Using a Ladder of 5-year Treasury Notes

Research on Safe Withdrawal Rates

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

Using a Ladder of 5-year Treasury Notes

Post by JWR1945 »

This is my first investigation into more realistic modeling of non-stock holdings.

Using a Ladder of 5-year Treasury Notes
or
HSWR50L5 ladders

I have made a special calculator for a ladder of 5-year Treasury Notes. I pasted the interest rates from the ladder on top of the row with commercial paper interest rates. The ladder replaces commercial paper in 1953-2002. Commercial paper remains for years 1871-1952. The existing dummy data for commercial paper for 2003-2010 remain in place.

HSWR50L5 consists of 50% stocks (as represented by the S&P500 index) and 50% of this combination of commercial paper and 5-year Treasury Notes. I set the initial balance at $100000. I set expenses at 0.20%. I rebalanced annually. I adjusted withdrawals to match inflation according to the CPI.

I determined the 30-year Historical Surviving Withdrawal Rates of HSWR50L5 for the years 1940-1980. The portfolio has a positive balance at year 30 at the Historical Surviving Withdrawal Rate. But its balance is zero or negative at a withdrawal rate that is 0.1% higher.

I have tabulated these Historical Surviving Withdrawal Rates as well as those for HDBR50, which is an identical portfolio except that it always uses commercial paper. I have included a listing of the percentage earnings yield 100E10/P as well. The table follows this post.

I had Excel calculate regression lines using the data for 1940-1980, 1950-1980 and 1953-1972. The 1940-1980 data includes historical sequences without any Treasury Notes for an entire decade. It includes dummy data for 2003-2010. The dummy data assume heavy stock losses and low interest rates. The 1950-1980 data is a compromise, with almost all of the effects related to actual 5-year Treasury Notes. The 1953-1972 has no contaminated data whatsoever. None of its historical sequences extends into the dummy data area of 2003-2010.

Here are the equations for the lines for HSWR50L5.
For 1940-1980, y = 0.5066x + 1.8708 and R-squared is 0.8646.
For 1950-1980, y = 0.5178x + 1.81 and R-squared is 0.9082.
For 1953-1972, y = 0.6119x + 1.2681 and R-squared is 0.9172.
where x is the percentage earnings yield, 100E10/P or 100 / [P/E10], and y is the Historical Surviving Withdrawal Rate of the regression line (in percent).

Here are eyeball estimates of the confidence intervals about the regression lines for HSWR50L5. [We simply use the range of the data about the regression lines as our eyeball estimates.]
For 1940-1980, plus and minus 0.8%.
For 1950-1980, plus 0.8% and minus 0.9%. Use plus and minus 0.9%.
For 1953-1972, plus 0.4% and minus 0.5%. Use plus and minus 0.5%.

Here are the equations for the lines for HDBR50.
For 1940-1980, y = 0.4564x + 2.3614 and R-squared is 0.8225.
For 1950-1980, y = 0.4665x + 2.3197 and R-squared is 0.8731.
For 1953-1972, y = 0.6016x + 1.5609 and R-squared is 0.9057.
where x is the percentage earnings yield, 100E10/P or 100 / [P/E10], and y is the Historical Surviving Withdrawal Rate of the regression line (in percent).

Here are eyeball estimates of the confidence intervals about the regression lines for HDBR50. [We simply use the range of the data about the regression lines as our eyeball estimates.]
For 1940-1980, plus and minus 0.8%.
For 1950-1980, plus 0.9% and minus 1.0%. Use plus and minus 1.0%.
For 1953-1972, plus 0.4% and minus 0.5%. Use plus and minus 0.5%.

Here are the Safe, Calculated and High Risk Rates for HSWR50L5 at today's valuations (x = 3.5% since P/E10 is between 28 and 29).

1940-1980 data: 3.2% 4.0% 4.8%
1950-1980 data: 2.7% 3.6% 4.5%
1953-1972 data: 2.9% 3.4% 3.9%

Here are the Safe, Calculated and High Risk Rates for HSWR50L5 at the January 2000 valuations (x = 100/44.77 since P/E10 was 44.77).

1940-1980 data: 2.2% 3.0% 3.8%
1950-1980 data: 2.1% 3.0% 3.9%
1953-1972 data: 2.2% 2.7% 3.2%

Here are the Safe, Calculated and High Risk Rates for HDBR50 at today's valuations (x = 3.5% since P/E10 is between 28 and 29).

1940-1980 data: 3.2% 4.0% 4.8%
1950-1980 data: 3.0% 4.0% 5.0%
1953-1972 data: 3.2% 3.7% 4.2%

Here are the Safe, Calculated and High Risk Rates for HDBR50 at the January 2000 valuations (x = 100/44.77 since P/E10 was 44.77).

1940-1980 data: 2.6% 3.4% 4.2%
1950-1980 data: 2.4% 3.4% 4.4%
1953-1972 data: 2.4% 2.9% 3.4%

Interpretation:

Care must be taken because of the relatively short availability of 5-year Treasury Notes. Within the interval examined, the relationship between Calculated Rates and the Percentage Earnings Yield 100E10/P was very strong. Historically, many investments have taken a very long time before establishing reliable behavior.

Still, the relationship between the ladder of 5-year Treasury Notes and commercial paper seems close enough to give us confidence that these results are reasonable.

In addition, the percentage earnings yield varied from 4% to 11% for both the Treasury Notes and commercial paper when the interval was 1940-1980 and 1950-1980. The range was 4% to 8.5% in the narrowest (1953-1972) interval. This suggests that predictions are good when the earnings yield is small (and valuations are high), which is true today.

Somewhat surprisingly, the commercial paper almost always did just a little bit better than the Treasury Note ladder. This may be nothing more than the result of randomness. What we do not see is a strong advantage in favor of having a Treasury Note ladder.

Comparing Safe Withdrawal Rates, we notice that the difference between using a ladder of 5-year Treasury Notes and commercial paper has been in the neighborhood of 0.3%. You should allow yourself that much tolerance related to the details of your actual holdings.

Safe Withdrawal Rates are currently around 3%. They were around 2.2% to 2.4% at the peak of the bubble. Withdrawal rates in the neighborhood of 3.5% to 4.0% have a 50-50 chance of lasting 30 years from today.

Have fun.

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

Post by JWR1945 »

HSWR50L5 uses a bond ladder using 5-year Treasury Notes (in the years 1953-2002).

HDBR50 uses commercial paper.

Both portfolios are 50% stocks (S&P500 index).

Notice how close the Historical Surviving Withdrawal Rates of HSWR50L5 and HDBR50 are.

Year, 100E10/P, HSWR50L5 Historical Surviving Withdrawal Rate, HDBR50 Historical Surviving Withdrawal Rate.

Code: Select all

1940    6.10    4.5    4.5
1941    7.19    5.3    5.4
1942    9.90    6.2    6.2
1943    9.80    6.1    6.1
1944    9.01    5.9    5.9
1945    8.33    5.7    5.7
1946    6.41    5.8    5.9
1947    8.70    7.1    7.1
1948    9.62    7.4    7.4
1949    9.80    7.2    7.3
1950    9.35    7.5    7.6
1951    8.40    6.9    7.1
1952    8.00    6.5    6.7
1953    7.69    6.3    6.5
1954    8.33    6.4    6.6
1955    6.25    5.5    5.6
1956    5.46    4.9    5.2
1957    5.99    5.0    5.3
1958    7.25    5.4    5.7
1959    5.56    4.6    4.9
1960    5.46    4.6    4.9
1961    5.41    4.6    4.8
1962    4.72    4.3    4.6
1963    5.18    4.4    4.8
1964    4.63    4.1    4.4
1965    4.29    3.9    4.2
1966    4.15    3.9    4.1
1967    4.90    4.2    4.4
1968    4.65    4.1    4.3
1969    4.72    4.2    4.3
1970    5.85    4.6    4.7
1971    6.06    4.6    4.8
1972    5.78    4.5    4.7
1973    5.35    4.6    4.7
1974    7.41    5.6    5.6
1975   11.24    6.7    6.7
1976    8.93    6.0    6.0
1977    8.77    6.1    6.2
1978   10.87    7.0    7.0
1979   10.75    7.4    7.3
1980   11.24    7.8    7.4
Here are the HSWR50L5 30-year Historical Surviving Withdrawal Rates in a form easy to download.

Code: Select all

4.5
5.3
6.2
6.1
5.9
5.7
5.8
7.1
7.4
7.2
7.5
6.9
6.5
6.3
6.4
5.5
4.9
5.0
5.4
4.6
4.6
4.6
4.3
4.4
4.1
3.9
3.9
4.2
4.1
4.2
4.6
4.6
4.5
4.6
5.6
6.7
6.0
6.1
7.0
7.4
7.8
Have fun.

John R.
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