What is the gambler’s equivalent of Amdahl’s Law? | Hacker News Reader

What is the gambler’s equivalent of Amdahl’s Law?

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11 pointsjmount10 comments

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

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

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

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.

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

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).

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.

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.

Does anyone have a copy of this paper ("The Kelly Criterion and the Stock Market" Louis M Rotando, Edward O Thorp, The American Mathematical Monthly (1992) vol. 99 (10) pp. 922-931) I am having a very difficult time locating it. Thanks

I certainly agree with you. In, say, a gambling situation (which provides a "special case type" of situation where the answer that satisfies the Kelly Criterion is equal to the Optimal f answer) we know that the optimal is very "delicate," (vs "robust") with respect to the distribution of future outcomes mimicing the past. We know that if it is off, even if just a little (magnified by the number of data points!) the outcomes are monstrously different. Profit maximization is clearly a very dangerous game.

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