a) I never made a claim about frequency distributions (not even sure what you are referring to here)
b) One can cluster future possible outcomes and attach probabilities to them of occurring. One can indeed also attach probabilities to ANY future possible outcome via a probability distribution in a continuous realm (as opposed to discretized steps)
c) your assertion why sometimes normal distributions are used is incorrect. They are used because they sometimes reasonably well approximate the true distribution of future events, but most importantly it is used because they greatly ease the mathematics behind them, especially in options pricing theory.
d) Without probability concepts one would never be able to accurately price and trade options, for example. In fact everything in options theory is based on measure theory that is intricately linked to probability theory.
e) It is not true that it "has been proven that a normal distribution does not apply to market behavior", as pointed out above, it does approximate market behavior in some cases and in fact much more sophisticated distributional models are used than normal distributions in other cases.
f) your cynical comment re "convenient probability distribution choice" is somewhat mislead; in fact convenience does not preclude accuracy. Risk-free pricing is an incredible convenience and it at the same time leads to laser sharp and accurate options pricing, where closed-form solutions are available.
g) Your comment of William Eckhardt re trading size has nothing whatsoever to do with probabilities.
Frederick, I have huge respect for your laser sharp line of reasoning and political stance in P&R but judging from your comments to which I reply right now, this topic is maybe something you don't want to get onto too thin ice. I get the very strong impression that this is not an area you earn your daily bread with, but others do (wink)
b) One can cluster future possible outcomes and attach probabilities to them of occurring. One can indeed also attach probabilities to ANY future possible outcome via a probability distribution in a continuous realm (as opposed to discretized steps)
c) your assertion why sometimes normal distributions are used is incorrect. They are used because they sometimes reasonably well approximate the true distribution of future events, but most importantly it is used because they greatly ease the mathematics behind them, especially in options pricing theory.
d) Without probability concepts one would never be able to accurately price and trade options, for example. In fact everything in options theory is based on measure theory that is intricately linked to probability theory.
e) It is not true that it "has been proven that a normal distribution does not apply to market behavior", as pointed out above, it does approximate market behavior in some cases and in fact much more sophisticated distributional models are used than normal distributions in other cases.
f) your cynical comment re "convenient probability distribution choice" is somewhat mislead; in fact convenience does not preclude accuracy. Risk-free pricing is an incredible convenience and it at the same time leads to laser sharp and accurate options pricing, where closed-form solutions are available.
g) Your comment of William Eckhardt re trading size has nothing whatsoever to do with probabilities.
Frederick, I have huge respect for your laser sharp line of reasoning and political stance in P&R but judging from your comments to which I reply right now, this topic is maybe something you don't want to get onto too thin ice. I get the very strong impression that this is not an area you earn your daily bread with, but others do (wink)
Let's be clear. As far as the markets are concerned, the frequency distribution of the past is not a probability distribution of the future. You simply cannot account for all of the possible variables going forward because it is not a closed system like a casino. The more heavily and doggedly you rely on "probability," the more likely you are to hurt yourself by placing more confidence where it is not due.
It has already been proven that a normal distribution does not apply to market behavior, but people use it because it allows for more "confidence" of probabilities. Sort of like looking for a lost item not where you misplaced it, but where the lighting is good. It's convenient. While some people may play such "probabilities" better than others, I think you need to give these numbers a much wider berth than the numbers themselves would suggest. I think the term "balance of probability" is more apropos than "probability." As I recall, John Meriwether of LTCM relied a bit too heavily on the probabilities. And remember what William Eckhardt said: "Trading size is one aspect you don't want to optimize. The optimum comes just before the precipice." That's in part because you can't rely too heavily on probability when you are in fact operating in an environment of uncertainty. Uncertainty demands much more respect than probability.
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