Saturday, October 25, 2008

Social Security, Part II

To read this, I suggest reading my proposal for funding Social Security
which precedes this in the BLOG. (egb)


This is a followup to the original posting. I have heard many times
that if someone had invested in the stockmarket he would have done much
better than the Social Security interest rate of 1.23%. I heard
something to the effect that "no 10 year period ever did worse than
1.23%. It's hard to propose an alternative to the current scheme based
on hearsay so I searched around and found daily Dow Jones records for
all trading days between Oct 1, 1928 and Oct 1, 2008.

I wrote a program that created three accounts: a cash account that
simply accumulated what was deposited without interest; a Social
Security (SS) account that accumuates deposits and grows at the SS
rate of 1.23%; and a dollar cost averaging account that grows
and shrinks at the rate of the Dow Jones averages.

The program is nothing more than you could do with pencil and paper,
but it is a lot faster. Assuming 'A' is the amount deposited in
each account per month:

          DJ   CASH       INTR                DCA
  DATE   CLOSE ACCT        ACCT               ACCT
               (x)        (y)                (z)

  month 1  w1  x = A     y = A                z = A
  month 2  w2  x = x+A   y = 1.0123 * y + A   z = (w2/w1) * z + A
  month 3  w3  x = x+A   y = 1.0123 * y + A   z = (w3/w2) * z + A

  ...

The program shows that there is no 30 year period where dollar cost
averaging did not do better than SS. Here are the results of analyzing
all dates using periods of from 1 to 60 years:

  YEARS INTR DCA
   1     341 609
   2
    296 641
   3
    262 663
   4     228 686
   5     199 703
   6     167 723
   7     159 719
   8     144 721
   9     135 719
  10     121 721
  11     118 712
  12     117 701
  13     105 700
  14      94 699
  15      88 694
  16      79 691
  17      76 682
  18      69 677
  19      63 670
  20      60 661
  21      52 658
  22      50 648
  23      42 644
  24      33 641
  25      23 638
  26      13 637
  27       9 629
  28       6 620
  29       3 611
  30       0 601
  31       0 589
  32       0 578
  33       0 566
  34       0 554
  35       0 542
  36       0 529
  37       0 518
  38       0 506
  39       0 494
  40       0 482
  41       0 469
  42       0 457
  43       0 446
  44       0 434
  45       0 422
  46       0 410
  47       0 397
  48       0 385
  49       0 374
  50       0 362
  51       0 350
  52       0 338
  53       0 325
  54       0 314
  55       0 302
  56       0 290
  57       0 278
  58       0 265
  59       0 253
  60       0 242


To read this table, the first column represents the total length
of time for the investment. The second column ("INTR") is the SS
Interest account accruing at 1.23% per year. The third column
is the Dollar Cost averaging account that follows the Dow Jones average.

Any line can be read as follows (choose 22, for example):

  Of all of the 22 year spans within Oct 1, 1928 and Oct 1,2008,
  50 of them would have shown a greater gain for a SS account
  than Dollar Cost Averaging, and 648 would have shown a greater
  gain for Dollar Cost Averaging than SS. There are a total of

  50 + 648 = 698 22-year spans each starting at the beginning
  of a month.

The results suggest that the risk of this plan is very low over a
30 year investment plan.

Using the example in the Heritage paper of a person starting out at age
21 and collecting at 67 (46 years) my program shows that the
worst 4 periods that person could have started investing in the time
from 1928 to 1962 [1962 + 46 = 2008 <- the present] are:   CASH = cash account, no interest   INT = interest account   DCA = dollar cost average of DJ close value. START    PERIOD   DJ
YEAR     (yrs)   CLOSE  CASH     INT       DCA    Difference
                (END)  (0.0%)   (1.23%)
------------------------------------------------------------------
1936/07/01 46    803.27 55300.00 74356.11 142633.01 68276.90
1936/06/01 46    814.97 55300.00 74356.11 145142.28 70786.18
1936/08/03 46    822.11 55300.00 74356.11 145559.27 71203.16
1936/03/02 46    828.39 55300.00 74356.11 148855.72 74499.61

and the best 4 periods are:

1953/06/01 46  10596.26 55300.00 74356.11 635346.00 560989.89
1953/12/01 46  10998.39 55300.00 74356.11 635604.09 561247.98
1953/09/01 46  10937.88 55300.00 74356.11 644034.34 569678.23
1954/01/04 46  11357.51 55300.00 74356.11 652417.48 578061.38
1953/07/01 46 11066.42 55300.00 74356.11 659513.43 585157.32


The program also showed that if an interest rate of 3.64% were
yielded in Social Security, then an Interest account would have equaled
the worst starting period (1936/07/01). That indicates that the worst
the DJ has done in ANY 46 year period since October 1928 was 3.64%
annally. All of these calculations are done without adjusting for
inflation. The results are what an investor would see, not what
he could buy.


Ed

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