## Some Accumulation Multipliers and Examples

Research on Safe Withdrawal Rates

Moderator: hocus2004

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

### Some Accumulation Multipliers and Examples

I have already looked at dollar cost averaging and switching portfolio allocations during the accumulation phase. If you are starting from scratch, the numbers suggest starting by dollar cost averaging into a 100% stock portfolio. Later, after you have built up your resources, trade-offs favor preserving capital through switching. In particular, if you invested \$1000 per year for 15 years and then switched portfolio allocations between stocks and 2% TIPS, you would gain enough in terms of safety to justify your giving up part of your portfolio's upside potential.

But what if you are not starting from scratch? And what if you are not immediately making withdrawals for retirement? I have collected some data to help you calculate your own numbers and to reach your own conclusions.

I have collected multipliers for the 15 years of leaving a balance untouched (except for switching stock allocations) and for 15 years of dollar cost averaging (into an all-stock portfolio).

Here is how you use them. Just multiply your starting balance by the first multiplier, the switching multiplier. Multiply any additional amounts that you wish to add by dollar cost averaging by the second multiplier, the dollar cost averaging multiplier. Add these two balances together and you have the (interim) total after 15 years.

If you wish to see what happens by leaving your portfolio alone for the following 15 years, multiply again after you align the new starting dates with the new switching multipliers. For example, if you are starting from 1923, you initially use the first (switching) and second (dollar cost averaging) multipliers for 1923. Fifteen years later is 1938. Multiply the interim balances by the first multiplier (i.e., for when the balance is left untouched) for 1938.

In all cases I used my latest Deluxe Calculator V1.1A07, which is a modified version of the Retire Early Safe Withdrawal Calculator, Version 1.61, dated November 7, 2002.

The details are simple. All investments were in the S&P500 index and in 2% TIPS. All dividends and interest were reinvested. All expenses were set at zero for these calculations. The portfolio consisted of 100% stocks with dollar cost averaging. Allocation switching was based upon Professor Shiller's P/E10 (the price of the index divided by the average of the previous ten years of earnings). Thresholds were set at P/E10 levels of 9-12-21-24 with allocations of 100-50-30-20-0% respectively. [When the P/E10 was below 9, the stock allocation was 100%. When P/E10 was between 9 and 12, the stock allocation was 50%. And so forth. The investment other than stocks was TIPS with a 2% interest rate.]

I have included two examples.

In the first, I started with \$200000 and add \$10000 per year through dollar cost averaging. The sums are 15-year balances.

The worst case outcome started in 1960. The \$200000 grew only to \$273916. Fifteen years of investing \$10000 each year lost money. It fell to \$126784. The total after 15 years is a frustratingly low \$400700.

I started with \$100000 in the second example and I added \$10000 per year for 15 years. After that, I left the portfolio untouched (except for switching allocations) for 15 years.

The worst case outcome was in 1961. The \$100000 grew to \$171536 at the 15-year point. Dollar cost averaging of \$10000 for 15 years produced \$161362. The 15-year total was \$332897. By leaving the account untouched except for allocation shifts, we would have ended up with \$749925 after 30 years of investing. The best case balance almost twice as big at \$1425707.

[When comparing this with the first example, remember that we started it with \$200000 already invested and we started this example with \$100000.]

This is a starting point. It is very easy for me to collect this kind of data.

Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Switching with 2% TIPS starting with \$100K. The thresholds are 9-12-21-24 and the corresponding stock allocations are 100-50-30-20-0%.

Year, 15-Year Balances, Switching Multipliers

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``````1871   221086    2.21
1872   219918    2.20
1873   211470    2.11
1874   214667    2.15
1875   214470    2.14
1876   202680    2.03
1877   226686    2.27
1878   210446    2.10
1879   182631    1.83
1880   169457    1.69
1881   155931    1.56
1882   161875    1.62
1883   166735    1.67
1884   177832    1.78
1885   174662    1.75
1886   170585    1.71
1887   172853    1.73
1888   175154    1.75
1889   165056    1.65
1890   172071    1.72
1891   186808    1.87
1892   172013    1.72
1893   162455    1.62
1894   190347    1.90
1895   188561    1.89
1896   188912    1.89
1897   188086    1.88
1898   179531    1.80
1899   163589    1.64
1900   161369    1.61
1901   169592    1.70
1902   160266    1.60
1903   136700    1.37
1904   137678    1.38
1905   127351    1.27
1906   105413    1.05
1907   128675    1.29
1908   173362    1.73
1909   151196    1.51
1910   184006    1.84
1911   199227    1.99
1912   209010    2.09
1913   231876    2.32
1914   269066    2.69
1915   279974    2.80
1916   242776    2.43
1917   222381    2.22
1918   263021    2.63
1919   398832    3.99
1920   387477    3.87``````

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``````1921   548188    5.48
1922   492615    4.93
1923   367319    3.67
1924   382007    3.82
1925   313603    3.14
1926   278473    2.78
1927   248759    2.49
1928   234943    2.35
1929   224885    2.25
1930   240256    2.40
1931   287458    2.87
1932   294066    2.94
1933   281376    2.81
1934   198140    1.98
1935   222705    2.23
1936   198706    1.99
1937   195649    1.96
1938   215249    2.15
1939   206474    2.06
1940   231235    2.31
1941   256883    2.57
1942   273313    2.73
1943   254424    2.54
1944   258580    2.59
1945   245204    2.45
1946   213209    2.13
1947   242038    2.42
1948   249547    2.50
1949   253783    2.54
1950   239777    2.40
1951   220723    2.21
1952   207580    2.08
1953   206616    2.07
1954   208221    2.08
1955   179175    1.79
1956   166510    1.67
1957   169555    1.70
1958   180679    1.81
1959   152181    1.52
1960   136958    1.37
1961   171536    1.72
1962   166814    1.67
1963   155723    1.56
1964   151251    1.51
1965   147755    1.48
1966   159147    1.59
1967   147138    1.47
1968   172883    1.73
1969   193149    1.93
1970   200953    2.01
1971   219461    2.19
1972   242152    2.42
1973   229234    2.29
1974   254449    2.54
1975   290853    2.91
1976   225272    2.25
1977   237937    2.38
1978   259382    2.59
1979   259593    2.60
1980   257586    2.58
1981   255765    2.56
1982   276640    2.77
1983   229009    2.29
1984   203506    2.04
1985   201659    2.02
1986   184924    1.85
1987   163802    1.64``````
Switching multipliers for 1871-1987 in a form suitable for copying into spreadsheets.

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``````2.21
2.20
2.11
2.15
2.14
2.03
2.27
2.10
1.83
1.69
1.56
1.62
1.67
1.78
1.75
1.71
1.73
1.75
1.65
1.72
1.87
1.72
1.62
1.90
1.89
1.89
1.88
1.80
1.64
1.61
1.70
1.60
1.37
1.38
1.27
1.05
1.29
1.73
1.51
1.84
1.99
2.09
2.32
2.69
2.80
2.43
2.22
2.63
3.99
3.87``````

Code: Select all

``````5.48
4.93
3.67
3.82
3.14
2.78
2.49
2.35
2.25
2.40
2.87
2.94
2.81
1.98
2.23
1.99
1.96
2.15
2.06
2.31
2.57
2.73
2.54
2.59
2.45
2.13
2.42
2.50
2.54
2.40
2.21
2.08
2.07
2.08
1.79
1.67
1.70
1.81
1.52
1.37
1.72
1.67
1.56
1.51
1.48
1.59
1.47
1.73
1.93
2.01
2.19
2.42
2.29
2.54
2.91
2.25
2.38
2.59
2.60
2.58
2.56
2.77
2.29
2.04
2.02
1.85
1.64``````
Dollar cost averaging is next.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Dollar Cost Averaging of \$1000 per year for 15 years.

Year, 15-Year Balances, DCA Multipliers

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``````1871   39583    39.58
1872   39679    39.68
1873   36678    36.68
1874   37276    37.28
1875   37609    37.61
1876   29865    29.87
1877   40634    40.63
1878   33953    33.95
1879   22268    22.27
1880   26819    26.82
1881   22644    22.64
1882   25020    25.02
1883   28839    28.84
1884   35083    35.08
1885   27476    27.48
1886   30051    30.05
1887   31358    31.36
1888   31917    31.92
1889   26462    26.46
1890   29583    29.58
1891   36504    36.50
1892   28773    28.77
1893   26513    26.51
1894   30571    30.57
1895   28307    28.31
1896   28477    28.48
1897   26277    26.28
1898   24552    24.55
1899   18852    18.85
1900   20088    20.09
1901   22703    22.70
1902   19641    19.64
1903   15481    15.48
1904   14350    14.35
1905   14430    14.43
1906   12248    12.25
1907   16052    16.05
1908   19648    19.65
1909   18068    18.07
1910   25955    25.96
1911   28875    28.88
1912   29573    29.57
1913   40999    41.00
1914   58459    58.46
1915   50204    50.20
1916   37075    37.08
1917   23054    23.05
1918   23431    23.43
1919   32588    32.59
1920   31039    31.04``````

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``````1921   46528    46.53
1922   47523    47.52
1923   28523    28.52
1924   30850    30.85
1925   27675    27.67
1926   23966    23.97
1927   18442    18.44
1928   19123    19.12
1929   21574    21.57
1930   26507    26.51
1931   35976    35.98
1932   26562    26.56
1933   20860    20.86
1934   20446    20.45
1935   23792    23.79
1936   26839    26.84
1937   29889    29.89
1938   34026    34.03
1939   32478    32.48
1940   43974    43.97
1941   48811    48.81
1942   48900    48.90
1943   41876    41.88
1944   51589    51.59
1945   49723    49.72
1946   41198    41.20
1947   48898    48.90
1948   45706    45.71
1949   48914    48.91
1950   44518    44.52
1951   43168    43.17
1952   35662    35.66
1953   35119    35.12
1954   33810    33.81
1955   25222    25.22
1956   22891    22.89
1957   23548    23.55
1958   25629    25.63
1959   18211    18.21
1960   12678    12.68
1961   16136    16.14
1962   16392    16.39
1963   13989    13.99
1964   14665    14.67
1965   14827    14.83
1966   16349    16.35
1967   14330    14.33
1968   17513    17.51
1969   19713    19.71
1970   20641    20.64
1971   24889    24.89
1972   30957    30.96
1973   27047    27.05
1974   29412    29.41
1975   34841    34.84
1976   30632    30.63
1977   36427    36.43
1978   35377    35.38
1979   34193    34.19
1980   31554    31.55
1981   38635    38.63
1982   45684    45.68
1983   50045    50.05
1984   57646    57.65
1985   57906    57.91
1986   47921    47.92
1987   35623    35.62``````
Dollar Cost Averaging multipliers for 1871-1987 in a form suitable for copying into spreadsheets.

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``````39.58
39.68
36.68
37.28
37.61
29.87
40.63
33.95
22.27
26.82
22.64
25.02
28.84
35.08
27.48
30.05
31.36
31.92
26.46
29.58
36.50
28.77
26.51
30.57
28.31
28.48
26.28
24.55
18.85
20.09
22.70
19.64
15.48
14.35
14.43
12.25
16.05
19.65
18.07
25.96
28.88
29.57
41.00
58.46
50.20
37.08
23.05
23.43
32.59
31.04``````

Code: Select all

``````46.53
47.52
28.52
30.85
27.67
23.97
18.44
19.12
21.57
26.51
35.98
26.56
20.86
20.45
23.79
26.84
29.89
34.03
32.48
43.97
48.81
48.90
41.88
51.59
49.72
41.20
48.90
45.71
48.91
44.52
43.17
35.66
35.12
33.81
25.22
22.89
23.55
25.63
18.21
12.68
16.14
16.39
13.99
14.67
14.83
16.35
14.33
17.51
19.71
20.64
24.89
30.96
27.05
29.41
34.84
30.63
36.43
35.38
34.19
31.55
38.63
45.68
50.05
57.65
57.91
47.92
35.62``````
Now for a couple of examples.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Example 1

15-Year Balances starting from \$200000 with switching and adding \$10000 each year (i.e., dollar cost averaging) into a 100% stock portfolio.

Start Year, Contributions from the initial portfolio, Contributions from dollar cost averaging, Total Amounts after 15 Years.

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``````1923   734639    285230   1019869
1924   764014    308496   1072510
1925   627205    276749    903955
1926   556947    239660    796607
1927   497517    184424    681941
1928   469886    191225    661111
1929   449771    215743    665513
1930   480512    265068    745580
1931   574917    359760    934677
1932   588131    265622    853754
1933   562751    208600    771351
1934   396279    204459    600739
1935   445411    237918    683329
1936   397413    268387    665799
1937   391298    298891    690189
1938   430499    340263    770762
1939   412948    324780    737728
1940   462470    439743    902213
1941   513766    488106   1001872
1942   546626    488998   1035624
1943   508848    418757    927605
1944   517161    515890   1033051
1945   490408    497231    987639
1946   426418    411984    838401
1947   484076    488979    973055
1948   499094    457059    956153
1949   507567    489141    996707
1950   479554    445178    924732
1951   441446    431682    873128
1952   415161    356623    771784
1953   413232    351192    764425
1954   416442    338097    754539
1955   358350    252217    610567
1956   333020    228908    561927
1957   339110    235483    574593
1958   361359    256293    617652
1959   304362    182111    486473
1960   273916    126784    400700
1961   343071    161362    504433
1962   333627    163921    497549
1963   311446    139887    451334
1964   302502    146653    449155
1965   295510    148270    443780
1966   318294    163493    481786
1967   294276    143295    437571
1968   345766    175132    520897
1969   386298    197134    583432
1970   401906    206414    608320
1971   438923    248886    687808
1972   484304    309574    793878
1973   458469    270465    728934
1974   508898    294119    803016
1975   581707    348409    930115
1976   450544    306319    756864
1977   475875    364269    840144
1978   518765    353772    872537
1979   519187    341929    861116
1980   515171    315536    830707
1981   511530    386345    897875
1982   553280    456840   1010119
1983   458017    500451    958468
1984   407012    576458    983470
1985   403317    579061    982379
1986   369848    479212    849060
1987   327603    356230    683833``````
The second example follows.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Example 1

15-Year Interim Balances starting from \$100000 with the switching of stock allocations and adding \$10000 each year (i.e., dollar cost averaging) into a 100% stock portfolio followed by 15 years of switching alone.

Start Year, Contributions from the initial portfolio, Contributions from dollar cost averaging, Total Amounts after 15 Years, Switching Multiplier after 15 Years, Final 30-Year Balances.

Code: Select all

``````1923   367319    285230    652550    2.15    1404609
1924   382007    308496    690503    2.06    1425707
1925   313603    276749    590352    2.31    1365101
1926   278473    239660    518134    2.57    1330998
1927   248759    184424    433183    2.73    1183946
1928   234943    191225    426168    2.54    1084275
1929   224885    215743    440628    2.59    1139377
1930   240256    265068    505324    2.45    1239076
1931   287458    359760    647219    2.13    1379928
1932   294066    265622    559688    2.42    1354657
1933   281376    208600    489976    2.50    1222719
1934   198140    204459    402599    2.54    1021730
1935   222705    237918    460624    2.40    1104469
1936   198706    268387    467093    2.21    1030981
1937   195649    298891    494540    2.08    1026566
1938   215249    340263    555513    2.07    1147779
1939   206474    324780    531254    2.08    1106182
1940   231235    439743    670978    1.79    1202227
1941   256883    488106    744989    1.67    1240479
1942   273313    488998    762311    1.70    1292535
1943   254424    418757    673181    1.81    1216299
1944   258580    515890    774471    1.52    1178596
1945   245204    497231    742435    1.37    1016826
1946   213209    411984    625193    1.72    1072427
1947   242038    488979    731017    1.67    1219437
1948   249547    457059    706606    1.56    1100349
1949   253783    489141    742924    1.51    1123679
1950   239777    445178    684955    1.48    1012055
1951   220723    431682    652405    1.59    1038283
1952   207580    356623    564203    1.47     830156
1953   206616    351192    557808    1.73     964355
1954   208221    338097    546318    1.93    1055208
1955   179175    252217    431392    2.01     866894
1956   166510    228908    395417    2.19     867788
1957   169555    235483    405038    2.42     980808
1958   180679    256293    436973    2.29    1001691
1959   152181    182111    334292    2.54     850602
1960   136958    126784    263742    2.91     767102
1961   171536    161362    332897    2.25     749925
1962   166814    163921    330735    2.38     786943
1963   155723    139887    295611    2.59     766762
1964   151251    146653    297904    2.60     773339
1965   147755    148270    296025    2.58     762518
1966   159147    163493    322640    2.56     825198
1967   147138    143295    290433    2.77     803454
1968   172883    175132    348014    2.29     796983
1969   193149    197134    390283    2.04     794249
1970   200953    206414    407367    2.02     821491
1971   219461    248886    468347    1.85     866086
1972   242152    309574    551726    1.64     903735
1973   229234    270465    499699
1974   254449    294119    548567
1975   290853    348409    639262
1976   225272    306319    531592
1977   237937    364269    602206
1978   259382    353772    613155
1979   259593    341929    601523
1980   257586    315536    573122
1981   255765    386345    642110
1982   276640    456840    733479
1983   229009    500451    729460
1984   203506    576458    779964
1985   201659    579061    780720
1986   184924    479212    664136
1987   163802    356230    520032``````
Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
I consider it highly significant that dollar cost averaging (DCA) lost money in several 15-year periods.

[This corresponds to DCA multipliers below 15 and/or DCA balances below \$150000 with an annual investment of \$10000.]

This means that investing in anything that matches inflation (e.g., TIPS and/or ibonds at 0% interest) can be a superior choice when looking into an extended bear market.

Our best estimate, based upon Professor Shiller's work and today's P/E10 level, is that we are looking into an extended bear market.

An alternative to buying TIPS and/or ibonds is purchasing income streams directly. This leads us to dividend-based investments.

Both of these accumulation alternatives are consistent with the results of our Safe Withdrawal Rate investigations.

Have fun.

John R.