The stock price for Boston Beer (Ticker: NYSE:SAM) went down to $0.01 from ~$60 (at one point although it bounced back soon after) on Thursday, May 6, 2010. The question is, given market data up to May 5, 2010 (and closing price on May 6), what is the probability that the stock price (of Boston Beer) goes down to $0.01 the next day? (Source: http://www.google.ca/finance/historical?q=NYSE:SAM). How would you calculate this probability?It does not have to be technical and/or using a sophisticated model or anything. An intuitive approach is fine, or giving some sort of (intuitive) upper/lower bounds is also fine. Sure the probability is (intuitively) really small (nearly 0), but I am not too sure how to quantify this. Any ideas?

it does rather depend how if Boston Beer stock price makes such excursions regularly. I guess not. SO you need to assume some distribution of stock price changes and the usually opt for a normal distribution.

Could you elaborate a little more?

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

Well... normal distribution would not really help here because such drop is clearly not consistent with normal distribution or standard black-scholes. I guess I can try with it, and will probably get 0 (I at least tried on Excel, and it does not even leave any non-zero digit; it just returned 0 whereas the answer should not be 0 since it did happen). I was more like trying to think of some other creative way. That's why I said an intuitive approach would be good (or better).daveangel said "assume some distribution of stock price changes", and that was what I hope he would elaborate on because for now, I have no idea what kind of distribution could explain this (or return non-zero value for such probability)...

i think you will find that its extremely unlikely - except if the stock does that frequently ! sorry not much more help

QuoteOriginally posted by: hjjindaveangel said "assume some distribution of stock price changes", and that was what I hope he would elaborate on because for now, I have no idea what kind of distribution could explain this (or return non-zero value for such probability)...Well you can't really quantify it with standard distributions (non that I've had experience with at least) because it's caused by broken market mechanics. There is no common distribution that would exhibit this kind of behaviour but you could maybe find something approximating it if this was a cyclical thing as daveangel pointed out.

There's also the nasty issue that those 0.01 cent trades were busted. That means that people that sold at 0.01 for a massive loss suddenly got their loss reversed and people that bought at 0.01 cent (and later sold the bounce a handsome intra-day profit) probably got screwed. It also means that the actual worst-case decline was 60% (the threshold for busted trades). But that 60% figure is not codified in regulations, so the future might be different.The original question of the probability of another crash the following day is not answerable with statistical methods both because we have a sample size of one and because subsequent market participant behavior is not independent of the results of the flash crash.Factors that make such a crash more likely or that widen the span of price movement:1) the likelihood that the same systemic interactions (e.g, HFT withdrawal in downday, NYSE slowing, stop-loss cascades) will induce the another flash crash2) the likelihood that sellers become even more fearful and sell more aggressively3) the likelihood that buyers avoid the market during a flash crash due to the risk of busted tradesFactors that make such a crash less likely or that narrow the span of price movement:1) the likelihood that the authorities intervene on subsequent days (or change the regulations) to halt a flash crash more quickly2) the likelihood that buyers anticipate a big bounce and buyAt this point we have a sample size of one on flash crashes and a near certainty that the participants will behave very differently the next time it happens. In other words, P("stock price (of Boston Beer) goes down to $0.01 the next day") is unknown but not zero and anyone that tries to assign a more concrete value to the probability should be extremely careful. In particular, they might want to model the impact of assigning any of a range of P values and seeing the impact on their model.

are you sure that it was a genuine price move ? i mean two more possibilities arise :1. there is a flaw in the data released by the exchange2. the company hinted at a bankruptcy and then was saved by a messiah before end of day close.now in the first case no probability can fit into. the second is a case of once in a lifetime experience and i am sure no probability modelling can fit into it.whatever it is what u need to look at is what caused such a fluctuation and then find out a mathematical model for the possibility of that cause happening the next day. for example what is the probability of the messiah ditching the company again the very next day should be a better questions.

QuoteOriginally posted by: ankitkare you sure that it was a genuine price move ? i mean two more possibilities arise :1. there is a flaw in the data released by the exchange2. the company hinted at a bankruptcy and then was saved by a messiah before end of day close.now in the first case no probability can fit into. the second is a case of once in a lifetime experience and i am sure no probability modelling can fit into it.whatever it is what u need to look at is what caused such a fluctuation and then find out a mathematical model for the possibility of that cause happening the next day. for example what is the probability of the messiah ditching the company again the very next day should be a better questions.In this case the move was "real", happened on multiple stocks (over 250 different stocks had a drop of 60% or more), and the move wasn't associated with any news. In other words, it was a true panic.

The only thing i can suggest is a GARCH like model as these conditional heteroskedastic models were built to capture a phenomena like this that is in a an asset price, large volatility breeds large volatility at least for the short term and low volatility breeds low volatility. And a GARCH model also helps in forecasting in the sense that it gives you expected volatility and expected returns from where you can get some probabilities for a large move next day.hope tht helped