Option Investor
Educational Article

A BIG Correction, and Ruminations on Trading

Printer friendly version

In my haste to finish last week's article and get back to the casino (Vegas, not Wall Street), I made one heck of a blunder in my math on the Butterfly trade on AZO. So I'll spend most of today's article correcting that error and showing you, my loyal fans, where I went wrong. But first, I want to talk a bit about my reference above to the casino. That's right. I spent a good portion of last week in Las Vegas. I only live 3 hours away, but until last year, had never been to the "City of Sin". I've found that enjoy short trips there for several reasons, not the least of which is the observations I can make about human nature.

I've actually watched people lose 5 and 6 figure chunks of cash in a short span of time, and then head right for the cashier to get a wad of dough, to keep the game going. Do you know anyone that has done that in the Financial markets? I sure do! I personally know people that ran 6 and 7 figure accounts down to NOTHING during the tech crash of 2000-2001, because they just "knew" the next trade would work and they could win back all their losses. Ouch! It's painful just thinking about some of the tales of woe that I've witnessed. If you're in the market, risking more than you can afford to lose, on the hopes of finally winning it all back, get help!! You have a gambler mentality and are risking your own financial security. Before you place one more trade, go back to my Monday article, What To Do When You Can't Do Anything Right. Read it and then apply the lessons contained within. It won't make you an overnight success, but it will help to get you back on the right path.

There's another interesting observation that I've come across when playing for a few days in Vegas. See, I became a trader many years before I ever tried my hand at gambling. And to be honest, I'm not much of a gambler, as I don't like having such a lack of control. But I have found that I can apply the same money management rules that work in trading to gambling. I'll sit down at a table and start with $1000. Immediately the stop loss goes in place at $500, as that is all that I am willing to lose in that one sitting. If I run the lot up to $1500, the stop loss goes up to breakeven, so that no matter what happens, I get to keep my original capital. Regardless of where I initially place my stop, it NEVER gets lowered! Not only has trading taught me how to gamble more effectively and enjoy the experience, gambling on occasion has solidified my adherence to my stops when trading. It is kind of funny, but somehow the money seems more real (and thus commands greater respect) at the BlackJack table than it does when it is put to work in the option market. But it is just as real, and we need to remain cognizant of that fact at all times.

But enough about my ruminations on the commonalities between trading and gambling, we're here to talk about options. Recall last week, that we were (or so I thought) wrapping up our discussion of Online Volatility Tools. I concluded the article with an example of Probability on a butterfly spread on AZO. I concluded that we could just average the probability of each end of the spread being successful to arrive at a probability of success for the entire spread. Boy was I wrong!! Fortunately, I've got a bunch of vigilant readers out there (some of which have a firmer grasp on the math than I! Don't tell my old colleagues at NASA -- I'd never hear the end of it. (BIG GRIN)

Alright, in the pursuit of both accuracy and clarity, I'm going to rectify that error so that everyone understands the error I made and also how to correctly determine the probability of success for this Butterfly Spread.

From last week's article (full text Here ):

" The net result is that we have a 72% chance of AZO finishing above $66 on expiration Friday next month and a 70% chance of the stock finishing below $74. Although it is a rather crude way to do the math, I can just average those 2 numbers and come up with a 71% chance of success."

And here's an excerpt from the email I received, correcting my error:

It's been a long time since my finite math classes, but I remember enough to question your conclusion on the AZO butterfly example. The part I have a problem with is your averaging of the probabilities that AZO will be above 66 and below 74 to get the probability it will be between those two prices.

Your first calculator gives a 72.6% chance of AZO will be above 66, but also a 27.3% chance of it being BELOW 66. So, when you look at the second calculator and find a 70.4 % chance of the stock being below 74, 27.3% of that is also below 66 leaving a 43.1% chance of it being above 66 AND below 74. You can reach the same conclusion the other way -- The second calculator showed the probability of being above 74 as 29.5%. The first calculator gave the chance of being over 66 as 72.6%. When you subtract 72.6-29.5, you again get a 43.1% chance of the stock being in the 66 to 74 range. Another way to look at it is that the first calculator showed 27.3% chance of <66, the second one showed 29.5% chance of >74, leaving a 43,1% chance of it being between 66 and 74 (100 - 27.3 - 29.5 = 43.1).

I know it "just math" but the result has a significant bearing on whether or not you would want to do that butterfly!

Hoping I've been helpful, Al"

Indeed you have, Al! Many thanks for pointing out the error of my ways, as doing the math correctly has a significant effect on the probability of success and hence our willingness to put on the trade.

I had to remove some cobwebs from a dusty corner of my brain to confirm that Al's calculations are correct and in my continuing effort to be accurate, let me restate the process for figuring the probability on the Butterfly spread in case anyone is still confused.

First, take the probability of AZO being below $66, which is 27.3%. Then take the probability of AZO being above $74, which is 29.5%. Subtract both of those numbers from 100% (100 - 27.3 - 29.5) to arrive at the correct probability of success, which is 43.1%. What we are actually calculating is the probability that AZO will not be between $66-74, as that is the area where we would be unprofitable on the trade at expiration.

My apologies for the inaccuracy and any confusion that it caused. Hopefully this helps to clarify the process of figuring probabilities on this type of spread trade.

See you next week!


Options 101 Archives