A couple of weeks ago, I watched the theoretical profit and loss (PnL) of my live RUT butterfly trade vary within a few scant minutes by as much as $2,500 when the RUT's price changed very little. My delta--the Greek that measures how much the PnL changes with price movement of the underlying--was under +20 at the time. The theoretical PnL wouldn't have been expected to change much due to small price movements, anyway, with the delta that low. What was up?

Let's look at a simpler trade to illustrate what could have been happening. Let's examine a hypothetical SPX split-strike iron butterfly established on 1/15 and composed of the following strikes: +10 FEB 1920 calls/-10 FEB 1850 Calls/-10 FEB 1840 Puts/+10 FEB 1770 Puts. Now let's look at the expiration graph PnL line two days later, on January 17.

Expiration Graph and Theoretical PnL for SPX Iron Butterfly on January 17:

The dark blue line shows the expiration tent, the profit or loss at each price point at expiration. The light blue line (colored red on the far right) is the current theoretical PnL. The speckled green dots are actual intra-day prices overlaid on the graph. As you can see, those green dots are not always tracking the theoretical PnL loss exactly. Why is that?

Notice that vega for this trade was a whopping -2,461.27, with this number visible on the pull-down tab beneath the expiration graph. Vega measures how much the profit-and-loss line should theoretically change for any changes in implied volatility. Since the absolute value of the vega was so large, this trade was going to be extremely sensitive to changes in implied volatility. Since vega was negative, the PnL was likely going to benefit by a drop in implied volatility and was likely going to be hurt by an expansion in implied volatility.

What was happening to volatility on the SPX at the time the expiration graph was snapped? Although the SPX's volatility index, the VIX, isn't always an exact proxy for implied volatilities on the options involved in individual trades, it serves as a decent proxy for our needs.

Graph of the VIX:

From the annotation at the far left-hand side of the graph, we can see that VIX was dropping at the time the first graph, the expiration graph, was snapped. Although the VIX rose later in that day, its behavior was relatively tame, staying in the 12-13 region that day. If this chart were a daily chart covering many months, we would see that this is a low level for the VIX, and the behavior on the right-hand side of this chart shows how quickly volatility can rise and how tame it was by comparison that January day. The early morning drop in the VIX on January 17 may have resulted in some fills, then, that returned more profit than the theoretical PnL line would suggest.

There may have been something else working to produce those profits that were above the theoretical PnL line. That was a Friday morning, and several important economic numbers were released. The expiration graph, with its theoretical profit-and-loss, was snapped before the last of those numbers was released. Market makers tend to keep implied volatilities high in that first thirty minutes of trading when important market events are occurring at 10:00 am ET. Then the volatility gets released afterwards if the economic event doesn't result in a huge move, particularly a huge move to the downside. Moreover, this was a Friday, and market makers start rolling out weekend decay Friday morning, barring a big move in the markets that would keep implied volatilities high. Those theoretical PnL lines don't factor in these actions by market makers.

Another possibility relates to the skew of the options involved in the trade. Not all options in the FEB14 series have the same implied volatility. Since the 1987 collapse, out-of-the-money equity puts tend to have higher implied volatilities than at-the-money puts, for example. That's because big money and individuals tend to buy out-of-the-money puts for Armageddon insurance. Higher demand for these products drives their prices higher than they would otherwise be, and that translates into higher implied volatilities. When the implied volatilities of a series of options (such as the FEB14 options) is graphed, a curve results. That curve can be relatively flat near the current price of the underlying but kick up more sharply as the strikes move further out of the money.

Sample Skew Graph of the SPX FEB 14 Options:

This graph was snapped on January 29 when the SPX was at 1,774.20. I did not have the ability to go back in time to January 17 for the skew graph, but this graph shows the general shape of a skew curve, particularly when the underlying has been dropping hard. IV rises quite sharply the further out of the money those put strikes are. Implied volatility also rises for the out-of-the-money calls, although not as sharply because of the way that puts are used. When markets are in a rabid rally, however, the skew curve can kick up on the upside, despite a dropping VIX.

What does all that "skew" stuff mean? It means that the implied volatilities in the individual options that make up one's trade can be changing at different rates. For a deeper understanding--deeper than the cursory knowledge I have--you might investigate the books of Jeff Augen, such as The Volatility Edge in Options Trading. You can trade without digging into Augen's or someone else's books that describe minutia about options skews, but you should not trade without understanding that some of your trades are volatility trades as much as they are price-related trades.

On January 17, the huge absolute value of the vega on that iron butterfly proves that volatility changes were likely going to make the most immediate impact on that trade, particularly in the OTM options most impacted by changes in skew. Understand where your risk lies. It's not always just about price action.

We've just been through a period when the VIX jumped all the way to 21.48 before dropping back into the mid-teens by Friday. We're seeing the volatility measures themselves become more volatile. It make take a while before we know whether the VIX will find support at 14-15 and then streak higher again or whether it will sink all the way back into the 12-13 range as equities rise again. In all my backtesting of my particular trade, I found this the most problematic time to enter a new trade. It can be more difficult to manage rapid changes in implied volatility than it is to manage rapid price changes, and the two together sometimes makes for a stressful trade. Assess your risk levels before entering new trades and size them accordingly.

Linda Piazza