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.
HDBR80 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 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
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 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
Have fun.
John R.