## More on Rebalancing

Research on Safe Withdrawal Rates

Moderator: hocus2004

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

### 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 30-year historical sequences starting in 1921-1980. Gummy's data are for the years 1928-2000. I used Professor Shiller's S&P500 stock data prior to 1928. I used the stock returns of 2000 for the years 2001-2010. Be cautious about any conclusions based on sequences starting in years 1921-1927 and ending in 2001-2010. (Those 30-year sequences start in 1971-1980.)

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 1977-1980. This special behavior for the 1977-1980 sequences is probably an artifact of the calculator. These sequences end at year 30 in 2007-2010. The calculator returns for Portfolio A and Portfolio B have different dummy values in 2001-2010.

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.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
DISTRIBUTION: Without rebalancing Portfolios A and B

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``````
More follows.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
DISTRIBUTION: With rebalancing of Portfolios A and B

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``````
The rebalancing bonuses (penalties) are next.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
DISTRIBUTION: Rebalancing bonus (penalty).

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)
``````
Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
DISTRIBUTION: With Rebalancing, Failed=1.

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``````
One more table about distribution follows.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
DISTRIBUTION: Without Rebalancing, Failed=1.

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
``````
Accumulation tables follow.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
ACCUMULATION: Without rebalancing Portfolios A and B

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
``````
The initial balance is \$100000. Deposits are made using dollar cost averaging (in real dollars).

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
ACCUMULATION: With the annual rebalancing of Portfolios A and B

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``````
Next are the rebalancing bonus (penalty) numbers.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
CCUMULATION: Rebalancing bonus (penalty).

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``````
Read the comments about 1977-1980 sequences. The reason that these numbers are positive is likely to be no more than an artifact of the calculator.

Have fun.

John R.

Delawaredave
* Rookie
Posts: 19
Joined: Sun Dec 26, 2004 2:21 am
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.

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

If you are willing to ask, I am confident that you are not the only person who was confused.

The tables are attachments to the first post. They are described in these sections:
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.
...
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.

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.