Do You Own a "Bernoulli Fund" In this game “B”, the hedge fund manager, in effect tosses a coin by repeatedly entering into a risky tax transactions. "A", the fund investor unknowingly assumes the role of The House and implicitly agrees to reduce the value of A’s investment if A loses the bet when the fund eventually settles the tax audit with the IRS. B keeps flipping the coin because the day of reckoning with the IRS will not happen unless and until the IRS happens to audit the fund. The funds outside auditors are not required to disclose to A that B is playing this game as long as the probability of tax audit failure for each risky transaction is .5 of less. So in a Bernoulli Fund, B -- the manager, keeps playing the St. Petersburg Paradox by doing one undisclosed risky tax transaction after another as the contingent liability builds. The question is: If the IRS eventually wins on audit – does The House (i.e. A – the fund investor) go broke?
-- But Don't Know It?
A Bernoulli Fund plays the famous St. Petersburg Paradox game.
Play Now – Pay Later (Here is how Financial Accounting Standards Board (FASB) Interpretation no. 48 Permits this to happen) Contemplate entering into a transaction with significant but uncertain tax risk. Equate the transaction to a coin flip. Think of this risky tax transaction as a fair coin with a .5 probability of being tax-free and a .5 probability of being fully taxable.
Example of The St. Petersburg Paradox as applied to a Fund:
Bob, a fund manager, tosses a fair coin repeatedly until it shows heads. He knows he will pay the IRS two dollars of the fund's (say Adam the investor’s) money if it shows heads on the first toss, four dollars if the first head appears on the second toss, eight dollars if the first head appears on the third toss, sixteen if on the fourth toss, etc. How much of the investor's money should Bob escrow for eventual payment to the IRS so that the game will be fair? How many times should Peter be allowed to flip the coin before the fund has to set aside cash in an escrow account to pay the IRS?
Bernstein, P. L. (1996), Against the Gods: The Remarkable Story of Risk, New York: Wiley. p. 106
Szekley, Gábor J. and St. P. Richards, Donald The American Statistician, August 2004, Vol. 58, No.3
Certainty has a probability of 1.0. The rules of FIN 48 disclosure operate so that only tax transactions with a probability of tax audit failure of greater than .5 must be disclosed. Imagine a fund that does hundreds of risky tax transactions -- but the risk of tax audit failure is .50 for each transaction. That means that the fund could have hundreds of tax transactions each with a 50% chance of losing on IRS audit without any disclosure to the investor in the audited financial statements of the fund.
Let's call a Fund that takes Contingent Tax Risk a “Bernoulli Fund” --
Are You Invested in a “Bernoulli Fund”? -- The St. Petersburg Paradox and the “Bernoulli Fund”
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