Many of our brokerages or charting programs will calculate the probability of profit of an options trade we're considering. At the time this article was first roughed out, I had already taken profit in my SPX JUL11 iron condor, but what if I had been considering opening an iron condor on June 3, 2011, 41 days before the JUL expiration? How would I go about determining my probability of profit?

I set my SPX iron condors up by selling the first call strike with a delta under 10 (or 0.10, depending on your quote source) and selling the first put strike with a delta above -9, which means that it has a delta of say -8.20 or -8.83 or something similar. Remember that with puts we're dealing with negative numbers for the delta; hence, that "above -9." Then I hedge by buying the strikes 10 points away. On June 3, that would have translated into a 1385/1375/1165/1155 iron condor. Remember that I had already closed my own iron condor and didn't trade this trade. This is just for discussion purposes.

A glance at think-or-swim's Risk Analysis page tells me that this trade has a 79.02 percent probability of profit at expiration. We can figure out a rough-and-ready estimation, too, without even needing an analysis chart or wicked mathematical calculations. We can simply add the absolute values of the deltas of both sold strikes, multiply them by 100 if your quote source hasn't already done so, and subtract them from 100. Here's how it works. The 1375 had a delta of 8.52. The 1165 put had a delta of -8.21, so we would use the 8.21 as its absolute value. Obviously this different quote source has already applied the 100 multiplier, so we don't need to do that. We can just add the two absolute values together (8.52 + 8.21 = 16.73). Then we can subtract this value from 100 to obtain a rough-and-ready estimation of the probability of profit of the proposed iron condor. That would be 100 - 16.73 = 83.27. This method provides a little higher probability of profit than think-or-swim's calculation, but it's a good estimation.

Not too long ago, I ran across an article saying that the unadjusted iron condor wouldn't be profitable over a minimally statistically significant number of trades. For me, that's at least 30 trades, although even 30 would not satisfy most mathematicians. Remember back to your days in your elementary grade classroom, sitting on the floor tossing coins to see how many would come up heads and how many, tails? You surely tossed those coins more than 30 times. Still, many traders consider that enough data points to give them some insight into how well a strategy or adjustment works across different market conditions even if that test might not provide enough data points to satisfy a statistician.

That brings us back to that assertion I'd read, that unadjusted iron condors wouldn't be profitable over a long period of time, even given their high probability of profit at expiration. I have at various times back tested unadjusted iron condors for 30 to 36 months of trades to see if they would be profitable, given the huge losses that would occur in smaller percentage of trades that were likely to be losers. They were profitable over the long run, even when including commissions and some haphazard attempts to account for slippage. Of course, in order to be profitable, I had to assume that there would be plenty of funds to absorb drawdowns if they occurred in back-to-back months, and particularly if they occurred right at the beginning of the test, when no profits had yet accrued. The times I tested it, however, I didn't encounter any situations in which back-to-back losses stacked up at the beginning of the test. And, it must be acknowledged that the brokerage earned about as much in commissions as the strategy earned the options trader.

I recently tried another route after I heard options expert Dan Harvey speak to a Sheridan trading group. He told traders that a javalinux site offers an "Option Trade Outcome Percentile" for trades. The site allows traders to run the proposed trade through a number of possible simulated price paths, with the number of paths set by you. I used the default number of paths, 100,000. I input the options set out in the previous paragraphs, June 3 as the start date, and a risk-free interest rate of 0.5 percent. Then I ran the simulator.

Option Trade Outcome Percentile for Expiration, JUL 16 2011:

Note that the probability of breakeven is 74.8367 percent, a little below both TOS's calculation and the rough-and-ready calculation based on the deltas of the sold strikes. Still, an almost 75 percent chance of breaking even or making a profit in a trade is a pretty hefty percentage of gains in the options-trading world. A slider along a chart that I did not include here indicates that the probability of earning the full \$1.27 credit taken in for this trade, if it were a one-contract trade, is 74.2 percent. That's pretty nice, isn't it?

But did you happen to notice the "Mean P/L" for this trade after those 100,000 simulations? That's a sobering -\$108.96, and no one disputes the fact that 100,000 simulations is enough to be statistically significant. I have never recommended no-touch iron condors, although for different reasons than this one. They are prone to big losses when losses do occur. Those losses are much more than the potential gain. That's hard for most traders and their accounts to endure. The allure of the iron condor lies in the number of times it's profitable as compared to those it's not.

I don't know how the calculations were made. My many-decades-ago, pre-computer single class in statistics wouldn't give me the tools I would need to evaluate it. Also understand that this is not the calculation of the likely profit or loss of separate iron condor trades set up each month, but is rather the calculation of all the different price paths for the SPX over the life of this single trade. They're different. My knowledge of statistics isn't strong enough to argue that one or the other is more persuasive, and I certainly can't argue that my 30-36 back-tested trades refutes the calculation performed above. The possibility that the unadjusted strategy might not provide profit over the long run proves to us that we must develop a loss-management and/or adjustment strategy.