HDBR80 Returns versus Earnings Yield

Research on Safe Withdrawal Rates

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

HDBR80 Returns versus Earnings Yield

Post by JWR1945 »

These are the final balances of the HDBR80 portfolio at years 10, 14, 18, 22, 26 and 30 when there are no withdrawals and when the initial balances are all $100000.

The HDBR80 portfolio consists of 80% stocks and 20% commercial paper. It is rebalanced annually. Expenses are 0.20%. In this case, all dividends were 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.

HDBR80 curves from sequences beginning in 1923-1984
At year 10: Final balance = 1716300/[P/E10] + 50728 and R-squared equals 0.3934.
At year 14: Final balance = 3395500/[P/E10] - 23666 and R-squared equals 0.6086.
At year 18: Final balance = 4828400/[P/E10] - 65804 and R-squared equals 0.5971.

HDBR80 curves from sequences beginning in 1923-1972
At year 22: Final balance = 5148800/[P/E10] - 26246 and R-squared equals 0.5281.
At year 26: Final balance = 4377700/[P/E10] + 107864 and R-squared equals 0.3645.
At year 30: Final balance = 4623500/[P/E10] + 209013 and R-squared equals 0.3316.

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 22. [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). At the top of the bubble, even year 22 is too early.]

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

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 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 26. Year 14 is the best, but years 18 and 22 are also good.

Have fun.

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

Post by JWR1945 »

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    306203    328869    476450
1872   14.5     6.90    258288    373757    476698
1873   15.3     6.54    253265    381278    416523
1874   13.9     7.19    255594    350956    487973
1875   13.6     7.35    233232    337895    428953
1876   13.3     7.52    265707    338888    385152
1877   10.6     9.43    323921    353864    458776
1878    9.7    10.31    266067    369944    405343
1879   10.7     9.35    228654    290273    341571
1880   15.3     6.54    222923    253356    336182
1881   18.5     5.41    163653    212172    316874
1882   15.7     6.37    212753    233111    299166
1883   15.3     6.54    198506    233587    338411
1884   14.4     6.94    188228    249763    362841
1885   13.1     7.63    197549    295035    346864
1886   16.7     5.99    161093    206741    251912
1887   17.5     5.71    155161    224791    278619
1888   15.4     6.49    181898    264250    339942
1889   15.8     6.33    203647    239423    306711
1890   17.2     5.81    162096    197513    234036
1891   15.4     6.49    205769    255043    312122
1892   19.0     5.26    190052    244490    261435
1893   17.7     5.65    188598    241603    279008
1894   15.7     6.37    173788    205924    292055
1895   16.5     6.06    196720    240747    269950
1896   16.6     6.02    223139    238603    248959
1897   17.0     5.88    205318    237105    224505
1898   19.2     5.21    155190    220101    240073
1899   22.9     4.37    161199    180753    189508
1900   18.7     5.35    185920    193990    158396
1901   21.0     4.76    163661    154964    127787
1902   22.3     4.48    151507    165255    112185
1903   20.3     4.93    153745    161192    106370
1904   15.9     6.29    159205    129993    140199
1905   18.5     5.41    125025    103099    142397
1906   20.1     4.98    128459     87206    123656
1907   17.2     5.81    125828     83034    152892
1908   11.9     8.40    109707    118320    208434
1909   14.8     6.76     84245    116356    185785
1910   14.5     6.90     81553    115642    236411
1911   14.0     7.14     71902    132395    311451
1912   13.8     7.25     83426    146964    280199
1913   13.1     7.63    103769    165687    254843
1914   11.6     8.62    110831    226577    207271
1915   10.4     9.62    139825    328932    226043
1916   12.5     8.00    134737    256888    260742
1917   11.0     9.09    158032    243070    249390
1918    6.6    15.15    277493    253848    468554
1919    6.1    16.39    398886    274116    596305
1920    6.0    16.67    378413    384089    460154

Code: Select all

1921    5.1    19.61    368344    377922    560897
1922    6.3    15.87    235369    434445    478075
1923    8.2    12.20    198467    431740    357031
1924    8.1    12.35    270870    324513    295888
1925    9.7    10.31    205245    304617    262111
1926   11.3     8.85    246617    271384    258788
1927   13.2     7.58    270396    223606    259222
1928   18.8     5.32    158737    144735    252271
1929   27.1     3.69    129489    111420    140514
1930   22.3     4.48    142341    135734    139032
1931   16.7     5.99    145378    168534    163882
1932    9.3    10.75    158216    275769    244804
1933    8.7    11.49    162136    204472    274448
1934   13.0     7.69    133728    136977    219894
1935   11.5     8.70    164262    159729    266586
1936   17.1     5.85    149403    132628    193777
1937   21.6     4.63     93994    126161    215232
1938   13.5     7.41    114334    183545    343619
1939   15.6     6.41    107622    179620    312293
1940   16.4     6.10    120524    176093    280322
1941   13.9     7.19    152560    260270    392974
1942   10.1     9.90    201302    376862    491756
1943   10.2     9.80    208749    362937    476693
1944   11.1     9.01    184664    293967    476439
1945   12.0     8.33    224510    338981    412601
1946   15.6     6.41    216215    282133    374335
1947   11.5     8.70    287791    377994    542660
1948   10.4     9.62    286993    465137    628596
1949   10.2     9.80    348602    424311    547706
1950   10.7     9.35    317820    421684    517884
1951   11.9     8.40    281617    404299    465551
1952   12.5     8.00    289744    391566    375159
1953   13.0     7.69    254233    328166    342310
1954   12.0     8.33    288614    354457    364454
1955   16.0     6.25    236984    272888    296832
1956   18.3     5.46    209156    200392    199432
1957   16.7     5.99    188751    196886    148556
1958   13.8     7.25    222663    228943    196007
1959   18.0     5.56    180736    196594    157952
1960   18.3     5.46    153572    152837    133156
1961   18.5     5.41    149902    113105    134668
1962   21.2     4.72    141260    120938    118825
1963   19.3     5.18    161516    129769    134425
1964   21.6     4.63    115192    100359    105403
1965   23.3     4.29     78784     93804    112355
1966   24.1     4.15     89490     87926    117665
1967   20.4     4.90    100533    104140    131591
1968   21.5     4.65     81716     85824    140343
1969   21.2     4.72     81462     97573    164790
1970   17.1     5.85     91771    122811    176386
1971   16.5     6.06     99837    126154    192626
1972   17.3     5.78     83470    136493    202468
1973   18.7     5.35     89702    151498    173744
1974   13.5     7.41    123403    177236    258175
1975    8.9    11.24    167196    255293    347310
1976   11.2     8.93    159429    236489    303473
1977   11.4     8.77    188561    216250    288845
1978    9.2    10.87    203431    296334    405389
1979    9.3    10.75    214416    291700    459236
1980    8.9    11.24    240695    308870    548986
1981    9.3    10.71    208759    278838    616435
1982    7.4    13.48    282150    385986    753575
1983    8.7    11.51    243535    383409    590537
1984    9.8    10.25    230804    410232    460201
1985    9.9    10.07    220670    487841    367041
1986   11.7     8.57    236042    460834    260215
1987   14.7     6.78    227017    349659    174686
1988   13.7     7.28    285630    320421    150617
1989   15.2     6.60    319496    240382    112994
1990   17.0     5.88    310671    175424     82460
1991   15.6     6.42    304889    152319     71599
1992   19.6     5.11    219967    103398     48603
1993   20.4     4.90    176695     83057    
1994   21.5     4.65    136704     64259    
1995   20.5     4.89    114037     53604    
1996   25.4     3.93     75582     35528    
1997   29.2     3.43     52757       
1998   33.8     2.96     36153       
1999   40.9     2.44     24247       
2000   44.7     2.24     18198       
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.
unclemick
*** Veteran
Posts: 231
Joined: Sat Jun 12, 2004 4:00 am
Location: LA till Katrina, now MO

Post by unclemick »

Thanks for the numbers John R

A good Bear Bryant reminder of the importance of defense in the distribution phase.
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    604846    711736   1031134
1872   14.5     6.90    541775    718891   1044362
1873   15.3     6.54    540011    806493    948171
1874   13.9     7.19    534667    686172    836093
1875   13.6     7.35    504759    731274    906385
1876   13.3     7.52    511065    742446    955113
1877   10.6     9.43    685170    805535   1031925
1878    9.7    10.31    520203    633861    751072
1879   10.7     9.35    494854    613351    750622
1880   15.3     6.54    488385    628279    671822
1881   18.5     5.41    372540    477239    551126
1882   15.7     6.37    364531    431938    612604
1883   15.3     6.54    419447    513321    575588
1884   14.4     6.94    466774    499124    520787
1885   13.1     7.63    444348    513143    485873
1886   16.7     5.99    298494    423345    461761
1887   17.5     5.71    340975    382336    400855
1888   15.4     6.49    363502    379279    309687
1889   15.8     6.33    354196    335373    276557
1890   17.2     5.81    331926    362046    245778
1891   15.4     6.49    349984    366936    242141
1892   19.0     5.26    272782    222731    240217
1893   17.7     5.65    264180    217850    300887
1894   15.7     6.37    318558    216255    306646
1895   16.5     6.06    283026    186769    343900
1896   16.6     6.02    203279    219239    386215
1897   17.0     5.88    185133    255699    408273
1898   19.2     5.21    162975    231097    472442
1899   22.9     4.37    125056    230269    541694
1900   18.7     5.35    170831    300939    573766
1901   21.0     4.76    176495    281809    433452
1902   22.3     4.48    159076    325207    297497
1903   20.3     4.93    195861    460753    316631
1904   15.9     6.29    246977    470883    477946
1905   18.5     5.41    227364    349710    358803
1906   20.1     4.98    252796    231256    426852
1907   17.2     5.81    359670    247166    537681
1908   11.9     8.40    397398    403359    483240
1909   14.8     6.76    285757    293187    435137
1910   14.5     6.90    216267    399187    439276
1911   14.0     7.14    214030    465597    385028
1912   13.8     7.25    284402    340726    310670
1913   13.1     7.63    261470    388064    333913
1914   11.6     8.62    382581    421003    401461
1915   10.4     9.62    491729    406638    471408
1916   12.5     8.00    312379    284824    496446
1917   11.0     9.09    370135    318486    401648
1918    6.6    15.15    515609    491676    503623
1919    6.1    16.39    493119    571663    555886
1920    6.0    16.67    419564    731297    649183

Code: Select all

1921    5.1    19.61    482629    608650    816946
1922    6.3    15.87    455884    466962    749631
1923    8.2    12.20    413899    402476    671727
1924    8.1    12.35    515730    457821    668906
1925    9.7    10.31    330551    443674    756914
1926   11.3     8.85    265076    425536    796655
1927   13.2     7.58    252068    420699    731437
1928   18.8     5.32    223945    327198    520866
1929   27.1     3.69    188601    321757    485811
1930   22.3     4.48    223193    417844    545232
1931   16.7     5.99    273518    475544    624596
1932    9.3    10.75    357675    569381    922811
1933    8.7    11.49    468212    706939    860472
1934   13.0     7.69    411669    537175    712725
1935   11.5     8.70    463493    608766    873964
1936   17.1     5.85    308474    499951    675644
1937   21.6     4.63    324973    395550    510581
1938   13.5     7.41    448378    594909    730628
1939   15.6     6.41    410175    588861    678074
1940   16.4     6.10    454324    613983    588256
1941   13.9     7.19    478320    617421    644032
1942   10.1     9.90    652463    801312    823913
1943   10.2     9.80    684356    788037    857182
1944   11.1     9.01    643870    616890    613934
1945   12.0     8.33    532590    555544    419174
1946   15.6     6.41    459734    472700    404697
1947   11.5     8.70    624874    679702    546100
1948   10.4     9.62    602256    599370    522190
1949   10.2     9.80    571312    431071    513252
1950   10.7     9.35    532491    455887    447921
1951   11.9     8.40    506400    406862    421462
1952   12.5     8.00    373361    325284    341636
1953   13.0     7.69    258283    307523    368342
1954   12.0     8.33    312024    306572    410264
1955   16.0     6.25    238487    247045    312165
1956   18.3     5.46    173751    182486    298408
1957   16.7     5.99    176877    211858    357806
1958   13.8     7.25    192583    257720    370148
1959   18.0     5.56    163620    206750    315688
1960   18.3     5.46    139850    228688    339225
1961   18.5     5.41    161301    272420    312423
1962   21.2     4.72    159015    228384    332681
1963   19.3     5.18    169860    259360    352843
1964   21.6     4.63    172360    255671    328088
1965   23.3     4.29    189757    217621    290676
1966   24.1     4.15    168995    246172    336767
1967   20.4     4.90    200928    273350    430347
1968   21.5     4.65    208178    267143    474821
1969   21.2     4.72    188989    252432    558058
1970   17.1     5.85    256938    351495    686237
1971   16.5     6.06    262055    412565    635445
1972   17.3     5.78    259815    461796    518046
1973   18.7     5.35    232069    513042    386001
1974   13.5     7.41    353188    689542    389358
1975    8.9    11.24    546785    842174    420743
1976   11.2     8.93    539394    605095    284431
1977   11.4     8.77    638556    480436    225833
1978    9.2    10.87    791456    446905    210072
1979    9.3    10.75    707328    353375    166107
1980    8.9    11.24    615856    289489    136077
1981    9.3    10.71    463792    218010    
1982    7.4    13.48    425515    200017    
1983    8.7    11.51    295027    138680    
1984    9.8    10.25    216322    101684    
1985    9.9    10.07    172531       
1986   11.7     8.57    122317       
1987   14.7     6.78     82113       
1988   13.7     7.28     70799       
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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