MonteCarlo 'Fat-Tails' and Chebyshev's Inequality

Quote from MGJ:

Actually, people do. In the field of nonlinear optimization, the "Least Pth approximation" applies exactly this idea (raising deviations to the power P, summing, and taking the Pth root).

Note that in the limit as P approaches infinity, this calculation merely returns the largest of the individual deviations.

In other words, it is a continuous approximation of the (discontinuous) "MAX" function. Since the fastest optimization algorithms require the objective function to be continuous (with continuous 1st and 2nd derivatives too), the Least Pth Approximation is incredibly valuable; it lets you use the best optimizers on minimax problems. Do a google search for Least Pth Algorithm and/or Least Pth Approximation. It's good stuff.
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Beautiful idea :)
I have some experience with nonlinear optimization, so it's easy for me to understand what you're talking about. Maybe I saw this least Pth idea many years ago, my memory fails me.

I'd like to hear more about "equiripple polynomials" but I fear we strayed too far off topic :)
 
All these probability and statistics concepts are only targeted to make more or less precise statement:

"The probability that tomorrow max price deviation will exceed $P is x%".

The more interesting is a question what to do with this information ?

If one selects too high threshold $P, it could be necessary to wait 20-50 years until such event happens,
and when it happens, one is in holliday.

If the $P is selected to low, it can end up with the catching falling knife exercise.

So one is still at the begining of decission on selecting trade off between efficient using of capital and limiting risk.
And everyone must do that according to his own preferecnes. Statistics does help here not too much.
 
Quote from waxwing:


But I'm not sure I buy the argument as to stdev being more pessimistic and therefore better.
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I agree. Variance, standard deviation, mean, etc, are parameters that belong to a distribution, and give information about it. The better values are simply the values that belong to the distribution that better describes my process
 
Quote from ElectricSavant:

New ET guests...

You have often heard "gems among the sand".

This is one of those occurances
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I've been waiting...
But nobody has even bothered to relate any of this to making money in the financial markets...
And one has to question why a dusty paper from the 60s ressurected by Taleb is a "gem".

I'm fairly certain of one thing...
None of this stuff is useful to > 95% of quants...
Most of whom avoid "black swan outlier" events like the plague...
But rather trade/scalp ONLY events 1-2 SD away from the mean/median.

Also...
Even extreme "outlier" events such as 1987's "Black Friday" or the 1998 "Russian Crisis"...
Have a minimal effect on a properly hedged and diversified portfolio.
If either of those 2 events happened suddenly tomorrow...
Victor Niederhoffer would go bankrupt 2 times over...
While my portfolio would take a max 5% hit...
And then for a few weeks I'd make a killing on the volatility.

So for most sane quants...
It's a waste of time to focus on rare events other than to be well hedged...
While the long-shot specialists who buy/sell options on extreme events...
Are more gamblers than traders.

Is not a person who waits 10 years to profit from a terrible tragedy... a sociopath?
 
Quote from HoundDogOne:

I've been waiting...
But nobody has even bothered to relate any of this to making money in the financial markets...
And one has to question why a dusty paper from the 60s ressurected by Taleb is a "gem".
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I'm afraid you've entirely missed the point if this is how you feel. Maybe someone will be kind enough to generate some buy/sell signals based on some pretty red and green arrows, perhaps? :eek:

I'm fairly certain of one thing...
None of this stuff is useful to > 95% of quants...
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What a rather crude and unbased generalization. Would you be kind enough as to inform us as to which 'quants' you've polled and the strategies they employ?

Most of whom avoid "black swan outlier" events like the plague...
But rather trade/scalp ONLY events 1-2 SD away from the mean/median.
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You've invalidated your aforementioned claim with this statement. Do share how they come about getting these SD measurements, and why they choose to use the particular measurement of 1-2 SD? Also the choice of mean or median as a point of central tendency, as shown in previous posts, makes a material difference on the results. Which of these 'scalping quants' that you've polled use which measurement, and why?

Also...
Even extreme "outlier" events such as 1987's "Black Friday" or the 1998 "Russian Crisis"...
Have a minimal effect on a properly hedged and diversified portfolio.
If either of those 2 events happened suddenly tomorrow...
Victor Niederhoffer would go bankrupt 2 times over...
While my portfolio would take a max 5% hit...
And then for a few weeks I'd make a killing on the volatility.
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Again, would you care to support your claims? Some rather bold statements, considering the markets have become more correlated.
How delightfully humble you are to compare yourself to Niederhoffer. I suppose you know more about portfolio management than this former Ivy League professor? I guess Soros should have sent his son to study with you then.

So for most sane quants...
It's a waste of time to focus on rare events other than to be well hedged...
While the long-shot specialists who buy/sell options on extreme events...
Are more gamblers than traders.

Is not a person who waits 10 years to profit from a terrible tragedy... a sociopath?
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You've contradicted yourself again. If these events are so rare, why even bother hedging? Are you not focusing on these rare events by allocating time and capital to hedge against them? Yet how do you know that you're not overhedging, leading to an inefficient portfolio?

It is unfortunate that this type of knee-jerk post from those who refuse to even attempt the slightest bit of their own study in the concepts before flaming them become increasingly frequent on ET.
 
Quote from tireg:


What a rather crude and unbased generalization. Would you be kind enough as to inform us as to which 'quants' you've polled and the strategies they employ?
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Very good question. I'm very curious to know how pros do it.
 
I assume there is a normal distribution. The rest comes down to money management. I might also add that practically all normal distributions found in the market undergoe skewness. When prices have been going up for an extended period of time this tends to result in positive skewness and vice versa.

I usually find that taking the natural LOG of most time series data gets rid of any major skewness. Also one thing to take into note when using past data is price volatility. As the market increases in price, so does its underlying volatility. It is useful therefore to have past movements scaled by a volatility factor. (a bit like the present compounded value of a past sum)

P.S if you assume that prices follow a particular distribution please do so for your STOPS not just your returns.

The rest gets a bit specific on the strat i use.

by the way why is it that whenever the discussion turns to statistics do people bag neiderhoffer? IMO neiderhoffer is a brilliant trader and just cause he had one bad week doesnt automatically invalidate his method of trading. Pre-bust the best funds in the buisness were:

Neiderhoffer investments
Renaissance Technologies - Medallion fund.

both used QA (RT-statarb)
 
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