Using a Ladder of 5-year Treasury Notes
Posted: Sun Jan 23, 2005 6:09 pm
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.
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.