Trading Math - Part I

You examples however shows a case where ruin depends on price series. It does not answer whether ruin is certain regardless the price series for non negative expectancy. That was the question. Do you see the difference?
 
I think I answered the right question: it depends on the price series and the strategy! If there's finite stopping time, then it all depends on the dynamics of the price series and the strategy.

If there isn't a stopping time, then it's certain - but that's a fairly irrelevant technical limiting result.

I'm sure you were hoping for a certain answer (not that I see you aren't being sarcastic) - but there's no simple, universal answer to this question.

Quote from intradaybill:

You examples however shows a case where ruin depends on price series. It does not answer whether ruin is certain regardless the price series for non negative expectancy. That was the question. Do you see the difference?
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Don'tMissTheBus,
Thanks for this concrete example. Can you explain what the results demonstrate in your view? For either your original, or restated Case A.

Thanks

Quote from DontMissTheBus:

Absolutely.

You can convince yourself with a simple experiment (you can do this in Excel if you don't have matlab or something similar):

Trading strategy: Long/short when Price > MA(50) (doesn't matter), Exit with time stop or simple stop loss.

Simulate the drawdowns over 1000 days under:

A. Purely normal random returns: r(t) = e(t) where e(t) = norm(0,1)

B. Random returns with a long memory: r(t) = 0.8*r(t-1) + 0.2*e(t).
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That the distribution of either maximum draw-down or probability of NAV < 0 with finite trading time is sensitive to the specification of the returns series - even when they are in the same general family.

Quote from abattia:

Don'tMissTheBus,
Thanks for this concrete example. Can you explain what the results demonstrate in your view? For either your original, or restated Case A.

Thanks
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Quote from kut2k2:

The original question is silly. To prove it or disprove it, you have to first assume you have an infinite price series, which is a fantasy.

For example suppose I posted a disproof via a counter-example that was profitable from the IPO of a price series to now. Then the OP can claim the series didn't go long enough to reach failure.

This fails the test of being mathematics. Next.
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You are correct.

This thread points out how most analysts cannot even get a foothold in assessing how markets work.

Time has to be replaced by an events series.
 
Quote from DontMissTheBus:

That the distribution of either maximum draw-down or probability of NAV < 0 with finite trading time is sensitive to the specification of the returns series - even when they are in the same general family.
More...
Thanks

[But your dig at JH was unnecessary and out of place]
 
Why? He's about to pepper this discussion with unadulterated nonsense anyway (nonsense, not as in unorthodox thoughts that reasonable men can reasonably have divergent opinions on, but random words strung together).

To be fair, I do believe there was a thread a while back that purported his demise.

Quote from abattia:

Thanks

[But your dig at JH was unnecessary and out of place]
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Quote from braincell:

Adaptive MAs you say? Funny name. I'd like to know how they're "adaptive"? By definition an MA is supposed to be one thing and nothing else - a moving average. I've made several of my own also, I'm not sure if they qualify as competition to your "adaptive MAs" but they give weight to values with logarithmic, exponential or sqrt decay, and on top of that adjust for volatility (also with various weighing curves available). Is that something similar to what you seem to consider very valuable? Math discussion is much easier when everyone is using the same definitions - hence why definitions are so strictly taught in schools.
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Adaptive moving averages come in different forms but I think the most common form is that of a variable exponential moving average, i.e., the smoothing constant is replaced by a smoothing variable that depends on the raw data or changes according to some other criterion.

The oldest adaptive MA appears to be called "adaptive response rate"

http://web.uconn.edu/cunningham/econ397/smoothing.pdf

The most famous is probably Kaufman's adaptive moving average, which is also in the public domain. There are several blackbox AMAs for sale, such as Jurik's moving average or the Ocean moving average. The subject is wide open for experimentation.
 
Quote from kut2k2:

Adaptive moving averages come in different forms but I think the most common form is that of a variable exponential moving average, i.e., the smoothing constant is replaced by a smoothing variable that depends on the raw data or changes according to some other criterion.

The oldest adaptive MA appears to be called "adaptive response rate"

http://web.uconn.edu/cunningham/econ397/smoothing.pdf

The most famous is probably Kaufman's adaptive moving average, which is also in the public domain. There are several blackbox AMAs for sale, such as Jurik's moving average or the Ocean moving average. The subject is wide open for experimentation.
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Right, it's basically just applications of different curves (variables) that may or may not be modulated by other derived or direct information. Their usefulness is highly subjective and fairly hard to quantify experimentally. Different AMA approaches have (for me anyway) so far proven to be more/less useful for different situations. It just becomes all about what you think will work.

I was just trying to say AMAs are nothing fancy and I'm suprised anyone would think so. I'd also like more discussion on them, but that's for another thread.
 
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