HDBR50T2 Returns versus Earnings Yield

Research on Safe Withdrawal Rates

Moderator: hocus2004

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

HDBR50T2 Returns versus Earnings Yield

Post by JWR1945 »

These are the final balances of the HDBR50T2 portfolio at years 10, 14, 18, 22, 26 and 30 when there are no withdrawals and when the initial balances are all $100000.

The HDBR50T2 portfolio consists of 50% stocks and 50% TIPS at 2% interest. It is rebalanced annually. Expenses are 0.20%. 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.

Curves from sequences beginning in 1923-1984
At year 10: Final balance = 925330/[P/E10] + 87166 and R-squared equals 0.3932.
At year 14: Final balance = 1743700/[P/E10] + 58789 and R-squared equals 0.6071.
At year 18: Final balance = 2271000/[P/E10] + 59332 and R-squared equals 0.5936.

Curves from sequences beginning in 1923-1972
At year 22: Final balance = 2707800/[P/E10] + 74087 and R-squared equals 0.5292.
At year 26: Final balance = 2403900/[P/E10] + 147550 and R-squared equals 0.3623.
At year 30: Final balance = 2510800/[P/E10] + 208245 and R-squared equals 0.3198.

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 14. [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.

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 26. 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 »

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    202352    210493    269573
1872   14.5     6.90    183861    228709    268257
1873   15.3     6.54    181263    231620    247355
1874   13.9     7.19    181758    223124    274781
1875   13.6     7.35    170602    218486    256860
1876   13.3     7.52    186877    219191    237534
1877   10.6     9.43    210872    225197    263605
1878    9.7    10.31    191339    235636    249012
1879   10.7     9.35    174312    204927    224868
1880   15.3     6.54    166911    180879    219197
1881   18.5     5.41    137925    161448    212737
1882   15.7     6.37    160524    169636    207714
1883   15.3     6.54    154957    170035    225219
1884   14.4     6.94    148907    180452    239002
1885   13.1     7.63    155204    204509    238223
1886   16.7     5.99    136372    166984    193640
1887   17.5     5.71    133067    176254    207877
1888   15.4     6.49    146997    194692    234412
1889   15.8     6.33    159689    186014    221871
1890   17.2     5.81    142366    165092    188340
1891   15.4     6.49    165042    194653    227275
1892   19.0     5.26    158092    190345    206306
1893   17.7     5.65    158224    188724    212070
1894   15.7     6.37    152344    173796    222030
1895   16.5     6.06    166292    194161    213651
1896   16.6     6.02    180120    195224    203622
1897   17.0     5.88    171988    193264    191809
1898   19.2     5.21    143414    183217    200407
1899   22.9     4.37    147350    162142    174387
1900   18.7     5.35    159435    166294    157915
1901   21.0     4.76    145910    144811    140638
1902   22.3     4.48    138333    151312    131179
1903   20.3     4.93    139195    149708    124911
1904   15.9     6.29    143402    136176    147629
1905   18.5     5.41    122782    119244    148564
1906   20.1     4.98    125673    108951    136351
1907   17.2     5.81    125513    104723    155786
1908   11.9     8.40    119368    129407    190464
1909   14.8     6.76    102128    127240    175280
1910   14.5     6.90    100522    125802    202682
1911   14.0     7.14     93195    138636    244918
1912   13.8     7.25    101294    149088    229721
1913   13.1     7.63    115633    159290    213576
1914   11.6     8.62    120613    194323    185883
1915   10.4     9.62    139688    246777    193828
1916   12.5     8.00    136300    210016    213954
1917   11.0     9.09    148105    198579    206960
1918    6.6    15.15    204634    195746    301596
1919    6.1    16.39    254099    199579    347730
1920    6.0    16.67    242249    246792    295608

Code: Select all


1921    5.1    19.61    238000    248045    337774
1922    6.3    15.87    180560    278198    310149
1923    8.2    12.20    160190    279103    259568
1924    8.1    12.35    197199    236206    235286
1925    9.7    10.31    166742    227061    220097
1926   11.3     8.85    189016    210724    219004
1927   13.2     7.58    202607    188427    221314
1928   18.8     5.32    146610    146039    218949
1929   27.1     3.69    128528    124586    156026
1930   22.3     4.48    136759    142132    157482
1931   16.7     5.99    140533    165062    176529
1932    9.3    10.75    152669    228890    229176
1933    8.7    11.49    158619    198648    251940
1934   13.0     7.69    139516    154583    217409
1935   11.5     8.70    158377    169380    243677
1936   17.1     5.85    148557    148743    197184
1937   21.6     4.63    114013    144600    210896
1938   13.5     7.41    129056    181506    279864
1939   15.6     6.41    124384    178944    263660
1940   16.4     6.10    133420    176871    247449
1941   13.9     7.19    155483    226768    306042
1942   10.1     9.90    182216    280958    344662
1943   10.2     9.80    184606    272002    334912
1944   11.1     9.01    170184    238094    332949
1945   12.0     8.33    193070    260564    302782
1946   15.6     6.41    187399    229889    282659
1947   11.5     8.70    217193    267426    344854
1948   10.4     9.62    214887    300497    372333
1949   10.2     9.80    243639    283114    341183
1950   10.7     9.35    229602    282306    329402
1951   11.9     8.40    210858    271908    304420
1952   12.5     8.00    213662    264739    264801
1953   13.0     7.69    196792    237157    250420
1954   12.0     8.33    212953    248479    260315
1955   16.0     6.25    186433    208725    226521
1956   18.3     5.46    171697    171737    177248
1957   16.7     5.99    160957    169959    149979
1958   13.8     7.25    177607    186067    178743
1959   18.0     5.56    154659    167845    155580
1960   18.3     5.46    139995    144487    140519
1961   18.5     5.41    138034    121807    141474
1962   21.2     4.72    133057    127820    131403
1963   19.3     5.18    144442    133887    141493
1964   21.6     4.63    117513    114285    120993
1965   23.3     4.29     94458    109709    125887
1966   24.1     4.15    103159    106051    129216
1967   20.4     4.90    111099    117411    138000
1968   21.5     4.65     97946    103694    143756
1969   21.2     4.72     97992    112442    159407
1970   17.1     5.85    106026    129186    165943
1971   16.5     6.06    111192    130691    174618
1972   17.3     5.78     98980    137220    179949
1973   18.7     5.35    103608    146883    164046
1974   13.5     7.41    125170    160784    209774
1975    8.9    11.24    148101    197879    248439
1976   11.2     8.93    142842    187323    226846
1977   11.4     8.77    158463    176979    219015
1978    9.2    10.87    165324    215698    270766
1979    9.3    10.75    170372    213904    293079
1980    8.9    11.24    182215    220661    326413
1981    9.3    10.71    167466    207242    352971
1982    7.4    13.48    203740    255754    401101
1983    8.7    11.51    186415    255415    345546
1984    9.8    10.25    181101    267893    298440
1985    9.9    10.07    176322    300308    262404
1986   11.7     8.57    184482    289324    213510
1987   14.7     6.78    180165    243741    167809
1988   13.7     7.28    208554    232335    154643
1989   15.2     6.60    224762    196393    130720
1990   17.0     5.88    220623    162812    108368
1991   15.6     6.42    218240    150253    100009
1992   19.6     5.11    178076    118528     78892
1993   20.4     4.90    156425    104117    
1994   21.5     4.65    134445     89487    
1995   20.5     4.89    121415     80814    
1996   25.4     3.93     94422     62847    
1997   29.2     3.43     75990       
1998   33.8     2.96     60495       
1999   40.9     2.44     47449       
2000   44.7     2.24     40074       
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    316919    347758    460621
1872   14.5     6.90    290705    352289    466594
1873   15.3     6.54    289542    381523    444418
1874   13.9     7.19    290378    355560    412320
1875   13.6     7.35    281854    373328    440310
1876   13.3     7.52    287854    381252    459031
1877   10.6     9.43    347347    404607    482602
1878    9.7    10.31    304908    353582    403372
1879   10.7     9.35    297848    351286    410159
1880   15.3     6.54    290318    349546    378857
1881   18.5     5.41    247807    295575    332140
1882   15.7     6.37    240873    274791    351055
1883   15.3     6.54    265628    310144    341277
1884   14.4     6.94    287762    311891    325308
1885   13.1     7.63    284144    319294    316890
1886   16.7     5.99    220907    282217    308695
1887   17.5     5.71    242715    267079    287249
1888   15.4     6.49    254068    264998    251646
1889   15.8     6.33    249317    247440    240310
1890   17.2     5.81    240610    263185    228166
1891   15.4     6.49    250090    268977    224425
1892   19.0     5.26    215181    204338    221524
1893   17.7     5.65    210473    204408    254670
1894   15.7     6.37    242862    210547    263497
1895   16.5     6.06    229786    191725    285209
1896   16.6     6.02    193362    209625    308531
1897   17.0     5.88    186282    232086    319711
1898   19.2     5.21    173741    217434    350313
1899   22.9     4.37    145502    216448    382384
1900   18.7     5.35    171196    251971    388248
1901   21.0     4.76    175219    241374    323633
1902   22.3     4.48    164168    264495    253007
1903   20.3     4.93    185816    328268    257835
1904   15.9     6.29    217285    334802    341079
1905   18.5     5.41    204656    274401    285982
1906   20.1     4.98    219678    210137    323768
1907   17.2     5.81    275216    216165    376629
1908   11.9     8.40    293476    298979    358118
1909   14.8     6.76    235015    244934    333538
1910   14.5     6.90    193879    298720    333028
1911   14.0     7.14    192368    335167    311708
1912   13.8     7.25    234028    280320    279228
1913   13.1     7.63    222590    303111    293815
1914   11.6     8.62    286399    319292    331838
1915   10.4     9.62    337710    314074    368891
1916   12.5     8.00    256275    255277    382725
1917   11.0     9.09    281827    273183    342122
1918    6.6    15.15    336234    349445    387183
1919    6.1    16.39    323392    379836    406223
1920    6.0    16.67    294457    441465    442017

Code: Select all


1921    5.1    19.61    327415    410039    520042
1922    6.3    15.87    322335    357146    502296
1923    8.2    12.20    304872    326052    469071
1924    8.1    12.35    352753    353194    468219
1925    9.7    10.31    275639    349586    509863
1926   11.3     8.85    242655    341274    526210
1927   13.2     7.58    236689    340510    501714
1928   18.8     5.32    219222    290617    406584
1929   27.1     3.69    197883    288608    389501
1930   22.3     4.48    221485    341507    418940
1931   16.7     5.99    253961    374191    460736
1932    9.3    10.75    303812    425044    594380
1933    8.7    11.49    367448    495902    576250
1934   13.0     7.69    335222    411229    505625
1935   11.5     8.70    359038    442078    570073
1936   17.1     5.85    275868    385773    477995
1937   21.6     4.63    284622    330737    398575
1938   13.5     7.41    343319    422127    492548
1939   15.6     6.41    324640    418634    468690
1940   16.4     6.10    346032    428753    428854
1941   13.9     7.19    355628    428571    452540
1942   10.1     9.90    423777    494474    518026
1943   10.2     9.80    431879    483519    524745
1944   11.1     9.01    412544    412640    425882
1945   12.0     8.33    364885    385292    339999
1946   15.6     6.41    329814    345523    331922
1947   11.5     8.70    386088    419007    388388
1948   10.4     9.62    372421    384371    373814
1949   10.2     9.80    360265    317914    369243
1950   10.7     9.35    345092    331508    340800
1951   11.9     8.40    330376    306234    323630
1952   12.5     8.00    273298    265792    281393
1953   13.0     7.69    220982    256661    294508
1954   12.0     8.33    250068    257077    313234
1955   16.0     6.25    209968    221895    260807
1956   18.3     5.46    172380    182498    253004
1957   16.7     5.99    174194    199881    283367
1958   13.8     7.25    183753    223892    287596
1959   18.0     5.56    164418    193250    258205
1960   18.3     5.46    148767    206241    270463
1961   18.5     5.41    162335    230139    257030
1962   21.2     4.72    160107    205661    268326
1963   19.3     5.18    166305    222203    278977
1964   21.6     4.63    167738    219970    266382
1965   23.3     4.29    178467    199321    246663
1966   24.1     4.15    165982    216556    271843
1967   20.4     4.90    184384    231495    317183
1968   21.5     4.65    188520    228296    337707
1969   21.2     4.72    178033    220319    375244
1970   17.1     5.85    216505    271779    426232
1971   16.5     6.06    219234    300383    406381
1972   17.3     5.78    217917    322353    359110
1973   18.7     5.35    203010    345763    302121
1974   13.5     7.41    263329    412980    304764
1975    8.9    11.24    340398    460517    317055
1976   11.2     8.93    335562    373825    248819
1977   11.4     8.77    373022    325939    216946
1978    9.2    10.87    424643    313371    208581
1979    9.3    10.75    396500    272981    181697
1980    8.9    11.24    363632    242035    161099
1981    9.3    10.71    308419    205285    
1982    7.4    13.48    295997    197017    
1983    8.7    11.51    237900    158347    
1984    9.8    10.25    198643    132217    
1985    9.9    10.07    174657       
1986   11.7     8.57    142113       
1987   14.7     6.78    111694       
1988   13.7     7.28    102931       
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.
Post Reply