HDBR80T2 Returns versus Earnings Yield

Research on Safe Withdrawal Rates

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

HDBR80T2 Returns versus Earnings Yield

Post by JWR1945 »

These are the final balances of the HDBR80T2 portfolio at years 10, 14, 18, 22, 26 and 30 when there are no withdrawals and when the initial balances are all $100000.

The HDBR80T2 portfolio consists of 80% stocks and 20% TIPS at 2% interest. It is rebalanced annually. Expenses are 0.20%. All dividends are reinvested. There were no withdrawals. The initial balances were all $100000.

Curve fit equations

These are the equations for fitting a straight line to the final balances as a function of Professor Robert Shiller's P/E10.

P/E10 is the current value of the S&P500 index (in real dollars) divided by the average of the most recent ten years of (real) earnings.

Excel calculated the curve fit equations as a function of the percentage earnings yield 100E10/P.

The calculator uses dummy data with heavy stock market losses after 2002. I excluded all sequences that ended after 2002.

Curves from sequences beginning in 1923-1984
At year 10: Final balance = 1642800/[P/E10] + 58294 and R-squared equals 0.3702.
At year 14: Final balance = 3293200/[P/E10] - 10682 and R-squared equals 0.5666.
At year 18: Final balance = 4688200/[P/E10] - 45165 and R-squared equals 0.5553.

Curves from sequences beginning in 1923-1972
At year 22: Final balance = 5581300/[P/E10] - 31825 and R-squared equals 0.4879.
At year 26: Final balance = 5115800/[P/E10] + 90712 and R-squared equals 0.3359.
At year 30: Final balance = 5711000/[P/E10] + 175812 and R-squared equals 0.3211.

Predictability

Look at R-squared. We see that P/E10 (actually, 100E10/P) predicts a portfolio's return best in the medium-term.

There is considerable randomness in the short-term.

We cannot rely upon significant portfolio gains prior to year 18. [Put today's P/E10 of 28 or so into the equations. While you are at it, put in a P/E10 of 44 to see what happened at the top of the bubble (in December 1999).]

Valuations always matter. We can take best advantage of them in the medium term.

At a 4% earnings yield (with P/E10 = 25), the calculated balances at years 10, 14 and 18 are all very close at $124K, $121K and $142K respectively. They separate considerably as the earnings yield increases (and as P/E10 decreases). At a 10% earnings yield (and P/E10 =10), the calculated balances are $223K, $319K and $424K, differences of $96K and $105K. The downward scatter is about $100K. Even though the likelihood of a higher balance increases with time, there is considerable overlap until the earnings yield has increased to 6% (with P/E10 = 17).

By years 22, 26 and 30, the lines are almost parallel. This is can be seen by looking at their slopes (which are the numbers just before the "/[P/E10]"￾Â￾ terms). They are all close to 55000. The calculated balances at a 4% earnings yield (with P/E10 = 25) are $201K, $295K and $394K respectively with differences of $94K and $99K. It is arguable as to whether it is worth waiting 4 years for the earnings yield to increase from 4% (with P/E10 = 25) to 6% (with P/E10 = 17). It is not worth waiting for 8 years.

Relationship with previous findings

In the New Tool we found that knowing a portfolio's total return at year 14 allowed us to estimate its 30-year Historical Surviving Withdrawal Rate with the greatest accuracy. R-squared was around 90%. When we waited much later to make estimates, R-squared was much lower. There was almost no variation of Historical Surviving Withdrawal Rates at year 30 based upon a portfolio's 30-year total return.

These results help to explain why. We have only a limited ability to estimate total returns as a function of earnings yield before year 10 and after year 22. Years 14 and 18 are best, but year 22 is also good.

Considering only the predictability of returns, we would expect the best estimate at year 14, but year 18 is almost as good. Historical Surviving Withdrawal Rates are most sensitive to the returns during the earliest years. This pulls the best number of years for predicting Historical Surviving Withdrawal Rates forward slightly, favoring 14 years over 18.

Have fun.

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

Post by JWR1945 »

HDBR80T2

Year, P/E10, 100E10/P, balance at year 10, balance at year 14, balance at year 18

Code: Select all


1871   13.3     7.52    269976    275217    387879
1872   14.5     6.90    231694    312175    384940
1873   15.3     6.54    226551    318415    337837
1874   13.9     7.19    227540    299773    397629
1875   13.6     7.35    205828    290085    357312
1876   13.3     7.52    236433    291544    315406
1877   10.6     9.43    287430    304962    373560
1878    9.7    10.31    246355    326774    341655
1879   10.7     9.35    213540    263028    292070
1880   15.3     6.54    199759    216108    280873
1881   18.5     5.41    148326    181690    268600
1882   15.7     6.37    188254    196828    258182
1883   15.3     6.54    177917    197562    292633
1884   14.4     6.94    166848    216850    321173
1885   13.1     7.63    178230    263486    319483
1886   16.7     5.99    146084    191621    230608
1887   17.5     5.71    140565    208207    257044
1888   15.4     6.49    164598    243783    310635
1889   15.8     6.33    186955    226687    284490
1890   17.2     5.81    155398    187016    217592
1891   15.4     6.49    196238    242267    291811
1892   19.0     5.26    183788    234188    251248
1893   17.7     5.65    184036    230964    262602
1894   15.7     6.37    172868    201130    282742
1895   16.5     6.06    197779    238226    265946
1896   16.6     6.02    223987    240304    246054
1897   17.0     5.88    207998    236490    223483
1898   19.2     5.21    154753    217547    238918
1899   22.9     4.37    161143    179894    192244
1900   18.7     5.35    183198    187582    161940
1901   21.0     4.76    159659    150877    135104
1902   22.3     4.48    146884    161313    121102
1903   20.3     4.93    148363    158549    111748
1904   15.9     6.29    155869    134562    145770
1905   18.5     5.41    122211    109435    147156
1906   20.1     4.98    126597     95039    128719
1907   17.2     5.81    126335     89043    158549
1908   11.9     8.40    115653    125287    219498
1909   14.8     6.76     90855    122172    193518
1910   14.5     6.90     88586    119979    241571
1911   14.0     7.14     78315    139447    321639
1912   13.8     7.25     89123    156140    289947
1913   13.1     7.63    109438    173347    257134
1914   11.6     8.62    117175    235926    202407
1915   10.4     9.62    147564    340360    216594
1916   12.5     8.00    142173    264011    250461
1917   11.0     9.09    162211    240615    237138
1918    6.6    15.15    273283    234457    431674
1919    6.1    16.39    380095    241880    538442
1920    6.0    16.67    351675    333627    409034

Code: Select all

1921    5.1    19.61    341385    336452    506355
1922    6.3    15.87    216429    398483    443548
1923    8.2    12.20    179878    400422    335261
1924    8.1    12.35    246333    302010    285109
1925    9.7    10.31    188956    284375    257352
1926   11.3     8.85    227449    253172    255402
1927   13.2     7.58    252795    211657    259578
1928   18.8     5.32    149996    141603    255496
1929   27.1     3.69    123291    111575    149501
1930   22.3     4.48    136337    137538    151807
1931   16.7     5.99    142689    174994    182802
1932    9.3    10.75    165052    297806    281746
1933    8.7    11.49    175331    234929    326466
1934   13.0     7.69    144978    160019    262145
1935   11.5     8.70    177560    185482    314799
1936   17.1     5.85    161749    153026    228538
1937   21.6     4.63    105535    146656    252290
1938   13.5     7.41    130519    213817    400328
1939   15.6     6.41    123245    209171    364642
1940   16.4     6.10    137478    205318    329000
1941   13.9     7.19    175159    301325    458126
1942   10.1     9.90    226492    424059    556663
1943   10.2     9.80    231135    402932    532051
1944   11.1     9.01    203525    326127    527285
1945   12.0     8.33    245698    373552    453669
1946   15.6     6.41    235024    308517    409081
1947   11.5     8.70    300714    397078    567325
1948   10.4     9.62    295472    477722    641567
1949   10.2     9.80    357598    434293    557218
1950   10.7     9.35    326104    432400    527804
1951   11.9     8.40    285743    408255    467119
1952   12.5     8.00    291612    391626    373204
1953   13.0     7.69    255889    328317    341756
1954   12.0     8.33    289528    353410    363372
1955   16.0     6.25    237317    271535    295066
1956   18.3     5.46    209170    199330    198754
1957   16.7     5.99    188334    196043    150061
1958   13.8     7.25    220552    226769    197652
1959   18.0     5.56    178598    194075    159945
1960   18.3     5.46    151847    151408    135485
1961   18.5     5.41    148467    113644    136947
1962   21.2     4.72    140257    122249    121994
1963   19.3     5.18    159802    131699    137250
1964   21.6     4.63    114188    102179    106806
1965   23.3     4.29     79541     95851    113487
1966   24.1     4.15     91029     90839    118194
1967   20.4     4.90    102646    106972    131514
1968   21.5     4.65     83709     87500    140061
1969   21.2     4.72     83772     99186    164202
1970   17.1     5.85     95323    124028    175526
1971   16.5     6.06    102766    126342    190228
1972   17.3     5.78     85101    136221    199318
1973   18.7     5.35     91276    151107    171985
1974   13.5     7.41    124387    176034    255553
1975    8.9    11.24    165056    248518    339617
1976   11.2     8.93    156288    228680    295451
1977   11.4     8.77    183351    208684    279298
1978    9.2    10.87    196724    285589    390465
1979    9.3    10.75    206230    281828    441391
1980    8.9    11.24    229156    296066    521677
1981    9.3    10.71    200243    268001    587839
1982    7.4    13.48    273215    373547    722692
1983    8.7    11.51    238031    372797    571104
1984    9.8    10.25    227546    400942    450794
1985    9.9    10.07    217990    478143    364172
1986   11.7     8.57    233367    451488    260753
1987   14.7     6.78    225188    344976    177179
1988   13.7     7.28    283309    318535    154410
1989   15.2     6.60    317564    241869    117246
1990   17.0     5.88    308562    178207     86386
1991   15.6     6.42    303098    155671     75461
1992   19.6     5.11    219418    106363     51559
1993   20.4     4.90    176990     85796    
1994   21.5     4.65    137933     66863    
1995   20.5     4.89    116313     56383    
1996   25.4     3.93     77794     37711    
1997   29.2     3.43     54780       
1998   33.8     2.96     37947       
1999   40.9     2.44     25705       
2000   44.7     2.24     19492       
2001   37.0     2.70          
2002   30.3     3.30          
2003   22.9     4.37          
CAUTION: 2003-2010 data are dummy values with heavy stock market losses.

More follows.

Have fun.

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

Post by JWR1945 »

Year, P/E10, 100E10/P, balance at year 22, balance at year 26, balance at year 30

Code: Select all


1871   13.3     7.52    477770    530523    785823
1872   14.5     6.90    416447    541250    801636
1873   15.3     6.54    413829    611784    741803
1874   13.9     7.19    415737    545329    656283
1875   13.6     7.35    396764    587697    725546
1876   13.3     7.52    409929    607139    773633
1877   10.6     9.43    552251    669618    840363
1878    9.7    10.31    448155    539338    627514
1879   10.7     9.35    432621    534095    643319
1880   15.3     6.54    415996    530073    568688
1881   18.5     5.41    325685    408731    464721
1882   15.7     6.37    310712    361511    508202
1883   15.3     6.54    361273    435154    485790
1884   14.4     6.94    409247    439060    449566
1885   13.1     7.63    400948    455871    430797
1886   16.7     5.99    268311    377183    414238
1887   17.5     5.71    309610    345637    369367
1888   15.4     6.49    333264    341238    294592
1889   15.8     6.33    323460    305669    273715
1890   17.2     5.81    305884    335934    252194
1891   15.4     6.49    325767    348132    245370
1892   19.0     5.26    257260    222093    240592
1893   17.7     5.65    248158    222216    298811
1894   15.7     6.37    310519    233114    315724
1895   16.5     6.06    284204    200313    356674
1896   16.6     6.02    212419    230112    403148
1897   17.0     5.88    200120    269099    426247
1898   19.2     5.21    179362    242923    489113
1899   22.9     4.37    135498    241265    556486
1900   18.7     5.35    175429    307344    570728
1901   21.0     4.76    181673    287767    426858
1902   22.3     4.48    164017    330240    283322
1903   20.3     4.93    198978    458948    292060
1904   15.9     6.29    255383    474238    449900
1905   18.5     5.41    233093    345758    340762
1906   20.1     4.98    259169    222348    409380
1907   17.2     5.81    365699    232719    518049
1908   11.9     8.40    407599    386681    474080
1909   14.8     6.76    287054    282907    425770
1910   14.5     6.90    207250    381582    424737
1911   14.0     7.14    204681    455634    381488
1912   13.8     7.25    275067    337238    318366
1913   13.1     7.63    253418    381390    345148
1914   11.6     8.62    372665    414811    418465
1915   10.4     9.62    482153    403692    495090
1916   12.5     8.00    307072    289888    523050
1917   11.0     9.09    356889    322974    432758
1918    6.6    15.15    480494    484726    535016
1919    6.1    16.39    450821    552889    577556
1920    6.0    16.67    386144    696727    659153

Code: Select all


1921    5.1    19.61    458237    613999    853235
1922    6.3    15.87    447455    493878    809077
1923    8.2    12.20    411166    429509    728962
1924    8.1    12.35    514427    486685    726846
1925    9.7    10.31    344829    479187    824340
1926   11.3     8.85    281900    461812    864645
1927   13.2     7.58    271158    460209    802269
1928   18.8     5.32    241717    360996    578456
1929   27.1     3.69    207752    357394    543372
1930   22.3     4.48    248692    465623    611225
1931   16.7     5.99    310251    540851    714166
1932    9.3    10.75    420777    674249   1090132
1933    8.7    11.49    561616    853864   1036995
1934   13.0     7.69    490812    644290    854302
1935   11.5     8.70    548780    724637   1035324
1936   17.1     5.85    366207    592087    795155
1937   21.6     4.63    383575    465841    597696
1938   13.5     7.41    525512    696807    850550
1939   15.6     6.41    481491    687930    787120
1940   16.4     6.10    531930    714365    680762
1941   13.9     7.19    556382    713863    743084
1942   10.1     9.90    738112    900969    926367
1943   10.2     9.80    760167    869772    945145
1944   11.1     9.01    708128    674818    672867
1945   12.0     8.33    582078    605904    463791
1946   15.6     6.41    499341    513417    447496
1947   11.5     8.70    649125    705377    581330
1948   10.4     9.62    611387    609620    545507
1949   10.2     9.80    580027    443983    535023
1950   10.7     9.35    542683    473004    472021
1951   11.9     8.40    507599    418333    435966
1952   12.5     8.00    372125    332989    348070
1953   13.0     7.69    261598    315239    373242
1954   12.0     8.33    316716    316058    411232
1955   16.0     6.25    243176    253426    311567
1956   18.3     5.46    177851    185906    297578
1957   16.7     5.99    180832    214104    354448
1958   13.8     7.25    197242    256637    363195
1959   18.0     5.56    166687    204928    308552
1960   18.3     5.46    141621    226691    331693
1961   18.5     5.41    162145    268429    305517
1962   21.2     4.72    158730    224637    326111
1963   19.3     5.18    168738    254062    347195
1964   21.6     4.63    170964    250154    323195
1965   23.3     4.29    187877    213836    286193
1966   24.1     4.15    167269    242828    332002
1967   20.4     4.90    198015    270602    423809
1968   21.5     4.65    204937    264775    466541
1969   21.2     4.72    186889    250128    548635
1970   17.1     5.85    254815    348390    674021
1971   16.5     6.06    259961    407143    623720
1972   17.3     5.78    257516    453750    510168
1973   18.7     5.35    230181    504883    384538
1974   13.5     7.41    349400    675974    390403
1975    8.9    11.24    531899    814839    418501
1976   11.2     8.93    520592    585321    283734
1977   11.4     8.77    612618    466593    226181
1978    9.2    10.87    755422    436287    211490
1979    9.3    10.75    676185    347288    168348
1980    8.9    11.24    586541    284325    137827
1981    9.3    10.71    447721    217032    
1982    7.4    13.48    417384    202327    
1983    8.7    11.51    293319    142186    
1984    9.8    10.25    218522    105929    
1985    9.9    10.07    176532       
1986   11.7     8.57    126400       
1987   14.7     6.78     85888       
1988   13.7     7.28     74850       
1989   15.2     6.60          
1990   17.0     5.88          
1991   15.6     6.42          
1992   19.6     5.11          
1993   20.4     4.90          
1994   21.5     4.65          
1995   20.5     4.89          
1996   25.4     3.93          
1997   29.2     3.43          
1998   33.8     2.96          
1999   40.9     2.44          
2000   44.7     2.24          
2001   37.0     2.70          
2002   30.3     3.30          
2003   22.9     4.37          

CAUTION: 2003-2010 data are dummy values with heavy stock market losses.

Have fun.

John R.
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