Additional tables for the accumulation stage
Posted: Tue Dec 28, 2004 3:57 pm
Here are some tables for planning during the accumulation stage.
The first set of tables has historical growth multipliers with dollar cost averaging. Multiply the entries by $1000 to find out how much investing $1000 per year for 5, 10, 15, 20, 25 and 30 years into an all-stock portfolio would have returned.
The second set of tables has historical growth multipliers for an account that switches allocations between stocks and TIPS at 2% interest depending upon P/E10. The P/E10 thresholds are 9-12-21-24 and the corresponding stock allocations are 100%-50%-30%-20%-0%. (As examples: if P/E10 equals 14, the stock allocation is 30%. If P/E10 equals 22, the stock allocation is 20%.) Multiply the initial balance by these growth multipliers to determine the balances after 5, 10, 15, 20, 25 and 30 years.
All balances are in real dollars. That is, they are adjusted to compensate for inflation. The very long-term historical return of the stock market is around 6.5% to 7.0% above inflation. A growth multiplier of 2 at ten years corresponds to an annualized real return of 7%+, which is just a little bit higher than the long-term return of stocks overall. At 20 years, a growth multiplier of 4 corresponds to the same annualized real return of 7%+.
[Reference approximation: the rule of 72. The interest rate in percent times the number of years for an investment to double equals 72.]
Switching stock allocations reduces the maximum stock market returns. Switching increases the minimum returns.
In general, one has done best by dollar cost averaging into a 100% stock portfolio over a long time period, typically 25 years or longer. Once an investor has built up some capital, it makes sense for him to protect some of his money. He should take part of his money out of his 100% stock portfolio. He should put it into an account that varies allocations between stocks and TIPS in a gradual manner according to valuations.
Doing this becomes more and more important as the investor approaches his retirement. He can no longer tolerate losses that delay his retirement by a decade or more, which is typical of what can happen with stocks.
With these growth multiplier tables, you can construct historical sequences for such a transition. You would start out with an initial allocation. Normally, this would be zero dollars as you begin by dollar cost averaging into a 100% stock portfolio. At some point later on, you remove money from the account. First, you determine the balance at that time by using the dollar cost averaging growth multipliers. Then you split your money into two [actually, three] separate accounts, one with dollar cost averaging and the other [two] with an initial balance. This is where it gets to be a little tricky.
The money that you remove from the account must be put into a sequence that begins at the right time. For example, if you remove some money from the 1942 sequence after ten years, you need to place the balance at the start of the 1952 historical sequence. Then you look up the 1952 growth multipliers that apply to switching stock allocations.
You need to break off the money that you leave in the dollar cost averaging account and treat it separately. For example, if you withdraw $5000 from the 1942 historical sequence in 1952, you look up the dollar cost averaging growth multiplier after ten years. It is 18.84. Your annual $1000 investment would have grown to $18840. After withdrawing $5000, the remaining balance is $13840. You use a table of growth multipliers for 100% stocks for the $13840 that you leave untouched, beginning from 1952. You now treat the dollar cost averaging account as brand new, but beginning in 1952.
[It is simpler if you remove all of your money from the dollar cost averaging account. Then you do not have to include a 100% stock portfolio without deposits and/or withdrawals.]
This process is difficult to do manually, but it is easy to do with an Excel spreadsheet. You end up with a complete set of Historical Surviving Withdrawal Rates.
Additional material:
Some Accumulation Multipliers and Examples dated Tue Nov 09, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=3067
Annualized Real Total Returns 100% stocks dated Tue Mar 16, 2004.
[These tables have annualized real returns. Let r be the annualized real return expressed as a fraction. Let the number of years equal N. Then to calculate growth multipliers, use this equation: (the growth multiplier at N years) = (1 + r)^N.]
http://nofeeboards.com/boards/viewtopic.php?t=2226
Have fun.
John R.
The first set of tables has historical growth multipliers with dollar cost averaging. Multiply the entries by $1000 to find out how much investing $1000 per year for 5, 10, 15, 20, 25 and 30 years into an all-stock portfolio would have returned.
The second set of tables has historical growth multipliers for an account that switches allocations between stocks and TIPS at 2% interest depending upon P/E10. The P/E10 thresholds are 9-12-21-24 and the corresponding stock allocations are 100%-50%-30%-20%-0%. (As examples: if P/E10 equals 14, the stock allocation is 30%. If P/E10 equals 22, the stock allocation is 20%.) Multiply the initial balance by these growth multipliers to determine the balances after 5, 10, 15, 20, 25 and 30 years.
All balances are in real dollars. That is, they are adjusted to compensate for inflation. The very long-term historical return of the stock market is around 6.5% to 7.0% above inflation. A growth multiplier of 2 at ten years corresponds to an annualized real return of 7%+, which is just a little bit higher than the long-term return of stocks overall. At 20 years, a growth multiplier of 4 corresponds to the same annualized real return of 7%+.
[Reference approximation: the rule of 72. The interest rate in percent times the number of years for an investment to double equals 72.]
Switching stock allocations reduces the maximum stock market returns. Switching increases the minimum returns.
In general, one has done best by dollar cost averaging into a 100% stock portfolio over a long time period, typically 25 years or longer. Once an investor has built up some capital, it makes sense for him to protect some of his money. He should take part of his money out of his 100% stock portfolio. He should put it into an account that varies allocations between stocks and TIPS in a gradual manner according to valuations.
Doing this becomes more and more important as the investor approaches his retirement. He can no longer tolerate losses that delay his retirement by a decade or more, which is typical of what can happen with stocks.
With these growth multiplier tables, you can construct historical sequences for such a transition. You would start out with an initial allocation. Normally, this would be zero dollars as you begin by dollar cost averaging into a 100% stock portfolio. At some point later on, you remove money from the account. First, you determine the balance at that time by using the dollar cost averaging growth multipliers. Then you split your money into two [actually, three] separate accounts, one with dollar cost averaging and the other [two] with an initial balance. This is where it gets to be a little tricky.
The money that you remove from the account must be put into a sequence that begins at the right time. For example, if you remove some money from the 1942 sequence after ten years, you need to place the balance at the start of the 1952 historical sequence. Then you look up the 1952 growth multipliers that apply to switching stock allocations.
You need to break off the money that you leave in the dollar cost averaging account and treat it separately. For example, if you withdraw $5000 from the 1942 historical sequence in 1952, you look up the dollar cost averaging growth multiplier after ten years. It is 18.84. Your annual $1000 investment would have grown to $18840. After withdrawing $5000, the remaining balance is $13840. You use a table of growth multipliers for 100% stocks for the $13840 that you leave untouched, beginning from 1952. You now treat the dollar cost averaging account as brand new, but beginning in 1952.
[It is simpler if you remove all of your money from the dollar cost averaging account. Then you do not have to include a 100% stock portfolio without deposits and/or withdrawals.]
This process is difficult to do manually, but it is easy to do with an Excel spreadsheet. You end up with a complete set of Historical Surviving Withdrawal Rates.
Additional material:
Some Accumulation Multipliers and Examples dated Tue Nov 09, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=3067
Annualized Real Total Returns 100% stocks dated Tue Mar 16, 2004.
[These tables have annualized real returns. Let r be the annualized real return expressed as a fraction. Let the number of years equal N. Then to calculate growth multipliers, use this equation: (the growth multiplier at N years) = (1 + r)^N.]
http://nofeeboards.com/boards/viewtopic.php?t=2226
Have fun.
John R.