More on Rebalancing
Moderator: hocus2004
More on Rebalancing
I continue to look at what the data show about rebalancing. My question is this: Is rebalancing portfolio allocations a good idea? In my earlier study, Hobby Stocks and Rebalancing, the answer was NO! except under the most stressful conditions. Rebalancing took away far more from the upside than it gave back in the form of downside protection.
This time I took matters to an extreme. I investigated the rebalancing of mirror portfolios. I looked at both the distribution and accumulation phases.
This is what I mean by mirror portfolios: Portfolio A had 80% stocks and 20% Treasury Bills while Portfolio B had 20% stocks and 80% Treasury Bills.
I rebalanced each individual portfolio annually.
I allowed the two portfolios to grow independently. I compared this to what happens if the two individual portfolios are rebalanced as well.
The Portfolios
Portfolio A consisted of 80% stocks and 20% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
Portfolio B consisted of 20% stocks and 80% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
The Conditions
I started with an initial balance of $100000. I set the investment expenses at 0.20%.
I allocated 50% of the initial balance to Portfolio A and 50% to Portfolio B.
For the distribution phase, I withdrew 3%, 4% and 5% of the initial balance (plus inflation) annually from the individual portfolios in proportion to their balances.
For the accumulation phase, I deposited 3%, 4% and 5% of the initial balance (plus inflation) annually to the individual portfolios in proportion to their balances. The calculator treats deposits as negative withdrawals.
I recorded balances of the combined portfolio at year 30 when I rebalanced Portfolios A and B and when I let them grow separately.
Calculator Conditions
I used the Gummy 04 version of the Deluxe Calculator V1.1A08 dated January 28, 2005. This calculator includes a complete set of Gummy's data, which can be entered separately as if they were stocks and commercial paper.
Portfolio A appears as stock holdings and Portfolio B appears as if it were commercial paper.
Here are the key entries:
Portfolio A: Entered as stocks
Portfolio B: Entered as commercial paper
Portfolio A: 80% S&P500 stocks and 20% Treasury Bills
Portfolio B: 20% S&P500 stocks and 80% Treasury Bills
Stock allocation: 50%
Fixed Income Series: commercial paper
Front end/back end?: 50%
Inflation: CPI
Investment expenses: 0.20%
Rebalance? NO!, the basic condition, and YES for making comparisons.
Others: Gummy's Algorithms 1 and 2: NO. Remove gains? NO.
Others: Reinvest Dividends? Yes, 100%. Reinvest Interest? Yes, 100%.
The calculator automatically rebalances the holdings within a portfolio. It offers a choice as to whether to rebalance between the two portfolios.
I examined 30year historical sequences starting in 19211980. Gummy's data are for the years 19282000. I used Professor Shiller's S&P500 stock data prior to 1928. I used the stock returns of 2000 for the years 20012010. Be cautious about any conclusions based on sequences starting in years 19211927 and ending in 20012010. (Those 30year sequences start in 19711980.)
Be especially careful about what happens after 2000. The calculator holds separate return sequences for Portfolios A and B. Portfolio A freezes at the year 2000 stock return while Portfolio B freezes at the year 2000 return for commercial paper.
Dollar Allocations
I set the initial balance equal to $100000.
I allocated 50% of this initial balance to portfolio A. This is $50000. I put 80% of this into the S&P500 index and 20% into Treasury Bills.
I allocated 50% of this initial balance to portfolio B. This is $50000. I put 20% of this into the S&P500 index and 80% into Treasury Bills.
Portfolio A started with $40000 in the S&P500 index and $10000 in Treasury Bills.
Portfolio B started with $10000 in the S&P500 index and $40000 in Treasury Bills.
The combination of the two portfolios started out with $50000 in the S&P500 index and $50000 in Treasury Bills.
Tables for the distribution phase
I am including tables of the balances at year 30 with withdrawal rates of 3%, 4% and 5% of the initial balance (plus inflation). All balances are in terms of real dollars. That is, after adjusting for inflation.
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
[In making these calculations, I substituted zero for any negative balance. This prevents any big losses from distorting the results.]
The fourth table has a 1 whenever the money ran out by year 30 with rebalancing. The fifth table has a 1 whenever the money ran out by year 30 without rebalancing.
[These two tables turn out to be identical except in 1934, 1937, 1938 and 1965. At year 30, the rebalanced portfolios failed in 1934 and 1938, but not the portfolios that were allowed to grow independently. In year 20, the rebalanced portfolios failed in 1937 but not the portfolios that were allowed to grow independently. In contrast, in the 1965 sequence at year 20, the rebalanced portfolio combination still had a positive balance while the portfolios that had been allowed to grow independently were depleted.]
Tables for the accumulation phase
I am including tables of the balances at year 30 with annual deposits of 3%, 4% and 5% of the initial balance (plus inflation). That is, these annual deposits were $3000, $4000 and $5000 plus inflation. All balances are in terms of real dollars (i.e., after adjusting for inflation).
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
There was no need for the additional tables. There are no failures during accumulation.
Analysis
During the distribution phase, only a few conditions show a rebalancing bonus. Those with a bonus show only a small improvement. The sequences with a rebalancing bonus are those associated with high valuations and times of severe portfolio stress: a few years around 1929 and the entire decade of the 1960s.
Typically, there was a penalty for rebalancing. Typically, it was huge.
This is the same as we have seen before when looking at hobby stocks.
During the accumulation phase, all of the sequences favored leaving the two portfolios alone except for the years 19771980. This special behavior for the 19771980 sequences is probably an artifact of the calculator. These sequences end at year 30 in 20072010. The calculator returns for Portfolio A and Portfolio B have different dummy values in 20012010.
Conclusions
During distribution, the message remains unchanged. Except in times of severe portfolio stress, let the two portfolios grow independently.
This happens to be a time of severe portfolio stress. Today's valuations are higher than during the Great Depression and during the 1960s (and stagflation).
For those who are still in the accumulation phase, the message is simpler. Allow the two portfolios to grow independently.
Have fun.
John R.
This time I took matters to an extreme. I investigated the rebalancing of mirror portfolios. I looked at both the distribution and accumulation phases.
This is what I mean by mirror portfolios: Portfolio A had 80% stocks and 20% Treasury Bills while Portfolio B had 20% stocks and 80% Treasury Bills.
I rebalanced each individual portfolio annually.
I allowed the two portfolios to grow independently. I compared this to what happens if the two individual portfolios are rebalanced as well.
The Portfolios
Portfolio A consisted of 80% stocks and 20% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
Portfolio B consisted of 20% stocks and 80% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
The Conditions
I started with an initial balance of $100000. I set the investment expenses at 0.20%.
I allocated 50% of the initial balance to Portfolio A and 50% to Portfolio B.
For the distribution phase, I withdrew 3%, 4% and 5% of the initial balance (plus inflation) annually from the individual portfolios in proportion to their balances.
For the accumulation phase, I deposited 3%, 4% and 5% of the initial balance (plus inflation) annually to the individual portfolios in proportion to their balances. The calculator treats deposits as negative withdrawals.
I recorded balances of the combined portfolio at year 30 when I rebalanced Portfolios A and B and when I let them grow separately.
Calculator Conditions
I used the Gummy 04 version of the Deluxe Calculator V1.1A08 dated January 28, 2005. This calculator includes a complete set of Gummy's data, which can be entered separately as if they were stocks and commercial paper.
Portfolio A appears as stock holdings and Portfolio B appears as if it were commercial paper.
Here are the key entries:
Portfolio A: Entered as stocks
Portfolio B: Entered as commercial paper
Portfolio A: 80% S&P500 stocks and 20% Treasury Bills
Portfolio B: 20% S&P500 stocks and 80% Treasury Bills
Stock allocation: 50%
Fixed Income Series: commercial paper
Front end/back end?: 50%
Inflation: CPI
Investment expenses: 0.20%
Rebalance? NO!, the basic condition, and YES for making comparisons.
Others: Gummy's Algorithms 1 and 2: NO. Remove gains? NO.
Others: Reinvest Dividends? Yes, 100%. Reinvest Interest? Yes, 100%.
The calculator automatically rebalances the holdings within a portfolio. It offers a choice as to whether to rebalance between the two portfolios.
I examined 30year historical sequences starting in 19211980. Gummy's data are for the years 19282000. I used Professor Shiller's S&P500 stock data prior to 1928. I used the stock returns of 2000 for the years 20012010. Be cautious about any conclusions based on sequences starting in years 19211927 and ending in 20012010. (Those 30year sequences start in 19711980.)
Be especially careful about what happens after 2000. The calculator holds separate return sequences for Portfolios A and B. Portfolio A freezes at the year 2000 stock return while Portfolio B freezes at the year 2000 return for commercial paper.
Dollar Allocations
I set the initial balance equal to $100000.
I allocated 50% of this initial balance to portfolio A. This is $50000. I put 80% of this into the S&P500 index and 20% into Treasury Bills.
I allocated 50% of this initial balance to portfolio B. This is $50000. I put 20% of this into the S&P500 index and 80% into Treasury Bills.
Portfolio A started with $40000 in the S&P500 index and $10000 in Treasury Bills.
Portfolio B started with $10000 in the S&P500 index and $40000 in Treasury Bills.
The combination of the two portfolios started out with $50000 in the S&P500 index and $50000 in Treasury Bills.
Tables for the distribution phase
I am including tables of the balances at year 30 with withdrawal rates of 3%, 4% and 5% of the initial balance (plus inflation). All balances are in terms of real dollars. That is, after adjusting for inflation.
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
[In making these calculations, I substituted zero for any negative balance. This prevents any big losses from distorting the results.]
The fourth table has a 1 whenever the money ran out by year 30 with rebalancing. The fifth table has a 1 whenever the money ran out by year 30 without rebalancing.
[These two tables turn out to be identical except in 1934, 1937, 1938 and 1965. At year 30, the rebalanced portfolios failed in 1934 and 1938, but not the portfolios that were allowed to grow independently. In year 20, the rebalanced portfolios failed in 1937 but not the portfolios that were allowed to grow independently. In contrast, in the 1965 sequence at year 20, the rebalanced portfolio combination still had a positive balance while the portfolios that had been allowed to grow independently were depleted.]
Tables for the accumulation phase
I am including tables of the balances at year 30 with annual deposits of 3%, 4% and 5% of the initial balance (plus inflation). That is, these annual deposits were $3000, $4000 and $5000 plus inflation. All balances are in terms of real dollars (i.e., after adjusting for inflation).
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
There was no need for the additional tables. There are no failures during accumulation.
Analysis
During the distribution phase, only a few conditions show a rebalancing bonus. Those with a bonus show only a small improvement. The sequences with a rebalancing bonus are those associated with high valuations and times of severe portfolio stress: a few years around 1929 and the entire decade of the 1960s.
Typically, there was a penalty for rebalancing. Typically, it was huge.
This is the same as we have seen before when looking at hobby stocks.
During the accumulation phase, all of the sequences favored leaving the two portfolios alone except for the years 19771980. This special behavior for the 19771980 sequences is probably an artifact of the calculator. These sequences end at year 30 in 20072010. The calculator returns for Portfolio A and Portfolio B have different dummy values in 20012010.
Conclusions
During distribution, the message remains unchanged. Except in times of severe portfolio stress, let the two portfolios grow independently.
This happens to be a time of severe portfolio stress. Today's valuations are higher than during the Great Depression and during the 1960s (and stagflation).
For those who are still in the accumulation phase, the message is simpler. Allow the two portfolios to grow independently.
Have fun.
John R.
DISTRIBUTION: Without rebalancing Portfolios A and B
Year, Real Balances at year 30 for withdrawal rates of 3%, 4% and 5%
More follows.
John R.
Year, Real Balances at year 30 for withdrawal rates of 3%, 4% and 5%
Code: Select all
1921 334611 269638 204665
1922 306606 245842 185078
1923 263106 202970 142833
1924 256442 198910 141378
1925 277505 207691 137877
1926 262176 180110 98044
1927 228916 151086 73255
1928 130082 66610 3138
1929 90037 16495 (57460)
1930 96571 12070 (73041)
1931 124212 36091 (52381)
1932 279041 170441 61841
1933 281312 195443 109574
1934 191354 102307 13260
1935 242434 145502 48570
1936 152167 57526 (37309)
1937 84473 3214 (78933)
1938 212637 116038 19439
1939 145489 52242 (41250)
1940 143749 64261 (15265)
1941 204209 134128 64047
1942 317339 242076 166814
1943 323124 242663 162202
1944 223048 160294 97540
1945 145846 101286 56726
1946 144232 101241 58251
1947 232673 183325 133978
1948 228631 182916 137201
1949 218082 174644 131206
1950 194798 157251 119704
1951 185287 144621 103954
1952 148303 110673 73043
1953 143979 103741 63504
1954 168620 124459 80298
1955 106798 63717 20636
1956 91720 44345 (3030)
1957 103774 52830 1885
1958 130487 79250 28013
1959 88184 35529 (17168)
1960 90330 31760 (26908)
1961 90380 35268 (19904)
1962 74273 12794 (49009)
1963 95856 34249 (27468)
1964 73355 11190 (51351)
1965 57461 (1809) (61640)
1966 60758 (7532) (76567)
1967 96279 20620 (55442)
1968 99011 10058 (78932)
1969 103321 7179 (89845)
1970 160206 52956 (54652)
1971 155308 56860 (41844)
1972 144134 52550 (39016)
1973 128519 51024 (26483)
1974 171500 103762 36023
1975 260390 195177 129964
1976 191577 133534 75490
1977 159061 107921 56782
1978 185779 140520 95261
1979 193745 154736 115727
1980 185220 149547 113874
John R.
DISTRIBUTION: With rebalancing of Portfolios A and B
Year, Real Balances at year 30 for withdrawal rates of 3%, 4% and 5%
The rebalancing bonuses (penalties) are next.
John R.
Year, Real Balances at year 30 for withdrawal rates of 3%, 4% and 5%
Code: Select all
1921 261000 206608 152215
1922 232955 183353 133751
1923 208714 159047 109379
1924 204655 156540 108424
1925 220342 164003 107665
1926 211975 146241 80508
1927 188243 125292 62340
1928 120149 64021 7893
1929 84481 19609 (45544)
1930 86578 14587 (57825)
1931 100601 28584 (43688)
1932 174890 96258 17625
1933 176959 113288 49617
1934 126418 58868 (8691)
1935 155671 83699 11727
1936 103394 30171 (43321)
1937 61662 (6241) (74956)
1938 133934 59933 (14095)
1939 93747 20126 (53919)
1940 96356 31151 (34250)
1941 138908 81440 23972
1942 208781 148488 88195
1943 215264 150782 86300
1944 163315 108848 54382
1945 118965 76411 33857
1946 120921 80366 39812
1947 188448 143149 97851
1948 191132 147782 104432
1949 183542 141907 100272
1950 167496 131370 95245
1951 162379 123502 84625
1952 137631 100221 62811
1953 135208 95346 55484
1954 155233 112023 68813
1955 104045 61125 18204
1956 90952 44104 (2745)
1957 102515 52517 2520
1958 125429 75438 25448
1959 87853 36084 (15719)
1960 89709 32754 (24281)
1961 90297 36206 (17933)
1962 75265 15149 (45249)
1963 94449 34903 (24734)
1964 73786 13327 (47459)
1965 58991 737 (58023)
1966 61815 (4392) (71277)
1967 93032 21841 (49685)
1968 95459 12344 (70803)
1969 97871 9572 (79470)
1970 143421 48759 (46179)
1971 141447 52624 (36399)
1972 136071 50634 (34787)
1973 125625 50821 (23992)
1974 164297 99067 33837
1975 236754 174441 112128
1976 183105 125632 68159
1977 156790 105018 53246
1978 183199 136953 90707
1979 193431 153105 112780
1980 187498 150306 113113
John R.
DISTRIBUTION: Rebalancing bonus (penalty).
Year, Differences in the real balances at year 30 for withdrawal rates of 3%, 4% and 5%
Have fun.
John R.
Year, Differences in the real balances at year 30 for withdrawal rates of 3%, 4% and 5%
Code: Select all
1921 (73611) (63030) (52450)
1922 (73651) (62489) (51327)
1923 (54392) (43923) (33454)
1924 (51787) (42370) (32953)
1925 (57163) (43687) (30212)
1926 (50201) (33868) (17536)
1927 (40674) (25794) (10915)
1928 (9934) (2589) 4755
1929 (5556) 3114 0
1930 (9992) 2516 0
1931 (23612) (7507) 0
1932 (104151) (74184) (44216)
1933 (104353) (82155) (59957)
1934 (64936) (43438) (13260)
1935 (86763) (61803) (36843)
1936 (48773) (27355) 0
1937 (22811) (3214) 0
1938 (78703) (56105) (19439)
1939 (51742) (32116) 0
1940 (47393) (33110) 0
1941 (65301) (52688) (40075)
1942 (108558) (93588) (78618)
1943 (107861) (91881) (75902)
1944 (59733) (51446) (43158)
1945 (26880) (24875) (22869)
1946 (23310) (20875) (18440)
1947 (44225) (40176) (36127)
1948 (37500) (35134) (32769)
1949 (34540) (32737) (30934)
1950 (27302) (25881) (24459)
1951 (22908) (21119) (19330)
1952 (10672) (10452) (10232)
1953 (8770) (8395) (8020)
1954 (13386) (12435) (11484)
1955 (2754) (2593) (2432)
1956 (768) (241) 0
1957 (1259) (312) 634
1958 (5058) (3812) (2566)
1959 (331) 555 0
1960 (621) 994 0
1961 (83) 938 0
1962 993 2356 0
1963 (1407) 654 0
1964 431 2137 0
1965 1530 737 0
1966 1057 0 0
1967 (3247) 1221 0
1968 (3553) 2286 0
1969 (5450) 2393 0
1970 (16785) (4197) 0
1971 (13861) (4236) 0
1972 (8063) (1916) 0
1973 (2895) (203) 0
1974 (7203) (4695) (2186)
1975 (23636) (20736) (17836)
1976 (8472) (7902) (7332)
1977 (2270) (2903) (3536)
1978 (2580) (3567) (4554)
1979 (314) (1631) (2947)
1980 2278 758 (761)
John R.
DISTRIBUTION: With Rebalancing, Failed=1.
Year, Failures (negative balances) at year 30 for withdrawal rates of 3%, 4% and 5%
One more table about distribution follows.
John R.
Year, Failures (negative balances) at year 30 for withdrawal rates of 3%, 4% and 5%
Code: Select all
1921 0 0 0
1922 0 0 0
1923 0 0 0
1924 0 0 0
1925 0 0 0
1926 0 0 0
1927 0 0 0
1928 0 0 0
1929 0 0 1
1930 0 0 1
1931 0 0 1
1932 0 0 0
1933 0 0 0
1934 0 0 1
1935 0 0 0
1936 0 0 1
1937 0 1 1
1938 0 0 1
1939 0 0 1
1940 0 0 1
1941 0 0 0
1942 0 0 0
1943 0 0 0
1944 0 0 0
1945 0 0 0
1946 0 0 0
1947 0 0 0
1948 0 0 0
1949 0 0 0
1950 0 0 0
1951 0 0 0
1952 0 0 0
1953 0 0 0
1954 0 0 0
1955 0 0 0
1956 0 0 1
1957 0 0 0
1958 0 0 0
1959 0 0 1
1960 0 0 1
1961 0 0 1
1962 0 0 1
1963 0 0 1
1964 0 0 1
1965 0 0 1
1966 0 1 1
1967 0 0 1
1968 0 0 1
1969 0 0 1
1970 0 0 1
1971 0 0 1
1972 0 0 1
1973 0 0 1
1974 0 0 0
1975 0 0 0
1976 0 0 0
1977 0 0 0
1978 0 0 0
1979 0 0 0
1980 0 0 0
John R.
DISTRIBUTION: Without Rebalancing, Failed=1.
Year, Failures (negative balances) at year 30 for withdrawal rates of 3%, 4% and 5%
Accumulation tables follow.
John R.
Year, Failures (negative balances) at year 30 for withdrawal rates of 3%, 4% and 5%
Code: Select all
Year 3% 4% 5%
1921 0 0 0
1922 0 0 0
1923 0 0 0
1924 0 0 0
1925 0 0 0
1926 0 0 0
1927 0 0 0
1928 0 0 0
1929 0 0 1
1930 0 0 1
1931 0 0 1
1932 0 0 0
1933 0 0 0
1934 0 0 0
1935 0 0 0
1936 0 0 1
1937 0 0 1
1938 0 0 0
1939 0 0 1
1940 0 0 1
1941 0 0 0
1942 0 0 0
1943 0 0 0
1944 0 0 0
1945 0 0 0
1946 0 0 0
1947 0 0 0
1948 0 0 0
1949 0 0 0
1950 0 0 0
1951 0 0 0
1952 0 0 0
1953 0 0 0
1954 0 0 0
1955 0 0 0
1956 0 0 1
1957 0 0 0
1958 0 0 0
1959 0 0 1
1960 0 0 1
1961 0 0 1
1962 0 0 1
1963 0 0 1
1964 0 0 1
1965 0 1 1
1966 0 1 1
1967 0 0 1
1968 0 0 1
1969 0 0 1
1970 0 0 1
1971 0 0 1
1972 0 0 1
1973 0 0 1
1974 0 0 0
1975 0 0 0
1976 0 0 0
1977 0 0 0
1978 0 0 0
1979 0 0 0
1980 0 0 0
John R.
ACCUMULATION: Without rebalancing Portfolios A and B
Year, Real Balances at year 30 for deposits of $3000, $4000 and $5000
The initial balance is $100000. Deposits are made using dollar cost averaging (in real dollars).
Have fun.
John R.
Year, Real Balances at year 30 for deposits of $3000, $4000 and $5000
Code: Select all
1921 724448 789421 854394
1922 671190 731954 792718
1923 623923 684059 744195
1924 601636 659168 716700
1925 696389 766203 836017
1926 754573 836640 918706
1927 695901 773731 851562
1928 510914 574386 637858
1929 531288 604830 678371
1930 603574 688075 772575
1931 652941 741062 829184
1932 930642 1039242 1147842
1933 796524 882393 968262
1934 725636 814684 903731
1935 824024 920956 1017888
1936 720007 814648 909288
1937 572022 653281 734539
1938 792231 888831 985430
1939 704970 798217 891464
1940 620678 700166 779654
1941 624696 694777 764858
1942 768915 844177 919440
1943 805892 886353 966814
1944 599574 662328 725082
1945 413204 457764 502324
1946 402173 445163 488153
1947 528759 578107 627454
1948 502923 548638 594353
1949 478710 522148 565586
1950 420079 457626 495173
1951 429285 469951 510618
1952 374085 411715 449345
1953 385402 425639 465876
1954 433585 477746 521907
1955 365285 408367 451448
1956 375970 423345 470719
1957 409440 460384 511329
1958 437909 489146 540383
1959 404113 456767 509422
1960 441745 500315 558884
1961 421053 476166 531278
1962 443147 504626 566105
1963 465500 527107 588714
1964 446349 508514 570680
1965 413079 472349 531619
1966 470445 538726 607008
1967 550235 625894 701553
1968 632734 721688 810642
1969 680170 776312 872453
1970 803707 910957 1018207
1971 746002 844451 942900
1972 693636 785219 876803
1973 593490 670985 748480
1974 577934 645672 713411
1975 651668 716881 782094
1976 539837 597881 655924
1977 465895 517034 568174
1978 457335 502594 547853
1979 427797 466805 505814
1980 399257 434930 470602
Have fun.
John R.
ACCUMULATION: With the annual rebalancing of Portfolios A and B
Year, Real Balances at year 30 for deposits of $3000, $4000 and $5000
Next are the rebalancing bonus (penalty) numbers.
Have fun.
John R.
Year, Real Balances at year 30 for deposits of $3000, $4000 and $5000
Code: Select all
1921 587355 641747 696140
1922 530566 580168 629770
1923 506717 556384 606051
1924 493348 541464 589580
1925 558375 614714 671053
1926 606375 672108 737841
1927 565949 628900 691851
1928 456914 513042 569169
1929 473712 538584 603456
1930 518530 590522 662514
1931 532702 604718 676735
1932 646687 725320 803953
1933 558985 622656 686327
1934 531715 599265 666814
1935 587501 659472 731444
1936 542726 615948 689170
1937 469038 536933 604829
1938 577938 651939 725940
1939 535473 609094 682715
1940 487588 552794 617999
1941 483716 541184 598652
1942 570539 630832 691125
1943 602155 666637 731119
1944 490116 544583 599050
1945 374291 416845 459400
1946 364250 404805 445360
1947 460242 505541 550839
1948 451231 494581 537930
1949 433352 474987 516622
1950 384250 420376 456502
1951 395643 434520 473398
1952 362093 399503 436913
1953 374380 414242 454104
1954 414494 457704 500914
1955 361567 404488 447408
1956 372044 418893 465741
1957 402503 452501 502498
1958 425372 475363 525353
1959 398466 450235 502003
1960 431435 488389 545344
1961 414844 468935 523026
1962 435961 496077 556193
1963 451726 511272 570818
1964 436541 497000 557459
1965 408516 466770 525024
1966 459045 525250 591455
1967 520174 591365 662555
1968 594147 677261 760376
1969 627667 715966 804265
1970 711393 806055 900717
1971 674387 763210 852033
1972 648691 734127 819564
1973 574445 649249 724052
1974 555680 620910 686141
1975 610633 672946 735259
1976 527945 585419 642892
1977 467424 519197 570969
1978 460674 506920 553166
1979 435382 475707 516032
1980 410654 447847 485039
Have fun.
John R.
CCUMULATION: Rebalancing bonus (penalty).
Year, Differences in the real balances at year 30 for deposits of $3000, $4000 and $5000. Initial balance=$100000.
Read the comments about 19771980 sequences. The reason that these numbers are positive is likely to be no more than an artifact of the calculator.
Have fun.
John R.
Year, Differences in the real balances at year 30 for deposits of $3000, $4000 and $5000. Initial balance=$100000.
Code: Select all
1921 (137093) (147673) (158254)
1922 (140624) (151786) (162948)
1923 (117206) (127675) (138144)
1924 (108287) (117704) (127121)
1925 (138014) (151490) (164965)
1926 (148199) (164532) (180864)
1927 (129951) (144831) (159711)
1928 (54000) (61344) (68689)
1929 (57576) (66245) (74915)
1930 (85044) (97553) (110062)
1931 (120239) (136344) (152448)
1932 (283954) (313922) (343889)
1933 (237539) (259737) (281935)
1934 (193921) (215419) (236916)
1935 (236523) (261483) (286444)
1936 (177282) (198700) (220118)
1937 (102985) (116347) (129709)
1938 (214293) (236891) (259490)
1939 (169497) (189123) (208749)
1940 (133089) (147372) (161655)
1941 (140980) (153593) (166206)
1942 (198376) (213346) (228315)
1943 (203736) (219716) (235695)
1944 (109458) (117745) (126032)
1945 (38913) (40919) (42924)
1946 (37923) (40358) (42793)
1947 (68517) (72566) (76615)
1948 (51692) (54057) (56423)
1949 (45358) (47161) (48964)
1950 (35829) (37250) (38671)
1951 (33642) (35431) (37220)
1952 (11992) (12212) (12432)
1953 (11021) (11397) (11772)
1954 (19091) (20042) (20993)
1955 (3718) (3879) (4040)
1956 (3926) (4452) (4978)
1957 (6937) (7884) (8830)
1958 (12537) (13783) (15029)
1959 (5647) (6533) (7419)
1960 (10311) (11926) (13541)
1961 (6210) (7231) (8252)
1962 (7186) (8549) (9912)
1963 (13774) (15835) (17896)
1964 (9808) (11514) (13221)
1965 (4564) (5579) (6595)
1966 (11400) (13477) (15553)
1967 (30060) (34529) (38998)
1968 (38587) (44426) (50266)
1969 (52503) (60346) (68188)
1970 (92314) (104903) (117491)
1971 (71615) (81241) (90866)
1972 (44945) (51092) (57239)
1973 (19044) (21736) (24427)
1974 (22254) (24762) (27271)
1975 (41035) (43935) (46835)
1976 (11892) (12462) (13032)
1977 1529 2162 2795
1978 3339 4326 5312
1979 7585 8902 10218
1980 11397 12917 14437
Have fun.
John R.

 * Rookie
 Posts: 19
 Joined: Sun Dec 26, 2004 2:21 am
If you are willing to ask, I am confident that you are not the only person who was confused.Delawaredave wrote:Sorry in advance for the stupid question, but these posts with tables of numbers  what do they mean ?
I assume they are some input or output data set for a calculator  but I can't put the puzzle together.
Thanks for any comments !
The tables are attachments to the first post. They are described in these sections:
The calculator produced the numbers in the first two tables for distribution and in the first two tables for accumulation. Other tables were derived from these.JWR1945 wrote:More on Rebalancing  Tables for the distribution phase
I am including tables of the balances at year 30 with withdrawal rates of 3%, 4% and 5% of the initial balance (plus inflation). All balances are in terms of real dollars. That is, after adjusting for inflation.
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
[In making these calculations, I substituted zero for any negative balance. This prevents any big losses from distorting the results.]
The fourth table has a 1 whenever the money ran out by year 30 with rebalancing. The fifth table has a 1 whenever the money ran out by year 30 without rebalancing.
[These two tables turn out to be identical except in 1934, 1937, 1938 and 1965. At year 30, the rebalanced portfolios failed in 1934 and 1938, but not the portfolios that were allowed to grow independently. In year 20, the rebalanced portfolios failed in 1937 but not the portfolios that were allowed to grow independently. In contrast, in the 1965 sequence at year 20, the rebalanced portfolio combination still had a positive balance while the portfolios that had been allowed to grow independently were depleted.]
Tables for the accumulation phase
I am including tables of the balances at year 30 with annual deposits of 3%, 4% and 5% of the initial balance (plus inflation). That is, these annual deposits were $3000, $4000 and $5000 plus inflation. All balances are in terms of real dollars (i.e., after adjusting for inflation).
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
There was no need for the additional tables. There are no failures during accumulation.
...
Here is an example. I will walk you through a single entry on each of the tables. I have selected the year 1932 and a withdrawal rate of 4% (plus inflation) or a deposit rate of $4000 (plus inflation).
Example: 1932 with 4% withdrawals.
Table 1) Without rebalancing Portfolios A and B: $170441.
Table 2) With the rebalancing of Portfolios A and B: $96258.
Table 3) Rebalancing bonus (penalty): ($74184).
Notice that $96258$170441= $74184 or ($74184) with a rounding error of 1.
Table 4) and Table 5) There were positive balances with both approaches at year 30.
Example: 1932 with $4000 deposits.
Table 1) Without rebalancing Portfolios A and B: $1039242.
Table 2) With the rebalancing of Portfolios A and B: $725320.
Table 3) Rebalancing bonus (penalty): ($313922).
Notice that $725320$1039242= $313922 or ($313922).
Have fun.
John R.