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.
HDBR80T2 Returns versus Earnings Yield
Moderator: hocus2004
HDBR80T2
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.
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
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 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
Have fun.
John R.