MonteCarlo 'Fat-Tails' and Chebyshev's Inequality

Taleb has a paper on his website:

http://www.fooledbyrandomness.com

It discusses the whole "slow bleed vs blow-up" that contrasts his and Niederhoffer's strategies. It's called something like Why Assymetric Payoffs are Preferred.

I'm not one to comment on the math in this discussion, but will say from my experience on the floor, that the "mean reversion" guys would scalp out money day after day, but when they dropped money, it was a bundle. The question I guess is how much of your prior profits the "bundle drop" takes away.

I've been playing with some ideas about using mean reversion, but being hedged against the rare, multi-sigma event. I'm not sure how one would program such a thing, and started a thread on learning programming and modeling which has gotten some useful responses. Please feel free to check that as well, as I'd love to hear from the posters here regarding that. I think applying the ideas discussed here would be challenging, yet potentially rewarding.
 
Asymmetric payoffs aren't necessary, either in theory or in practice, to achieve profitable results. Here's one way to make profits with symmetric payoffs:
  1. Obtain a technical entry signal with >55% accuracy rate (for example, following the protocols on pp. 170-179 of LeBeau and Lucas's book)
  2. Set your stoploss at a distance "R" away from your entry
  3. Set a profit target exit (a limit order) a distance "R" away from your entry
  4. >55% of trades make a profit equal to "R", <45% of trades make a loss equal to "-R"
  5. Average profit per trade is > (0.10 * R)
  6. Payoffs are symmetric
 
trader56 there is a method of hedging against the rare multi sigma event if your trading a countertrend strategy as i do.

Create a simple trend following system. there are quite a few on this website. One that doesnt generate signals very often but is pretty accurate. YOu might add a few things like:

ATR or RSI
MACD etc.

In fact i use the originial turtle trend following system as the basis of my simple trend following system.

The idea behind it is that if its not mean reverting then a trend trading strategy will profit, and that if it is mean reverting then a countertrend strategy will profit.

Use both to generate signals. Which one you wish to take is up to you, but understand that if your painfully wrong in one, it means there is a strong case for the other to be correct and so you would take the signal from the other system, which usually results in a profit.

ITs not a perfect hedge, but it does provide good insurance against teh black swans that taleb talkes about. The problem with most ppl is that they get too caught up in the trend-countertrend debate that they cant see that each one offsets the other and provides risk diversification.

I for one recommended almost all of my former retail clients to invest 50-50 in Neiderhoffer's Matador Fund and JWH Global Diversified Fund. On average those clients have gotten superior returns with much less volatility than normal.
 
Obtain a technical entry signal with >55% accuracy rate (for example, following the protocols on pp. 170-179 of LeBeau and Lucas's book)
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Done easily enough.

Set your stoploss at a distance "R" away from your entry
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You just changed the ratio of profitable to unprofitable trades. Your quoted 55% rate no longer applies.

Set a profit target exit (a limit order) a distance "R" away from your entry
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You just changed it again.

If you find a random (non-edged based) strategy that produces 10 winners for every loser, then it will tend to produce losers that are 10 times larger in value than the winners. It may take many, many trades for this to become obvious, but you will break even in the end, before commissions and other fees. Only your broker will profit from such a strategy.

-Raystonn
 
no not really. that trading strategy proposed by MGJ can become profitable.But in order to make it become profitable there needs to be an asymettric payoff.

Heres a method of doing that:


[*]Set a profit target exit (a limit order) a distance "R" away from your entry

IF this is edited to make it a floating profit target i.e - set a mental target of at minimum "R" away from entry. for every X points the market moves beyond "R" the limit order is increased to a certain % of the move X.

This floating target might make the system viable in theory.
 
Aus Splder,

Re past data price volatility: “have past movements scaled by a volatility factor”.

Could you expand on this, perhaps with a simple illustration?

Thank you.

Grant.
 
Quote from Grant:

Aus Splder,

Re past data price volatility: “have past movements scaled by a volatility factor”.

Could you expand on this, perhaps with a simple illustration?

Thank you.

Grant.
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I think by that, he means 'standardized' or 'normalized' (for lack of better word) historical return. This lets you compare apples to apples. A common way to do this is using %tages instead of actual dollars for 'past movements' (=returns).

To put it another way, if you were to look at a stock with huge arithmetic ATR like GOOG and compare it to a small $5 stock with a relatively smaller arithmetic ATR, to 'scale it by a volatility factor' you'd use % ATR instead of arith. ATR.

I probably have a picture of this somewhere.... but it makes sense if you think about it?

EDIT: I'm sorry.. just scrolled back and read his complete quote in context. My response was to his quote taken out of context.

Here's the quote:
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)
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In this context I think Aus was referring to historical volatility vs present volatility and making sure you're adjusting for the changes.
 
i like thits thread a lot. yet i admit that i use literally none of the referenced concepts for trading. but there is reason for this.

first of all i think that the time series we are usually looking at are too short to allow for too detailed tail discussion. 250 data points per year is not that much when it comes to 5+ sigma events. and if you lok at intraday data the fact that different times of the day must be treated differently makes the analysis problematic for intraday.

plus i assume as well that the time series as such have been consistently subject to change over the years. 1960, 1980 and 2000 are different. just think of the evolution of arbitrage ...

-
my paranoia is overfitting. our machines are so fast that just by pure chance some (actually quite many) of our backtests have to be very good just by mere chance.

yet i care about the tails, because most of our stuff is trend following in one or the other way with stop loss but no profit target. so i am actually "long" the tails. but to me analysing the tails with so few data points is a flawed concept to start with. so i rather backtest a strategy that exploits fat tails than search for time series that have some in the first place.

my second paranoia is system life cycle. each and every strategy has limited life time. that is my basic business assumption in trading. and i need to build more and more systems correlated as little as possible to account for that. and i assume this is the best way to ride the swan once she comes around next time ...
 
Thanks for the insight, man.

In my studies even a relatively small sample of one-year daily returns or 5-year (60mo) monthly returns also show fat tails. If you make the sample size larger, thereby theoretically encompassing many black swans and various market conditions then the tails become fatter.

It is up to each individual to decide how they want to utilize these concepts. In my experience, the average trader thinks not of this. I actually use these concepts as a way of managing risk.

Here are some pretty pictures that are quasi-related.

Red line = probability distribution with a stop-loss order entered.
<img src="http://i9.photobucket.com/albums/a79/tireg/stopreturn.gif">

Various volatilities. It says futures but it can apply to any vehicle. Which type of curve do you think a Treasury bill looks like?
<img src="http://i9.photobucket.com/albums/a79/tireg/volatilitydistributions.gif">

Wikipedia.org's picture of different types of distributions. Guess which one's the normal one :P
<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Normal_distribution_pdf.png/325px-Normal_distribution_pdf.png">
 
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