total Return Quotation. For the 1-, 5-, and 10-year periods ended on the date of the most recent balance sheet included in the registration statement (or for the periods the Fund has been in operation), calculate the Fund's average annual total return by finding the average annual compounded rates of return over the 1-, 5-, and 10-year periods (or for the periods of the Fund's operations) that would equate the initial amount invested to the ending redeemable value, according to the following formula:

P(1+T)^n = ERV

Where:

P = a hypothetical initial payment of $1,000.

T = average annual total return.

n = number of years.

ERV = ending redeemable value of a hypothetical $1,000 payment made at the beginning of the 1-, 5-, or 10-year periods at the end of the 1-, 5-, or 10-year periods (or fractional portion).

Note that in this formula, T is the average annual total return, so you must solve the equation for T. This is what I did a bit upthread (Bogleheads • View topic - Initial SEC yield and subsequent 5yr and 10yr returns), but I wrote the formula using the more common present value and future value notation:

Code: Select all

FV = PV * (1+r)^n 
So the formulas obviously are the same; simply make the following substitutions:

r = T
PV = P
FV = ERV

(While looking at this I realized that in an earlier post I showed the formula for cumulative total return percentage instead of geometric mean, and I have corrected that).

Kevin
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

For some more context on the issue of compounding "built in" to the SEC 30 day yield formula, it is instructive to read the "Compounding" section of this SEC document: https://www.sec.gov/rules/proposed/482.txt, which is a proposal for a yield formula to be used by unit investment trusts (UITs). Here's an extract:
The proposed Estimated Yield Formula would omit a step
proposed by the ICI in which a trust's average yield to maturity
is divided by twelve and re-annualized using a method that, in
effect, would compound a monthly yield
. The Commission is
concerned that such a calculation could materially overstate the
anticipated yield of a trust and is not proposing to provide for
compounding of a trust's average yield to maturity.

In its request for rulemaking and in other correspondence
with the staff, the ICI has argued that Fixed Income UITs
primarily compete with mutual funds.-[27]- Mutual funds
calculate yield according to a Commission formula that
effectively compounds earnings
.-[28]- The ICI believes that
Fixed Income UITs also should be permitted to compound earnings
or they would be placed at a competitive disadvantage to mutual
funds.-[29]-

The compounding element of the mutual fund yield formula
reflects the internal compounding of dividends within mutual
funds as a result of their reinvestment of interest from bonds
(and other securities) upon receipt
. Because of the fixed nature
of UITs, interest payments received are not reinvested, but are
held by the trust's custodian until they are distributed to
unitholders, and thus no compounding occurs within the UIT.
The proposed yield formula for UITs is simpler than the 30-day mutual fund yield formula:
Estimated Yield = [(a-b) * c] - x

Where,

a = sum of (market value of each security * yield to
maturity of each security * time to maturity of each
security)/sum of (market value of each security * time
to maturity of each security)

b = total annual expenses of the trust/net asset value of
the trust

c = 1 - sales load

x = sales load * r
(1+r)n-1

r = (a-b) * c

n = number of annual periods until amortization date.
Note that there is no raising to the power of 6 (and then doubling) in this formula, which is the compounding being discussed with respect to the mutual fund formula.

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Electron »

Assume annual returns of 5%, 4%, 6%, -2%, 3%. Kevin's formula gives a result of 3.16%, as does a normal CAGR formula.
I use a scientific calculator with the y to xth power function.

1.05 x 1.04 x 1.06 x 0.98 x 1.03 = 1.168400688

1.168400688 to the 0.2 power = 1.031616693 which translates to 3.1616693%.

If an investment increases by a factor of 2.5 after 10 years, I calculate the following: 2.5 to the 0.1 power = 1.095958226 which translates to 9.5958226%.

Compounding money at 5% for 14 years results in the following: 1.05 to the 14th power = 1.979931599

1.979931599 to the 1/14th power = 1.05
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

I haven't gone through your recent posts in detail but a couple of points stand out.

1)
Kevin M wrote:Note that instruction 1(a) requires calculating "yield to maturity of each obligation held by the Fund". This is why I think SEC yield commonly is thought of as a type of yield to maturity, although clearly the calculation has some other components.
OK. The SEC 30 day yield is the "'sum" of the YTM (IRR) of the funds components. I think that's what most of us thought - the SEC yield is like the bond YTM but for a fund.

2)
Kevin M wrote:The linked SEC document also includes the required formula for calculating "average annual total returns", which is based on the simple (two cash flows) version of the future value formula). Since I have the document handy, here is the formula for calculating "average annual total return":
This is where I got the "not quite". I took a five year example using gains of 1,1,1,5,1% and 5,1,1,1,1%. The simple two cash flow model starts with the FV of (1+a)*(1+b)*...(1+e). In this case the order of the gains doesn't matter since a*b*c = c*b*a. From this idea I reached the conclusion that the two cash flow model did not really take into account the sequence of returns if they were unequal and is therefore not a discounted cash flow model like the YTM (IRR) and by extension the SEC yield. The values are close at least with these low returns. I got "yields" of 1.829, 1.786 and 1.788 for the "early" five cash flow, the "late" cash flow and the "two" cash flow cases respectively. (The discounted cash flow calculations were done with Excel using both the IRR and XIRR formulas.) The results are in exactly the order you would expect by rigorous discounting of the cash flows. Your original chart (from sometime in the dark ages I think it was so long ago) had returns in the 4% range which would magnify the differences I found in my short model. It may be that a significant part of the difference you see is due to this slight oranges to grapefruits comparison. :idea:
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

Electron wrote:
Assume annual returns of 5%, 4%, 6%, -2%, 3%. Kevin's formula gives a result of 3.16%, as does a normal CAGR formula.
I use a scientific calculator with the y to xth power function.

1.05 x 1.04 x 1.06 x 0.98 x 1.03 = 1.168400688

1.168400688 to the 0.2 power = 1.031616693 which translates to 3.1616693%.

If an investment increases by a factor of 2.5 after 10 years, I calculate the following: 2.5 to the 0.1 power = 1.095958226 which translates to 9.5958226%.

Compounding money at 5% for 14 years results in the following: 1.05 to the 14th power = 1.979931599

1.979931599 to the 1/14th power = 1.05
If this was directed at my response to Richard - yes that's what I got, probably with the same calculator. I got hung up on the IRR/XIRR model because I screwed up the final cash flow by misapplying the "return of capital" in year four.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

It is instructive to simplify the SEC 30 day yield formula, ignore expenses, and assume it basically reduces to this:

Code: Select all

2 * ( ( YTM / 360 * 30 + 1) ^ 6 - 1 )
If we then plug in 2% for YTM, the result is 2.01%. If we plug in 5%, we get 5.05%, and 10% gives 10.21%. So there is a slight compounding effect relative to straight YTM. This is what the UIT folks were complaining about in not getting to apply similar compounding in the formula the SEC wanted them to use.

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Doc wrote:From this idea I reached the conclusion that the two cash flow model did not really take into account the sequence of returns if they were unequal and is therefore not a discounted cash flow model <snip>
.

This is correct.

One problem with applying a discounted cash flow model is that part of the total return is from capital appreciation, which is not a cash flow (unless you sell the security). To apply a discounted cash flow model you'd have to look at the annual distributions, which include dividends and possibly capital gain distributions. You can see the breakout between capital appreciation and distribution income for Vanguard funds back to 1999, and do the discounted cash flow calculation if you want, but you'd also have to calculate the final value, not including reinvested distributions, yourself. This is not the typical way to evaluate average annual total return (or annualized return or CAGR or whatever you want to call it). The SEC mandates that the 2-cash-flow future value formula is the basis for reporting average annual total returns.

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Doc »

Kevin M wrote:
Doc wrote:From this idea I reached the conclusion that the two cash flow model did not really take into account the sequence of returns if they were unequal and is therefore not a discounted cash flow model <snip>
.

This is correct.

One problem with applying a discounted cash flow model is that part of the total return is from capital appreciation, which is not a cash flow (unless you sell the security). To apply a discounted cash flow model you'd have to look at the annual distributions, which include dividends and possibly capital gain distributions. You can see the breakout between capital appreciation and distribution income for Vanguard funds back to 1999, and do the discounted cash flow calculation if you want, but you'd also have to calculate the final value, not including reinvested distributions, yourself. This is not the typical way to evaluate average annual total return (or annualized return or CAGR or whatever you want to call it). The SEC mandates that the 2-cash-flow future value formula is the basis for reporting average annual total returns.

Kevin
The assumed sale of the final market value is indeed needed for the discounted cash flow calculation but for a fund it is simply the shares times the ending price and you need the starting price to calculate the shares. That's not a big deal. If you want to know the "yield" on a fund that you don't own the discounted cash flow can be a problem if you don't have a source for the cash distributions then falling back on the CAGR calculation that the fund already gives you is a good substitute at least for bond funds. For equity funds what may have large and uneven distributions the "error" is somewhat different. If you are evaluating a fund that you own and make periodic purchase and sales the discounted cash flow is your best choice but you need the data and the software to do it. (Quicken does both jobs for you but the IRR calculation has some quirks which can lead to errors if the time periods are short or sometimes when you have add/remove shares transactions as in an upgrade from investor to admiral class. I would be surprised if other software didn't' have similar features. And there is always Excel.)

This has been a good discussion and I've learned or re-learned stuff I had forgotten. However I still have no comment on the Vanguard California Intermediate-Term Tax-Exempt bond fund chart. By the way what is California?)
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by grayfox »

I thought I would post the results for another bond fund: Vanguard Intermediate-Term Tax-Exempt Fund Investor Shares (VWITX). I used the same scale as the chart for VFITX to allow direct comparison. I am posting both here for comparison.

Image

Image

Compared to VFITX, the SEC-Yield model is a more accurate predictor of 5-year return. The actual result is closer to the 5-year return predicted by SEC Yield. VWITX prediction is also biased low, but only by half a s much (77 bps for VWITX vs. 151 bps for VFITX). The precision is also twice as good, 55 bps. vs 102 bps. Using 2 x measured precision, the prediction interval is about 220 bps wide(+/- 110 bps). About the same percentage (70%) fell inside the prediction interval, and most were higher than predicted.

Looking at the holdings of VWITX, there are bonds from 20 years down to under 1 year. This is unlike VFITX, which had all bonds between 3 and 10 years, and no bonds less than 3 years. BTW, currently the average duration = 4.7 years, and SEC Yield = 1.45%.

Code: Select all

Under 1 Year	12.4%
1 - 3 Years	10.0%
3 - 5 Years	8.7%
5 - 10 Years	26.6%
10 - 20 Years	41.8%
20 - 30 Years	0.5%
Over 30 Years	0.0%
Total	100.0%
Unlike VFITX, it appears that this VWITX holds its bonds to maturity. In other words, the IT muni fund is managed in a completely different way than the IT Treasury fund. This makes sense, because it is well known that muni bonds are not very liquid. In practical terms, this means if you sell a muni bond before maturity, you will get a haircut. There probably isn't much opportunity to "ride the yield curve" with muni bonds. The CD ladder bond fund model might not be a bad model for the IT muni fund, since the bonds are held to the bitter end.

Everyone can draw their own conclusions, but my guess is that 5-year return will be within about 100 or 150 basis points of SEC Yield most of the time.

Another thing I will add is that, from a Modern Portfolio Theory MPT point of view, the IT Muni bond fund is less risky than the IT Treasury fund. The Markowitz measure of risk, i.e. variance of the outcome, is only half as much. The outcome is more predictable.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Electron »

I just read the latest Annual Report on the Vanguard California Tax Exempt funds, one of which was referenced in the first post of this thread. It looks as though Vanguard may be managing these funds for total return and the dividend payout is a lower priority. See "Management of the Funds" on page 12. As an example, they recently sold a significant quantity of bonds rated A and replaced them with higher quality AA rated securities. They also reduced holdings in longer maturities.

https://personal.vanguard.com/us/funds/ ... =INT#tab=0

I've held several Vanguard Tax Exempt Bond funds going back as far as 1990 without reinvesting dividends and the reduction in the dividend payout has been very noticeable as rates came down. Shareholders undoubtedly benefit if total return management is successful but it is still disappointing to see the payout drop.

My next comment is a little off topic but quite interesting. If you look at the holdings of the California Tax Exempt Money Market fund and the Municipal Money Market fund, you will see many Nuveen VRDP VRDO securities. The coupons are in the range of 0.14%. These securities are used to provide leverage for Nuveen Closed End Municipal Bond funds. Closed End Leveraged funds often issue preferred shares paying a low rate to provide the leverage so the VRDP securities are considered quite safe. These replace the auction rate preferred securities used previously.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by siamond »

Kevin pointed to this 2015 thread in a more recent discussion, I posted one of my graphs below out there, then thought that I should add to Kevin's thread for future references, and run a few more tests. The primary value-added of my tests is that I started at the end of 1990, instead of 1993/94 for most previous tests. Oh, and I included returns up to yesterday (Nov 21st, 2017). I also computed the RMSE, which I find a good statistic for accuracy, and nicely complements correlation (which doesn't capture amplitude, only directionality).

So... this is about comparing the SEC Yield at one point in history and the subsequent 10-years (nominal) returns of the corresponding fund. Let's start by two intermediate-term funds:
- Vanguard Intermediate-Term Tax-Exempt Fund Investor Shares (VWITX)
- Vanguard Total Bond Market Index Fund Investor Shares (VBMFX)

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by siamond »

Let's keep going by using two more tax-exempts funds:
- Vanguard Short-Term Tax-Exempt Fund Investor Shares (VWSTX)
- Vanguard Long-Term Tax-Exempt Fund Investor Shares (VWLTX)

Image

I was expecting more accuracy on the short-term fund, and less accuracy on the long-term fund, I have to say.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by siamond »

And to finish, a simple treasury fund, plus a high-yield fund just for fun:
- Vanguard Intermediate-Term Treasury Fund Investor Shares (VFITX)
- Vanguard High-Yield Corporate Fund Investor Shares (VWEHX)

Image

Unsurprisingly, the HY fund has a life of its own, while I would have expected more accuracy on the treasury fund.

Overall, same result as previously posted. The SEC Yield is a pretty good predictor, but its accuracy sometimes leaves to be desired by 1% or more. It's a useful tool, but remains a blunt one, and should be used as such.

PS. data sources: Morningstar for annualized returns (total return); Vanguard for SEC Yields.

EDIT: chart updated, to fix a silly spreadsheet mistake of mine. :(
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

siamond wrote: Wed Nov 22, 2017 2:03 pm Kevin pointed to this 2015 thread in a more recent discussion, I posted one of my graphs below out there, then thought that I should add to Kevin's thread for future references, and run a few more tests.
As mentioned much earlier in this thread, I find the error charts to be much more informative, so I encourage you to produce those and share them as well. For reference, here's one post in which I show both: Initial SEC yield and subsequent 10yr returns:VBMFX. Here's the first part of that post, showing both types of charts:
Kevin M wrote: Mon Jan 19, 2015 8:04 pm OK, trying to get this thread back on track, here are results for initial SEC yield and subsequent 10-year return for Vanguard Total Bond Market Index Fund (VBMFX):

Image

So again, we see rough tracking, but significant deviations. The correlation of subsequent 10-year return to initial yield is 0.82, so not as high as the 0.92 number that we've seen for aggregate US bond market since 1972 (or whenever), but still pretty high.

I think it's also informative to view the subsequent 10-year return minus the initial SEC yield:

Image
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by siamond »

Kevin M wrote: Fri Nov 24, 2017 8:30 pmAs mentioned much earlier in this thread, I find the error charts to be much more informative, so I encourage you to produce those and share them as well.
Well, this is essentially what the RMSE metric summarizes in one number (it's similar to std-deviation, it's the square root of the average of the deltas to the power of two).

If you have a specific question about one of those funds, I can easily generate such error chart for more details, but it seems to me that the high-level conclusion didn't change, and there isn't much more to analyze.
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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

siamond wrote: Fri Nov 24, 2017 10:00 pm
Kevin M wrote: Fri Nov 24, 2017 8:30 pmAs mentioned much earlier in this thread, I find the error charts to be much more informative, so I encourage you to produce those and share them as well.
Well, this is essentially what the RMSE metric summarizes in one number (it's similar to std-deviation, it's the square root of the average of the deltas to the power of two).

If you have a specific question about one of those funds, I can easily generate such error chart for more details, but it seems to me that the high-level conclusion didn't change, and there isn't much more to analyze.
Your choice, of course. It's just that many people grasp things better with a graphic, and I think the graphic I'm emphasizing clarifies the lack of prediction accuracy much more clearly. The other graph gets the correlation point across, but I think it visually minimizes the lack of prediction accuracy.

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Re: Initial SEC yield and subsequent 5yr and 10yr returns

Post by Kevin M »

Since the Simba/siamond backtest spreadsheet has simulated returns for an intermediate-term Treasury (ITT) fund back to 1871, I thought it would be interesting to see if I could use that data to look at initial yield and subsequent 10-year returns over a much longer time period than we can do with actual fund data. The yields aren't available directly in the backtest spreadsheet (as far as I could tell), so I looked to the source of the ITT return data, which is a 10-year to 4-year simulated Treasury ladder, one of the simulated bond funds in longinvest's bond fund simulation spreadsheet.

To simulate the initial yield for a given start year, I took the average of the 4-year to 7-year yields for that year. The return for each year is provided directly in the spreadsheet, but without any correction for an assumed expense ratio as is done in the backtest spreadsheet.

As an initial sanity check, we can compare the 10-year annualized returns minus the initial SEC yields for the Vanguard intermediate-term Treasury fund, VFITX, to the 10-year annualized returns minus the initial yields for the simulated bond fund for start years 1993 through 2008. Here they are:

Image

Image

By no means a perfect match, but close enough I think to validate that using the simulated data for this purpose is as good as using it for any other backtest purpose.

To clarify what these charts are showing, consider the values for 2003. VFITX initial SEC yield was 3.03%, and the annualized 10-year return for 2003-2012 (inclusive) was 5.18%. The 10-year return minus the initial SEC yield is 2.15 percentage points, which is the value indicated by the 2003 bar in the VFITX chart (the vertical axis values indicate %, but they are actually percentage points).

Similarly, the initial 2003 yield for the simulated bond ladder was 3.47%, the 10-year return was 5.39%, and the difference is 1.92 percentage points.

Here's the chart for the simulated bond ladder for start years 1871 through 2008:

Image

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