A Survey using Minimum Balances
Posted: Wed Jul 28, 2004 10:48 am
I have taken a break from my latest calculator update, which will be named the Deluxe Calculator V1.1.
I am in the process of adding numerous data summaries similar what is already in rows 1 through 9 and columns L through P. I have completed my first new area. It tells us how many times the PORTFOLIO BALANCE would have fallen below a minimal balance that we specify. We can choose whether the threshold is in real dollars or nominal dollars. The range of years summarized remains as specified by cells M1 and M2.
I set the initial balance equal to $100000. I set the minimum balance threshold at $50000. I chose to use inflation adjusted (real) dollars. I selected start years 1921 through 1980. I set expenses equal to 0.20%.
I looked at a variety of portfolios.
I varied withdrawal rates as a percentage of the initial balance with adjustments to match inflation. I have focused on 30-year portfolio lifetimes.
I determined withdrawal rates in increments of 0.1%. I determined the minimum rates with 1 failure, 7 failures, 13 failures and 31 failures and then subtracted 0.1%. There are 60 historical sequences that begin from 1921 to 1980.
Data collection was very simple. I set up a portfolio in the traditional manner. I varied withdrawal rates in cell B9. I read the number of 30-year failures from cell W6, which is in a new summary table, instead of M6, which shows the number of portfolios that would have been depleted entirely (i.e., with a threshold of zero dollars).
In the results that follow, failure means that a portfolio's balance fell below its threshold (of 50% of its initial balance in real dollars) within 30 years.
Conventional Portfolios
I looked at HDBR50 first. It consists of 50% stocks and 50% commercial paper. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9% (or, more precisely, 3.91%). The portfolio would have fallen below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 2.8%.
Six failures (10%): 3.5%.
Twelve failures (20%): 3.7%.
Thirty failures (50%): 4.6%.
The first failure was with start year 1937. At a withdrawal rate of 3.6%, the (six) failures occurred with start years 1936, 1937, 1965, 1966, 1968 and 1969.
I looked at HDBR80. It consists of 80% stocks and 20% commercial paper. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9% (or, more precisely, 3.95%). The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 2.4%.
Six failures (10%): 3.1%.
Twelve failures (20%): 3.6%.
Thirty failures (50%): 5.5%.
The first failure was with start year 1966. At a withdrawal rate of 3.2%, the (six) failures occurred with start years 1965-1969 and 1973.
I looked at HDBR50T2. It consists of 50% stocks and 50% TIPS at a 2% (real) interest rate. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 3.3%.
Six failures (10%): 3.6%.
Twelve failures (20%): 3.9%.
Thirty failures (50%): 5.0%.
The first failure was with start year 1966. At a withdrawal rate of 3.7%, the failures occurred with start years 1962, 1964, 1965, 1966, 1968 and 1969.
I looked at HDBR80T2. It consists of 80% stocks and 20% TIPS at a 2% (real) interest rate. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 2.5%.
Six failures (10%): 3.2%.
Twelve failures (20%): 3.8%.
Thirty failures (50%): 5.6%.
The first failure was with start year 1966. At a withdrawal rate of 3.3%, the (seven) failures occurred with start years 1964-1969 and 1973.
Switching Portfolios
All portfolios consisted of stocks as represented by the S&P500 index (with all dividends reinvested) and 2% TIPS.
With two thresholds:
The simplest approach uses two thresholds and three stock allocations. The best choices are P/E10 thresholds of 11 and 24 and stock allocations of 100%-30%-0%, respectively.
Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 5.2%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 0.7%.
Six failures (10%): 4.3%.
Twelve failures (20%): 4.5%.
Thirty failures (50%): 5.6%.
This is a very strange result. It can be traced to the dummy data after 2002. The dummy data introduce heavy losses into hypothetical portfolios. Examining the real portfolio balances, it was these late declines that brought the portfolios down for start years 1976-1980.
The first failure occurred with the 1980 sequence. The second was in 1979. The third was in 1978. The fourth was in 1977. The fifth was in 1976. The sixth and seventh occurred at a withdrawal rate of 4.4%. They were in 1956 and 1959.
Without the effects caused by the dummy data, the first failure occurred at a withdrawal rate of 4.3%.
[It was this anomaly that caused me to reexamine the data and to report the start years associated with first few failures.]
With four thresholds:
The best choice with four thresholds and five stock allocations are 9-12-21-24 or 9-13-21-24 (with no preference) with 100%-50%-30%-20%-0%, respectively. There is relatively little sensitivity to changing the lowest adjustable allocation or the lower middle P/E10 threshold.
My choice was to us 9-12-21-24 and 100%-50%-30%-20%-0%.
Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 5.2%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 1.0%.
Six failures (10%): 4.4%.
Twelve failures (20%): 4.5%.
Thirty failures (50%): 5.2%.
This strange result follows the earlier pattern (with two thresholds and three allocations). The first failure occurred in 1980. The failures at 4.3% were for start years 1976-1980. At 4.4%, the new failures were with start years of 1956 and 1959.
Without the effects caused by the dummy data, the first failure occurred at a withdrawal rate of 4.4%.
Comments
This is a peek at the kind of information that we will be able to collect easily with the new Deluxe Calculator V1.1A.
This report makes use of only the first of the new data summaries. There will be more.
It took about three hours total to put this together, including this write up.
Have fun.
John R.
I am in the process of adding numerous data summaries similar what is already in rows 1 through 9 and columns L through P. I have completed my first new area. It tells us how many times the PORTFOLIO BALANCE would have fallen below a minimal balance that we specify. We can choose whether the threshold is in real dollars or nominal dollars. The range of years summarized remains as specified by cells M1 and M2.
I set the initial balance equal to $100000. I set the minimum balance threshold at $50000. I chose to use inflation adjusted (real) dollars. I selected start years 1921 through 1980. I set expenses equal to 0.20%.
I looked at a variety of portfolios.
I varied withdrawal rates as a percentage of the initial balance with adjustments to match inflation. I have focused on 30-year portfolio lifetimes.
I determined withdrawal rates in increments of 0.1%. I determined the minimum rates with 1 failure, 7 failures, 13 failures and 31 failures and then subtracted 0.1%. There are 60 historical sequences that begin from 1921 to 1980.
Data collection was very simple. I set up a portfolio in the traditional manner. I varied withdrawal rates in cell B9. I read the number of 30-year failures from cell W6, which is in a new summary table, instead of M6, which shows the number of portfolios that would have been depleted entirely (i.e., with a threshold of zero dollars).
In the results that follow, failure means that a portfolio's balance fell below its threshold (of 50% of its initial balance in real dollars) within 30 years.
Conventional Portfolios
I looked at HDBR50 first. It consists of 50% stocks and 50% commercial paper. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9% (or, more precisely, 3.91%). The portfolio would have fallen below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 2.8%.
Six failures (10%): 3.5%.
Twelve failures (20%): 3.7%.
Thirty failures (50%): 4.6%.
The first failure was with start year 1937. At a withdrawal rate of 3.6%, the (six) failures occurred with start years 1936, 1937, 1965, 1966, 1968 and 1969.
I looked at HDBR80. It consists of 80% stocks and 20% commercial paper. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9% (or, more precisely, 3.95%). The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 2.4%.
Six failures (10%): 3.1%.
Twelve failures (20%): 3.6%.
Thirty failures (50%): 5.5%.
The first failure was with start year 1966. At a withdrawal rate of 3.2%, the (six) failures occurred with start years 1965-1969 and 1973.
I looked at HDBR50T2. It consists of 50% stocks and 50% TIPS at a 2% (real) interest rate. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 3.3%.
Six failures (10%): 3.6%.
Twelve failures (20%): 3.9%.
Thirty failures (50%): 5.0%.
The first failure was with start year 1966. At a withdrawal rate of 3.7%, the failures occurred with start years 1962, 1964, 1965, 1966, 1968 and 1969.
I looked at HDBR80T2. It consists of 80% stocks and 20% TIPS at a 2% (real) interest rate. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 2.5%.
Six failures (10%): 3.2%.
Twelve failures (20%): 3.8%.
Thirty failures (50%): 5.6%.
The first failure was with start year 1966. At a withdrawal rate of 3.3%, the (seven) failures occurred with start years 1964-1969 and 1973.
Switching Portfolios
All portfolios consisted of stocks as represented by the S&P500 index (with all dividends reinvested) and 2% TIPS.
With two thresholds:
The simplest approach uses two thresholds and three stock allocations. The best choices are P/E10 thresholds of 11 and 24 and stock allocations of 100%-30%-0%, respectively.
Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 5.2%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 0.7%.
Six failures (10%): 4.3%.
Twelve failures (20%): 4.5%.
Thirty failures (50%): 5.6%.
This is a very strange result. It can be traced to the dummy data after 2002. The dummy data introduce heavy losses into hypothetical portfolios. Examining the real portfolio balances, it was these late declines that brought the portfolios down for start years 1976-1980.
The first failure occurred with the 1980 sequence. The second was in 1979. The third was in 1978. The fourth was in 1977. The fifth was in 1976. The sixth and seventh occurred at a withdrawal rate of 4.4%. They were in 1956 and 1959.
Without the effects caused by the dummy data, the first failure occurred at a withdrawal rate of 4.3%.
[It was this anomaly that caused me to reexamine the data and to report the start years associated with first few failures.]
With four thresholds:
The best choice with four thresholds and five stock allocations are 9-12-21-24 or 9-13-21-24 (with no preference) with 100%-50%-30%-20%-0%, respectively. There is relatively little sensitivity to changing the lowest adjustable allocation or the lower middle P/E10 threshold.
My choice was to us 9-12-21-24 and 100%-50%-30%-20%-0%.
Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 5.2%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.
No failures: 1.0%.
Six failures (10%): 4.4%.
Twelve failures (20%): 4.5%.
Thirty failures (50%): 5.2%.
This strange result follows the earlier pattern (with two thresholds and three allocations). The first failure occurred in 1980. The failures at 4.3% were for start years 1976-1980. At 4.4%, the new failures were with start years of 1956 and 1959.
Without the effects caused by the dummy data, the first failure occurred at a withdrawal rate of 4.4%.
Comments
This is a peek at the kind of information that we will be able to collect easily with the new Deluxe Calculator V1.1A.
This report makes use of only the first of the new data summaries. There will be more.
It took about three hours total to put this together, including this write up.
Have fun.
John R.