CHAPTER 12
Delta-Neutral Trading
Trading Implied Volatility
Many of the strategies covered so far have been option-selling strategies. Some had a directional bias; some did not. Most of the strategies did have a primary focus on realized volatility—especially selling it. These short volatility strategies require time. The reward of low stock volatility is theta. In general, most of the strategies previously covered were theta trades in which negative gamma was an unpleasant inconvenience to be dealt with.
Moving forward, much of the remainder of this book will involve more in-depth discussions of trading both realized and implied volatility (IV), with a focus on the harmonious, and sometimes disharmonious, relationship between the two types. Much attention will be given to how IV trades in the option market, describing situations in which volatility moves are likely to occur and how to trade them.
Direction Neutral versus Direction Indifferent
In the world of nonlinear trading, there are two possible nondirectional views of the underlying asset: direction neutral and direction indifferent. Direction neutral means the trader believes the stock will not trend either higher or lower. The trader is neutral in his or her assessment of the future direction of the asset. Short iron condors, long time spreads, and out-of-the-money (OTM) credit spreads are examples of direction-neutral strategies. These strategies generally have deltas close to zero. Because of negative gamma, movement is the bane of the direction-neutral trade.
Direction indifferent means the trader may desire movement in the underlying but is indifferent as to whether that movement is up or down. Some direction-indifferent trades are almost completely insulated from directional movement, with a focus on interest or dividends instead. Examples of these types of trades are conversions, reversals, and boxes, which are described in Chapter 6, as well as dividend plays, which are described in Chapter 8.
Other direction-indifferent strategies are long option strategies that have positive gamma. In these trades, the focus is on movement, but the direction of that movement is irrelevant. These are plays that are bullish on realized volatility. Yet other direction-indifferent strategies are volatility plays from the perspective of IV. These are trades in which the trader’s intent is to take a bullish or bearish position in IV.
Delta Neutral
To be truly direction neutral or direction indifferent means to have a delta equal to zero. In other words, there are no immediate gains if the underlying moves incrementally higher or lower. This zero-delta method of trading is called
delta-neutral trading
.
A delta-neutral position can be created from any option position simply by trading stock to flatten out the delta. A very basic example of a delta-neutral trade is a long at-the-money (ATM) call with short stock.
Consider a trade in which we buy 20 ATM calls that have a 50 delta and sell stock on a delta-neutral ratio.
Buy 20 50-delta calls (long 1,000 deltas)
Short 1,000 shares (short 1,000 deltas)
In this position, we are long 1,000 deltas from the calls (20 × 50) and short 1,000 deltas from the short sale of stock. The net delta of the position is zero. Therefore, the immediate directional exposure has been eliminated from the trade. But intuitively, there are other opportunities for profit or loss with this trade.
The addition of short stock to the calls will affect only the delta, not the other greeks. The long calls have positive gamma, negative theta, and positive vega.
Exhibit 12.1
is a simplified representation of the greeks for this trade.
EXHIBIT 12.1
20-lot delta-neutral long call.
With delta not an immediate concern, the focus here is on gamma, theta, and vega. The +1.15 vega indicates that each one-point change in IV makes or loses $115 for this trade. Yet there is more to the volatility story. Each day that passes costs the trader $50 in time decay. Holding the position for an extended period of time can produce a loser even if IV rises. Gamma is potentially connected to the success of this trade, too. If the underlying moves in either direction, profit from deltas created by positive gamma may offset the losses from theta. In fact, a big enough move in either direction can produce a profitable trade, regardless of what happens to IV.
Imagine, for a moment, that this trade is held until expiration. If the stock is below the strike price at this point, the calls expire. The resulting position is short 1,000 shares of stock. If the stock is above the strike price at expiration, the calls can be exercised, creating 2,000 shares of long stock. Because the trade is already short 1,000 shares, the resulting net position is long 1,000 shares (2,000 − 1,000). Clearly, the more the underlying stock moves in either direction the greater the profit potential. The underlying has to move far enough above or below the strike price to allow the beneficial gains from buying or selling stock to cover the option premium lost from time decay. If the trade is held until expiration, the underlying needs to move far enough to cover the entire premium spent on the calls.
The solid lines forming a V in
Exhibit 12.2
conceptually illustrate the profit or loss for this delta-neutral long call at expiration.
EXHIBIT 12.2
Profit-and-loss diagram for delta-neutral long-call trade.
Because of gamma, some deltas will be created by movement of the underlying before expiration. Gamma may lead to this being a profitable trade in the short term, depending on time and what happens with IV. The dotted line illustrates the profit or loss of this trade at the point in time when the trade is established. Because the options may still have time value at this point—depending on how far from the strike price the stock is trading—the value of the position, as a whole, is higher than it will be if the calls are trading at parity at expiration. Regardless, the plan is for the stock to make a move in either direction. The bigger the move and the faster it happens, the better.
Why Trade Delta Neutral?
A few years ago, I was teaching a class on option trading. Before the seminar began, I was talking with one of the students in attendance. I asked him what he hoped to learn in the class. He said that he was really interested in learning how to trade delta neutral. When I asked him why he was interested in that specific area of trading, he replied, “I hear that’s where all the big money is made!”
This observation, right or wrong, probably stems from the fact that in the past most of the trading in this esoteric discipline has been executed by professional traders. There are two primary reasons why the pros have dominated this strategy: high commissions and high margin requirements for retail traders. Recently, these two reasons have all but evaporated.
First, the ultracompetitive world of online brokers has driven commissions for retail traders down to, in some cases, what some market makers pay. Second, the oppressive margin requirements that retail option traders were subjected to until 2007 have given way to portfolio margining.
Portfolio Margining
Customer portfolio margining is a method of calculating customer margin in which the margin requirement is based on the “up and down risk” of the portfolio. Before the advent of portfolio margining, retail traders were subject to strategy-based margining, also called Reg. T margining, which in many cases required a significantly higher amount of capital to carry a position than portfolio margining does.
With portfolio margining, highly correlated securities can be offset against each other for purposes of calculating margin. For example, SPX options and SPY options—both option classes based on the Standard & Poor’s 500 Index—can be considered together in the margin calculation. A bearish position in one and a bullish position in the other may partially offset the overall risk of the portfolio and therefore can help to reduce the overall margin requirement.
With portfolio margining, many strategies are margined in such a way that, from the point of view of this author, they are subject to a much more logical means of risk assessment. Strategy-based margining required traders of some strategies, like a protective put, to deposit significantly more capital than one could possibly lose by holding the position. The old rules require a minimum margin of 50 percent of the stock’s value and up to 100 percent of the put premium. A portfolio-margined protective put may require only a fraction of what it would with strategy-based margining.
Even though Reg. T margining is antiquated and sometimes unreasonable, many traders must still abide by these constraints. Not all traders meet the eligibility requirements to qualify for portfolio-based margining. There is a minimum account balance for retail traders to be eligible for this treatment. A broker may also require other criteria to be met for the trader to benefit from this special margining. Ultimately, portfolio margining allows retail traders to be margined similarly to professional traders.
There are some traders, both professional and otherwise, who indeed have made “big money,” as the student in my class said, trading delta neutral. But, to be sure, there are successful and unsuccessful traders in many areas of trading. The real motivation for trading delta neutral is to take a position in volatility, both implied and realized.
Trading Implied Volatility
With a typical option, the sensitivity of delta overshadows that of vega. To try and profit from a rise or fall in IV, one has to trade delta neutral to eliminate immediate directional sensitivity. There are many strategies that can be traded as delta-neutral IV strategies simply by adding stock. Throughout this chapter, I will continue using a single option leg with stock, since it provides a simple yet practical example. It’s important to note that delta-neutral trading does not refer to a specific strategy; it refers to the fact that the trader is indifferent to direction. Direction isn’t being traded, volatility is.
Volatility trading is fundamentally different from other types of trading. While stocks can rise to infinity or decline to zero, volatility can’t. Implied volatility, in some situations, can rise to lofty levels of 100, 200, or even higher. But in the long-run, these high levels are not sustainable for most stocks. Furthermore, an IV of zero means that the options have no extrinsic value at all. Now that we have established that the thresholds of volatility are not as high as infinity and not as low as zero, where exactly are they? The limits to how high or low IV can go are not lines in the sand. They are more like tides that ebb and flow, but normally come up only so far onto the beach.
The volatility of an individual stock tends to trade within a range that can be unique to that particular stock. This can be observed by studying a chart of recent volatility. When IV deviates from the range, it is typical for it to return to the range. This is called
reversion to the mean
, which was discussed in Chapter 3. IV can get stretched in either direction like a rubber band but then tends to snap back to its original shape.
There are many examples of situations where reversion to the mean enters into trading. In some, volatility temporarily dips below the typical range, and in some, it rises beyond the recent range. One of the most common examples is the rush and the crush.
The Rush and the Crush
In this situation, volatility rises before and falls after a widely anticipated news announcement, of earnings, for instance, or of a Food and Drug Administration (FDA) approval. In this situation, option buyers rush in and bid up IV. The more uncertainty—the more demand for insurance—the higher vol rises. When the event finally occurs and the move takes place or doesn’t, volatility gets crushed. The crush occurs when volatility falls very sharply—sometimes 10 points, 20 points, or more—in minutes. Traders with large vega positions appreciate the appropriateness of the term crush all too well. Volatility traders also affectionately refer to this sudden drop in IV by saying that volatility has gotten “whacked.”
In order to have a feel for whether implied volatility is high or low for a particular stock, you need to know where it’s been. It’s helpful to have an idea of where realized volatility is and has been, too. To be sure, one analysis cannot be entirely separate from the other. Studying both implied and realized volatility and how they relate is essential to seeing the big picture.
The Inertia of Volatility
Sir Isaac Newton said that an object in motion tends to stay in motion unless acted upon by another force. Volatility acts much the same way. Most stocks tend to trade with a certain measurable amount of daily price fluctuations. This can be observed by looking at the stock’s realized volatility. If there is no outside force—some pivotal event that fundamentally changes how the stock is likely to behave—one would expect the stock to continue trading with the same level of daily price movement. This means IV (the market’s expectation of future stock volatility) should be the same as realized volatility (the calculated past stock volatility).
But just as in physics, it seems there is always some friction affecting the course of what is in motion. Corporate earnings, Federal Reserve Board reports, apathy, lulls in the market, armed conflicts, holidays, rumors, and takeovers, among other market happenings all provide a catalyst for volatility changes. Divergences of realized and implied volatility, then, are commonplace. These divergences can create tradable conditions, some of which are more easily exploited than others.
To find these opportunities, a trader must conduct a study of volatility. Volatility charts can help a trader visualize the big picture. This historical information offers a comparison of what is happening now in volatility with what has happened in the past. The following examples use a volatility chart to show how two different traders might have traded the rush and crush of an earnings report.
Volatility Selling
Susie Seller, a volatility trader, studies semiconductor stocks.
Exhibit 12.3
shows the volatilities of a $50 chip stock. The circled area shows what happened before and after second-quarter earnings were reported in July. The black line is the IV, and the gray is the 30-day historical.
EXHIBIT 12.3
Chip stock volatility before and after earnings reports.
Source
: Chart courtesy of
iVolatility.com
In mid-July, Susie did some digging to learn that earnings were to be announced on July 24, after the close. She was careful to observe the classic rush and crush that occurred to varying degrees around the last three earnings announcements, in October, January, and April. In each case, IV firmed up before earnings only to get crushed after the report. In mid-to-late July, she watched as IV climbed to the mid-30s (the rush) just before earnings. As the stock lay in wait for the report, trading came to a proverbial screeching halt, sending realized volatility lower, to about 13 percent. Susie waited for the end of the day just before the report to make her move. Before the closing bell, the stock was at $50. Susie sold 20 one-month 50-strike calls at 2.10 (a 35 volatility) and bought 1,100 shares of the underlying stock at $50 to become delta neutral.
Exhibit 12.4
shows Susie’s position.
EXHIBIT 12.4
Delta-neutral short ATM call, long stock position.
Her delta was just about flat. The delta for the 50 calls was 0.54 per contract. Selling a 20-lot creates 10.80 short deltas for her overall position. After buying 1,100 shares, she was left long 0.20 deltas, about the equivalence of being long 20 shares. Where did her risk lie? Her biggest concern was negative gamma. Without even seeing a chart of the stock’s price, we can see from the volatility chart that this stock can have big moves on earnings. In October, earnings caused a more than 10-point jump in realized volatility, to its highest level during the year shown. Whether the stock rose or fell is irrelevant. Either event means risk for a premium seller.
The positive theta looks good on the surface, but in fact, theta provided Susie with no significant benefit. Her plan was “in and out and nobody gets hurt.” She got into the trade right before the earnings announcement and out as soon as implied volatility dropped off. Ideally, she’d like to hold these types of trades for less than a day. The true prize is vega.
Susie was looking for about a 10-point drop in IV, which this option class had following the October and January earnings reports. April had a big drop in IV, as well, of about eight or nine points. Ultimately, what Susie is looking for is reversion to the mean.
She gauges the normal level of volatility by observing where it is before and after the surges caused by earnings. From early November to mid- to late- December, the stock’s IV bounced around the 25 percent level. In the month of February, the IV was around 25. After the drop-off following April earnings and through much of May, the IV was closer to 20 percent. In June, IV was just above 25. Susie surmised from this chart that when no earnings event is pending, this stock’s options typically trade at about a 25 percent IV. Therefore, anticipating a 10-point decline from 35 was reasonable, given the information available. If Susie gets it right, she stands to make $1,150 from vega (10 points × 1.15 vegas × 100).
As we can see from the right side of the volatility chart in
Exhibit 12.3
, Susie did get it right. IV collapsed the next morning by just more than ten points. But she didn’t make $1,150; she made less. Why? Realized volatility (gamma). The jump in realized volatility shown on the graph is a function of the fact that the stock rallied $2 the day after earnings. Negative gamma contributed to negative deltas in the face of a rallying market. This negative delta affected some of Susie’s potential vega profits.
So what was Susie’s profit? On this trade she made $800. The next morning at the open, she bought back the 50-strike calls at 2.80 (25 IV) and sold the stock at $52. To compute her actual profit, she compared the prices of the spread when entering the trade with the prices of the spread when exiting.
Exhibit 12.5
shows the breakdown of the trade.
EXHIBIT 12.5
Profit breakdown of delta-neutral trade.
After closing the trade, Susie knew for sure what she made or lost. But there are many times when a trader will hold a delta-neutral position for an extended period of time. If Susie hadn’t closed her trade, she would have looked at her marks to see her P&(L) at that point in time. Marks are the prices at which the securities are trading in the actual market, either in real time or at end of day. With most online brokers’ trading platforms or options-trading software, real-time prices are updated dynamically and always at their fingertips. The profit or loss is, then, calculated automatically by comparing the actual prices of the opening transaction with the current marks.
What Susie will want to know is why she made $800. Why not more? Why not less, for that matter? When trading delta neutral, especially with more complex trades involving multiple legs, a manual computation of each leg of the spread can be tedious. And to be sure, just looking at the profit or loss on each leg doesn’t provide an explanation.
Susie can see where her profits or losses came from by considering the profit or loss for each influence contributing to the option’s value.
Exhibit 12.6
shows the breakdown.
EXHIBIT 12.6
Profit breakdown by greek.
Delta
Susie started out long 0.20 deltas. A $2 rise in the stock price yielded a $40 profit attributable to that initial delta.
Gamma
As the stock rose, the negative delta of the position increased as a result of negative gamma. The delta of the stock remained the same, but the negative delta of the 50 call grew by the amount of the gamma. Deriving an exact P&(L) attributable to gamma is difficult because gamma is a dynamic metric: as the stock price changes, so can the gamma. This calculation assumes that gamma remains constant. Therefore, the gamma calculation here provides only an estimate.
The initial position gamma of −1.6 means the delta decreases by 3.2 with a $2 rise in the stock (–1.60 times the $2 rise in the stock price). Susie, then, would multiply −3.2 by $2 to find the loss on −3.2 deltas over a $2 rise. But she wasn’t short 3.2 deltas for the whole $2. She started out with zero deltas attributable to gamma and ended up being 3.2 shorter from gamma over that $2 move. Therefore, if she assumes her negative delta from gamma grew steadily from 0 to −3.2, she can estimate her average delta loss over that move by dividing by 2.
Theta
Susie held this trade one day. Her total theta contributed 0.75 or $75 to her position.
Vega
Vega is where Susie made her money on this trade. She was able to buy her call back 10 IV points lower. The initial position vega was −1.15. Multiplying −1.15 by the negative 10-point crush of volatility yields a vega profit of $1,150.
Conclusions
Studying her position’s P&(L) by observing what happened in her greeks provides Susie with an alternate—and in some ways, better—method to evaluate her trade. The focus of this delta-neutral trade is less on the price at which Susie can buy the calls back to close the position than on the volatility level at which she can buy them back, weighed against the P&(L) from her other risks. Analyzing her position this way gives her much more information than just comparing opening and closing prices. Not only does she get a good estimate of how much she made or lost, but she can understand why as well.
The Imprecision of Estimation
It is important to notice that the P&(L) found by adding up the P&(L)’s from the greeks is slightly different from the actual P&(L). There are a couple of reasons for this. First, the change in delta resulting from gamma is only an estimate, because gamma changes as the stock price changes. For small moves in the underlying, the gamma change is less significant, but for larger moves, the rate of change of the gamma can be bigger, and it can be nonlinear. For example, as an option moves from being at-the-money (ATM) to being out-of-the-money (OTM), its gamma decreases. But as the option becomes more OTM, its gamma decreases at a slower rate.
Another reason that the P&(L) from the greeks is different from the actual P&(L) is that the greeks are derived from the option-pricing model and are therefore theoretical values and do not include slippage.
Furthermore, the volatility input in this example is rounded a bit for simplicity. For example, a volatility of 25 actually yielded a theoretical value of 2.796, while the call was bought at 2.80. Because some options trade at minimum price increments of a nickel, and none trade in fractions of a penny, IV is often rounded.
Caveat Venditor
Reversion to the mean holds the promise of profit in this trade, but Susie also knows that this strategy does not come without risks of loss. The mean to which volatility is expected to revert is not a constant. This benchmark can and does change. In this example, if the company had an unexpectedly terrible quarter, the stock could plunge sharply. In some cases, this would cause IV to find a new, higher level at which to reside. If that had happened here, the trade could have been a big loser. Gamma and vega could both have wreaked havoc. In trading, there is no sure thing, no matter what the chart looks like. Remember, every ship on the bottom of the ocean has a chart!
Volatility Buying
This same earnings event could have been played entirely differently. A different trader, Bobby Buyer, studied the same volatility chart as Susie. It is shown again here as
Exhibit 12.7
. Bobby also thought there would be a rush and crush of IV, but he decided to take a different approach.
EXHIBIT 12.7
Chip stock volatility before and after earnings reports.
Source
: Chart courtesy of
iVolatility.com
About an hour before the close of business on July 21, just three days before earnings announcements, Bobby saw that he could buy volatility at 30 percent. In Bobby’s opinion, volatility seemed cheap with earnings so close. He believed that IV could rise at least five points over the next three days. Note that we have the benefit of 20/20 hindsight in the example.
Near the end of the trading day, the stock was at $49.70. Bobby bought 20 33-day 50-strike calls at 1.75 (30 volatility) and sold short 1,000 shares of the underlying stock at $49.70 to become delta neutral.
Exhibit 12.8
shows Bobby’s position.
EXHIBIT 12.8
Delta-neutral long call, short stock position.
With the stock at $49.70, the calls had +0.51 delta per contract, or +10.2 for the 20-lot. The short sale of 1,000 shares got Bobby as close to delta-neutral as possible without trading an odd lot in the stock. The net position delta was +0.20, or about the equivalent of being long 20 shares of stock. Bobby’s objective in this case is to profit from an increase in implied volatility leading up to earnings.
While Susie was looking for reversion to the mean, Bobby hoped for a further divergence. For Bobby, positive gamma looked like a good thing on the surface. However, his plan was to close the position just before earnings were released—before the vol crush and before the potential stock-price move. With realized volatility already starting to drop off at the time the trade was put on, gamma offered little promise of gain.
As fate would have it, IV did indeed increase. At the end of the day before the July earnings report, IV was trading at 35 percent. Bobby closed his trade by selling his 20-lot of the 50 calls at 2.10 and buying his 1,000 shares of stock back at $50.
Exhibit 12.9
shows the P&(L) for each leg of the spread.
EXHIBIT 12.9
Profit breakdown.
The calls earned Bobby a total of $700, while the stock lost $300. Of course, with this type of trade, it is not relevant which leg was a winner and which a loser. All that matters is the bottom line. The net P&(L) on the trade was a gain of $400. The gain in this case was mostly a product of IV’s rising.
Exhibit 12.10
shows the P&(L) per greek.
EXHIBIT 12.10
Profit breakdown by greek.
Delta
The position began long 0.20 deltas. The 0.30-point rise earned Bobby a 0.06 point gain in delta per contract.
Gamma
Bobby had an initial gamma of +1.8. We will use 1.8 for estimating the P&(L) in this example, assuming gamma remained constant. A 0.30 rise in the stock price multiplied by the 1.8 gamma means that with the stock at $50, Bobby was long an additional 0.54 deltas. We can estimate that over the course of the 0.30 rise in the stock price, Bobby was long an average of 0.27 (0.54 ÷ 2). His P&(L) due to gamma, therefore, is a gain of about 0.08 (0.27 × 0.30).
Theta
Bobby held this trade for three days. His total theta cost him 1.92 or $192.
Vega
The biggest contribution to Bobby’s profit on this trade was made by the spike in IV. He bought 30 volatility and sold 35 volatility. His 1.20 position vega earned him 6.00, or $600.
Conclusions
The $422 profit is not exact, but the greeks provide a good estimate of the hows and the whys behind it. Whether they are used for forecasting profits or for doing a postmortem evaluation of a trade, consulting the greeks offers information unavailable by just looking at the transaction prices.
By thinking about all these individual pricing components, a trader can make better decisions. For example, about two weeks earlier, Bobby could have bought an IV level closer to 26 percent. Being conscious of his theta, however, he decided to wait. The $64-a-day theta would have cost him $896 over 14 days. That’s much more that the $480 he could have made by buying volatility four points lower with his 1.20 vega.
Risks of the Trade
Like Susie’s trade, Bobby’s play was not without risk. Certainly theta was a concern, but in addition to that was the possibility that IV might not have played out as he planned. First, IV might not have risen enough to cover three days’ worth of theta. It needed to rise, in this case, about 1.6 volatility points for the 1.20 vega to cover the 1.92 theta loss. It might even have dropped. An earlier-than-expected announcement that the earnings numbers were right on target could have spoiled Bobby’s trade. Or the market simply might not have reacted as expected; volatility might not have risen at all, or might have fallen. Remember, IV is a function of the market. It does not always react as one thinks it should.