Bond Ladders?

Research on Safe Withdrawal Rates

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JWR1945
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Bond Ladders?

Post by JWR1945 »

Our historical sequence calculators do a poor job of handling the bonds and other investments other than stocks. Our calculators treat all non-stock investments as single year trading vehicles without any transaction fees and without any capital gains and losses.

For example, if you had bought a 13% 30-year treasury bond in 1984, you would have sold it immediately in 1985 and replaced it with a 10% 30-year treasury bond without any capital gain. In fact, by 2000, your brand new 30-year treasury bond would be yielding just above 6%. Its actual date of maturity would be irrelevant because replacements were available (on the secondary market) in 2001.

At no time beyond the first year would you have benefited from the 13% interest rate. You never would have received any capital gains. You would always replace the previous year's 30-year treasury bond with the latest available 30-year treasury bond.

We can do better.

It strikes me that we can construct surrogates for mutual bond funds. I cannot introduce capital gains and losses with the information that I have. But we should be able to simulate bond ladders, etc., that are held to maturity.

Our calculators need to have the equivalent of an interest rate for every year. If I am not mistaken, a rolling bond ladder does this. If so, we can create new Fixed Income investments to put into our calculators.

In contrast to simulating bond ladders, I do not know how I could lock-in the interest rates of particular issues. It would have to be preprogrammed. I will appreciate all of the assistance that I receive along these lines.

I have extracted the existing data that is in our calculators for commercial paper, 5-year treasury notes and 30-year treasury bonds. I have also extracted (via the device of examining 0% TIPS) both the CPI and the PPI. These can be used with TIPS and I-bond ladders.

For those who are knowledgeable, please help me get this right. I think that this will improve the realism of our calculators considerably.

Have fun.

John R.
JWR1945
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Posts: 1697
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Location: Crestview, Florida

Post by JWR1945 »

These are the interest rates of commercial paper in a form easy to download.
1871-1920

Code: Select all

6.35
7.81
8.35
6.86
4.96
5.33
5.03
4.90
4.25
5.10
4.79
5.26
5.35
5.65
4.22
4.26
6.11
5.02
4.68
5.41
5.97
3.93
8.52
3.32
3.09
5.76
3.44
3.55
3.36
4.64
4.30
4.72
5.50
4.34
4.17
5.47
6.23
5.32
3.65
5.26
4.00
4.35
5.65
4.64
3.65
3.64
4.25
5.98
5.56
7.30
1921-1980

Code: Select all

7.44
4.58
4.96
4.34
3.87
4.28
4.26
4.64
6.01
4.15
2.43
3.36
1.46
1.01
0.75
0.75
0.88
0.88
0.56
0.56
0.53
0.63
0.69
0.72
0.75
0.76
1.01
1.35
1.58
1.32
2.12
2.39
2.58
1.80
1.81
3.21
3.86
2.54
3.74
4.28
2.91
3.39
3.50
4.09
4.46
5.44
5.55
6.17
8.05
9.11
5.66
4.62
7.93
11.03
7.24
5.70
5.28
7.78
10.88
11.37
1981-2002

Code: Select all

17.63
14.60
9.37
11.11
8.35
7.31
6.25
7.63
9.29
8.43
6.92
3.91
3.44
4.35
6.45
5.68
5.78
5.49
5.14
6.22
3.95
1.76
Have fun.

John R.
JWR1945
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Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

These are the interest rates of 5-year treasury notes in a form easy to download.

1871-1952
No notes were available.

1953-1980

Code: Select all

2.94
1.92
2.59
2.97
3.83
2.46
4.50
4.12
3.81
3.64
3.81
4.02
4.15
4.97
5.01
5.85
6.75
7.85
6.53
5.91
6.69
8.10
7.51
7.61
6.76
8.36
8.85
9.21
1981-2002

Code: Select all

13.95
14.43
10.63
13.48
9.60
7.64
8.02
8.49
8.29
8.43
7.94
6.48
5.22
6.70
5.93
6.69
6.38
5.52
5.81
6.30
4.81
4.19
Have fun.

John R.
JWR1945
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Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

These are the interest rates of 30-year treasury bonds in a form easy to download.

1871-1924
No notes were available.

1925-1980

Code: Select all

3.79
3.67
3.34
3.29
3.69
3.25
3.13
3.76
3.21
2.98
2.72
2.69
2.81
2.58
2.22
2.40
2.01
2.43
2.45
2.49
2.35
2.16
2.22
2.41
2.38
2.33
2.65
2.61
3.13
2.55
2.82
2.93
3.58
3.19
4.09
3.99
3.88
3.90
4.00
4.13
4.14
4.63
4.86
5.23
6.06
6.99
5.94
5.59
6.32
7.03
6.86
6.92
6.99
7.94
8.32
9.40
1981-2002

Code: Select all

12.39
13.32
10.64
13.04
10.36
8.23
8.63
9.04
8.40
8.62
8.54
7.72
6.55
7.43
6.59
7.20
6.82
5.80
6.36
6.28
5.82
5.66
Have fun.

John R.
JWR1945
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Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

These are the consumer inflation rates. They correspond to 0% TIPS with inflation adjustments tied to the CPI. These data are in a form easy to download.

1871-1920

Code: Select all

1.53
1.53
2.26
(4.41)
(6.92)
(5.79)
0.88
(15.65)
(10.31)
20.69
(5.71)
8.08
(1.87)
(7.62)
(10.31)
(3.45)
0.00
4.76
(4.55)
(4.76)
2.50
(6.10)
7.79
(13.25)
(4.17)
1.45
(2.86)
2.94
1.43
16.90
(2.41)
2.47
9.64
(4.40)
2.30
0.00
4.49
(2.15)
3.30
10.64
(6.73)
(1.03)
7.29
2.04
1.00
2.97
12.50
19.66
17.86
16.97
1921-1980

Code: Select all

(1.55)
(11.05)
(0.59)
2.98
0.00
3.47
(2.23)
(1.14)
(1.16)
0.00
(7.02)
(10.06)
(9.79)
2.33
3.03
1.47
2.17
0.71
(1.41)
(0.71)
1.44
11.35
7.64
2.96
2.30
2.25
18.13
10.23
1.27
(2.08)
8.09
4.33
0.38
1.13
(0.74)
0.37
2.99
3.62
1.40
1.03
1.71
0.67
1.33
1.64
0.97
1.92
3.46
3.65
4.40
6.18
5.29
3.27
3.65
9.39
11.80
6.72
5.22
6.84
9.28
13.91
1981-2002

Code: Select all

11.83
8.39
3.71
4.19
3.53
3.89
1.46
4.05
4.67
5.20
5.65
2.60
3.26
2.52
2.80
2.73
3.04
1.57
1.67
2.68
3.14
1.78
Have fun.

John R.
JWR1945
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Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

These are the producer inflation rates. They correspond to 0% TIPS with inflation adjustments tied to the PPI. These data are in a form easy to download.

1871-1920

Code: Select all

1.49
1.49
2.30
(4.44)
(6.94)
(5.77)
0.90
(15.62)
(10.35)
20.65
(5.68)
8.08
(1.91)
(7.54)
(10.35)
(3.42)
0.00
4.76
(4.55)
(4.76)
2.45
(6.02)
7.73
(13.23)
(4.14)
1.36
(2.80)
2.88
1.46
16.91
(2.36)
2.42
9.64
(4.40)
2.35
0.00
4.49
(2.20)
3.27
10.69
(6.71)
(1.05)
7.27
(2.48)
0.00
12.71
32.33
22.73
7.41
17.24
1921-1980

Code: Select all

(27.94)
(19.90)
12.10
(2.27)
2.91
0.56
(7.87)
1.22
(0.60)
(3.64)
(15.09)
(14.07)
(9.48)
18.10
9.68
2.21
6.47
(5.41)
(5.00)
3.01
1.46
18.71
6.06
1.71
1.69
1.66
33.15
13.06
(1.44)
(5.13)
17.76
(1.64)
(3.00)
1.03
(0.68)
1.71
4.38
1.61
0.63
(0.32)
0.63
(0.31)
(0.32)
0.63
0.00
3.46
1.52
1.20
2.96
4.89
2.19
4.02
7.22
17.79
17.14
4.36
4.84
6.37
10.48
15.45
1981-2002

Code: Select all

11.74
4.73
0.50
2.69
0.49
(0.19)
(2.62)
4.08
5.64
3.98
3.57
(2.86)
2.08
0.93
3.19
2.77
2.69
(3.24)
(2.47)
4.82
9.12
(8.21)
Have fun.

John R.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

JWR1945:

This is a great idea. This is an effort at significant forward motion. Thanks very much for putting this on the table.

I hope that we will see a few community members with the appropriate skills set step forward and offer to help out. It is obviously not reasonable to expect you to move forward too far on something like this on your own, without the feedback you need to know that you are doing things right and are headed in the right direction.

In the event that no one steps forward at this time, my suggestion is that you do what you feel comfortable doing on your own, and then give this particular initiative a rest for a bit. The thread is available for public review, and in time we will have more community members participating here and you will be able to get the help you need.

You might want to keep a list of projects that have been stalled. Then, when we have more people willing and able to lend a hand on this sort of thing, we will have a list of opportunities for community service to which we can direct them.

It's exciting to me that we are getting out of the reactive mode of just trying to show the flaws of the REHP study. We are starting to see people come up with their own questions, questions that never occured to intercst (properly so--he examined the questions that needed to be examined for use of his own particular approach, which is just what most others do too). I see this expansion in the range of topics we discuss not only with this thread, but also in comments that have been made by UncleMick, Ben, Mike, Gummy, and our three newcomers--DelawareDave, Peterv and Martha. We should look at more real estate stuff than we have in the past. We should look at the demographics question. We should look at the option of going with the Vanguard Target fund (I don't recall the precise name, but I am speaking of the one that UncleMick often refers to). We should look at the Permanent Portfolio concept. We should look at the option of part-time work during retirement as a means of insuring a sufficiently large income stream.

This stuff does not take us off course. It was my purpose in putting up the May 13, 2002 post to encourage discussion of all of these various options, and lots of others. It is important that people understand that I do not care all that much whether people discuss TIPS or not. I went with TIPS, but, as has been pointed out, TIPS do not today provide the generous real returns that were provided when I purchased them. I think that there are good strategic uses to which TIPS can be put today, but I don't expect all to agree and I certainly don't think that TIPS are the only good option.

The point of the May 13, 2002, post was to open things up. I had seen a number of fine community members leave because of their frustration that the only investing ideas that could be discussed were those favored by intercst. I held my tongue for a long while because I did not want to see all the ugliness that we have seen transpire in the past 32 months. The Smear Campaign against Wanderer pushed things over the line. He was the most popular and the most effective poster in the community at the time. The cause of the Smear Campaign against Wanderer? He happened to observe that it sometimes makes sense to invest in real estate. Not acceptable. Not even close.

We have proven beyond any reasonable doubt that intercst got the number wrong in the study published at RetireEarlyHomePage.com. That's a good thing we did, aspiring early retirees have a right to know what the historical data really says. But we didn't walk down this road for the purpose of discrediting the REHP study. We did it because we want to learn together what it takes to win financial freedom early in life, and intercst's abusive use of the REHP study had made it impossible for the community to move forward on that project. Now we are taking small steps. We will be taking large steps in the future. You can't indefinitely stop people from learning things that they very much want to learn. If you put enough effort into it, you can pull it off for a time. But there is no man born of woman who can block the path of the history train for ever and ever. That was a foolish idea that intercst and the other DCMs got into their heads for awhile.

There will be people in our future who will recommend, as intercst did, that aspiring early retirees invest in 74 percent S&P stocks. That's one option. It will never be one of my favorites, but it will always be one of the packages sitting on the table awaiting purchase by newcomers to our movement. Never again, however, will our discussions be restricted by the dogmatic claim that any community member who offers an alternative idea is suffering from "mental illness." The Intercst era is in its twilight. The community era is dawning, post by post, thread by thread, board by board. This will be over when every board with the words "Retire Early" or "FIRE" in the title permit honest and informed discussions of investing. We are more than halfway there, in my estimation.

I hope this thread becomes a long one. I hope you receive the assistance you requested. But the bottom line is that I find this thread a most encouraging one even if these words of mine end up being the last post put to it. I never could have pulled it off without you, old friend.
JWR1945
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Post by JWR1945 »

hocus2004 wrote:I hope that we will see a few community members with the appropriate skills set step forward and offer to help out. It is obviously not reasonable to expect you to move forward too far on something like this on your own, without the feedback you need to know that you are doing things right and are headed in the right direction.

In the event that no one steps forward at this time, my suggestion is that you do what you feel comfortable doing on your own, and then give this particular initiative a rest for a bit. The thread is available for public review, and in time we will have more community members participating here and you will be able to get the help you need.
SUMMARY: Here is how I propose to create a bond ladder out of 5-year Treasury Notes.
I put $1000 per year into a bond account for each of five years. [I start the process by using the 1953-1957 interest rates as dummy data along with these initial $1000 deposits.] This starts the process. The actual data follow, starting from an initial balance of $5000.

Each year, I add the interest from each of the five previous years to the principal amount of the bond from 5 years earlier.

I calculate the total balance by adding the principal from each of the 5 most recent years.

Then I determine the percentage increase of this total balance from one year to the next. I convert this into an effective single-year interest rate.

All calculations are in terms of nominal dollars. There are no adjustments for inflation. This includes having no adjustment for the dummy data at the start of this process.

This bond ladder is constructed assuming there are no deposits and no withdrawals. This is never true in the real world. But what would be a realistic alternative suitable for our calculators? Our calculators require a single number for each year.

The final result is a new security, which is a 5-year ladder, with interest rates that vary each year. There are entries for all of the years from 1953-2002.

The actual data begin in 1953 and ends in 2002.

I made a copy of the interest rates in 1953-1957. I put these at the top of column K, beginning with cell K12. This copy is for dummy data.

I put the data from 1953-2002 underneath the dummy data.

I put in a column for the principal amount. It begins with $1000.00 of principal for each of the dummy values.

I put in a column with the interest payments associated with the principal of the same year. For example, the first dummy interest rate was 2.94%, the same as the interest in 1953. The interest payment in this new column was $29.40 since all of the dummy entries have a principal amount of $1000.00.

Later entries for the principal equaled the original principal from five years earlier plus the sum of the interest payments from the five previous years. The principal for the year 1953 is in cell L17. The formula that I wrote for cell L17 is =$L12+$M12+$M13+$M14+$M15+$M16. Cell L12 has the first dummy principal amount of $1000.00. The interest payments from each of the five previous years were in cells M12, M13, M14, M15 and M16.

I used the fill handle to drag the formulas in column L down from 1953 through 2002.

[It turned out that the $ signs were unnecessary. They keep the references to column L with $L and column M with $M when using Excel to copy formulas automatically.]

The formula in cell M12 is =$K12*$L12/100, which is the interest rate as a percentage times the principal divided by 100. I used the fill handle to drag the formula down from the top of the dummy data to year 2002.

In column N, I added the principal amounts of each individual Treasury Note from each of the previous five years. These are the total balances (assuming that there are no deposits and no withdrawals from the ladder). The formula for 1953 is in cell N17 and it is =$L13+$L14+$L15+$L16+$L17. I used the fill handle to drag this equation down to year 2002.

[The first five principal amounts in column N are with dummy data: $1000, $2000, $3000, $4000 and $5000.]

I put single year gain multipliers in column O. In cell O17, the formula is =N17/N16.

I put the single year increases for each total balance in column P. In cell P17, the formula is =(O17-1)*100.

The single year interest rates of the bond ladder are different from the single year interest rates of the 5-year Treasury Notes.

Have fun.

John R.
JWR1945
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Location: Crestview, Florida

Post by JWR1945 »

Year, Interest Rate for 5-Year Note, Interest Rate for Ladder

Code: Select all

1953    2.94     2.850
1954    1.92     2.852
1955    2.59     2.827
1956    2.97     2.820
1957    3.83     2.824
1958    2.46     2.852
1959    4.50     2.748
1960    4.12     3.282
1961    3.81     3.589
1962    3.64     3.746
1963    3.81     3.709
1964    4.02     3.965
1965    4.15     3.881
1966    4.97     3.896
1967    5.01     4.140
1968    5.85     4.409
1969    6.75     4.842
1970    7.85     5.415
1971    6.53     6.180
1972    5.91     6.461
1973    6.69     6.573
1974    8.10     6.722
1975    7.51     7.031
1976    7.61     7.007
1977    6.76     7.222
1978    8.36     7.327
1979    8.85     7.671
1980    9.21     7.875
1981   13.95     8.244
1982   14.43     9.678
1983   10.63    11.272
1984   13.48    11.550
1985    9.60    12.425
1986    7.64    12.168
1987    8.02    10.818
1988    8.49     9.652
1989    8.29     9.234
1990    8.43     8.381
1991    7.94     8.203
1992    6.48     8.230
1993    5.22     7.857
1994    6.70     7.149
1995    5.93     6.866
1996    6.69     6.403
1997    6.38     6.216
1998    5.52     6.209
1999    5.81     6.219
2000    6.30     6.047
2001    4.81     6.123
2002    4.19     5.735
Have fun.

John R.
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ben
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Post by ben »

I believe the Vanguard tot market bond fund have existed since about 1986. That gives close to 20 years of history to compare which ever method/mix further back one decides to create. The fund has a split of different bonds both gov/mortgage/tips Etc.
Average Eff Duration 4.45 Yrs
Average Eff Maturity 7.30 Yrs
Average Credit Quality AAA
Any mix one creates to go further back would have to have a similar broad diversification. Same applies for equities but believe it is easier to find the data or at least estimate the total US market returns?
Cheers, Ben
Normal; to put on clothes bought for work, go to work in car bought to get to work needed to pay for the clothes, the car and the home left empty all day in order to afford to live in it...
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Alec
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Location: Crofton, MD

Post by Alec »

Our historical sequence calculators do a poor job of handling the bonds and other investments other than stocks. Our calculators treat all non-stock investments as single year trading vehicles without any transaction fees and without any capital gains and losses.

For example, if you had bought a 13% 30-year treasury bond in 1984, you would have sold it immediately in 1985 and replaced it with a 10% 30-year treasury bond without any capital gain. In fact, by 2000, your brand new 30-year treasury bond would be yielding just above 6%. Its actual date of maturity would be irrelevant because replacements were available (on the secondary market) in 2001.

At no time beyond the first year would you have benefited from the 13% interest rate. You never would have received any capital gains. You would always replace the previous year's 30-year treasury bond with the latest available 30-year treasury bond.

We can do better.
John,

I'm a little confused. Are you saying that the returns your calculator has doesn't take into account cap gains and losses? I find that hard to believe. How on earth would you not have generated a capital gain on the 13% 30 year bond if you sold it one year later when long term bond yields were yielding 10%? I thought that is exactly what historical bond returns from people like Gummy or Ibbotson showed for each year. According to Gummy's historical return data, long term treasuries returned 31% in 1985 and 24.5% in 1986, and 5 year treasuries returned 20% and 15%. How does this not take into account cap appreciation? Do the spreadsheets you work with only use the yield for the newly issued bonds each year?

Definitely agree that unfortunately, transaction costs for buying or selling aren't factored into those returns. But returns like Gummy's aren't bad for approximating something like a fund that held nothing but long term gov't bonds, or nothing but 5 year treasuries, or nothing but Tbills. For Treasuries, you really only need to hold one bond, note, or bill, and turn it over every year to approximate a fund of similar duration and credit quality. And I'm pretty sure that those stock returns also don't factor in transaction costs for things like the S&P 500 or the MSCI EAFE. After all, an S&P 500 index fund wasn't even available until, what, 1976?

Perhaps I've missed the point of your gripe. Laddering is certainly and interesting idea. Good luck!

- Alec
JWR1945
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Location: Crestview, Florida

Post by JWR1945 »

Alec wrote:I'm a little confused. Are you saying that the returns your calculator has doesn't take into account cap gains and losses? I find that hard to believe. How on earth would you not have generated a capital gain on the 13% 30 year bond if you sold it one year later when long term bond yields were yielding 10%? I thought that is exactly what historical bond returns from people like Gummy or Ibbotson showed for each year.
This is exactly what I mean.

My calculators are developed from the Retire Early Safe Withdrawal Calculator. These calculators, along with dory36's FIRECalc, do exactly what I stated.

You may have read some of hocus's comments about earlier SWR studies. He has stated from time to time that they were biased in favor of stocks. He was right. Now you know how.

The calculators include capital gains and losses for stocks. They reinvest dividends. When it comes to the non-stock investment, the original idea was commercial paper. There is a single year's interest rate and that is all.

The algorithm makes sense with T-bills and commercial paper. It does not for notes and bonds. Notes and bonds are in the calculators, but only as an after thought and not with much attention to their fidelity.

Here is the complete input data for 5-year Treasury Notes and for 30-year Treasury bonds.

Year,30-year bond single-year total return (interest rate of coupon),5-Year Notes single-year total return (interest rate of coupon)

Code: Select all

1925   3.79    
1926   3.67    
1927   3.34    
1928   3.29    
1929   3.69    
1930   3.25    
1931   3.13    
1932   3.76    
1933   3.21    
1934   2.98    
1935   2.72    
1936   2.69    
1937   2.81    
1938   2.58    
1939   2.22    
1940   2.40    
1941   2.01    
1942   2.43    
1943   2.45    
1944   2.49    
1945   2.35    
1946   2.16    
1947   2.22    
1948   2.41    
1949   2.38    
1950   2.33    
1951   2.65    
1952   2.61    
1953   3.13    2.94
1954   2.55    1.92
1955   2.82    2.59
1956   2.93    2.97
1957   3.58    3.83
1958   3.19    2.46
1959   4.09    4.50
1960   3.99    4.12
1961   3.88    3.81
1962   3.90    3.64
1963   4.00    3.81
1964   4.13    4.02
1965   4.14    4.15
1966   4.63    4.97
1967   4.86    5.01
1968   5.23    5.85
1969   6.06    6.75
1970   6.99    7.85
1971   5.94    6.53
1972   5.59    5.91
1973   6.32    6.69
1974   7.03    8.10
1975   6.86    7.51
1976   6.92    7.61
1977   6.99    6.76
1978   7.94    8.36
1979   8.32    8.85
1980   9.40    9.21
1981  12.39    13.95
1982  13.32    14.43
1983  10.64    10.63
1984  13.04    13.48
1985  10.36    9.60
1986   8.23    7.64
1987   8.63    8.02
1988   9.04    8.49
1989   8.40    8.29
1990   8.62    8.43
1991   8.54    7.94
1992   7.72    6.48
1993   6.55    5.22
1994   7.43    6.70
1995   6.59    5.93
1996   7.20    6.69
1997   6.82    6.38
1998   5.80    5.52
1999   6.36    5.81
2000   6.28    6.30
2001   5.82    4.81
2002   5.66    4.19
dummy  6.00    5.00
The dummy rates are used for 2003-2010.

The calculator defaults to a zero percent interest rate when there an entry is missing. That is, every note prior to 1953 and every bond prior to 1925 is assigned a total annual return of zero percent (nominal).

I can put in substitute numbers easily. I make a special spreadsheet by copying something that I already have and then pasting the new rates on top of something that already exists. Typically, I would paste on top of the 5-year note or 30-year bond because I would want to keep commercial paper available.

If gummy has better data for 30-year bonds, I want it! Maybe that explains why I am not getting his numbers out of my latest version. I have just finished putting in two variants of a special algorithm that he has created. My numbers turn out different when I try to recreate his calculations. It could be a bug in my software. It could be different input data. Or it could be a bug in his software.

Have fun.

John R.
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