"Just because a basket of tomatoes costs $10 does not mean that basket of rotten tomatoes is a better buy for only $1."
That sentence appeared in a November 21, 1999 Options 101 article written by Jim Brown. In an article titled "Paycheck or Lottery Ticket," Jim was discussing the dangers in choosing cheap out-of-the-money (OTM) options for directional options trades. You can guess which direction Jim was headed when he discussed the cheap OTM options. They were the lottery tickets and the rotten tomatoes, too. This article will build on the thought that plump tomatoes, calls or puts purchased to hedge a portfolio, may rot over time.
As Jim pointed out in that article that first appeared more than a decade ago, "Nobel prize winners developed the theory for pricing options. They were not dummies, and some options are cheap for a reason." Presumably, Jim referenced the Black-Scholes option-pricing model. New models have surfaced, but those were likely developed by people just as smart as Fischer Black and Myron Scholes.
Jim's focus a decade ago was likely on single options purchased or sold for a directional trade. Obviously, those of us who are selling iron condors for a living are employing cheap OTM options, particularly those used to hedge the closer-in options that we sold. However, I want to extend Jim's caution to some degree to the options that are part of our complex options trades, especially if the primary purpose behind their purchase has been to hedge risk.
When I'm buying an at-the-money (ATM) OEX regular butterfly or selling an ATM iron butterfly, I typically place the wings 25 or 30 points away from the body of the butterfly. For those who are not used to trading butterflies, the body is composed of the strikes I sold. For example, a one-contract ATM regular call butterfly would consist of 2 sold ATM calls, the body of the butterfly, and one long OTM call 20-30 points below the sold strikes, in my case, and one long OTM call equidistance above the sold strikes. In an iron butterfly, an ATM put and call are sold. A put is purchased below the sold put and a call is purchased an equal distance above the call.
Let's take an example of a hypothetical 4-contract OEX iron butterfly. If I'd opened an OEX iron butterfly on Wednesday, December 16, 2009, 30 days before the January expiration, the body of the butterfly might have been composed of 4 sold OEX JAN 510 calls and 4 sold OEX JAN 510 puts. As some options traders might already recognize, this forms a sold or short straddle. Traders with a higher fear threshold than I have and with deep pockets could leave the trade at that. However, most of us prefer to hedge our risk and most of us prefer not to have exorbitant amounts of buying power withheld in order to hold those naked shorts in our accounts.
Without the long wings composed of 4 long calls and 4 long puts, that short straddle would theoretically have had a position delta of -33.42. It would have been long 138.92 theta and -465.72 vega. However tame that delta might have appeared, however, the buying-power effect or margin withheld would have been anything but tame, at least in the Reg T account that most of us have. The buying power effect of this trade would have been in excess of $200,000.
However, adding long puts and calls, the wings of the butterfly, 25 points away from the sold strikes of this hypothetical 4-contract JAN OEX iron butterfly would have lowered the margin requirement or buying-power effect to $3,740.00, depending on one software's theoretical calculations and commissions. I included commissions of $1.50 per contract.
That buying-power effect is derived from multiplying the number of butterfly contracts, 4 in this case, by the distance between wings, $25, and multiplying that result by the 100 multiplier. The total credit after commissions taken in when the butterfly was sold is then deducted from the requirement.
The wings significantly lower the margin requirement or buying-power effect of this iron butterfly. They can serve another purpose for the trader, however, in hedging losses. That's why the brokerage sets a lower margin requirement or buying-power effect, after all, but we traders are interested in how well they hedge a trade, too. Some strategists such as Dan Sheridan in his CBOE webinars also suggest buying an extra long OTM call when butterflies are established. This is because most butterflies are negative delta trades, and the extra long call also helps to hedge against price-related risk if prices should zoom upward.
Let's keep Jim's rotten tomatoes comparison in mind as we think about that extra long OTM call meant to hedge price-related risk. We have to be careful that the extra long OTM call, usually fairly cheap and destined to get cheaper as time goes by unless there's a strong upward move, still provides the help that we think it will provide. We don't want that nice, plump red tomato we bought to rot, to borrow from Jim's terminology.
Let's talk actual numbers. The hypothetical 4-contract OEX iron butterfly would have had a theoretical delta of -44.76 once 25-point wings were added. Flattening out those deltas so that the butterfly wouldn't suffer as much if prices happened to climb would be the purpose in buying an extra call. Long calls have positive deltas, you might remember, and delta measures how the position reacts as prices change. A negative delta for the entire position means that it would lose money as the prices climbed. Adding those extra positive deltas lessens the impact if prices should rally.
The choice of which extra long call to purchase might prove important, as it was to be in this expiration period. While it might have been tempting to buy a cheap far-OTM call, such a call would not have provided as much of a hedge in any sharp upside move. How could a trader tell which call would be useful and which not? The cheap cost of the call is one clue: its cost is lower because it doesn't work as hard for you. It's lower in long deltas, too. For example, a cheap $0.30 call wouldn't have added much to the buying-power effect or margin withheld for the iron butterfly, but neither it have provided much of a hedge. Its delta was only 4.54. After its purchase, the position delta would have been raised only 4.54, so would have been a resultant -40.22. If there had been a quick upside move the next day, the loss to the position would have demonstrated that the hedge wasn't providing much protection at all.
In contrast the purchase of 1 JAN10 OEX 525 call, a more expensive call with a higher delta, would have raised the position delta to -22.73. (For those not mathematically inclined, moving the delta from a -44.76 to -22.73 is raising the delta, because it's not as negative a number.) This raising of the position delta would have made the trade less susceptible to losses from an upside move.
That extra long was to come in handy when the OEX moved up toward the butterfly's upper expiration breakeven, 14 days into the trade. However, what if the upside move had occurred later, when the hedge call's value--and its delta--had eroded, when the tomato had begun to soften with the first signs of decay? Traders must evaluate whether a call or put's hedging abilities have eroded as time passes. Loss of value is one clue. The lower value is a sign that the absolute value of its delta has eroded and it's not hedging what it hedged in the beginning of the trade. It might be necessary to roll that call down to one with a lower strike and a higher delta. Such a roll would be a debit but would provide more of a hedge in case of an upside move.
Different traders and advisors might choose different proportions to hedge when a trade is begun or when a hedge is applied or adjusted later in the trade. There's no one right or wrong way, as is true of so many decisions we options traders make. If a trader is skilled in technical analysis and worries that an upside breakout might be imminent, that trader might choose to hedge more deltas than someone with no market view, who just routinely hedges half the deltas. I once mentioned that I had "over hedged" a position to my broker, meaning that I had accidentally completely flattened the deltas rather than cutting them by 1/2 to 2/3, as I had intended to do, but he didn't consider that too extreme.
Whatever your preference, remember that a passage of time, or a movement away from the strike of the hedging long all impact that long's value and tend to lower the absolute value of the hedge's delta. Just as you don't want to buy too cheap an option as a hedge for a complex options position, neither do you want to count on one that has devalued too much over time. That cheap price is a sign that its hedging ability may have waned. Check the deltas! As Jim said long ago, those cheap options are cheap for a reason.