Any quants here? What to do with mean reversion?

Hey,

I was wondering if anybody a way to calculate the probability of something reverting to the mean?

For example, if the mean is 100, and currently the security is at 120, what is the probability of it going higher and what is the probability of it going lower?  Ideally, I'd think that you would want to look at all the times historicaly, the security was at 120, and what happened afterwards, but let's say there isn't enough data to do that.

I also don't think you can just look at the frequency distribution and calculate a probability above and below because it's not independent.

What's the next best way?

Thanks!

I give up.... I know you can use MatLab and the price is right for student version.... If you qualify....

Good luck....  I can't find any reference to free library..... but I know it existed once before... 

Did some Googling: Haven't finished the entire article but so far I think it's shedding some light as to what to do next.

http://www.math.ncsu.edu/finmath/imsm2010/references/Mean_Reverting_Processes.pdf

mean, which mean. no math necessary - 50% it will revert, 50% it will not. if you want to be more precise and the issue has options, use delta of the option as the probability to reach the "mean"

made - one can calculate mean over different periods

This may be too much ...

A quantitative system for mean reversion and swing trading in market regimes

http://www.naaim.org/wp-content/uploads/2012/04/A-2011.pdf

TampaJake said: I think Oldfart is correct, 50/50 up or down. Remember past performance is not indicative of future values. Charts are just a pictograph of what a stock has done, not what it will do in the future. All stocks do not follow mean reversion. If so AAPL would not be at its current level. It may come back to 300, 200, 100 but over what time period? and what circumstances would precede that fall? It could just as easily go to $1000 per share.

Applying math to stock trading can be useful, but it definitely is not foolproof and can often send you in the wrong direction resulting in buying/selling too early or too late.

Stocks may follow the random walk theory but things like volatility and commodities tend to be mean reverting.  The VIX probabily isn't going to fall below 10 - I'm not even sure if that's possible.  This means that if it's at 10, the probability of it going up has to be greater than 50.

The reason why I want to apply math to it is two part:
-So I can take emotion out of trading.  If the model says to trade, I trade.  If it doesn't, I don't.  If I lose money, the model's wrong, not me haha.
-I'm hoping to eventually get paid to trade so that ways I'd have something to talk about in the interview.

Where are you getting paid to trade? I thought you've only been trading yourself for a few months. Traders are rarely that new to trading as most are analysts for a couple years first or work at risk management desks.

treeHamster said: Where are you getting paid to trade? I thought you've only been trading yourself for a few months. Traders are rarely that new to trading as most are analysts for a couple years first or work at risk management desks.

I'm not right now.  I applied to a few trading firms coming out of college but didn't make it.  Ended up taking an analyst position in finance but not in trading.  I'm in the Chicago area so there's a lot of prop shops around here.  I'm mainly looking at options market making.  If not that, move down to Houston for some energy trading.

Tree, you might fit in well at Spot Trading.  They do a lot of directional options trading, primarily on equities.  Your experience with Apple will probably help.  I heard they are just starting a market making group but they've primarily been doing directional trading.  Spot, is one of those firms where they pay you to trade, i.e. you get a salary.  You don't have to bring in your own capital either.  I visited their floor and it's sick, just like in the pictures on their website.

The good firms usually train you for 3-6 months (paid of course) then you go live.  But to get in is hard.  They test you extensively, speed math and logic tests.  I passed those but didn't have the trading experience/options knowledge (at the time) to get in.  At one of the firms I applied for, after 4 math/logic tests, they put you and all the remaining candidates who passed, into a room, and had you make markets on random stuff, like make a market on the number of windows on this building, with senior traders.  If you've never done that before, then you were lost, which happened to me.  I BSed through a couple rounds, because you can still trade, without knowing what to do, but eventually I was filtered out.  And you had to pass that just to get to an interview!

The Otter Way said: As more and more folks try different things... I have found a listing for math libraries that might be of use....

http://en.wikipedia.org/wiki/List_of_numerical_libraries

 This is actually pretty useful.  I was wondering what programs out there I should check out.

Tree - That's pretty cool.  Working at a hedge fund would be pretty cool but I don't know if I'm cut out to actually run one.  I don't like dealing with clients who are generally fickle.  If you are right in the long-term but wrong in the short-term, a client may pull out his money before you have a chance to show that you are right.