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Suppose you have a hedge fund and suppose you open a
"model account" with something like $1000.00, just to provide
an actual "real money" track record showing precisely what an
investor's account has done over the life of the fund.
If your hedge fund is wildly successful, the model account will
grow to a tremendous equity and the taxes on those profits would
be immense (it is feverishly hoped).
How do you pay the taxes on the model account? You certainly
don't want to withdraw funds from the model account to pay its
taxes; that'd ruin the very purpose of the model account.
I explored a wacky scheme that I will call Big Brother / Little Brother.
Perhaps some omega-list readers may enjoy seeing its operation.
If not, I apologize for boring you.
The idea is this: you open TWO accounts. The Little Brother
account is the Model Account and is opened for $1000.00. You
never withdraw funds from this account, never ever ever, so it
shows the exact real-money track record that investors received.
The Big Brother account is opened for 100X more initial money
(i.e. $100K). It pays taxes for BOTH itself AND for its little brother.
Naturally, Little Brother's equity will grow faster than Big Brother's:
BB is paying taxes and LB isn't. So, eventually, LB will catch up
to BB and overtake BB. But if that happens a long loooong time
after the fund begins, giving you a loooong unbroken track record
in the Model Account, it is probably good enough. If it gives you
a (plug in your favorite number here) 25 year track record, you
are probably happy.
So I fired up the LINUX box and ran the program AWK to see
where these "overtake" points might occur.
Not surprisingly, they are *strongly* dependent upon the taxation
rate, and the hedge fund's Compound Annual Growth Rate ("CAGR")
after deducting fees and performance bonuses.
Just as your intuition would predict, the computer results said:
* The lower the taxes, the longer it takes LB to overtake BB.
* The higher the profits (CAGR), the less time it takes LB to overtake.
Here is some of the output. In every case, BB was funded with
$100k and LB was funded with $1k. Taxation rates and compound
annual growth rates were varied.
Conculsion? 100X seems like a good ratio between BB and LB,
giving you at least a 15 year track record before LB overtakes BB.
UNLESS you hit very large (after fees) profit percentages, in which
case you might want to use 1000X.
tax 30% cagr 35% overtake in 50 yrs $ 2434191022
tax 35% cagr 35% overtake in 43 yrs $ 297864178
tax 40% cagr 35% overtake in 37 yrs $ 49205728
tax 45% cagr 35% overtake in 33 yrs $ 14814281
tax 50% cagr 35% overtake in 30 yrs $ 6021148
tax 55% cagr 35% overtake in 27 yrs $ 2447248
tax 60% cagr 35% overtake in 25 yrs $ 1342797
tax 65% cagr 35% overtake in 23 yrs $ 736789
tax 30% cagr 40% overtake in 45 yrs $ 2689264815
tax 35% cagr 40% overtake in 39 yrs $ 357162090
tax 40% cagr 40% overtake in 34 yrs $ 66408730
tax 45% cagr 40% overtake in 30 yrs $ 17286737
tax 50% cagr 40% overtake in 27 yrs $ 6299831
tax 55% cagr 40% overtake in 24 yrs $ 2295857
tax 60% cagr 40% overtake in 22 yrs $ 1171356
tax 65% cagr 40% overtake in 21 yrs $ 836683
tax 30% cagr 45% overtake in 42 yrs $ 4131312924
tax 35% cagr 45% overtake in 36 yrs $ 444508508
tax 40% cagr 45% overtake in 31 yrs $ 69348978
tax 45% cagr 45% overtake in 28 yrs $ 22747625
tax 50% cagr 45% overtake in 25 yrs $ 7461602
tax 55% cagr 45% overtake in 22 yrs $ 2447530
tax 60% cagr 45% overtake in 21 yrs $ 1687952
tax 65% cagr 45% overtake in 19 yrs $ 802831
tax 30% cagr 50% overtake in 39 yrs $ 4914369920
tax 35% cagr 50% overtake in 33 yrs $ 431439883
tax 40% cagr 50% overtake in 29 yrs $ 85222693
tax 45% cagr 50% overtake in 26 yrs $ 25251168
tax 50% cagr 50% overtake in 23 yrs $ 7481828
tax 55% cagr 50% overtake in 21 yrs $ 3325257
tax 60% cagr 50% overtake in 19 yrs $ 1477892
tax 65% cagr 50% overtake in 18 yrs $ 985261
tax 30% cagr 55% overtake in 36 yrs $ 4587852385
tax 35% cagr 55% overtake in 31 yrs $ 512803458
tax 40% cagr 55% overtake in 27 yrs $ 88843192
tax 45% cagr 55% overtake in 24 yrs $ 23857727
tax 50% cagr 55% overtake in 22 yrs $ 9930375
tax 55% cagr 55% overtake in 20 yrs $ 4133351
tax 60% cagr 55% overtake in 18 yrs $ 1720437
tax 65% cagr 55% overtake in 16 yrs $ 716103
tax 30% cagr 60% overtake in 34 yrs $ 5444517871
tax 35% cagr 60% overtake in 29 yrs $ 519229686
tax 40% cagr 60% overtake in 26 yrs $ 126765060
tax 45% cagr 60% overtake in 23 yrs $ 30948501
tax 50% cagr 60% overtake in 20 yrs $ 7555786
tax 55% cagr 60% overtake in 18 yrs $ 2951479
tax 60% cagr 60% overtake in 17 yrs $ 1844674
tax 65% cagr 60% overtake in 16 yrs $ 1152922
tax 30% cagr 65% overtake in 33 yrs $ 9109325374
tax 35% cagr 65% overtake in 28 yrs $ 744846007
tax 40% cagr 65% overtake in 24 yrs $ 100491821
tax 45% cagr 65% overtake in 22 yrs $ 36911596
tax 50% cagr 65% overtake in 19 yrs $ 8216957
tax 55% cagr 65% overtake in 18 yrs $ 4979974
tax 60% cagr 65% overtake in 16 yrs $ 1829191
tax 65% cagr 65% overtake in 15 yrs $ 1108601
tax 30% cagr 70% overtake in 31 yrs $ 8193465726
tax 35% cagr 70% overtake in 27 yrs $ 981006660
tax 40% cagr 70% overtake in 23 yrs $ 117456288
tax 45% cagr 70% overtake in 21 yrs $ 40642314
tax 50% cagr 70% overtake in 19 yrs $ 14063084
tax 55% cagr 70% overtake in 17 yrs $ 4866119
tax 60% cagr 70% overtake in 15 yrs $ 1683778
tax 65% cagr 70% overtake in 14 yrs $ 990458
tax 30% cagr 75% overtake in 30 yrs $ 11171292210
tax 35% cagr 75% overtake in 26 yrs $ 1191108207
tax 40% cagr 75% overtake in 22 yrs $ 126998626
tax 45% cagr 75% overtake in 20 yrs $ 41468939
tax 50% cagr 75% overtake in 18 yrs $ 13540878
tax 55% cagr 75% overtake in 16 yrs $ 4421511
tax 60% cagr 75% overtake in 15 yrs $ 2526578
tax 65% cagr 75% overtake in 14 yrs $ 1443759
tax 30% cagr 80% overtake in 29 yrs $ 14048506052
tax 35% cagr 80% overtake in 25 yrs $ 1338258845
tax 40% cagr 80% overtake in 22 yrs $ 229468252
tax 45% cagr 80% overtake in 19 yrs $ 39346408
tax 50% cagr 80% overtake in 17 yrs $ 12143953
tax 55% cagr 80% overtake in 15 yrs $ 3748134
tax 60% cagr 80% overtake in 14 yrs $ 2082296
tax 65% cagr 80% overtake in 13 yrs $ 1156831
tax 30% cagr 85% overtake in 28 yrs $ 16354477245
tax 35% cagr 85% overtake in 24 yrs $ 1396206814
tax 40% cagr 85% overtake in 21 yrs $ 220513188
tax 45% cagr 85% overtake in 18 yrs $ 34827266
tax 50% cagr 85% overtake in 17 yrs $ 18825549
tax 55% cagr 85% overtake in 15 yrs $ 5500526
tax 60% cagr 85% overtake in 14 yrs $ 2973257
tax 65% cagr 85% overtake in 13 yrs $ 1607166
tax 30% cagr 90% overtake in 27 yrs $ 17684534181
tax 35% cagr 90% overtake in 23 yrs $ 1356998042
tax 40% cagr 90% overtake in 20 yrs $ 197841966
tax 45% cagr 90% overtake in 18 yrs $ 54803869
tax 50% cagr 90% overtake in 16 yrs $ 15181127
tax 55% cagr 90% overtake in 14 yrs $ 4205298
tax 60% cagr 90% overtake in 13 yrs $ 2213315
tax 65% cagr 90% overtake in 12 yrs $ 1164903
tax 30% cagr 95% overtake in 26 yrs $ 17818259684
tax 35% cagr 95% overtake in 22 yrs $ 1232329482
tax 40% cagr 95% overtake in 20 yrs $ 324084019
tax 45% cagr 95% overtake in 17 yrs $ 43707280
tax 50% cagr 95% overtake in 16 yrs $ 22413990
tax 55% cagr 95% overtake in 14 yrs $ 5894540
tax 60% cagr 95% overtake in 13 yrs $ 3022841
tax 65% cagr 95% overtake in 12 yrs $ 1550175
tax 30% cagr 100% overtake in 26 yrs $ 33554432000
tax 35% cagr 100% overtake in 22 yrs $ 2097152000
tax 40% cagr 100% overtake in 19 yrs $ 262144000
tax 45% cagr 100% overtake in 17 yrs $ 65536000
tax 50% cagr 100% overtake in 15 yrs $ 16384000
tax 55% cagr 100% overtake in 14 yrs $ 8192000
tax 60% cagr 100% overtake in 12 yrs $ 2048000
tax 65% cagr 100% overtake in 11 yrs $ 1024000
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