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.
HDBR50T2 Returns versus Earnings Yield
Moderator: hocus2004
Year, P/E10, 100E10/P, balance at year 10, balance at year 14, balance at year 18
CAUTION: 2003-2010 data are dummy values with heavy stock market losses.
More follows.
Have fun.
John R.
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
More follows.
Have fun.
John R.
Year, P/E10, 100E10/P, balance at year 22, balance at year 26, balance at year 30
CAUTION: 2003-2010 data are dummy values with heavy stock market losses.
Have fun.
John R.
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
Have fun.
John R.