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Algorithm G2

 
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JWR1945
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Joined: 26 Nov 2002
Posts: 1697
Location: Crestview, Florida

PostPosted: Sat Feb 26, 2005 5:28 pm    Post subject: Algorithm G2 Reply with quote

Gummy recently came up with an interesting withdrawal algorithm. It adjusts withdrawals according to the percentage earnings yield, 100E10/P or 100/ [P/E10], and an offset. I have included two algorithms of this sort in each of my Gummy series of calculators. Algorithm G1 makes an adjustment as a percentage of a portfolio's current balance. Algorithm G2 makes an adjustment as a percentage of a portfolio's initial balance.

My implementation is highly flexible.

I used my Gummy 02 calculator in this survey. It is similar to the Deluxe Calculator V1.1A08 except that it includes Algorithms G1 and G2.

Algorithm G2 appears in row 9, columns A through H. It has the form:

Initial Withdrawal Rate = (the contents of cell B9)*(Initial Balance)+(special inflation term G2)*G3*(100E10/P-G4)*(Initial Balance)

Gummy's Inflation Term G2 (0=none,1=PPI, 2=CPI) is in cell I24.
Gummy's Multiplier G3 is in cell F25. This term should a negative number whenever withdrawals are to increase as the percentage earnings yield increases.
Gummy's Offset G4 is in cell I25.

To use the algorithm, set Gummy Algorithm 2? Y=1 equal to 1 in cell F23.

General Procedure

I examined two portfolios. One one consists of 50% stocks and 50% commercial paper. The other consists of 80% stocks and 20% commercial paper.

I decided to apply the algorithm to match inflation according to the CPI. That is, I set term G2 = 2 in all cases.

I decided to look at slopes of 0.25 and 0.50. That is, I set G3 equal to (0.25), which is minus 0.25, and to (0.50), which is minus 0.50.

I set the offset equal to 2.5%. That is, I set G4 = 2.5.

By setting the offset to 2.5%, there is no adjustment when the earnings yield 100E10/P is 2.5%. That is, there is no adjustment when P/E10 equals 40.

When P/E10 equals 20, the percentage earnings yield is 5.0%. The withdrawal rate adjustment is (slope)*(5%-2.5%) in real dollars. This is (0.25)*(2.5%) or (0.50)*(2.5%) depending upon the choice of the slope term G3. These adjustments increase the withdrawal rate by 0.625% or 1.250%.

When P/E10 equals 10, the percentage earnings yield is 10%. The withdrawal rate adjustment is (slope)*(10%-2.5%) in real dollars. This is (0.25)*(7.5%) or (0.50)*(7.5%), which is an increase of 1.875% or 3.75%.

My final step was to adjust the amount in cell B9, the regular input for the withdrawal rate, in increments of 0.1% as high as I could without any failures in 30 years.

I started with initial balances of $100000. I set the expenses to 0.20%. I adjusted withdrawals (the term in cell B9) to match inflation according to the CPI. I rebalanced the portfolio annually.

I determined the five-year rolling averages of the amount withdrawn at years 5, 10, 15, 20, 25 and 30 for historical sequences starting in 1921-1980.

Tables

Tables with all of these outputs follow this post.

Observations

Using a slope of 0.25 (that is, setting G3 equal to minus 0.25) was consistently better than using a slope of 0.50.

With a slope of 0.50, the withdrawal algorithm over-corrected during the bubble years in the late 1990s. We see this in the low withdrawal amounts at years 25 and 30. (Be careful when looking at sequences that extend beyond 2002 because they include dummy data.)

With a slope of 0.50 and a portfolio with 50% stocks, the (five-year averages of the) withdrawal amounts generally stay above $2500 with a few exceptions beginning in year 20. With 80% stocks, this lower limit (generally) falls to $2300.

In both cases, the maximum (five-year averages of the) withdrawal amounts are close to $6000. Overall, a portfolio with 50% stocks seems to do better than a portfolio with 80% stocks.

With a slope of 0.25, the income floors were $3300 with 50% stocks and $3200 with 80% stocks. (There were exceptions.) The ceilings were close to $5000 in both cases. Once again, the portfolio with 50% stocks generally did better than the portfolio with 80% stocks.

I determined the balances at years 10, 20 and 30 for both 50% stocks and 80% stocks when the slope was 0.25.

When the portfolio had 50% stocks, there were 13 times that the balance fell below $40000. They occurred in 9 separate sequences. There were 4 times that the balance fell below $30000. They occurred in 3 separate sequences. There were 3 times that the balance fell below $20000. They occurred in 3 separate sequences.

When the portfolio had 80% stocks, there were 9 times that the balance fell below $40000. They occurred in 5 separate sequences. There were 6 times that the balance fell below $30000. They occurred in 3 separate sequences. There were 2 times that the balance fell below $20000. They occurred in 2 separate sequences.

Comments about the Algorithm

This turns out to be one of the better variable withdrawal rate algorithms.

The portfolio with 50% stocks and 50% commercial paper provided a better income stream. The portfolio with 80% stocks and 20% commercial paper provided balances that did not fall as much.

Have fun.

John R.


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JWR1945
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Joined: 26 Nov 2002
Posts: 1697
Location: Crestview, Florida

PostPosted: Sat Feb 26, 2005 5:31 pm    Post subject: Reply with quote

Conditions
1921-1980
$100000 initial balance
Gummy Algorithm 2 is set for Yes (cell F23 equals 1)
Gummy Inflation Term G2 is set for CPI (cell I24 equals 2)
Gummy's Multiplier G3 = (0.50) in cell F25
Gummy's Offset G4 is 2.50 in cell I25

Stocks = 50%
Commercial Paper = 50%
Withdrawal Rate in cell B9 was set at 1.3%.
There were no failures at 30 years with B9 set at 1.3%.
There was one failure at 30 years with B9 set at 1.4%.
Expenses = 0.20%
With Rebalancing

Five Year Rolling Averages
Year, At Year 5, At Year 10, At Year 15
Code:
1921 6213 3049 4820
1922 5392 3388 4234
1923 4696 3988 3819
1924 3853 4395 3714
1925 3283 4798 3444
1926 2993 4751 3533
1927 3311 4138 4028
1928 3892 3695 4202
1929 4248 3520 4400
1930 4661 3257 4609
1931 4648 3396 4527
1932 4072 3949 4439
1933 3702 4209 4437
1934 3542 4423 4460
1935 3308 4657 4567
1936 3404 4535 4720
1937 3900 4392 4620
1938 4163 4390 4456
1939 4408 4445 4303
1940 4627 4536 4002
1941 4573 4758 3755
1942 4482 4712 3611
1943 4448 4520 3571
1944 4504 4371 3290
1945 4586 4064 3210
1946 4779 3785 3218
1947 4737 3649 3175
1948 4559 3630 3001
1949 4416 3359 2909
1950 4128 3308 2825
1951 3831 3287 2682
1952 3631 3149 2685
1953 3591 2946 2629
1954 3329 2867 2654
1955 3221 2710 2747
1956 3203 2570 2907
1957 3085 2599 3000
1958 2901 2570 3092
1959 2781 2543 3309
1960 2669 2697 3832
1961 2550 2883 4107
1962 2559 2955 4377
1963 2517 3034 4920
1964 2515 3278 5231
1965 2660 3794 5222
1966 2844 4067 5395
1967 2944 4365 5876
1968 2869 4761 5838
1969 3268 5222 5844
1970 3809 5235 5725
1971 4087 5414 5495
1972 4250 5773 4723
1973 4726 5839 4307
1974 5261 5887 4079
1975 5297 5797 3731
1976 5457 5549 3489
1977 5932 4877 3338
1978 6013 4501 3171
1979 5954 4179 3010
1980 5835 3788 2943

Year, At Year 20, At Year 25, At Year 30
Code:
1921 3627 4740 4928
1922 4144 4628 4860
1923 4335 4564 4645
1924 4594 4636 4525
1925 4784 4699 4207
1926 4654 4840 3871
1927 4516 4746 3663
1928 4430 4500 3541
1929 4437 4293 3170
1930 4517 3978 3078
1931 4712 3690 3080
1932 4668 3545 3028
1933 4508 3552 2892
1934 4320 3212 2708
1935 4041 3174 2647
1936 3701 3096 2427
1937 3471 2925 2386
1938 3474 2784 2417
1939 3185 2672 2402
1940 3114 2568 2570
1941 3175 2532 2863
1942 3122 2648 3056
1943 2919 2594 3119
1944 2815 2587 3356
1945 2695 2729 3865
1946 2591 2931 4155
1947 2719 3137 4555
1948 2700 3238 5110
1949 2708 3486 5418
1950 2891 4032 5441
1951 3039 4263 5582
1952 3099 4518 6023
1953 3159 5036 6066
1954 3429 5366 6004
1955 3884 5304 5806
1956 4131 5456 5547
1957 4421 5930 4874
1958 4974 6003 4487
1959 5259 5885 4076
1960 5257 5750 3659
1961 5433 5519 3444
1962 5888 4815 3250
1963 5948 4405 3040
1964 5855 4030 2807
1965 5708 3597 2689
1966 5471 3373 2439
1967 4800 3228 2315
1968 4306 2939 2075
1969 4014 2786 1887
1970 3621 2722 1670
1971 3408 2486 1545
1972 3163 2258 1427
1973 2940 2076 1126
1974 2874 2015 1080
1975 2867 1898 979
1976 2591 1718 609
1977 2462 1734 271
1978 2366 1550 322
1979 2213 1340 320
1980 2017 1107 306

Have fun.

John R.


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JWR1945
***** Legend


Joined: 26 Nov 2002
Posts: 1697
Location: Crestview, Florida

PostPosted: Sat Feb 26, 2005 5:36 pm    Post subject: Reply with quote

Conditions
1921-1980
$100000 initial balance
Gummy Algorithm 2 is set for Yes (cell F23 equals 1)
Gummy Inflation Term G2 is set for CPI (cell I24 equals 2)
Gummy's Multiplier G3 = (0.25) in cell F25
Gummy's Offset G4 is 2.50 in cell I25

Stocks = 50%
Commercial Paper = 50%
Withdrawal Rate in cell B9 was set at 2.6%.
There were no failures at 30 years with B9 set at 2.6%.
There was one failure at 30 years with B9 set at 2.7%.
Expenses = 0.20%
With Rebalancing

Five Year Rolling Averages
Year, At Year 5, At Year 10, At Year 15
Code:
1921 5160 3638 4544
1922 4753 3810 4255
1923 4403 4099 4037
1924 3993 4302 3990
1925 3712 4492 3845
1926 3563 4451 3866
1927 3722 4144 4097
1928 3997 3906 4151
1929 4155 3795 4219
1930 4359 3664 4318
1931 4355 3736 4277
1932 4083 4024 4247
1933 3913 4159 4255
1934 3817 4241 4243
1935 3711 4362 4303
1936 3741 4281 4357
1937 3974 4199 4296
1938 4114 4210 4229
1939 4228 4231 4148
1940 4336 4275 4001
1941 4322 4398 3902
1942 4290 4389 3858
1943 4268 4292 3838
1944 4287 4214 3694
1945 4322 4060 3653
1946 4417 3928 3664
1947 4412 3893 3682
1948 4328 3893 3608
1949 4257 3759 3559
1950 4120 3746 3530
1951 3970 3725 3447
1952 3870 3650 3439
1953 3851 3549 3408
1954 3726 3515 3426
1955 3659 3414 3441
1956 3643 3337 3505
1957 3588 3356 3554
1958 3506 3353 3610
1959 3434 3321 3694
1960 3379 3397 3950
1961 3322 3488 4083
1962 3323 3515 4208
1963 3308 3559 4479
1964 3300 3671 4623
1965 3368 3920 4611
1966 3456 4052 4695
1967 3512 4204 4939
1968 3405 4331 4871
1969 3668 4620 4918
1970 3942 4631 4867
1971 4077 4719 4753
1972 4093 4835 4308
1973 4296 4872 4106
1974 4662 4965 4074
1975 4694 4940 3931
1976 4761 4807 3796
1977 4998 4479 3727
1978 5049 4313 3671
1979 5026 4164 3605
1980 4972 3979 3579

Year, At Year 20, At Year 25, At Year 30
Code:
1921 3991 4512 4591
1922 4230 4446 4548
1923 4292 4389 4423
1924 4413 4420 4369
1925 4487 4433 4200
1926 4396 4474 4009
1927 4318 4417 3901
1928 4247 4269 3803
1929 4221 4137 3575
1930 4257 3978 3526
1931 4353 3839 3533
1932 4345 3791 3540
1933 4278 3817 3501
1934 4163 3614 3363
1935 4036 3616 3357
1936 3845 3542 3201
1937 3717 3435 3153
1938 3742 3397 3211
1939 3592 3332 3191
1940 3563 3287 3282
1941 3626 3314 3478
1942 3633 3417 3622
1943 3531 3385 3645
1944 3471 3370 3745
1945 3407 3431 3986
1946 3365 3538 4134
1947 3482 3697 4386
1948 3485 3758 4664
1949 3484 3868 4800
1950 3585 4144 4817
1951 3635 4231 4866
1952 3648 4338 5068
1953 3672 4584 5083
1954 3806 4744 5056
1955 3995 4680 4924
1956 4101 4742 4782
1957 4245 4979 4452
1958 4526 5024 4276
1959 4643 4943 4041
1960 4639 4875 3834
1961 4725 4760 3727
1962 4943 4402 3618
1963 4976 4206 3523
1964 4921 4008 3391
1965 4843 3785 3323
1966 4723 3671 3194
1967 4397 3611 3149
1968 4105 3421 2989
1969 4004 3386 2933
1970 3820 3369 2853
1971 3716 3254 2798
1972 3529 3077 2662
1973 3423 2991 2514
1974 3481 3071 2622
1975 3517 3083 2624
1976 3358 2968 2382
1977 3305 2994 2204
1978 3299 2954 2247
1979 3252 2858 2238
1980 3182 2731 2218

Balances
Year, At Year 10, At Year 20, At Year 30
Code:
1921 208091 251451 222313
1922 163726 187165 202918
1923 149772 159609 178222
1924 188012 175136 183615
1925 154770 161911 192254
1926 171938 161211 178114
1927 178923 114421 157605
1928 120006 74302 91695
1929 93805 43623 39523
1930 96837 44565 34880
1931 94639 49280 41885
1932 95442 72897 95627
1933 94299 84086 117078
1934 75682 51770 64301
1935 89613 79062 101270
1936 75551 49858 40282
1937 47171 27898 3375
1938 55505 53986 56336
1939 48871 51090 40605
1940 51730 55403 43509
1941 65892 86998 90937
1942 88314 137559 152313
1943 92590 133880 161398
1944 84021 132331 125693
1945 95612 132465 93066
1946 96212 126261 94784
1947 136255 182918 159298
1948 144406 222358 169373
1949 167174 225482 165775
1950 162790 200766 155589
1951 153328 182774 145057
1952 158679 178493 122058
1953 147439 180880 125303
1954 164797 163761 139883
1955 139790 99307 90616
1956 126986 90993 72526
1957 121614 92107 85889
1958 141423 94387 102884
1959 119451 69658 63677
1960 107982 63203 63972
1961 105933 63489 58640
1962 99184 47369 45776
1963 110525 55440 56621
1964 86313 45392 34998
1965 62844 35688 19804
1966 64340 32694 15241
1967 69204 46836 37592
1968 58292 41006 38311
1969 53734 36944 32892
1970 56877 53162 68929
1971 58492 50821 68387
1972 50347 55105 63006
1973 50411 51758 53682
1974 68196 82809 86978
1975 95336 130590 132929
1976 87454 120272 90308
1977 101496 139775 83667
1978 117864 203535 97917
1979 128492 245961 90903
1980 146111 281133 85175

Have fun.

John R.


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JWR1945
***** Legend


Joined: 26 Nov 2002
Posts: 1697
Location: Crestview, Florida

PostPosted: Sat Feb 26, 2005 5:39 pm    Post subject: Reply with quote

Conditions
1921-1980
$100000 initial balance
Gummy Algorithm 2 is set for Yes (cell F23 equals 1)
Gummy Inflation Term G2 is set for CPI (cell I24 equals 2)
Gummy's Multiplier G3 = (0.50) in cell F25
Gummy's Offset G4 is 2.50 in cell I25

Stocks = 80%
Commercial Paper = 20%
Withdrawal Rate in cell B9 was set at 1.1%.
There were no failures at 30 years with B9 set at 1.1%.
There was one failure at 30 years with B9 set at 1.2%.
Expenses = 0.20%
With Rebalancing

Five Year Rolling Averages
Year, At Year 5, At Year 10, At Year 15
Code:
1921 6031 2962 4699
1922 5217 3299 4126
1923 4517 3857 3695
1924 3691 4250 3603
1925 3121 4616 3310
1926 2821 4546 3371
1927 3132 3935 3851
1928 3688 3481 3996
1929 4024 3291 4176
1930 4436 3039 4395
1931 4432 3197 4335
1932 3894 3797 4308
1933 3547 4067 4334
1934 3359 4244 4311
1935 3139 4490 4437
1936 3208 4346 4552
1937 3689 4193 4435
1938 3968 4218 4313
1939 4208 4268 4154
1940 4428 4362 3864
1941 4386 4599 3666
1942 4313 4577 3591
1943 4274 4384 3545
1944 4322 4228 3249
1945 4398 3919 3161
1946 4580 3632 3142
1947 4553 3544 3177
1948 4384 3545 3033
1949 4246 3282 2941
1950 3961 3239 2860
1951 3658 3187 2672
1952 3458 3037 2649
1953 3419 2832 2582
1954 3166 2764 2618
1955 3039 2566 2640
1956 3012 2411 2765
1957 2896 2443 2855
1958 2725 2431 2962
1959 2589 2375 3140
1960 2480 2526 3656
1961 2363 2708 3924
1962 2367 2767 4182
1963 2332 2852 4725
1964 2321 3084 5025
1965 2460 3590 5011
1966 2640 3859 5183
1967 2745 4161 5669
1968 2669 4558 5638
1969 3063 5008 5631
1970 3611 5029 5520
1971 3885 5208 5289
1972 4052 5574 4523
1973 4527 5638 4107
1974 5056 5685 3889
1975 5111 5618 3588
1976 5257 5351 3316
1977 5728 4680 3164
1978 5817 4325 3034
1979 5757 4006 2882
1980 5637 3620 2820

Year, At Year 20, At Year 25, At Year 30
Code:
1921 3603 4727 4999
1922 4098 4630 4949
1923 4231 4523 4698
1924 4492 4608 4622
1925 4652 4635 4279
1926 4503 4736 3907
1927 4366 4639 3708
1928 4250 4353 3487
1929 4229 4101 3007
1930 4321 3802 2941
1931 4540 3561 3020
1932 4570 3578 3231
1933 4459 3686 3257
1934 4214 3222 2849
1935 3978 3271 2908
1936 3584 3058 2480
1937 3321 2816 2325
1938 3411 2819 2564
1939 3109 2676 2496
1940 3057 2592 2674
1941 3201 2693 3106
1942 3252 2965 3453
1943 3032 2867 3449
1944 2890 2794 3581
1945 2746 2877 4004
1946 2604 2999 4205
1947 2854 3327 4704
1948 2868 3450 5242
1949 2865 3656 5499
1950 3029 4154 5499
1951 3081 4284 5572
1952 3091 4484 5970
1953 3131 4966 5993
1954 3397 5284 5939
1955 3768 5165 5683
1956 3979 5293 5398
1957 4264 5764 4731
1958 4820 5847 4372
1959 5072 5703 3917
1960 5068 5566 3502
1961 5243 5334 3287
1962 5688 4622 3073
1963 5751 4221 2877
1964 5650 3832 2621
1965 5499 3390 2487
1966 5258 3161 2227
1967 4594 3030 2127
1968 4106 2740 1875
1969 3801 2574 1677
1970 3425 2537 1521
1971 3212 2302 1403
1972 2963 2056 1226
1973 2740 1877 926
1974 2705 1900 1020
1975 2773 1967 1069
1976 2451 1702 536
1977 2329 1730 157
1978 2309 1671 225
1979 2199 1447 186
1980 2055 1162 139

Have fun.

John R.


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JWR1945
***** Legend


Joined: 26 Nov 2002
Posts: 1697
Location: Crestview, Florida

PostPosted: Sat Feb 26, 2005 5:43 pm    Post subject: Reply with quote

Conditions
1921-1980
$100000 initial balance
Gummy Algorithm 2 is set for Yes (cell F23 equals 1)
Gummy Inflation Term G2 is set for CPI (cell I24 equals 2)
Gummy's Multiplier G3 = (0.25) in cell F25
Gummy's Offset G4 is 2.50 in cell I25

Stocks = 80%
Commercial Paper = 20%
Withdrawal Rate in cell B9 was set at 2.5%.
There were no failures at 30 years with B9 set at 2.5%.
There was one failure at 30 years with B9 set at 2.6%.
Expenses = 0.20%
With Rebalancing

Five Year Rolling Averages
Year, At Year 5, At Year 10, At Year 15
Code:
1921 5078 3653 4522
1922 4678 3822 4246
1923 4324 4067 4012
1924 3931 4256 3976
1925 3650 4409 3808
1926 3490 4346 3801
1927 3643 4041 4017
1928 3892 3791 4042
1929 4031 3666 4093
1930 4234 3545 4202
1931 4238 3637 4183
1932 4004 3970 4213
1933 3858 4116 4249
1934 3733 4161 4192
1935 3641 4294 4270
1936 3644 4191 4287
1937 3863 4098 4209
1938 4019 4137 4183
1939 4128 4153 4098
1940 4237 4200 3962
1941 4235 4339 3913
1942 4220 4353 3936
1943 4193 4254 3909
1944 4205 4170 3750
1945 4234 4014 3702
1946 4317 3875 3686
1947 4327 3887 3782
1948 4253 3908 3738
1949 4186 3780 3688
1950 4053 3775 3661
1951 3897 3724 3532
1952 3796 3635 3498
1953 3778 3532 3455
1954 3663 3509 3484
1955 3576 3368 3428
1956 3551 3275 3459
1957 3499 3298 3505
1958 3430 3311 3576
1959 3341 3251 3622
1960 3289 3324 3871
1961 3235 3410 3998
1962 3229 3426 4111
1963 3222 3476 4383
1964 3207 3575 4515
1965 3268 3816 4500
1966 3352 3942 4581
1967 3413 4099 4830
1968 3305 4228 4771
1969 3563 4505 4803
1970 3843 4523 4759
1971 3975 4611 4645
1972 3996 4736 4208
1973 4197 4772 4006
1974 4557 4861 3982
1975 4607 4859 3887
1976 4661 4708 3722
1977 4893 4380 3653
1978 4953 4237 3634
1979 4928 4091 3576
1980 4873 3910 3556

Year, At Year 20, At Year 25, At Year 30
Code:
1921 4070 4601 4768
1922 4283 4548 4737
1923 4285 4446 4574
1924 4408 4487 4558
1925 4452 4464 4363
1926 4342 4464 4134
1927 4264 4404 4033
1928 4164 4217 3839
1929 4111 4040 3504
1930 4158 3898 3483
1931 4278 3807 3569
1932 4344 3920 3836
1933 4325 4043 3952
1934 4152 3716 3590
1935 4068 3803 3703
1936 3822 3595 3341
1937 3663 3420 3183
1938 3775 3527 3449
1939 3613 3432 3378
1940 3604 3409 3483
1941 3752 3574 3820
1942 3861 3830 4115
1943 3740 3752 4068
1944 3641 3669 4063
1945 3553 3673 4217
1946 3475 3701 4279
1947 3713 3981 4630
1948 3748 4063 4891
1949 3734 4130 4975
1950 3815 4357 4969
1951 3769 4345 4949
1952 3734 4398 5109
1953 3737 4608 5104
1954 3868 4758 5085
1955 3974 4637 4895
1956 4045 4675 4727
1957 4184 4910 4403
1958 4469 4964 4255
1959 4554 4858 3976
1960 4548 4788 3769
1961 4632 4672 3663
1962 4841 4305 3534
1963 4878 4118 3454
1964 4814 3906 3299
1965 4731 3674 3214
1966 4607 3555 3077
1967 4288 3508 3056
1968 4005 3321 2890
1969 3888 3271 2821
1970 3721 3282 2803
1971 3618 3168 2758
1972 3429 2975 2560
1973 3323 2893 2413
1974 3412 3060 2671
1975 3523 3257 2818
1976 3318 3058 2413
1977 3272 3096 2192
1978 3343 3180 2251
1979 3338 3067 2205
1980 3320 2885 2152

Balances
Year, At Year 10, At Year 20, At Year 30
Code:
1921 278085 351276 470344
1922 183246 251801 445850
1923 152106 209923 378315
1924 213722 244125 392588
1925 160673 220753 423969
1926 187922 224729 398089
1927 206392 150454 351327
1928 112208 87082 182720
1929 77954 39869 64542
1930 85757 48161 80266
1931 92454 75426 145006
1932 115882 165367 412442
1933 125035 200369 459348
1934 92986 114667 281271
1935 120031 195954 414417
1936 95550 122054 205692
1937 51059 66224 81556
1938 72990 142023 272882
1939 63325 145938 222065
1940 69980 155844 204590
1941 99634 226358 308882
1942 144406 362544 479468
1943 148381 327226 492032
1944 127235 317258 335415
1945 151456 309138 218624
1946 143171 256718 201553
1947 214352 365483 335060
1948 221489 451339 335680
1949 272992 451567 329556
1950 255567 360209 293574
1951 223707 302808 258486
1952 229518 288742 197551
1953 203060 290401 206751
1954 236942 241769 236071
1955 186009 120949 140790
1956 159868 110495 109158
1957 146665 112523 133926
1958 180343 113832 160171
1959 139603 76119 90587
1960 118750 69177 92986
1961 115791 69784 81943
1962 105759 44923 60426
1963 123804 57286 80921
1964 84246 42361 42345
1965 53445 28639 15388
1966 56963 23949 4598
1967 65524 45144 46869
1968 50123 33549 37457
1969 45626 28609 27920
1970 53298 57204 115585
1971 55145 52929 109962
1972 42091 55340 83413
1973 41113 46894 56204
1974 67829 106634 125699
1975 109370 196047 208084
1976 93820 170721 116632
1977 112631 202050 96372
1978 137158 335498 112469
1979 150140 421305 94230
1980 174007 482836 80054

Have fun.

John R.


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