Checking Out an Old Rule of Thumb for Forward Price Probability For Option Trades

This brief post tries to compare an old option trader's rule of thumb (for a one standard deviation range/move of a stock at future dates) that I once learned from an old-school trader against the new-ish Interactive Brokers "market (option) implied probability" in their Probability Lab. I just wanted to see how the quick-and-dirty rule stacked up in very, very general terms to something that attempts to go a step further and mathematically infer probability from market (option price) data.  I claim no skill in options trading...or numeracy in statistics (or options) for that matter.   Just checking it out the best I can. 

• The Rule of Thumb:  a one standard deviation move at a future date = [ (price x implied vol. x square root of days to expiration ) / square root of 365 ]    

• Interactive Brokers: this is embarrassing but since I do not have access to their data or formulas, I had to hand draw, the best I could, box plots (it is a standard deviation range, by the way, not a quartile range; the center line is a median price. Mode is quite a bit different due to the skew) based on the graphical probability distributions presented in their tool.  Quants have very specific math protocols on how to do this. I have no idea on that math, nor am I going to try....

The security is IWM as of 8/5/16. I am projecting info out to the expiration dates of Aug 19, Sep 16, and Oct 21 of 2016.

This is what I came up with:

Any conclusions?

• Uh, well, since some of the graph is hand drawn, I don't know about all this. On the other hand… 

• The general shape is pretty darn close.  If I were to be moving quickly and had a couple simple trades to evaluate -- rather than billions of dollars in client's money at stake in a hedge fund -- then it looks like it might be an informative approximation.  There may be some use to this for a plugger-type trader like me. 

• I didn't take expiration dates out very far...

• It absolutely, positively does not capture the skew implied in the market data.  The options implied distributions at the various dates have a very significant downside skew.  

• Past one standard deviation the accuracy looks like it falls off quite a bit.  The negative skew takes over in the real market data.  The two-standard-deviation line looks like it is not helpful in the Rule of Thumb. 

• If I had no other data to go on I could maybe use this to help me set strike price estimates or guess spread strike ranges or maybe plan a trade exit.  I don't know.  I have not used it yet and my trading volume in this area is super low for now.   

• It looks like it is, for this security anyway (at one standard deviation anyway and allowing for errors in the hand-drawing), ever so slightly more conservative than what the market data would imply.  For that alone it might be useful.  

Just for fun, let me give the last word to Thomas Peterffy, founder of Interactive Brokers, with respect to forecasting prices: 

"Some may say that these are all very sloppy approximations. Yes, that is the nature of predicting prices; they are sloppy and there is no point in pretending otherwise. Everybody is guessing. Nobody knows. Computer geeks with complex models appear to the uninitiated to be doing very precise calculations, but the fact is that nobody knows the probabilities and your educated guess based on your understanding of the situation may be better than theirs based on statistics of past history."