On February 9, I bought a MAR/APR RUT 590 calendar. As all calendars do, this one had a positive vega. Late the afternoon of February 12, that vega measured 24.59, which meant that my calendar should benefit from any increase in volatility. Specifically, it should gain $24.59 for each one-percentage-point gain in implied volatility.

Not so fast, though, says Mark Sebastian when writing "How Well Do You Know Your Vega?" for the February, 2010 issue of Stocks, Futures and Options Magazine. As volatility changes, Sebastian explains, the front-month and back-month options that make up calendars react differently. He likens the front-month option to a shorter-but-faster sports figure and the back-month option to a taller-but-slower sports figure.

If they're just asked to take one step, the taller figure is going to travel a farther distance with that single step. And that's the basis upon which the position vega that we see on our brokerage pages is predicated, a single step. That's also the way we think calendars will work for us. We think that, if volatility expands after we buy the calendar, the back-month option is going to travel farther. In other words, it's going to gain more in price than the front-month option, so that when we sell to close the back-month option and buy to close the front-month one in an expanding volatility environment, we'll collect more than we originally paid. The trade will be profitable.

Upon that basis, the calendar would always benefit from any expansion in volatility. And it mostly does. However, it's possible and maybe likely that volatility won't move that single step and stop. It might keep moving in a kind of foot race. In a foot race, the shorter-but-faster sports figure is going to outpace the taller-but-slower one and our calendar may not perform as well as we thought it would, Sebastian advises. The position may not perform as well as those neat little profit-loss or analysis charts predicted it would if volatility expanded. If the sold front-month option is responding more to volatility changes than the back-month option, we may not make the profit we thought we'd make.

That's what happened to my calendar the morning of February 12. The sharp drop in the RUT at the open that morning popped the sold MAR 590 call's implied volatility above the APR 590's, creating a negative skew. While that condition persisted, my calendar lost money from the previous day's closing profit rather than gained. This was true although the RVX, the volatility index that measures the volatility on the RUT, popped that morning from the previous day's close of 26.63 to a value of about 27.60 at the time this paragraph was first typed.

One can't equate a gain in the RVX exactly to a gain in implied volatilities in RUT options, of course. Still, that 24.59 position vega from late afternoon on February 11 would have led me to expect some gain and probably something in the approximate (27.60 - 26.63) X 24.59 = $23.85 range. Instead, my profit was down by a few dollars.

Later in the day, the profit waxed and waned according to the skew in the two different options, but I wanted to present a real-life example from my portfolio to corroborate what Sebastian was suggesting. In fact, Sebastian suggests that any option strategy that involves options from different expiration cycles may not perform exactly as expected unless this effect is considered. The different vegas for each option must be weighted differently in such strategies, he suggested.

I used OptionOracle's Strategy Analysis page to increase the RUT's volatility from 25.66 to 26.66. At the RUT's closing price of 610.72 on 2/12/10 (DTNIQ feed), the MAR 590 put's vega had risen from 67.95 percent to 68.10 percent. Under the same conditions, the APR 590 put's vega rose from 94.56 percent to 94.60 percent, a much smaller climb. As a result of this action, the position vega theoretically decreased from 26.61 to 26.51 although volatility was climbing. This confusing result was due to the difference in the way the options from different expiration months responded.

This action describes why some positions comprised of options from different expiration months might not always behave exactly as our risk-analysis charts lead us to believe they might. In the past, we've thought that because those further-out options have more extrinsic or time value--it's that extrinsic value that contracts or expands with changing volatility--those further-out options will react more strongly to rising volatility. Sebastian's article and these calculations show that might not be true, however.

This result makes sense when we think about it a little. Options with further-out expiration may not respond as readily to a short-term move. Implied volatility is a measure of the best estimate of future movement of the underlying, and a further-out option's implied volatility may not respond as much to a change if the move is thought to be a short-term one.

Sebastian's research took him to Nassim Taleb's Dynamic Hedging. That's not a book I currently own, so I searched James Bittman's Trading Options as a Professional for more information. Bittman points out that volatility changes may also impact vega differently depending on whether an option is in the money, out of the money or at the money. Someone establishing a RUT butterfly with in the money, out of the money and at the money strikes may run up against this same impact, although perhaps to a lesser degree. A profit or loss may not react exactly as predicted by the position vega before the volatility change. However, Bittman doesn't seem to discuss this concept of weighted vega, or at least I couldn't locate it in his book.

I use OptionOracle, BX's option pricer function or TOS's platform to look at vega changes for individual options. That gets a bit clunky, but I'm hoping that I'll eventually develop enough experience with the way vega changes according to time to expiration to "eyeball" it, as Sebastian suggests in one method for weighting vega for different option expiration periods. Using these platforms doesn't take too long, but since the calculations constantly change, it can become cumbersome. I don't worry about it too much with a single calendar position--and I'm not suggesting that you worry about it, either--but big positions with many different options may require traders to make these calculations or at least consider whether the listed position vega will be impacted by the different weighting.

Sebastian draws from Taleb's book for a rough calculation describing how vegas of the different expiration months can be weighted. "The formula," Sebastian writes in his SFO article, "is to divide base days to expiration [he uses 30] by days to expiration [for each option] and then find the square root of that quotient." He used the example of one option 22 days to expiration. The weighting determined for that option's vega was 1.17, which was calculated by taking the square root of 30/22. Another option in the calendar he was weighting was 51 days from expiration. The square root of 30/51 returned a weighting of 0.77 for that option. In the example he cited, the position vega that would have been shown by the brokerage was calculated by subtracting the sold front-month's vega (51.5) from the long back-month's vega (76.6). That would have resulted in a positive vega of +24.76, close to the position vega that was showing up for my calendar. However, after weighting the two vegas as described, the new position vega was -1.28! A position that might have been expected to return $82.45 after a 3.33 rise in the underlying's volatility instead theoretically dropped $4.26 if nothing changed other than that 3.33 rise in volatility. In fact, my calendar responded as if it had a negative and not a positive vega, although the days to expiry were different than those quoted in Sebastian's example.

The mathematically inclined among you will have realized that the closer both options are to expiration, the bigger the weighting of the short front-month option. Since in calendars, the about-to-expire option is the sold one, it would seem that the calendars would grow more and more negative vega as expiration of the front-month option approaches. However, that would ignore two realities. As Bittman teaches and shows through multiple charts (p. 106), the vega of an option collapses as expiration approaches. If an option is only 5 days from expiration, it might have a weighting of 2.45 (square root of 30/5), but that weighting multiplies a collapsing vega number. In addition, Sebastian warns that the closer an option is to expiration, the less reliable any model becomes, including the one for weighting the vegas.

Perhaps you don't want to run all these calculations, especially many times over the course of a trade. I don't blame you, but whether you run these calculations or not, Sebastian's advice that vegas may be weighted may explain why our positions don't always behave exactly as theory or risk graphs say they should. When he's explaining his "eyeball" technique, he points out the usefulness of experience in watching how options respond differently to changes in volatility, depending on their time to expiration. I think he'd agree with Bittman, too, that they respond differently according to their distance from the current underlying price.

I always think it worthwhile to get to know how your underlying and its options behave. I've advised doing so for years, and now I'm doing so with Sebastian's advice in mind. Of course, I've dabbled in calendars before, but now I'm trying to add them as a regular part of my strategy repertoire, and I'm trying them on the RUT. What I've been doing is putting up a simulated calendar trade, if I don't have a live trade open at the moment, and just watching, when I have a moment here and there, how the different options' implied volatilities respond to certain market conditions.

If you're used to trading a certain strategy on a certain underlying, you probably have an inherent feel for how they'll behave when volatilities change. I know, for example, that if volatilities expand rapidly, my delta-based adjustment point on my iron condors is going to be reached sooner, while prices are further away from my sold option than in lower-volatility periods. I know I'm going to pay more to exit since the closer-in sold strike is going to react more to the rising volatility than the further-out long strike.

So, we don't have to set up spreadsheets that are constantly recalculating our position vega. However, it doesn't have to be an onerous task to watch and familiarize ourselves with how implied volatilities change in certain options. We all have slow market days or days when we're not going to be trading for other reasons. On those days, consider picking out options at several different price points in a couple of different expiration months and watching how they respond to changing volatilities. Or you can do it in a few minutes using an option pricing calculator on your platform or on CBOE. You can't run a whole spread or position through that calculator, however, because it's going to weight each option's vega the same. And, if you don't want to bother with this whole Greeks thing at all, just put up a simulated calendar or out-of-the-money spread and watch how the profit or loss changes as market conditions change.

The topic seems weighty, but it's worth some time spent testing it for those who are so inclined. However, the point is not to get bogged down in computations but rather to realize that, under certain conditions, our risk graphs or other tools for determining when a trade might be profitable might not be entirely accurate. If a trade isn't performing as well as expected, we may be forced realize that risk-analysis graphs and tables aren't always entirely accurate, as helpful as they are. I wouldn't trade without them, but I'm going to be making decisions based on my actual profits and losses and not on what a risk-analysis graph promised me two days previously that my profit or loss would be at a certain price point.

And that's the point of this article. As always, just get to know your preferred vehicle and strategy. Get a feel for how the position tends to react under certain circumstances. None of this weighty talk should scare you off from trading calendars if they're your preferred strategy and you understand how they work. My RUT calendar has required adjustments, but I'm still hanging in there with it as I type, still looking at potential profits on risk-analysis graphs. I'm still learning the ins and outs of this strategy that has not previously been a major part of my trading repertoire, although I've of course traded calendars, and have traded them with some frequency over the last 18 months or so. Now, I'm going to be more aware than ever that the profit-loss graph is just another trading tool and not the end-all, be-all of trading.