

What is the gambler’s equivalent of Amdahl’s Law? - jmount
http://www.win-vector.com/blog/2009/10/what-is-the-gamblers-equivalent-of-amdahls-law/

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jmount
I try and answer the question "What is the gambler’s equivalent of Amdahl’s
Law?" with "The Kelly Betting System."

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SwellJoe
Unfortunately, but realistically, this is a much more complicated formula than
Amdahl's law.

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jmount
Yes, the extra complexity (and it is there) is the biggest strain on the
analogy.

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BearOfNH
For financial markets, _Portfolio Management Formulas_ by Ralph Vince develops
a similar strategy. It too is based on the Kelly Criterion. But it assumes you
already have a profitable strategy as opposed to saying "do this system".

I'm not in any way related to the above authors, nor their books.

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rvince
Portfolio Management Formulas is _not_ based on the Kelly Criterion (i.e.
maximizing the expected value of the logs of the returns). The latter is not
applicable to trading (Academic promotion of such notwithstanding. Kelly
himself in his 1956 paper only shows it as applied to gambling. Are we to
believe he was unaware of a potential trading application, or that brevity
precluded that?) It is specifically because the Kelly Criterion is applicable
to gambling and not trading that prompted Portfolio Management Formulas and
what followed. -Ralph Vince

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jmount
The Kelly Criterion is controversial (proponents of utility theory hate it)
but has been used in financial situations (see: "The Kelly Criterion and the
Stock Market" Louis M Rotando, Edward O Thorp, The American Mathematical
Monthly (1992) vol. 99 (10) pp. 922-931). Now no system can make money unless
the underlying game is favorable to the player (which is why "system" has a
bad name). Also the Kelly System can be used with portfolios- it is
appropriate when you are investing in anti-correlated instruments (like stocks
and bonds at the same time).

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rvince
I beg to differ. It is appropriate only in certain, special circumstances. It
is misapplied and misunderstood, and though I respect the work of those you
cite, but it does NOT yield the growth optimal fraction in trading unless two
specific criteria occur (aside from a positive expectation). Peculiarly, it
has not been illuminated for what it is and when it is applicable -- an
absence of critical thinking on the part of its proponents have promulgated an
enormous degree of disinformation out there. Regularly, I would get called in
by hedge funds and witness this firsthand. Sorry I cannot be more specific
about this at this time -- I will be in the coming months, suffice to say for
the time being that one must be extremely careful if they think that the Kelly
Criterion is giving them the optimal fractin to risk in trading. More often
than not, it is giving them something different and very dangerous.

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jmount
First, I really appreciate your politeness in the discussion. One huge mis-use
I can think of in using a Kelly type system would be to use past frequencies
directly as your probabilities. At best this would give you the CAPM and at
worst it would give you a disastrous "momentum trade" strategy. The Kelly
System is a little sneaky in that it assumes you have good estimates of the
probabilities of future events. So when the system fails it can turn around
and say that you had bad estimates or un-modeled dependencies.

