Options Trading: Volatility and Volatility Derivatives

VOLATILITY AND VOLATILITY DERIVATIVES

Until recently, the challenge of even quantifying volatility, much less managing it, was focused on the one instrument that we know to be dependent on volatility—options. But, volatility has now become a focus in and of itself as a measurable, manageable, tradable entity. Some even view volatility as an asset class in its own right. Today’s traders and portfolio managers would do well to take advantage of the volatility products that exist, for they not only give clues to market direction, they can often provide protection and facilitate hedging strategies in an even more efficient manner than conventional puts. We feel this area of listed derivatives is sure to continue expanding in the future and is important to include here.

What Is Volatility?

As we have mentioned elsewhere in the book, there are two types of volatility—historical (also called actual or statistical) and implied. Historical volatility refers to how fast a stock, ETF, index, or futures contract has moved around in the past. It is usually measured as the standard deviation of daily percentage price changes. Though widely accepted, this definition can yield strange results. It allows, for example, that if a stock advances by the exact same percentage every day, day after day, its historical volatility is zero! That’s why there are other measures of volatility as well, but the one defined here is the most common. Typically, one observes the 10-, 20-, 50-, and 100-day historical volatilities for any particular entity.

Historical volatility is a backward-looking measure. Implied volatility, on the other hand, is forward looking. The part of an option’s price that is time value premium is somewhat of a misnomer, as in reality, it is much more related to volatility than it is to time. Yes, the time value premium will steadily shrink to zero as time passes. But, in the interim, the time component of an option’s price is heavily dependent on implied volatility.

In essence, every time an option trades, the market is making an estimate of the stock’s future volatility. If you expect the underlying stock to be volatile, you will pay a higher price for an option—put or call. Conversely, if you expect the underlying stock to be docile, you won’t pay much for the options at all. Thus, implied volatility is an estimate of how volatile the underlying entity is expected to be during the remaining life of the option. Events that can cause implied volatility to increase are those that are expected to cause the stock to deviate from its usual pattern of trading—takeover bids or rumors, large price drops (severe bear markets), Food and Drug Administration (FDA) hearings, lawsuits, and so on.

Measuring Volatility

For as long as listed options have existed (since 1973), option analysts have attempted to determine an overall composite volatility measure. In other words, just how high-priced (or low-priced) are options, in general? In 1993, the process was finally quantified when the CBOE began publishing its Volatility Index, VIX. The index has been quite successful and has become an effective measure of sentiment: rising wildly during crashing or severely bearish markets, and dropping to extremely low values during times of complacency.

The original formula for calculating VIX was derived for the CBOE by Robert E. Whaley of Duke University. It used a small subset of the options on the CBOE’s heavily traded (at the time) S&P 100 (OEX) options. The calculation involved only two strikes (one above and below the OEX current price) and the two nearest months, but was sufficient for the desired purpose. There was no way to trade VIX; it could only be observed and utilized as an indicator. If traders thought volatility was too low, they might, for example, buy straddles on the broad-based indexes or on a package of individual stocks.

As time passed, though, OEX options began to wane in popularity— having been replaced by the more liquid and institutionally favored S&P 500 (SPX) options that also trade on the CBOE. Furthermore, there were complaints that the VIX calculation did not take into account the OTM index puts, which were often the ones with wildly exaggerated implied volatilities. So, in 2003, the definition of VIX was changed. The old VIX was renamed VXO (for “volatility of OEX”) and a new VIX was created, using SPX options.

This new VIX takes into account a large strip of options—all the strikes at which valid option markets are being made—hundreds in this case. (With SPX recently near 1,200, there are currently strikes from 100 to 2,500!) Still, only the two front months are used. The actual formula for VIX—which is complicated—can be found in a white paper on the CBOE’s web site. The main point to note is that VIX is a 30-day volatility estimate. Thus, if you want to simulate VIX, you need to stay short-term with the various VIX products in order to do so.

Before getting into the definitions and uses of volatility derivatives, we will briefly discuss how VIX itself can be useful to investors.

Using VIX as a Market Indicator

Option pricing and volume data can often be used to help explain, and even forecast the direction of the underlying market. In some cases, this option data is direct, meaning that it reflects the direct actions of so-called “smart money” players, the assumption being that when the smart money is “operating,” it is wise to follow along. More often, though, the option data is contrary. In that case, prices reflect the general public piling incorrectly in at a market extreme, when a reversal of price is about to occur. For this reason, VIX, in general, is a contrary indicator.

The best example of this is the occasional buy signal that VIX generates: when the broad market is falling rapidly (even crashing), and VIX is skyrocketing upward. When this happens, a spike peak in VIX is usually a buy signal for the broad market.

When VIX is very high or spiking, implied volatility is very high and options are of course expensive, so a call purchase on a market-based ETF might not work so well due to its inflated price. If the market does rally, a call could lose implied volatility, and that could offset much or all of the benefit of being correct on the market’s direction. It would still be possible to make money if the market rallies enough, but one is generally advised against buying overly expensive options as the odds are not in your favor. A better speculative approach would be a bull call spread: buying an at-the-money call and selling a call against it at a strike well above that of the purchased call.

As an alternate approach, these spike peaks in VIX may be good indicators for buying the underlying, and for potentially selling covered calls if one is so inclined. In general, covered call writes and/or naked put sales can be entered with a reasonable degree of confidence after a spike peak in VIX.

FIGURE 9.1 Historical VXO

Those with a short-term horizon might use the VIX spike peak as a trigger for entering long trades, but anything bought on a spike peak in VIX should be stopped out if VIX goes to a higher high—then wait for another peak in VIX to form before re-entering a bullish, speculative trade.

The effectiveness of this approach, on a broad scale, can be seen from the long-term chart in Figure 9.1. When the CBOE first commissioned the creation of the old VIX (now VXO), in 1993, it backdated the data to 1986. Hence we have a longer history for VXO than we do for VIX. One of the reasons for backdating it that far may have been to include the crash of’87 in its history. (VXO did not actually exist at the time of the crash, but if it had, VXO would have valued at a high of approximately 150 that day.)

In Figure 9.1, you can see all of the market scares over the years that have caused VXO to spike up and then back down again. Many of them are identified. Some of the most notable were the Dow trading down the limit (the only time that’s ever happened) in October, 1997; the dual market scares—Russian debt crisis followed by the long-term capital hedge fund crisis—in 1998; the severe bear market in the summer of 2002; and, of course, the credit crisis of 2008, during which VXO rose to 103 at its peak.

In all of these cases, the market recovered substantially. On an everyday basis, there are other spike peaks in VIX (and VXO) that are perhaps not as dramatic (spikes up to say 20 or 30), but they can be just as effective in identifying an exhaustion of bearish sentiment, which leads to an intermediate-term rally in the broad stock market.

There is no particular level of VIX that marks these buying opportunities. Rather it’s the climactic effect of VIX spiking up and reversing back down again. What causes this? Generally, it is fear in the marketplace. It usually takes place as the broad market is declining sharply (even crashing), and traders begin to panic. When they do, they rush to buy SPX puts as protection. As you might imagine, these puts get rather expensive at such times. It’s akin to waiting until your house is on fire before you decide to get quotes on fire insurance; needless to say, it would be very expensive. The same applies here. Protection is expensive when the market is crashing. Since VIX measures the implied volatility of SPX options, VIX races upward as traders rush to buy the protection. Then, at the peak, when the “last” trader has bought the “last” put, demand dries up, VIX plummets, and the market rallies. It is one of the consummate contrarian indicators.

VIX as a Trend Indicator

Another feature of VIX that is important is its trend. In general, VIX trades opposite to the market’s direction about 75 percent of the time. Over longer time periods, the percentage is slightly higher. So, if VIX is trending up, the stock market is likely trending down, and vice versa. Figure 9.2 shows a snapshot of the market in 2008—2009, and various trends in VIX are shown as well. The lines denote periods in which the stock market was rising and VIX was trending lower or vice versa.

Sometimes the market action is so violent (as in October and November, 2008, for example) that a trend in VIX is not discernible. At other specific times, there also doesn’t appear to be much of a trend (as in February 2009). But, if one is in doubt about the trend of the market, it might be instructive to look at the trend of VIX. If the trend in VIX is clearer, that should be an aid to discerning the true trend of the broad market.

We have also observed that there is a seasonality to VIX as well. This can be useful, although experienced traders know that seasonal trends are just a general guideline—any particular year can provide variations. Figure 9.3 shows the seasonality of VIX, using data from 1989 through 2009. To construct this chart, we took the closing price of VIX on the first trading day of each year, summed them, and divided by 21. Then the process was repeated for the second trading day of the year, and so forth.

The result shows some noticeable trends. Initially, VIX trends slowly higher into March (point B). Then there is a general decline into the yearly low—which, on average, is just about the first of July (point C). This may not be too surprising.

FIGURE 9.2 VIX versus SPX

FIGURE 9.3 VXO Composite by Trading Day of Year, 21-Year Composite Spread: 1989 to 2009

Neither is the fact that VIX then rises all through the fall of the year, eventually peaking in October (point F). What happens after that, though, is a bit of a mystery. We speculate that naive traders get hurt by the volatility explosion of August through October, so that by the time it’s near its peak, they think they should buy volatility. But from October through the end of the year, there is such a drain of volatility that VIX ends the year almost back at the July lows. Then the process begins anew.

Of course, not every year conforms exactly to this roadmap. Sometimes the process is similar, but accelerated, as occurred in both 2006 and 2010. (Interestingly, and perhaps coincidentally, both were mid-term election years). In those years, the whole process appears “squashed” to the left. The seasonal peak came in the early summer, and the drain was lengthy for the rest of the year.

Figure 9.4 shows the VIX annual chart for 2006, while Figure 9.5 shows it for 2010. Notice that the same general pattern exists as in Figure 9.4, but at slightly different times of the year. The years start with VIX rising into February, then declining into the lows in April. Then a large volatility spike takes place, peaking in May or June, and finally, there is a general volatility decline throughout the remainder of the year.

FIGURE 9.4 2006 Volatility

FIGURE 9.5 2010 Volatility

Even in the craziest of years—2008—the seasonal pattern was quite accurate. That year, VIX actually bottomed in August, streaked to unexpected highs in October, and finished the year substantially below that October peak.

Does VIX Accurately Predict Volatility on SPX?

Before leaving this subject, let’s examine the ability of VIX to predict the actual volatility of SPX. Recall that VIX is a 30-day volatility estimate. Those are calendar days, so it’s a one-month volatility estimate. There are about 21 or 22 trading days in most months, so if we were to look back at the fairly common measure of 20-day historical volatility of SPX, we’d have a pretty good comparison: VIX versus the 20-day historical volatility of SPX.

Does the level of VIX “predict” the actual volatility that SPX will experience over the coming month? Actually no—not very well. VIX is almost always higher than actual volatility turns out to be. On average, we found VIX to be about four points higher than the subsequent 20-day historical volatility, but sometimes even much higher than that.

FIGURE 9.6 Distribution: VIX minus SPX Historical Volatility

 Why is this? We surmise that SPX option buyers are simply willing to overpay for those options to a certain extent—particularly for protective puts. This is not terribly surprising as there are few alternatives for quick portfolio protection and market makers probably just raise the offering prices when they see institutions come in to buy hundreds or thousands of contracts. Figure 9.6 shows the distribution of daily data points. Notice that is fairly common for VIX to be two to eight points higher than actual volatility turns out to be. For this reason, in general, SPX options are somewhat overpriced and may thus represent an attractive sale. The overpricing tends to be mostly in OTM puts, so those are the particularly best sale, and that is one of the strategies espoused in this book.

Volatility Futures

In order to understand VIX options, it is necessary to understand VIX futures—regardless of whether you trade the futures directly or not. In the following discussion, the description of expiration dates and settlement procedures are the same for both VIX futures and VIX options.

Volatility futures began trading in 2004. Prior to that time, one could measure volatility (VIX), but not directly trade it. If one wanted to be “long” volatility, they would have to buy a neutral package of options that had long vega (the amount of movement in an option resulting from a change in volatility) but were more or less neutral with respect to other risk measures. This was very difficult and complicated to do, so most people who wanted to be long volatility merely bought SPX straddles and adjusted the position as time went along.

This was not the first time that option traders found themselves in such a situation. Stock options were listed in 1973, but the first index option—OEX—was not listed until 1983. Hence, during that time, if someone had an opinion on the broad market, he or she couldn’t directly trade it. It would have been necessary to buy a package of options on big-cap stocks like IBM, GM, and the like, and use it as a proxy for an index. After 1983, though, if one wanted to trade “the market,” it was easy—all that was necessary was to buy an OEX (or other index) option.

To be technically correct, the introduction of VIX futures did not allow one to trade VIX directly, but rather to trade derivatives on VIX—which, as we will explain, is not exactly the same thing. That aside, VIX futures came about because the CBOE created a futures exchange—the CFE (CBOE Futures Exchange)—and came up with some very creative thinking in order to create these futures.

One of the greatest impediments to the actual introduction of trading was figuring out how market makers could viably hedge a futures position. No marketplace survives without arbitrage, which supplies necessary liquidity. For example, in stock options, market makers can create positions that are “equivalent” to stock and then hedge them with stock itself.

But recall that VIX is two strips of options (the two nearest months), and the strips are weighted differently each day in order to produce a 30-day volatility estimate. So, even if a market maker were to take down a large futures position to facilitate a customer order, and then hedge it with all the options in those two strips—a Herculean task in its own right—he or she would then have to change the quantities of the options in those strips each day in order to produce the proper hedge all the way to expiration. This, of course, is next to impossible, and thus market makers were not eager to trade such a product.

The CBOE solved this by asking, “If you only had to hedge with one strip of options whose weight never changed, would that be acceptable?” It was agreed that it would be, and so the definition of the futures is that they apply only to the SPX options that are traded one month hence. In fact, on expiration day, the futures would settle at a price based on the price of SPX options expiring 30 days in the future. So, for example, February VIX futures are based on March SPX options.

Working backward, then, VIX futures expire 30 days prior to the “normal” SPX option expiration. SPX December options expired on December 17, 2010. Thirty calendar days prior to that is November 17 (meaning, on November 17, there are 13 days in November and 17 days in December—a total of 30 days—until the SPX expiration). November 17 is a Wednesday. All VIX derivatives—futures or options—expire on a Wednesday. It is either the Wednesday just before or just after the “regular” third Friday expiration of stock and index options. In this example, “regular” November stock and index option expiration was Friday, November 19. But November VIX derivatives expired two days before—on Wednesday, November 17.

Futures and futures option traders are accustomed to seeing options expire at odd times. In fact it is quite rare that a futures option expires on the third Friday of the month. However, stock option traders might be a little taken aback by this, since they have probably never seen any option expire on a Wednesday (except, perhaps, end-of-the-month options, if they happen to trade any of those).

The last trading day for VIX futures, then, is a Tuesday. The settlement actually takes place in an “A.M.” settlement on that designated Wednesday. The procedure is described in detail on the CBOE’s web site. Suffice it to say that the settlement procedure uses the initial trade of each pertinent SPX option (those expiring in 30 days) or—if there is no trade—the average of the bid and asked prices of the option. These are then combined in the usual VIX formula to determine a settlement price. The settlement price is broadcast by the CBOE using the symbol $VRO. The futures then settle for cash.

For those actually wanting to trade the futures, they are worth $1,000 per point of movement, and they are quoted in VIX-like terms. So, for example, if the November VIX futures contracts were purchased at 21.25, and it rose to 22.00, you would have an unrealized profit of $750. There are VIX futures expiring in every month of the year, just as there are SPX options expiring in every month. VIX futures contracts are typically listed for the next seven or eight months.

As with most futures contract margins, the margin for the VIX futures contract is fairly low (the complete table of margin requirements is on the CBOE web site).

Variance Futures

Before moving on to discuss the behavior of VIX futures, it should be noted that there are variance futures available for trading as well. Variance is actual (historic, statistical) volatility squared. Thus variance futures track the true volatility of SPX. The product was successful as an over-the-counter contract (traded by Goldman Sachs or Morgan Stanley to institutional customers), but has not been a success as a listed futures product. Nevertheless, we will describe it here, for it may still prove to be viable at some time in the future—or some may still want to trade it despite its illiquidity.

The listed variance futures are futures on 90-day SPX variance. That is, at settlement (which is the third Friday of the expiration month), the futures settle at the 90-day historical volatility of SPX. That is of course the 90 days preceding expiration. Variance futures are listed only for March, June, September, and December each year. Three contracts are typically listed at any one time.

The expiring contract is said to be in the expiration period during the last 90 days. As each day passes, the actual volatility of SPX is calculated, and that number is broadcast by the CBOE. Furthermore, since we know the price of the near-term variance futures, one can imply the remaining volatility that is being estimated by that futures contract. These can be very useful numbers if one wants to trade that near-term contract.

Example: suppose that about halfway through the expiration period, SPX’s actual volatility has been 15 percent, but the futures are trading at 20 percent. They are therefore implying that SPX will experience volatility of about 25 percent the rest of the way, in order to bring the total 90-day volatility up to 20 percent (the futures price) by expiration. You might think that there is little chance of SPX being that volatile for that long, and so you would sell the variance futures if that were the case. (Variance futures are worth $50 per point of movement, because they are very volatile and can move great distances in a short time.)

To convert a variance price to volatility, merely take the square root. Thus, in the above example, one would not see those volatilities as actual prices. Rather one would see the SPX variance at 225 (15 squared), and the futures trading at 400 (20 squared). But, for most people, it is easier to convert things back into volatility terms for analysis. If you are correct, and SPX variance remains at 225 on expiration date (and you hold until expiration), you would make 175 points, or $8,750 per contract.

Variance futures quotes are wide—first because of the squaring factor, but also because of their illiquidity. For example, if one were quoting markets in terms of volatility, a market maker might say that a volatility market is 20 bid, offered at 21 (in reality, volatility futures have tighter markets than that, but in the illiquid market of variance, that’s about as close as it gets). Squaring that means that the variance futures would be 400 bid, offered 441. That’s bad enough, but often at higher volatility levels, the quote widens. This has been a problem for this contract, and the CBOE has promised to address it in the future.

For now, the variance futures are something that can be looked at and perhaps lightly traded, but they aren’t liquid enough for regular trading.