I had an idea about butterflies: the trading kind. For those who are unfamiliar with traditional butterflies, the body is formed by selling options and the wings, by buying options equidistant on either side of the body. Butterflies can be all call, all put or a combination of puts and calls. The idea is that you sell twice as many options at the body as you buy for each wing. Usually the wings are equal distance from the body but that doesn't have to be true.

Many people set the wings of their butterflies at about a standard deviation for the period in which one expects to be in the trade. For example, if they expect to be in a butterfly trade for three weeks, they would calculate a standard-deviation move for a three week period and buy their wings at or just outside that distance. For an explanation of how standard deviation calculations are calculated, and particularly how they're related to implied volatilities, see my December 25, 2009 article. Since the calculation of a standard deviation depends on the implied volatility of the options, traders who use this calculation will have wider wings and expiration breakevens when the volatilities are higher, and narrower wings and expiration breakevens when the volatilities are lower.

That's a danger inherent in that reasoning for placing the wings, I thought. When volatilities sink really low, you'd be building butterflies with the narrowest wings, the little wood satyr versions of butterflies. Let's think, however, of what happens when volatilities sink really low. Where are they likely going to go next? Maybe higher, right? If they go higher, that means the span of a standard deviation expands. If you've just put on a little wood satyr of a butterfly when volatilities were low just before that expansion, that butterfly's wing span isn't going to carry very far. You most need a swallowtail's wingspan with its wider breakevens, I reasoned, when volatilities are most likely to expand. Using a standard deviation calculation to determine wing width might be a bad idea when volatilities are low.

I should have remembered that some of those people using a standard deviation calculation to set the wing span were experienced butterfly traders. While I do trade butterflies, I don't rank my butterfly trading skills with theirs. I'm more of a frequent but still-lots-to-learn butterfly trader.

Turns out, I might have been all wrong in my thinking. The other day, I heard former market maker Dan Sheridan give advice that was the exact opposite of my own theory. Let's look at some particulars to see why.

OEX May Iron Butterfly Centered at 600, with 30-Point Wings:

This classic iron butterfly's expiration breakevens may be difficult to see on this graph, but they're at 582.45 and 617.50, a nice wide range for this butterfly. The Greeks for the trade were as follows: delta, 10.18; gamma, -1.22; theta, 5.56; and vega, -53.10. Theoretically, a credit of \$17.60 was available. When this credit is deducted, the buying-power effect (without commissions) is \$1,240. This is calculated as follows: (\$30-point wings - \$17.60 credit) x 100 multiplier = \$1,240.

What if those wings were narrower, say at 25 points? The new expiration breakevens are 583.80 and 616.34. Those aren't much narrower than the previous 582.45 and 617.50, as it turns out. If the risk parameters are set to examine a time period shorter than the time to expiration, say three weeks into the future, the differences in the "today's" profit/loss line are likely to be even less. With the exception of the delta, the Greeks aren't that much different, either: delta, 5.41; gamma, -1.02, theta, 5.34; and vega, -46.58. What is much different, however, is the buying-power effect. With the exclusion of commissions, the buying power effect and total risk for the trade is \$875.00.

That was Sheridan's point. When volatilities are extremely low and, therefore, more likely to steady or even rise than sink further, we do well to remember that a rising-volatility environment is one that's often difficult for traders of all kinds. Wouldn't you rather have less money at stake in such an environment, Sheridan reasoned, if the breakevens for the strategy aren't so very different than they would be with a wider wingspan for the butterfly? Moreover, if the butterfly starts getting into trouble, those closer-in longs will be more helpful than a way-out-in-space long.

So, it turns out that although my supposition seemed logical, perhaps it wasn't. I had been thinking that, to avoid having my wings narrowed at the very time I might need those wider expiration breakevens, I might just continue to use a standard size for my wings all the time, as I had been previously. Maybe not. I think I have some back testing ahead of me.