Is SEC Yield the Best Predictor of a Bond Fund's Performance?

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Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by #Cruncher »

A bond fund's SEC Yield is basically the weighted average yield-to-maturity (waYTM) of its holdings less the fund's expenses. On the forum it's sometimes stated that this is probably the best predictor of what a fund's future return will be if yields don't change. But is this really so? To check this out I computed the waYTM of three TIPS indexes: maturing in 1 to 5 years, 1 or more years, and 15 or more years. But then I also computed for all the bonds comprising these indexes what the gain or loss would be in one year if the yield curve was unchanged. I then summed the gains or losses for each index. In all three cases the return exceeded the waYTM.

Code: Select all

   Market                      1 Year    Gain /
    Value    waYTM   Index      Value    (Loss)  Percent  Vs Avg
  728,768  -2.243%     1-5    717,446  (11,322)  (1.55%)  +0.69%
1,657,297  -1.550%      1+  1,644,604  (12,693)  (0.77%)  +0.78%
  341,334  -0.370%     15+    341,868      534    0.16%   +0.53%
For example, the waYTM of the "1+" index (all TIPS maturing in more than one year) is -1.55%. However, if the yield curve is unchanged in one year, I estimate that the value of the bonds in the index will fall from $1,657.3B to $1,644.6B (in real terms), a loss of $12.7B or -0.77%. This is 0.78% points better than the waYTM. Similar results obtain for the "1-5" and "15+" indexes. So my question is: which is the better predictor of future bond fund performance?

Notes
  1. For simplicity I'm ignoring fund expenses and just looking at yield-to-maturity. This does not affect the comparison between the waYTM and the one-year value estimates. The latter are better because at the moment, the TIPS yield curve rises. Therefore, if the yield curve doesn't change over time, the value of a bond will be more over time than it would be if its yield stayed the same. This is related to the strategy of Riding the Yield Curve.
  2. The waYTM values are for 7/16/2021 and comes from the last edit to my post, Re: Consistent Yield & Duration to Help Choose TIPS Fund
  3. Here is a table showing my calculations. (Scroll to the bottom to see the totals and averages for the "1+" index.)

    Code: Select all

                           Market    Yield    Yield             1 Year    Gain /
        Mature  Coupon      Value      Now  in 1 Yr    Term      Value    (Loss)

    Code: Select all

     1/15/2023  0.125%     49,600  -2.838%  -3.248%    1.50     48,294   (1,306)
     4/15/2023  0.625%     53,533  -2.621%  -3.031%    1.75     52,294   (1,239)
     7/15/2023  0.375%     50,093  -2.766%  -3.176%    2.00     48,913   (1,180)
     1/15/2024  0.625%     50,592  -2.428%  -2.838%    2.50     49,676     (916)
     4/15/2024  0.500%     36,800  -2.277%  -2.621%    2.75     36,184     (615)
     7/15/2024  0.125%     49,634  -2.391%  -2.766%    3.00     48,822     (813)
    10/15/2024  0.125%     39,512  -2.270%  -2.766%    3.25     39,060     (452)
     1/15/2025  2.375%     46,140  -2.173%  -2.428%    3.50     45,433     (707)
     1/15/2025  0.250%     50,070  -2.145%  -2.428%    3.50     49,352     (718)
     4/15/2025  0.125%     39,710  -2.057%  -2.277%    3.75     39,134     (576)
     7/15/2025  0.375%     50,745  -2.112%  -2.391%    4.00     50,100     (645)
    10/15/2025  0.125%     38,438  -2.022%  -2.270%    4.25     37,972     (466)
     1/15/2026  2.000%     31,687  -1.914%  -2.145%    4.50     31,338     (349)
     1/15/2026  0.625%     53,018  -1.897%  -2.145%    4.50     52,475     (543)
     4/15/2026  0.125%     44,200  -1.813%  -2.057%    4.75     43,805     (395)
     7/15/2026  0.125%     44,996  -1.870%  -2.112%    5.00     44,592     (404)
     
     1/15/2027  2.375%     26,765  -1.706%  -1.897%    5.50     26,540     (225)
     1/15/2027  0.375%     47,140  -1.670%  -1.897%    5.50     46,838     (303)
     7/15/2027  0.375%     45,016  -1.654%  -1.870%    6.00     44,760     (256)
     1/15/2028  1.750%     24,123  -1.502%  -1.670%    6.50     23,984     (138)
     1/15/2028  0.500%     47,179  -1.480%  -1.670%    6.50     46,977     (202)
     4/15/2028  3.625%     37,444  -1.476%  -1.670%    6.75     37,312     (132)
     7/15/2028  0.750%     44,818  -1.461%  -1.654%    7.00     44,686     (132)
     1/15/2029  2.500%     22,689  -1.350%  -1.480%    7.50     22,575     (114)
     1/15/2029  0.875%     44,274  -1.323%  -1.480%    7.50     44,143     (131)
     4/15/2029  3.875%     45,107  -1.321%  -1.476%    7.75     44,985     (121)
     7/15/2029  0.250%     46,295  -1.279%  -1.461%    8.00     46,297        2 
     1/15/2030  0.125%     46,853  -1.159%  -1.323%    8.50     46,891       37 
     7/15/2030  0.125%     49,360  -1.149%  -1.279%    9.00     49,309      (51)
     1/15/2031  0.125%     49,013  -1.055%  -1.159%    9.50     48,931      (82)
     4/15/2032  3.375%     11,119  -1.005%  -1.055%   10.75     11,062      (57)
     
     2/15/2040  2.125%     28,036  -0.528%  -0.566%   18.58     28,076       40 
     2/15/2041  2.125%     44,223  -0.490%  -0.528%   19.59     44,320       97 
     2/15/2042  0.750%     33,407  -0.388%  -0.490%   20.59     33,952      545 
     2/15/2043  0.625%     32,042  -0.354%  -0.388%   21.59     32,154      112 
     2/15/2044  1.375%     36,558  -0.361%  -0.354%   22.58     36,371     (187)
     2/15/2045  0.750%     32,320  -0.313%  -0.361%   23.59     32,571      251 
     2/15/2046  1.000%     30,152  -0.318%  -0.313%   24.59     30,020     (131)
     2/15/2047  0.875%     26,744  -0.318%  -0.318%   25.59     26,659      (85)
     2/15/2048  1.000%     27,146  -0.319%  -0.318%   26.58     27,053      (94)
     2/15/2049  1.000%     22,078  -0.316%  -0.319%   27.59     22,026      (52)
     2/15/2050  0.250%     18,442  -0.291%  -0.316%   28.59     18,516       74 
     2/15/2051  0.125%     10,187  -0.293%  -0.291%   29.59     10,151      (36)
     Total/avg          1,657,297  -1.550%                   1,644,604  (12,693)
  4. "Market value" used for weighting the individual bond's YTMs are from the "Weight" sheet of the 6/30/2021 update to my YTM/Duration Calculator Excel workbook, excluding the 7/15/2022 maturity which now matures in less than one year.
  5. "Yield Now" is from the 7/16/2021 WSJ TIPS Quotes.
  6. "Yield in 1 Year" is the critical element of the calculation. On the assumption that the yield curve is unchanged I try to estimate what it would be for each bond if it matured one year sooner. For example, the 1/15/2023 maturity currently has a YTM of -2.838%. Therefore I assume that will be the yield of the 1/15/2024 maturity in one year. For cases where there is no bond maturing one year earlier, I guess what the YTM will be.
  7. "Term" is the number of years from 7/16/2021 to maturity.
  8. "One Year Value" assumes, for simplicity, that each bond is a zero coupon bond. So for example, the estimated $49,676 value of the 1/15/2024 maturity is calculated as follows:
    49,676 = 50592 * (1 - 2.428%) ^ 2.50 / (1 - 2.838%) ^ 1.50
Last edited by #Cruncher on Sat Jul 17, 2021 8:35 am, edited 1 time in total.
UpperNwGuy
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by UpperNwGuy »

I don't understand all your math, but the title of your thread immediately made me remember that I don't buy bond funds for performance. I buy stock funds for performance.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by grabiner »

This has been discussed before: Expected return of a bond fund My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration. This may not be a particularly good predictor, but it should be a relatively unbiased predictor.

The return of a bond over one year is the sum of its current yield and the effect of a change in yield. And that change comes from two factors: the "roll yield" of the difference between yields at different maturities, and the change of the yield curve itself.

Assuming an efficient market, the yield curve should reflect investors' expectations. Thus, if the yield curve is inverted, investors should expect yields to fall. If yields don't fall, long-term bonds will earn less than short-term bonds. Since bond investors prefer lower-risk bonds, they are unlikely to trade long-term bonds at prices which give them lower expected returns than short-term bonds. If yields do fall, long-term bonds will benefit more from the falling yields, and all bonds will earn more than the SEC yield.

Conversely, if the yield curve is steep and doesn't change, bonds will earn much more than the SEC yield. However, the steep curve implies that investors expect yields to rise, which will reduce bond returns. As long as yields don't rise too fast (for example, next year's 9-year yield is lower than this year's 10-year yield), bonds may still earn more than the SEC yield.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by JackoC »

grabiner wrote: Sat Jul 17, 2021 1:16 pm 1. This has been discussed before: Expected return of a bond fund My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration. This may not be a particularly good predictor, but it should be a relatively unbiased predictor.

2. Conversely, if the yield curve is steep and doesn't change, bonds will earn much more than the SEC yield. However, the steep curve implies that investors expect yields to rise, which will reduce bond returns. As long as yields don't rise too fast (for example, next year's 9-year yield is lower than this year's 10-year yield), bonds may still earn more than the SEC yield.
Starting with 2 I agree. The yield curve is upsloping (if so, and more commonly than not historically) for some combination of
a) the market clearing price includes an expectation that rates will go up between now t=0 and some future calendar date T1.
b) the market clearing price contains the effect of a mismatch in the eagerness/reluctance of borrowers and lenders to lock in rates for longer terms, which has historically usually resulted in the forward rate between T1 and a subsequent calendar date T2, calculated now at t=0, being lower than the actual expected rate from T1 to T2 when t=T1. That difference is called the term premium (the term premium does not mean the slope of the curve as the term is sometimes mistakenly used). That direction is a positive term premium.

Assuming the curve does not change at all between now and T1, with an upsloping curve, is assuming a positive term premium. The problem is, the steeper the curve, the bigger a positive term premium it's assuming. And I do not agree with your point 1, historical results don't agree, that the term premium can be well estimated from the slope of the curve. Yield curve modeling is required to derive the expected term premium. Various models have been presented. The NY Fed's ACM is one often referred to, see link. And one can see by clicking "Treasury Term Premia: 1961-Present" on that page a paper giving the results of ACM and some other models from 1961-2014. They vary, but not usually that dramatically and the models examined agree term premium has been declining in recent years.

However, the answer for expected term premium varies quite widely over time. For example, clicking 'download the data' on the first page, ACM now calculates a term premium in 6yr (a possible 'medium term' bond fund maturity) at -15 bps (although jumps around day to day, was around 0 the beginning of this month for example). The average result since 1961 was +115 bps, +71 bps this century. I ball park the 'roll gain', in stationary yield curve, of a 6.5 yr issue in a 6 yr fund, which is sold out of the fund when it becomes a 5.5 yr as 77 bps. IOW in the big picture* the gain assumed by 'yield curve doesn't change' in today's curve wouldn't be that out of line with historical term premium, but much higher than the ACM result now.

So unfortunately while Cruncher's exercise would be useful to forensically investigate why a bond fund returned more than the SEC yield in a past period where 'rates didn't change much' in an upsloping curve, it has no predictive power. The neutral sounding assumption 'the yield curve doesn't change' assumes a particular term premium based on curve slope, but expected term premium is not actually a simple function of curve slope. Nor would I strongly claim ACM or similar models can be counted on 100%. So the question is harder than it looks.

But, I personally would assume the models are more accurate than not, and as a planning estimate I would neglect term premium now and assume expected return=SEC yield for a riskless bond fund. For a Total Bond Market fund it's more outright overoptimistic IMO to add anything to the SEC yield to get expected return. Because in that case you've got potentially significant drag from credit losses (mainly IG corporates that get sold out of the fund at a loss if downgraded to junk, rather than defaulting outright which is much less common) and embedded options the investor is short (calls, prepayment options in mortgage backed).
https://www.newyorkfed.org/research/dat ... remia.html

*the two measures I gave are not exactly the same. 'Term premium' in the ACM output means the model's estimate of expected return of rolling over short term treasury investments for 6 yrs v the 6 yr rate. The 'roll yield' is a particular snapshot on the 5-7yr portion of the curve. But the expected 'roll' pick up over time if the expected term premium is zero is basically zero, not 77 bps.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by grabiner »

JackoC wrote: Sat Jul 17, 2021 3:14 pm
grabiner wrote: Sat Jul 17, 2021 1:16 pm 1. This has been discussed before: Expected return of a bond fund My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration. This may not be a particularly good predictor, but it should be a relatively unbiased predictor.

2. Conversely, if the yield curve is steep and doesn't change, bonds will earn much more than the SEC yield. However, the steep curve implies that investors expect yields to rise, which will reduce bond returns. As long as yields don't rise too fast (for example, next year's 9-year yield is lower than this year's 10-year yield), bonds may still earn more than the SEC yield.
Starting with 2 I agree. The yield curve is upsloping (if so, and more commonly than not historically) for some combination of
a) the market clearing price includes an expectation that rates will go up between now t=0 and some future calendar date T1.
b) the market clearing price contains the effect of a mismatch in the eagerness/reluctance of borrowers and lenders to lock in rates for longer terms, which has historically usually resulted in the forward rate between T1 and a subsequent calendar date T2, calculated now at t=0, being lower than the actual expected rate from T1 to T2 when t=T1. That difference is called the term premium (the term premium does not mean the slope of the curve as the term is sometimes mistakenly used). That direction is a positive term premium.

Assuming the curve does not change at all between now and T1, with an upsloping curve, is assuming a positive term premium. The problem is, the steeper the curve, the bigger a positive term premium it's assuming. And I do not agree with your point 1, historical results don't agree, that the term premium can be well estimated from the slope of the curve.
And I don't agree with that either. The term premium should not depend on the current slope of the curve; that would imply a negative term premium when the curve is inverted.

I made the simplest assumption which leads to a consistent model, which is that the term premium is essentially constant; investors demand the same compensation for the additional risk. In the linked post, my model compares a two-year bond versus a one-year bond bought this year and the proceeds used to purchase a new one-year bond next year. The two-year bond should have a slightly higher expected return.
Yield curve modeling is required to derive the expected term premium.
And I agree with this point; I don't claim that I have the best model. It may be possible to infer the term premium from the yield curve and other economic data.
*the two measures I gave are not exactly the same. 'Term premium' in the ACM output means the model's estimate of expected return of rolling over short term treasury investments for 6 yrs v the 6 yr rate. The 'roll yield' is a particular snapshot on the 5-7yr portion of the curve. But the expected 'roll' pick up over time if the expected term premium is zero is basically zero, not 77 bps.
Thanks for giving this definition; it ensures that we talk about the same model.

But your last point illustrates what I mean about consistency. A zero term premium, and no expectation that rates will rise or fall, would require a flat yield curve. A zero term premium and a positive roll yield are only possible if investors expect that rates will rise; if rates don't change, longer-term bonds not only have higher yields but will return more than their yields as their durations decrease. Since we assume that rates are as likely to rise as to fall in the long run, and the roll yield is known to be usually positive, the expected term premium should be positive.

This does not prevent the term premium from becoming negative at times (as your model suggests), although that seems suspicious. If investors expect a lower return over the next three months on a six-year Treasury bond than on a three-month Treasury bill, why would most investors buy the six-year bond? (There are some exceptional situations, such as insurance companies with future fixed-dollar liabilities; they would have negative exposure to interest-rate risk, and want to hedge their liabilities.)
But, I personally would assume the models are more accurate than not, and as a planning estimate I would neglect term premium now and assume expected return=SEC yield for a riskless bond fund. For a Total Bond Market fund it's more outright overoptimistic IMO to add anything to the SEC yield to get expected return. Because in that case you've got potentially significant drag from credit losses (mainly IG corporates that get sold out of the fund at a loss if downgraded to junk, rather than defaulting outright which is much less common) and embedded options the investor is short (calls, prepayment options in mortgage backed).
And this is an important point. For a fund with risky bonds, the expected yield to maturity is less than the SEC yield. And for GNMAs, the fund cannot set an SEC yield as the yield to call (as it does with callable bonds), because GNMAs are callable at any time. If it reports a yield to maturity, the actual return will be less than on Treasuries because the call time varies.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by JackoC »

grabiner wrote: Sat Jul 17, 2021 10:52 pm
JackoC wrote: Sat Jul 17, 2021 3:14 pm
grabiner wrote: Sat Jul 17, 2021 1:16 pm 1. This has been discussed before: Expected return of a bond fund My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration. This may not be a particularly good predictor, but it should be a relatively unbiased predictor.

2. Conversely, if the yield curve is steep and doesn't change, bonds will earn much more than the SEC yield. However, the steep curve implies that investors expect yields to rise, which will reduce bond returns. As long as yields don't rise too fast (for example, next year's 9-year yield is lower than this year's 10-year yield), bonds may still earn more than the SEC yield.
Starting with 2 I agree. The yield curve is upsloping (if so, and more commonly than not historically) for some combination of
a) the market clearing price includes an expectation that rates will go up between now t=0 and some future calendar date T1.
b) the market clearing price contains the effect of a mismatch in the eagerness/reluctance of borrowers and lenders to lock in rates for longer terms, which has historically usually resulted in the forward rate between T1 and a subsequent calendar date T2, calculated now at t=0, being lower than the actual expected rate from T1 to T2 when t=T1. That difference is called the term premium (the term premium does not mean the slope of the curve as the term is sometimes mistakenly used). That direction is a positive term premium.

Assuming the curve does not change at all between now and T1, with an upsloping curve, is assuming a positive term premium. The problem is, the steeper the curve, the bigger a positive term premium it's assuming. And I do not agree with your point 1, historical results don't agree, that the term premium can be well estimated from the slope of the curve.
1. And I don't agree with that either. The term premium should not depend on the current slope of the curve; that would imply a negative term premium when the curve is inverted.

I made the simplest assumption which leads to a consistent model, which is that the term premium is essentially constant
Yield curve modeling is required to derive the expected term premium.
2. And I agree with this point; I don't claim that I have the best model. It may be possible to infer the term premium from the yield curve and other economic data.
*the two measures I gave are not exactly the same. 'Term premium' in the ACM output means the model's estimate of expected return of rolling over short term treasury investments for 6 yrs v the 6 yr rate. The 'roll yield' is a particular snapshot on the 5-7yr portion of the curve. But the expected 'roll' pick up over time if the expected term premium is zero is basically zero, not 77 bps.
Thanks for giving this definition; it ensures that we talk about the same model.

3. But your last point illustrates what I mean about consistency. A zero term premium, and no expectation that rates will rise or fall, would require a flat yield curve. A zero term premium and a positive roll yield are only possible if investors expect that rates will rise; if rates don't change, longer-term bonds not only have higher yields but will return more than their yields as their durations decrease. Since we assume that rates are as likely to rise as to fall in the long run, and the roll yield is known to be usually positive, the expected term premium should be positive.

4. This does not prevent the term premium from becoming negative at times (as your model suggests), although that seems suspicious. If investors expect a lower return over the next three months on a six-year Treasury bond than on a three-month Treasury bill, why would most investors buy the six-year bond?
1, 2. Yes on reflection after writing, I realized your idea was to assume the term premium is a constant derived from long term average slope of the curve, not to infer a varying term premium from the current slope of the curve (as the 'assume the yield doesn't move', does). However as to 2, the models that have been devised to derive the term premium from the yield at a given time show it to vary quite widely, and again ACM and some other well known models agree it's much lower in recent years than the average over last several decades. This calls into serious question in my mind the assumption that the term premium is a constant whose value we can derive as the average over long term history. Again I would basically and roughly accept the models and assume the expected term premium now is close enough to zero to neglect.

3. 'a zero term premium and a positive roll yield'. This makes me unsure we really are on the same page via my definition. If the expected term premium is zero, the expected 'roll yield' (if meaning expected return pick up v the SEC yield) is zero, basically, over time.

4. It's not suspicious IMO. Say borrowers and lenders enter into loans of 6 yrs at the benchmark short rate, say one month, reset every month. Now one or the other proposes the rate be fixed for the whole 6 yrs. If both were indifferent to rate risk, they'd agree on a 6 yr rate which was the compounded current and future expected one month rates over the 6 yrs. In that world the term premium is zero. And likewise we refer to the short forward rates off the market curve for particular future periods as the 'risk neutral expected rates'. However we might generally assume borrowers would accept the fixed rate being at some premium to the expected compounding floating rate to avoid the possibility of a floating rate outcome much higher, that they couldn't afford. And, lenders might have a preference in the same direction, if for example banks lending long term fixed but funding themselves short rate floating (banks normally do, forget interest rate swaps for the moment, and the liquidity risk of borrow short/lend long is another issue, even if the long lending is floating rate). They may need to receive a premium on fixed over expected floating as some cushion against much higher than expected floating rate funding cost. So, positive term premium is natural, arguably. However, it's not hard to conceive of a situation where it's negative. Say the 'borrower' is a government and a lot of buyers government affiliated central banks. They won't typically be driven just by own rate risk management concerns, but concerns like stimulating the economy, providing liquid benchmark bond issues of a certain size across the yield curve and so forth. In particular, they might want to see term rates drop to add stimulus even after the central bank lowered short rates to zero. In fact many surmise that the output of term structure models like ACM in recent years, negative term premium, reflects the general QE/'(term) rate repression' policies of central banks, noting that the policies of foreign central banks also feed back into the USD curve in a globalized market. And the now huge market in interest rate derivatives, by which fixed v floating risk can find its way more easily to the parties most able to take it, might tend to shrink such premia from previous levels even if still going in the same direction.

And to reiterate the definition of term premium in ACM output, it's the expected return of eg. rolling over short term treasury investments *for 6 yrs* vs. the 6 yr treasury rate, not merely the expected return over the next short period of 6yr bond and short term treasury (not that that's fundamentally different on average, but that's what that column of the spreadsheet means).
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by Doc »

grabiner wrote: Sat Jul 17, 2021 1:16 pm This has been discussed before: Expected return of a bond fund My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration. This may not be a particularly good predictor, but it should be a relatively unbiased predictor.
I belive it was Larry Swedroe who said it something like this: "The SEC yield is the best predictor of a bond funds future performance. Just not a very good one."

I don't know if David agrees with Larry or the other way around but they are both basically saying the same thing.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by HootingSloth »

JackoC and grabiner,

I wonder if either of you could share how your analysis of the best predictor of the difference between actual returns and SEC yield might change when looking at bond funds that hold bonds callable at certain specified dates--where the SEC yield may use yield-to-call, instead of yield-to-maturity, depending on whether the call is likely to be exercised--such as municipal bonds, or bonds that may be prepaid at any time--where the SEC yield, I believe, just ignores the prepayment risk--such as mortgage-backed bonds.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by grabiner »

Doc wrote: Sun Jul 18, 2021 2:12 pm
grabiner wrote: Sat Jul 17, 2021 1:16 pm This has been discussed before: Expected return of a bond fund My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration. This may not be a particularly good predictor, but it should be a relatively unbiased predictor.
I belive it was Larry Swedroe who said it something like this: "The SEC yield is the best predictor of a bond funds future performance. Just not a very good one."

I don't know if David agrees with Larry or the other way around but they are both basically saying the same thing.
I almost agree. The expected return is slightly higher than the SEC yield for non-callable, high-quality bonds because of the roll effect; is lower for callable bonds (unless the SEC yield uses yield-to-call; such bonds will have a higher yield-to-maturity if not called); and is lower for low-quality bonds because of defaults and downgrades.

But the more important issue is the uncertainty. A bond fund with a 2% SEC yield and a five-year duration can easily return -3% or +7% next year if the rates on its bonds change by 1% either way.

If the average error is close to zero, it still makes sense to use SEC yield for comparing bond funds, and other characteristics of the funds for estimating the likely error. For example, long-term bond funds will deviate more from their SEC yield than short-term bond funds, and funds holding callable bonds will deviate more because changes in interest rates affect which bonds will be called.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by Doc »

grabiner wrote: Sun Jul 18, 2021 2:50 pm The expected return is slightly higher than the SEC yield for non-callable, high-quality bonds because of the roll effect; is lower for callable bonds (unless the SEC yield uses yield-to-call; such bonds will have a higher yield-to-maturity if not called); and is lower for low-quality bonds because of defaults and downgrades.
Maybe that's part of Larry's "not a very good one".
grabiner wrote: Sun Jul 18, 2021 2:50 pm If the average error is close to zero, it still makes sense to use SEC yield for comparing bond funds, and other characteristics of the funds for estimating the likely error.
If the the funds both have similar maturity ranges then any roll down effect would not make much of a difference in comparing those funds even if the actual amount gained may not be the SEC yield for either of them.

I don't use SEC yield myself. It's like dancing on the point of a pin. Ouch.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by #Cruncher »

grabiner wrote: Sat Jul 17, 2021 1:16 pmThis has been discussed before: Expected return of a bond fund[.] My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration.
Thanks for posting the link to the other thread, grabiner. But, how exactly do you determine the "average slope" of the yield curve, especially for a fund that doesn't hold many bonds? (For example, most TIPS funds follow the index of TIPS maturing in more than one year ("1+") and there are only 43 of those. The funds that follow subsets of that index naturally hold even fewer.)

It seems to me that the slope should reflect the weighting of the different bonds. For example, even though there are TIPS maturing in 30 years, over 80% of the market value of the 1+ index is for ones that mature within ten years. And the yield curve rises much faster for those than it does for the less than 20% that mature in 2040 to 2051. It therefore seems reasonable to compute the weighted average (by market value) of the difference between each bond's yield and what I estimate to be its yield if it matured one year earlier. When I do this for the 43 bonds in the 1+ index as shown in my original post I get a weighted average of +0.207% points per year.

If I multiply 0.207% by my computed duration of the 1+ index of 8.89 [*] I get 1.84% points. But this much more than the 0.78% point difference I previously calculated (in my original post) between the expected -0.77% return of the 1+ index and its -1.55% weighted average yield-to-maturity (waYTM). As shown in the two right-hand columns below, only for the 15+ index does this method produce a value close to the difference between the waYTM and the expected return (+0.60% vs +0.53%).

Code: Select all

          Market    Yield    Yield    Yield            1 Year    Gain /                     Roll
Index      Value      Now  in 1 Yr     Diff   Life      Value    (Loss)  Percent  Vs Avg   Yield
-----  ---------  -------  -------  -------  -----  ---------  --------  -------  ------  ------
  1-5    728,768  -2.243%  -2.565%  +0.322%   3.35    717,446  (11,322)  (1.55%)  +0.69%  +1.08%
   1+  1,657,297  -1.550%  -1.757%  +0.207%   8.89  1,644,604  (12,693)  (0.77%)  +0.78%  +1.84%
  15+    341,334  -0.370%  -0.396%  +0.026%  23.26    341,868      534    0.16%   +0.53%  +0.60%
I'm likely making some conceptual error. Several times in past posts you've pointed out other errors I've made, grabiner. I'm hoping you can do it again. :wink:

* I'm weighting the life of each bond which I think is OK since I'm treating each one as a zero-coupon bond for which the duration equals the remaining life.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by grabiner »

#Cruncher wrote: Sun Jul 18, 2021 3:49 pm
grabiner wrote: Sat Jul 17, 2021 1:16 pmThis has been discussed before: Expected return of a bond fund[.] My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration.
Thanks for posting the link to the other thread, grabiner. But, how exactly do you determine the "average slope" of the yield curve, especially for a fund that doesn't hold many bonds? (For example, most TIPS funds follow the index of TIPS maturing in more than one year ("1+") and there are only 43 of those. The funds that follow subsets of that index naturally hold even fewer.)

It seems to me that the slope should reflect the weighting of the different bonds.

It therefore seems reasonable to compute the weighted average (by market value) of the difference between each bond's yield and what I estimate to be its yield if it matured one year earlier.
I agree. The expected return of a 10-year bond is based on the average slope of the yield curve at 10 years, so you would multiply this by the fraction of 10-year bonds in the fund. (Mathematically, you would integrate the density of bonds by duration, times the average slope, times the duration, over the range of all durations.) For an intermediate-term fund, taking the slope over the range of 5-10 years would give a pretty good estimate of the relevant slope for all the bonds. For an all-duration fund, the different slopes for short-term and long-term bonds would have different effects.

For a TIPS fund, it's even harder, because there isn't much data. Treasury bonds have a long history, so we know what the curve looks like in many different economic conditions. TIPS have not existed during a period of high inflation, and the yields in the first few years were probably higher than a reasonable economic estimate of their value.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by hudson »

Doc wrote: Sun Jul 18, 2021 2:12 pm
grabiner wrote: Sat Jul 17, 2021 1:16 pm This has been discussed before: Expected return of a bond fund My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration. This may not be a particularly good predictor, but it should be a relatively unbiased predictor.
I belive it was Larry Swedroe who said it something like this: "The SEC yield is the best predictor of a bond funds future performance. Just not a very good one."

I don't know if David agrees with Larry or the other way around but they are both basically saying the same thing.
Thanks for the quote!

I don't try to predict future changes in a bond funds price.
I look for a fund with high quality holdings and ignore performance.

I do look hard at the SEC Yield, to see the estimated payout over the duration of the fund.

I like to study the monthly distribution table. I like to predict the payout over the next year or two.
Example VWIUX (Vanguard Intermediate-Term Tax-Exempt Fund)
SEC is .72%
VWIUX's July 1st dividend was 2.18% (annualized)
Look at VWIUX's monthly distribution table and predict the payout over the next year. https://investor.vanguard.com/mutual-fu ... ions/vwiux
Will it be .72%
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by JackoC »

#Cruncher wrote: Sun Jul 18, 2021 3:49 pm
grabiner wrote: Sat Jul 17, 2021 1:16 pmThis has been discussed before: Expected return of a bond fund[.] My conclusion there is that the best estimate of the expected return of a bond fund is the SEC yield, plus the product of the duration and the average slope (the historical average, not the current slope) at that duration.
Thanks for posting the link to the other thread, grabiner. But, how exactly do you determine the "average slope" of the yield curve, especially for a fund that doesn't hold many bonds? (For example, most TIPS funds follow the index of TIPS maturing in more than one year ("1+") and there are only 43 of those. The funds that follow subsets of that index naturally hold even fewer.)
I would again speak up for the concept of term premium (no term premium, no 'roll yield pickup'), and modeling the term premium. The modeling results uniformly say (though far from completely agreeing at all times in detail, see link to NY Fed papers above) that the expected term premium has not been nearly a constant. Grabiner's idea is a stationary estimate of the term premium based on the *historical average* slope of the curve, not the slope right now. I disagree with Grabiner that it's useful to estimate the term premium and hence 'roll pick up' as a constant but I believe we two are agreeing that you cannot derive it by close study of the current components of the fund, as your question still seems to imply.

The good news is you don't have to waste time trying to predict the 'roll yield' from detailed crunching lots of numbers of the current components of a fund. That's not possible.

The bad news is that 'what's the expected return of riskless non-callable funds compared to the SEC yield' has no simple, transparent answer. However if you believe the ACM model (and other major models don't have wildly different findings) the term premium is not remotely constant over time, has tended to decrease in recent decades (I believe the growth of the interest rate derivatives market, rate risk ending up in 'stronger hands' on average, might partly explain this, see my earlier post) and is zero-ish lately. I would now neglect 'roll yield' and say expected return=SEC yield for treasury funds. Not everyone has to agree, but I struggle to see why this take on it would be ignored. I believe it's the one best founded in recent financial research, though we all know that's not infallible.

On the effect of issuer call options in bond fund, some fund providers though not Vanguard have for years offered the metric 'option adjusted spread', meaning the spread over treasuries of the fund minus the value of the call options derived from putting each fund component through an options model. IOW the state of the art got beyond 'yield to call' or 'yield to worst' a long time ago. However as with the term premium it leaves the retail investor relying on a black box result (or no result in case of Vanguard funds). It's certainly preferable to DIY simple answers where possible but useful, simple ones don't always exist and estimating expected term premium/expected 'roll yield pick up' and embedded option values would be two examples IMO.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by Doc »

JackoC wrote: Mon Jul 19, 2021 10:20 am The good news is you don't have to waste time trying to predict the 'roll yield' from detailed crunching lots of numbers of the current components of a fund. That's not possible.
Yes it's possible. Both Grabiner and I have done it using different models. At least for Treasuries once you have set up your spreadsheet all you have to do is copy and paste the Treasury data into it. The data for non Treasury funds is available from sites like Morningstar but is more complicated to use.

A caveat is there in an inherent assumption in the calculation is that the yield curve remains unchanged.

But so what. Just because the current interest rates change over the duration of the fund doesn't mean that the current SEC yield isn't still the "best" predictor. And it is probably very good predictor that fund A will outperform fund B if risk factors are ignored or at least remain unchanged.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by jeffyscott »

Most of this discussion is beyond me, but is it reasonable to assume the YTM of a longer term bond would equal the one year return? Wouldn't the annual returns be uneven, rather than the same each year?

For example if I have a 10 year bond with a YTM of 2% and value of $1000, that means that after 10 years I expect a total return of $218.99. But I don't think it means that the return would be 2% (or ~$20) in year 1. Assuming no change in the yield curve, wouldn't my return be higher in year 1 and then gradually lower in each subsequent year?
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by #Cruncher »

jeffyscott wrote: Mon Jul 19, 2021 1:56 pm... if I have a 10 year bond with a YTM of 2% and value of $1000, that means that after 10 years I expect a total return of $218.99. ... Assuming no change in the yield curve, wouldn't my return be higher in year 1 and then gradually lower in each subsequent year?
It depends on the slope direction of the yield curve. Your conclusion would be true, jeffyscott, with an unchanged rising yield curve; i.e., longer term bonds have higher yields than shorter term. But it would be false with a falling or flat yield curve that doesn't change during the ten-year period.

Code: Select all

       -- Rising Yield Curve -    - Falling Yield Curve -    --- Flat Yield Curve --
Term   Yield     Value  Yr Chg    Yield     Value  Yr Chg    Yield     Value  Yr Chg
  10    2.0%  1,000.00             2.0%  1,000.00             2.0%  1,000.00         
   9    1.9%  1,029.04  2.904%     2.1%  1,011.04  1.104%     2.0%  1,020.00  2.000% 
   8    1.8%  1,056.86  2.704%     2.2%  1,024.22  1.304%     2.0%  1,040.40  2.000% 
   7    1.7%  1,083.32  2.503%     2.3%  1,039.61  1.503%     2.0%  1,061.21  2.000% 
   6    1.6%  1,108.25  2.302%     2.4%  1,057.31  1.702%     2.0%  1,082.43  2.000% 
   5    1.5%  1,131.54  2.101%     2.5%  1,077.41  1.901%     2.0%  1,104.08  2.000% 
   4    1.4%  1,153.05  1.901%     2.6%  1,100.05  2.101%     2.0%  1,126.16  2.000% 
   3    1.3%  1,172.66  1.701%     2.7%  1,125.36  2.301%     2.0%  1,148.69  2.000% 
   2    1.2%  1,190.26  1.500%     2.8%  1,153.49  2.500%     2.0%  1,171.66  2.000% 
   1    1.1%  1,205.73  1.300%     2.9%  1,184.64  2.700%     2.0%  1,195.09  2.000% 
   0          1,218.99  1.100%           1,218.99  2.900%           1,218.99  2.000%
The "Yr Chg" columns show the yearly change in market value of a zero-coupon bond with a redemption value of $1,218.99 (= 1000 * 1.02 ^ 10). If the YTM is 1.9% with nine years to maturity, the market value would be $1,029.04 (= 1218.99 / 1.019 ^ 9), a gain of 2.904%. If the YTM is 1.1% with one year until maturity, the market value would be $1,205.73 (= 1218.99 / 1.011). So the gain in the final year would be only 1.100% (= 1218.99 / 1205.73 - 1).
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by jeffyscott »

#Cruncher wrote: Mon Jul 19, 2021 7:24 pm
jeffyscott wrote: Mon Jul 19, 2021 1:56 pm... if I have a 10 year bond with a YTM of 2% and value of $1000, that means that after 10 years I expect a total return of $218.99. ... Assuming no change in the yield curve, wouldn't my return be higher in year 1 and then gradually lower in each subsequent year?
It depends on the trend of the yield curve. Your conclusion would be true, jeffyscott, with an unchanged rising yield curve; i.e., longer term bonds have higher yields than shorter term. But it would be false with a falling or flat yield curve that doesn't change during the ten-year period.
Thanks.

So for the bond you only expect the return to equal the YTM, if it's held to maturity. That's sort of like SEC yield as an estimate of expected return, over a time period equal to the duration of the fund (which is the usual way this has been stated, I think). But neither is a good estimate of return over a much shorter period.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by acegolfer »

YTM is not the expected return of a bond. It's an annualized return, IF you hold the bond till maturity and reinvest all the coupons at YTM. Both don't apply when evaluating annual performance of a bond fund.
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Estimate of return over a shorter period...

Post by hudson »

jeffyscott wrote: Mon Jul 19, 2021 9:17 pm
#Cruncher wrote: Mon Jul 19, 2021 7:24 pm
jeffyscott wrote: Mon Jul 19, 2021 1:56 pm... if I have a 10 year bond with a YTM of 2% and value of $1000, that means that after 10 years I expect a total return of $218.99. ... Assuming no change in the yield curve, wouldn't my return be higher in year 1 and then gradually lower in each subsequent year?
It depends on the trend of the yield curve. Your conclusion would be true, jeffyscott, with an unchanged rising yield curve; i.e., longer term bonds have higher yields than shorter term. But it would be false with a falling or flat yield curve that doesn't change during the ten-year period.
Thanks.

So for the bond you only expect the return to equal the YTM, if it's held to maturity. That's sort of like SEC yield as an estimate of expected return, over a time period equal to the duration of the fund (which is the usual way this has been stated, I think). But neither is a good estimate of return over a much shorter period.
Yield to maturity doesn't estimate one or two year returns.
SEC Yield doesn't estimate one or two year returns.
Trailing twelve months yield doesn't estimate one or two year returns.
There isn't a number that I know of that estimates one or two year returns.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by JackoC »

Doc wrote: Mon Jul 19, 2021 10:48 am
JackoC wrote: Mon Jul 19, 2021 10:20 am The good news is you don't have to waste time trying to predict the 'roll yield' from detailed crunching lots of numbers of the current components of a fund. That's not possible.
1. Yes it's possible. Both Grabiner and I have done it using different models. At least for Treasuries once you have set up your spreadsheet all you have to do is copy and paste the Treasury data into it. The data for non Treasury funds is available from sites like Morningstar but is more complicated to use.

A caveat is there in an inherent assumption in the calculation is that the yield curve remains unchanged.

2. But so what. Just because the current interest rates change over the duration of the fund doesn't mean that the current SEC yield isn't still the "best" predictor. And it is probably very good predictor that fund A will outperform fund B if risk factors are ignored or at least remain unchanged.
1. A caveat which blows the whole exercise out of the water as I've said from the beginning in pretty long posts explaining why, but perhaps too long to expect people to read. :happy But to simply reiterate, 'roll yield pick up' is a function of the term premium. The 'yield curve remains unchanged' is assuming a particular term premium, and a high term premium in a strongly upsloping curve. But the actual term premium is not a function of the slope of the curve and good evidence suggests its expected value is now low if not slightly negative. Therefore calculating 'roll yield pick' assuming a stationary curve is a useless exercise IMO for predictive purposes: calculate something under an implicit assumption we have reason to believe is way off.

2. If you're saying that at the end of day the SEC yield is best simple predictor of expected return of 'riskless' non-callable bond funds, we basically agree. However again I think this is true because of actual predictive information from term structure models indicating a low expected term premium. If all the well know models were saying the term premium was historically high, I *would* probably factor in an expected 'roll yield pick up' in my estimate.
Last edited by JackoC on Wed Jul 21, 2021 9:44 am, edited 1 time in total.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by Doc »

hudson wrote: Wed Jul 21, 2021 7:02 am There isn't a number that I know of that estimates one or two year returns.
It is possible to calculate one or two year returns under several assumptions:

1) The yield curve remains constant.
2) You sell the bond at the end of the period.
3) You make an assumption of whether or not to reinvest coupons. (I think that the SEC assumption is that you don't but I don't remember. Ask Grabiner.)

I belive this is the same as the SEC yield calculation except for not holding to maturity.
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Re: Is SEC Yield the Best Predictor of a Bond Fund's Performance?

Post by grabiner »

Doc wrote: Wed Jul 21, 2021 9:42 am
hudson wrote: Wed Jul 21, 2021 7:02 am There isn't a number that I know of that estimates one or two year returns.
It is possible to calculate one or two year returns under several assumptions:

1) The yield curve remains constant.
2) You sell the bond at the end of the period.
3) You make an assumption of whether or not to reinvest coupons. (I think that the SEC assumption is that you don't but I don't remember. Ask Grabiner.)

I belive this is the same as the SEC yield calculation except for not holding to maturity.
The SEC assumption is that you reinvest coupons at the current yield of the bond. If a bond has an SEC yield of 2%, this implies a 1% semiannual yield to maturity (2.01% annualized become of compounding). If you reinvest all coupons at a 1% semiannual return, and hold the bond and all reinvested coupons to maturity, your semiannualized return will be 1% and your annualized return will be 2.01%; thus, for example, on a five-year bond, a $1000 bond will give you 1000*(1.01)^10=$1105 at maturity.

Not reinvesting dividends is mathematically equivalent. If the $1000 bond pays a $10 semiannual coupon, and you spend the coupon, your total rate of return is 1% semiannually, since you turn $1000 in cash now into $1010 in cash six months from now, and you spend $10 of that cash.
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