More about Imperfect Allocation Switching

Research on Safe Withdrawal Rates

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

More about Imperfect Allocation Switching

Post by JWR1945 »

This extends my investigation into the effects of switching allocations between stocks (i.e., the S&P500 index) and TIPS according to P/E10 (i.e., the current price of the S&P500 index divided by the average of the last ten years of earnings) in a less-than-perfect manner.

These investigations let you know the penalty of buying high and selling low as well as the rewards of investing properly.

This particular investigation shows what can happen in the accumulation stage.

Procedure

I set up 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) for switching allocations between stocks and TIPS. I set the expense ratio at 0.00%. I rebalanced all portfolios annually. I selected the CPI for making inflation adjustments.

I made deposits of $1000 per year for 30 years. To do this, I set the initial balance to $1000 and I set the withdrawal rate equal to (100%), which means minus 100%, of the initial balance. I recorded portfolio balances.

I set the P/E10 thresholds to 3-12-20-80. The thresholds of 3 and 80 eliminate the effects of allocations other than the three programmable selections. [The allocation with P/E10 less than 3 was 100%. The allocation with P/E10 greater than 80 was 0%. The software sets both of these extreme conditions. They never occur because P/E10 has always been between 3 and 80 throughout the historical record.]

I collected data for TIPS with interest rates of 0.0%, 2.0% and 4.0%.

Conditions Examined

In this investigation, I set the stock allocation equal to 50% when P/E10 was below 20 and either 100% or 10% when P/E10 was above 20. Both conditions are selected to highlight the effects of emotional decisions on long-term investment results. The first condition shows what happens when an investor is caught up in the euphoria of high stock returns and jumps in when valuations are high. The second condition shows what happens when an investor is reluctant to invest when valuations are high but still wants a little bit of exposure to the market at all times.

P/E10 is not perfect for revealing these effects. The best comparisons would be made strictly on price drops. However, the earnings part of P/E10 varies slowly (since it is the average of the most recent ten years of earnings) while the price component (or index value) is current. If prices drop 25% or 30%, P/E10 will not change by an identical amount but it will come close.

Summary

I have included tables that show real balances at 10, 20 and 30 years in the post that follows this one.

When the TIPS interest rate is 4.0%, the data generally favor keeping stock allocations at 10% when valuations are high.

There are exceptions, however. There are instances that favor 100% stock allocations while prices are continuing to rise. We see the effect of the 1960s in the data. At 10 years, 1955-1956 and 1958-1959 show the effect of rising prices during the late 1960s. At 20 years, we can see the same thing for sequences beginning in 1945-1946 and 1948-1949. At 30 years, we can still see this in 1936 (but not 1935) and 1938-1939.

We see the effect of the recent bubble in the 1966-1972 data at 30 years.

We see similar effects when the TIPS interest rate is 2.0%. There are a few more conditions favoring the 100% stock allocation when P/E10 exceeds 20.

When the interest rate of the TIPS is set to 0.0%, there are numerous conditions favoring the 100% stock allocation.

This is the story behind these numbers. The return of alternative investments must be considered when making comparisons such as these. The data generally favor lowering stock allocations when prices are high (e.g., when P/E10 is greater than 20). But the data will favor the 100% stock allocation if the investment alternative is sufficiently poor.

Have fun.

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

Post by JWR1945 »

Accumulation Phase: 4% TIPS
Real balances after investing $1000 per year.

50% stocks / 50% TIPS at 4.0% when P/E10 < 20.
10% stocks when P/E10 > 20.
4.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   22822    57561    116931
1922   16150    44579    106151
1923   14654    42307    102216
1924   17536    44742     99937
1925   14985    43627    110740
1926   18208    50195    124180
1927   19227    41323    118210
1928   17563    37805    106779
1929   17599    37131    118272
1930   18516    42268    126169
1931   17681    47158    128516
1932   15956    49249    135139
1933   14382    44549    115746
1934   14497    41793    117334
1935   15248    49693    117269
1936   16473    52568    112314
1937   14137    51830    109571
1938   13804    49120    111042
1939   14000    55416    108427
1940   14792    54158    102996
1941   14914    49121     92054
1942   16011    52861     95706
1943   16780    52556    100516
1944   16139    54404     85263
1945   18754    53083     70215
1946   17653    45084     66805
1947   18401    46515     70765
1948   17916    48793     68067
1949   20263    48216     68520
1950   17756    41438     59977
1951   17226    40286     61944
1952   18031    41253     57270
1953   16959    41293     60734
1954   17657    35569     63698
1955   16578    28758     61211
1956   15689    30898     63524
1957   15098    30726     69989
1958   15225    28552     67670
1959   14707    28462     69373
1960   14198    28100     72672
1961   14001    29454     69589
1962   14093    26860     76458
1963   14571    29474     76102
1964   12693    31264     76559
1965   10839    31215     75510
1966   12200    33466     76420
1967   12455    37503     77744
1968   11507    35646     78746
1969   11685    36599     79289
1970   11958    39196     80510
1971   12878    38102     80944
1972   12003    42238     78999
50% stocks / 50% TIPS at 4.0% when P/E10 < 20.
100% stocks when P/E10 > 20.
4.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   17333    34660     76968
1922   12505    27601     71483
1923   11618    27042     70643
1924   14261    29541     70929
1925   12522    29815     80871
1926   15677    35594     93524
1927   17030    30381     91625
1928   11444    28926     85434
1929   12151    29509     97519
1930   13551    34823    107055
1931   13623    40077    111808
1932   12666    42531    119078
1933   11791    39192     96557
1934   12362    37720    100131
1935   13454    45814    111080
1936   15138    49765    113718
1937   13479    50231    100108
1938   13804    49120    111075
1939   14000    55416    110051
1940   14792    54158     88680
1941   14914    49121     79400
1942   16011    52861     82711
1943   16780    49012     87056
1944   16139    50810     74029
1945   18754    54058     61147
1946   17653    47943     58357
1947   18401    43736     62013
1948   17916    48902     59880
1949   20263    49040     60544
1950   17756    35795     53236
1951   17226    34959     55274
1952   18031    35977     51383
1953   15839    36202     54790
1954   16566    31371     57789
1955   16992    25554     55884
1956   16775    27659     58330
1957   14279    27702     64613
1958   15377    25938     62825
1959   15080    26086     64834
1960   12410    25965     68313
1961   12395    27444     65814
1962   12644    25243     72771
1963   13299    27990     73002
1964   11657    29806     76553
1965    9986    29796     71886
1966   11399    32182     89595
1967   11941    36588    106723
1968   11090    34872    127383
1969   11414    36082    155177
1970   11958    39196    169671
1971   12878    38102    151570
1972   12003    42238    122617
Differences in favor of a 10% allocation when P/E10 > 20.
4.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   5489    22901    39962
1922   3645    16979    34668
1923   3036    15265    31573
1924   3275    15201    29008
1925   2462    13812    29869
1926   2531    14601    30656
1927   2197    10942    26585
1928   6119     8879    21345
1929   5448     7622    20752
1930   4965     7445    19114
1931   4058     7081    16708
1932   3290     6718    16061
1933   2590     5358    19189
1934   2134     4073    17203
1935   1794     3879     6189
1936   1335     2804    (1405)
1937    658     1599     9463
1938      0        0      (33)
1939      0        0    (1624)
1940      0        0    14315
1941      0        0    12654
1942      0        0    12996
1943      0     3543    13460
1944      0     3594    11233
1945      0     (976)    9069
1946      0    (2859)    8448
1947      0     2779     8752
1948      0     (109)    8187
1949      0     (824)    7976
1950      0     5644     6741
1951      0     5327     6670
1952      0     5276     5887
1953   1120     5091     5944
1954   1090     4198     5909
1955   (414)    3204     5327
1956  (1085)    3238     5194
1957    819     3024     5376
1958   (152)    2613     4845
1959   (372)    2376     4539
1960   1788     2135     4359
1961   1606     2011     3776
1962   1449     1617     3688
1963   1272     1485     3100
1964   1036     1458        7
1965    853     1418     3624
1966    800     1284    (13176)
1967    514      914    (28980)
1968    417      773    (48637)
1969    271      517    (75888)
1970      0        0    (89160)
1971      0        0    (70626)
1972      0        0    (43618)
2.0% TIPS tables are next.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Accumulation Phase: 2% TIPS
Real balances after investing $1000 per year.

50% stocks / 50% TIPS at 4.0% when P/E10 < 20.
10% stocks when P/E10 > 20.
2.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   21207    49906     94821
1922   14979    38650     86219
1923   13612    36772     83230
1924   16345    38996     81530
1925   13985    38133     90692
1926   17064    44050    102066
1927   18062    36291     97308
1928   16397    33292     88044
1929   16475    32788     97788
1930   17364    37407    104362
1931   16585    41793    106254
1932   14951    43628    111606
1933   13489    39468     94756
1934   13636    37093     96275
1935   14364    44181     95477
1936   15564    46835     90868
1937   13353    46172     87968
1938   13049    43704     88437
1939   13236    49306     85632
1940   13985    48101     80614
1941   14094    43524     71948
1942   15128    46809     74833
1943   15860    46164     78740
1944   15250    47805     66802
1945   17736    46268     55025
1946   16683    38959     52476
1947   17366    39862     55673
1948   16891    41542     53683
1949   19121    40805     54267
1950   16742    34846     47667
1951   16245    33989     49509
1952   17013    34928     45960
1953   15876    35078     48993
1954   16548    30283     51627
1955   15439    24578     49868
1956   14518    26554     51968
1957   13884    26503     57447
1958   13931    24706     55654
1959   13413    24770     57293
1960   12902    24557     60173
1961   12789    25858     57717
1962   12948    23664     63618
1963   13466    26087     63424
1964   11776    27773     63416
1965   10099    27797     62124
1966   11435    29874     62462
1967   11719    33543     63108
1968   10851    31884     63473
1969   11046    32748     63443
1970   11322    35074     63923
1971   12200    34041     63732
1972   11362    37725     61684
50% stocks / 50% TIPS at 4.0% when P/E10 < 20.
100% stocks when P/E10 > 20.
2.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   16666    31533    65677
1922   11983    25078    60989
1923   11126    24588    60282
1924   13669    26873    60483
1925   11982    27125    69009
1926   15008    32400    79792
1927   16283    27576    77998
1928   11023    26215    72530
1929   11677    26700    82656
1930   12974    31431    90362
1931   12994    36097    94000
1932   12057    38248    99878
1933   11221    35197    81576
1934   11774    33860    84578
1935   12805    41110    94496
1936   14407    44623    97480
1937   12787    44916    86375
1938   13049    43704    96283
1939   13236    49306    96139
1940   13985    48101    78038
1941   14094    43524    69669
1942   15128    46809    72481
1943   15860    43811    76283
1944   15250    45424    64737
1945   17736    48748    53347
1946   16683    43566    50900
1947   17366    40057    54027
1948   16891    45181    52123
1949   19121    45698    52722
1950   16742    33620    46342
1951   16245    32806    48168
1952   17013    33730    44750
1953   15084    33894    47741
1954   15779    29281    50347
1955   16333    23788    48674
1956   16248    25729    50765
1957   13926    25707    56160
1958   15091    23992    54450
1959   14885    24086    56103
1960   12304    23910    58971
1961   12218    25211    56611
1962   12393    23103    62452
1963   12952    25544    62390
1964   11279    27139    65850
1965    9596    27037    62194
1966   10918    29121    77932
1967   11390    33012    93266
1968   10540    31360   111932
1969   10827    32368   137042
1970   11322    35074   150543
1971   12200    34041   135357
1972   11362    37725   110207
Differences in favor of a 10% allocation when P/E10 > 20.
2.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   4541    18373    29145
1922   2997    13572    25230
1923   2486    12184    22948
1924   2676    12122    21047
1925   2003    11008    21683
1926   2056    11650    22274
1927   1780     8715    19310
1928   5375     7077    15514
1929   4798     6088    15133
1930   4391     5976    13999
1931   3591     5696    12254
1932   2894     5380    11728
1933   2268     4271    13180
1934   1862     3233    11697
1935   1559     3071      981
1936   1157     2212    (6613)
1937    567     1256     1593
1938      0        0    (7846)
1939      0        0   (10507)
1940      0        0     2575
1941      0        0     2279
1942      0        0     2352
1943      0     2353     2457
1944      0     2381     2065
1945      0    (2480)    1678
1946      0    (4607)    1576
1947      0     (194)    1646
1948      0    (3638)    1560
1949      0    (4893)    1544
1950      0     1225     1326
1951      0     1183     1342
1952      0     1199     1211
1953    792     1185     1252
1954    769     1002     1279
1955   (894)     790     1194
1956  (1730)     825     1203
1957    (42)     796     1287
1958  (1160)     714     1204
1959  (1471)     684     1190
1960    598      647     1202
1961    571      647     1106
1962    555      561     1166
1963    514      544     1034
1964    497      634    (2434)
1965    503      759      (70)
1966    517      753   (15470)
1967    328      531   (30158)
1968    311      524   (48459)
1969    219      381   (73599)
1970      0        0   (86619)
1971      0        0   (71624)
1972      0        0   (48524)
Next comes data for 0.0% TIPS.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Accumulation Phase: 0% TIPS
Real balances after investing $1000 per year.

50% stocks / 50% TIPS at 4.0% when P/E10 < 20.
10% stocks when P/E10 > 20.
0.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   19703    43359    77339
1922   13893    33587    70447
1923   12647    32042    68180
1924   15242    34078    66916
1925   13058    33424    74722
1926   16002    38765    84383
1927   16979    31959    80557
1928   15315    29396    72989
1929   15428    29030    81270
1930   16288    33187    86742
1931   15560    37128    88257
1932   14014    38742    92594
1933   12658    35051    77908
1934   12833    32999    79330
1935   13539    39370    78040
1936   14713    41815    73785
1937   12619    41212    70866
1938   12339    38954    70664
1939   12519    43946    67853
1940   13226    42792    63312
1941   13324    38630    56451
1942   14299    41517    58762
1943   14995    40607    61972
1944   14413    42068    52610
1945   16779    40382    43372
1946   15771    33708    41488
1947   16393    34203    44111
1948   15927    35417    42664
1949   18047    34587    43336
1950   15789    29355    38223
1951   15323    28744    39944
1952   16057    29659    37245
1953   14864    29899    39921
1954   15511    25879    42271
1955   14378    21095    41040
1956   13434    22928    42944
1957   12768    22972    47621
1958   12751    21486    46212
1959   12238    21668    47753
1960   11732    21571    50263
1961   11694    22815    48271
1962   11911    20946    53348
1963   12460    23190    53239
1964   10938    24770    52870
1965    9420    24841    51408
1966   10730    26752    51321
1967   11035    30085    51474
1968   10239    28589    51393
1969   10447    29368    50983
1970   10724    31450    50970
1971   11562    30473    50401
1972   10759    33759    48386
50% stocks / 50% TIPS at 4.0% when P/E10 < 20.
100% stocks when P/E10 > 20.
0.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   16030    28724    56255
1922   11484    22816    52233
1923   10656    22386    51634
1924   13103    24479    51766
1925   11465    24710    59103
1926   14369    29531    68321
1927   15569    25063    66634
1928   10618    23791    61792
1929   11224    24195    70308
1930   12423    28416    76552
1931   12396    32570    79324
1932   11480    34457    84083
1933   10681    31664    69178
1934   11216    30446    71703
1935   12190    36952    80683
1936   13715    40080    83867
1937   12133    40231    74800
1938   12339    38954    83777
1939   12519    43946    84294
1940   13226    42792    68919
1941   13324    38630    61339
1942   14299    41517    63722
1943   14995    39228    67047
1944   14413    40676    56774
1945   16779    44033    46670
1946   15771    39654    44515
1947   16393    36746    47193
1948   15927    41807    45486
1949   18047    42646    46025
1950   15789    31621    40441
1951   15323    30822    42077
1952   16057    31652    39066
1953   14370    31757    41698
1954   15033    27346    43968
1955   15703    22154    42493
1956   15742    23943    44287
1957   13584    23864    48931
1958   14812    22199    47305
1959   14693    22247    48669
1960   12200    22029    51038
1961   12043    23174    48829
1962   12145    21159    53753
1963   12611    23334    53489
1964   10911    24739    56836
1965    9220    24567    54006
1966   10458    26392    68049
1967   10866    29838    81830
1968   10020    28253    98747
1969   10273    29093   121503
1970   10724    31450   134085
1971   11562    30473   121311
1972   10759    33759    99384
Differences in favor of a 10% allocation when P/E10 > 20.
0.0% TIPS, Real balances after investing $1000 per year.
Year, at year 10, at year 20, at year 30

Code: Select all

1921   3674    14635    21083
1922   2409    10771    18213
1923   1991     9656    16545
1924   2139     9599    15150
1925   1594     8713    15619
1926   1633     9234    16062
1927   1410     6896    13924
1928   4696     5606    11197
1929   4204     4835    10961
1930   3866     4771    10189
1931   3164     4558     8932
1932   2534     4285     8510
1933   1977     3387     8730
1934   1617     2552     7627
1935   1349     2418    (2643)
1936    997     1735   (10082)
1937    486      981    (3934)
1938      0        0   (13112)
1939      0        0   (16441)
1940      0        0    (5607)
1941      0        0    (4888)
1942      0        0    (4959)
1943      0     1379    (5075)
1944      0     1392    (4164)
1945      0    (3652)   (3298)
1946      0    (5946)   (3027)
1947      0    (2543)   (3082)
1948      0    (6390)   (2822)
1949      0    (8060)   (2689)
1950      0    (2266)   (2217)
1951      0    (2077)   (2133)
1952      0    (1994)   (1820)
1953    494    (1858)   (1777)
1954    478    (1467)   (1697)
1955  (1325)   (1059)   (1453)
1956  (2308)   (1015)   (1342)
1957   (816)    (892)   (1310)
1958  (2062)    (713)   (1093)
1959  (2455)    (580)    (916)
1960   (468)    (458)    (775)
1961   (350)    (359)    (558)
1962   (234)    (214)    (405)
1963   (151)    (144)    (250)
1964     27       31    (3966)
1965    199      273    (2598)
1966    272      360   (16727)
1967    169      247   (30356)
1968    219      335   (47354)
1969    174      275   (70521)
1970      0        0   (83115)
1971      0        0   (70910)
1972      0        0   (50998)
Have fun.

John R.
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