Trading Ideas for Volatility Futures Contracts

Mean Reversion

It is a well-known mathematical fact that realized volatility is mean reverting. What this means, quite simply, is that, within a reasonable period of time, one can expect current realized volatility to revert, or return, to its mean, which is to say, to levels that are normal, or average, or customary, for the particular asset under consideration.

A Mean-Reversion Trade, or strategy, seeks to exploit this phenomenon by trading a VolatilityContract (VolContract futures) in a direction, long or short, that corresponds to the direction of reversion to the mean volatility of the underlying asset. For example, suppose that the long-term historical mean volatility for Asset A is 30%. And, suppose further that a current three-month VolContract futures (3Vol), about to begin its Realized-Volatility Period (RVP), is trading at 40.00. One might consider selling the contract at 40.00, with the expectation that, over the next three months, the underlying’s volatility will revert to historical norms of 30.00, thereby creating the potential for a profitable trade should this reversion to the mean take place within the life of the contract.

Naturally, there can be no guarantee that such a movement will actually transpire within this given time frame. But, of course, a complete return to historical levels of 30 is not required for the trade to be profitable. All that is necessary is for the movement to be in the direction of the mean for the VolContract futures’ value to decrease from 40, creating a profitable opportunity for the seller of the contract.

The buyer of VolContract futures, for the purpose of profiting from mean reversion, would have just the opposite mind-set from the above scenario. Here, the idea would be for a current volatility lower than normal, say, 20.00, to revert to higher historical levels, such as the aforementioned 30.00.

Arbing with Volatility Swaps

Before the advent of listed VolContract futures, the only mechanism available to capture, in its purest fashion, the realized volatility of an asset was the volatility swap. Such an instrument is a contractual obligation between buyer and seller, over the designated time period, to pay a predetermined amount of dollars per realized-volatility point, with reference to an initial strike-price volatility. For example, suppose an investor is convinced that the realized volatility of Asset A is going to increase over the next three months. He might engage in a volatility swap, with an initial strike price of, say, 25.00, and a agreement stating that, upon expiration, in three months, each realized-volatility point of the underlying, above or below 25.00, will have a value of $100,000.

While no funds need change hands at the inception of the trade, it is understood that the buyer will receive from the seller (r – 25.00) x $100,000, upon expiration, where r = the realized volatility of Asset A over the designated three-month life of the swap, and r > 25.00. Conversely, if r < 25.00, the buyer remits to the seller (25.00 – r) x $100,000 upon expiration.

It is reasonable to assume that, under normal circumstances, a three-month VolContract futures (3Vol), beginning its Realized-Volatility Period (RVP) on the same day as the inception of the above-referenced volatility swap, would be trading at a price ostensibly equal to the strike price of the swap. After all, the two instruments would have identical payouts after three months. However, theory and reality do not always coincide, and it is possible to imagine a scenario where the current quote for a 3Vol, just beginning its RVP, could differ from the strike price proposed by an OTC vendor for a corresponding three-month volatility swap on the same asset. In such circumstances, there might exist the opportunity for arbitrage between the two contracts.

In the above instance, if, for example, the 3Vol were trading at a level higher than 25.00, it would suffice for the trader to sell that contract while simultaneously buying the swap, struck at 25.00, to lock in a riskless arbitrage (absent counterparty risk) for a value of (VolContract futures – 25.00) x $100,000, where VolContract futures = the current price of the 3Vol.

Again, such opportunities ought not to exist, in theory, but the realities of market dynamics do not always coincide with mathematical formulas, and so the wise investor/trader would do well to keep an eye out for such potential arbitrage opportunities.

Spreading with Variance Swaps

Similar to the volatility swap, the variance swap rewards the buyer/seller with a payout that reflects the realized variance (square of volatility) of the underlying asset, with respect to a predetermined reference price, or starting variance. Such variance swaps have proven to be somewhat more popular than volatility swaps, in the OTC markets, because the variance-swap payouts are more easily and directly replicated with options on the underlying asset than is the case for volatility-swap payouts, and thus, the variance swaps are often deemed more suitable for hedging purposes than their vol-swap counterparts.

Once again, one might envision the possibility of an arbitrage between VolContract futures and a variance swap, but, in this instance, no completely riskless arbitrage is feasible. Whereas the payout from a vol swap or VolContract futures is purely linear, at $X per realized-volatility point above or below the strike, the payout from a variance swap is a squared function and is thus subject to the absolute levels of realized variance, which are not symmetrical around the current strike. A single example will suffice.

Suppose the current volatility strike price for a vol swap and the current price of VolContract futures were both 30.00. The corresponding strike for the variance swap might, therefore, be 30.00² = 900.00. (In actuality, because of the aforementioned asymmetry of prices around the strike, an adjustment would be made, such that the variance-swap strike would not be 900.00, but somewhat higher.) Suppose realized volatility were 35.00 over the period. Difference in variance would be 35.00² – 30.00² = 1,225.00 – 900.00 = 325.00. On the other hand, suppose realized volatility were 25.00 over the period. Difference in variance would now be 30.00² – 25.00² = 900.00 – 625.00 = 275.00.

Compared to the vol swap, whose linear difference of five volatility points is the same up or down (35.00 – 30.00 = 5, and 30.00 – 25.00 = 5), it is clear that such is not the case for the variance differentials, which were shown to be 325.00 and 275.00 respectively. What is more, all such five-point volatility/variance differentials are not created equal! Were we to begin from a realized-volatility level of, say 40.00, a five-point move in either direction would produce corresponding variance differentials, this time, of 425.00 and 375.00 (we leave the math to the reader), although the payouts for the five-point moves in the VolContract futures would remain unchanged.

For all of the above reasons, direct arbitrage between VolContract futures and variance swaps is not possible, although creating a spread between the two vehicles, when prices appear to be out of line, is certainly a reasonable possibility.

Spreading against VIX

The CBOE Volatility Index on the S&P 500, or VIX, is a calculation that reflects current levels of option implied volatilities over the entire range of current strike prices for the underlying asset. While it is not possible to trade this VIX value directly, futures contracts on the VIX are readily available and trade on the Chicago Futures Exchange (CFE). Such contracts, in theory, reflect predictions of future levels of option implied volatilities, which, themselves, are often related to, though rarely equal to, future levels of the underlying asset’s realized volatility.

It is possible to conceive of spread trading between VolContract futures and VIX futures. But, one must proceed with caution. Suppose the perception is that current implied volatilities, as represented by VIX futures prices, are higher than one’s forecast for upcoming realized volatility of the S&P 500. One might envision a spread trade, whereby VIX futures are sold and VolContract futures are bought. The thinking might be that, if realized volatility does, in fact, turn out to be lower than the implied volatility represented by VIX futures, a profit could be made.

While this, indeed, may be the case during the Anticipatory Period of VolContract futures, when they are expected to trade mostly on sentiment and, therefore, ought to closely match VIX futures in their pricing, such may not be the case once VolContract futures enter the Realized-Volatility Period (RVP) of their existence. VolContract futures always settle to the past realized volatility over a given RVP, and, thus reflect, upon their expiration, what has already occurred, while VIX futures, upon their expiration, settle to yet another forecast of what implied volatilities will be. As a result, there can be no guarantee that such settlement price will reflect either past levels of implied volatility or realized volatility.

In short, spreading between VolContract futures and VIX futures has inherent subtleties that must be taken into consideration, since the values that the two contracts represent are not only different as to their calculation but also as to the time period to which they apply. These dissimilarities might make spreading, at best, a tricky undertaking, and, at worst, a sometimes challenging endeavor with frequently unpredictable outcomes. So, proceed with caution!

Volatility Hedging a Delta-Neutral Options Book

Before the advent of VolContract futures and volatility and variance swaps, there was no direct method for trading pure realized volatility. In the absence of the above vehicles, traders turned to options contracts, specifically to at-the-money straddles (long call, long put), in an attempt to capture the realized volatility of the underlying asset. To this day, buying and selling ATM straddles, and then hedging them actively, to remain delta-neutral, remains the staple strategy of traders, market-makers, and portfolio managers, worldwide, wishing to “trade volatility.”

Now, one might contemplate the use of VolContract futures, in conjunction with straddle selling and buying, so that, in times of uncertainty, the straddle trader might, in turn, hedge not only the deltas of his options position but the very volatility that such a position is intended to capture in the first place.

It would suffice for the straddle buyer to sell VolContract futures, or for the straddle seller to buy VolContract futures, in order to hedge much or all of the volatility exposure that the original straddle was designed to capture. What’s more, the original options book need not be a pure volatility play, or straddle, in order to have, nonetheless, as one of its risk exposures, or “Greeks,” sensitivity to changing volatility. One might imagine, then, the use of VolContract futures as a more general, global, hedge against the vega, or kappa (sensitivity of options prices to changes in implied volatility) of an entire options portfolio.

What’s more, the maturities of the options and the VolContract futures used as a hedge need not necessarily be the same. One might contemplate a long-term exposure, through sold options, to profitability through declining volatility. However, in periods of stress, or market turbulence, one might envision buying shorter-dated VolContract futures as a form of protection against rising volatility and as a means of “riding out the storm,” without necessarily disturbing or liquidating the underlying, longer-dated, options positions.

Clearly, many such strategies, involving hedging the volatility exposure of an options portfolio with VolContract futures, are readily available.

Trading the Decrease in Sensitivity to Changing Volatility As We Progress Through the Realized-Volatility Period

Once VolContract futures reach the Realized-Volatility Period (RVP), their value going forward is no longer purely a function of anticipated realized volatility, as it was during the Anticipatory Period (AP). In essence, once the RVP begins, the formula for calculating the final settlement price of a VolContract futures is invoked, and, with each passing day, the Partial Realized Volatility (PVOL) plays an increasingly important role in the determination of the final value of the VolContract futures.

We might say that, the more days that have been logged into the formula, the less sensitive the VolContract futures becomes to any changes in future realized volatility, since such data points now become just one, or a few, of the many that have been entered into the formula for the ongoing determination of the expiration value.

Suppose we are 15 trading days into the life of the RVP of a 1Vol, with six trading days left to expiration. And, further suppose that the PVOL for the first 15 days of the RVP has already been calculated as 40.00. We now feel that, from here until expiration, the underlying asset will display a somewhat lower volatility of, say, 30.00. How might we determine if the current price of the 1Vol justifies a trade in one direction or the other?

First, let us observe that, just because the PVOL is currently 40.00 does not mean that the VolContract futures will be trading at 40.00. Although, in essence, a good part of the VolContract futures’s terminal value has already been input into the VolX formula, six more trading days remain. As a result, depending on trader sentiment, the VolContract futures may be trading above or below the PVOL value of 40.00. Suppose, nonetheless, for simplicity, that the VolContract futures’ price is, indeed, exactly 40.00. We are forecasting 30% vol for the remainder of the contract’s life. How do we determine how such a remaining volatility would affect the potential final price of the VolContract futures? We use a calculation referred to as the root mean square.

There are a total of 21 days in the RVP. For 15 of those days, vol has already been calculated to be 40.00. In addition, we are forecasting vol of 30.00 for the remaining six days. First, we square the 40.00, yielding 1,600.00, which we multiply by 15, to obtain a weighted average: 15 x 1,600.00 = 24,000.00. Next, we square the projected 30.00 volatility for the last six days, yielding 900.00. Multiplying by six gives 5,400.00. We then add the two weighted values, giving 29,400.00, and we divide by the total number of trading days in the RVP, which is 21. 29,400.00/21 = 1,400.00. Finally, we take the square root of this weighted average, or mean, of the squared results (the so-called root mean square), thus obtaining a projected final value of the VolContract futures of √1,400 = 37.42.

Finally, we compare this forecast of the terminal value of the VolContract futures, namely 37.42, which incorporates the PVOL of 40.00 and our estimate of the next six days’ realized volatility of 30.00, to the current price of the VolContract futures to see if a trade is advisable. Clearly, values above 37.42 might induce us to sell the VolContract futures, while values below 37.42 might trigger a purchase. At values near 37.42, we would conclude that the market has assessed remaining realized volatility levels in the same manner as we have, and we would probably pass on taking a position.

Trading the Difference in the Volatilities of Three-Month VolContract Futures and One-Month VolContract Futures

As volatility represents the tendency of an asset’s prices to fluctuate around its mean, or average, return, it should be clear that the dispersion, or the range of values that such volatility may assume, differs according to the time period considered. For example, while it is not unreasonable to assume that an asset with average volatility of, say, 30% might realize levels as high as 70%, or as low as 8%, over a one-month time horizon, it is much more difficult to imagine sustaining such extreme values of volatility over the longer time frame of, say, a year, or even a quarter (three months).

The above is simply another way of stating that the volatility of volatility itself is much greater over the short term than it is over the long term. Studies of what is referred to as the “vol of vol,” for the S&P 500, for example, indicate one-month vol of vol to be about 90–95%, whereas three-month vol of vol is a more subdued 30–35%. And, herein lies the germ of a possible spread trade, between a 3Vol and a 1Vol.

Suppose a trader expects that, near-term, volatility is likely to increase dramatically. And, let us further suppose that, at the moment, it is April 1, and the 1Vol with April expiration is about to begin its 21-day RVP, while the June 3Vol is also beginning its 63-day RVP. What’s more, both contracts are currently priced at 25.00. Feeling that volatility is about to increase sharply, a trader might simply consider the outright purchase of either contract. Clearly, however, if the increase is imminent, its effect on the price of the 1Vol will be more dramatic than on that of the 3Vol, as the 1Vol has only 21 days in its RVP, while the 3Vol has 63. The price of the 1Vol will, therefore, be more sensitive to a sharp move in volatility than will be the price of its three-month counterpart.

As an alternative, to mitigate the risk of an outright purchase, the trader might consider a spread trade, once again with the outlook of sharply increasing vol over the near term. In this case, he should buy the shorted-dated 1Vol and sell the longer-dated 3Vol to take advantage of the greater sensitivity of the 1Vol’s price to a shock in volatility compared to that of the 3Vol. Conversely, when the expectation is for a marked drop in realized volatility, the trader might reverse the spread, thereby buying the 3Vol and selling the 1Vol, with the expectation that a sharp decline in volatility will impact the price of the 1Vol more severely than that of the 3Vol.

Gaining Longer-Term Exposure: Comparisons and Contrasts of Volatility Swaps, “Strips” of 3Vols, and Delta-Hedged ATM Options Straddles

Although, in the future, VolContract futures with Realized-Volatility Periods (RVPs) longer than three months may be listed, for now, no such contracts exist. Nonetheless, three-month contracts (3Vols) are actually listed well in advance of the start of their RVP and can be traded, during their Anticipatory Period (AP), a full year before the start of the RVP. In this section, we discuss the various vehicles and methodologies that exist in the marketplace for gaining exposure, longer-term, to realized volatility. Specifically, we compare and contrast the pros and cons of volatility swaps (vol swaps), “strips” of 3Vols, and delta-hedged ATM options straddles.

Suppose it is January 1, and an investor wishes to “buy” volatility over the coming year. Now, there are two interpretations of such an investment. The first might be exposure to varying volatility, as the year progresses. Shorter-term VolContract futures, traded in sequence, will provide just such exposure on a recurring basis. But, a second investment would involve actually capturing the volatility displayed by the underlying for the entire yearlong period. And, it is that investment that we discuss here.

The most efficient vehicle currently available in the marketplace to gain such exposure is the volatility swap, whose dynamics were discussed in a previous section, above. One simply chooses a dollar multiplier for each point of realized volatility achieved over the year, compares to the starting reference point, or strike price, at which the vol swap was created, and a final settlement is made at year-end. This over-the-counter process is relatively simple, both to execute and to understand, but, for the most part, is available only to very large, institutional investors and involves the counterparty risk inherent in all non-listed OTC transactions.

Since VolContract futures with a one-year RVP are not currently available, how might an investor utilize 3Vols to achieve the desired exposure to a full year of realized volatility? For that, we turn to a “strip” of four 3Vols, whose RVPs of three months each, can be purchased simultaneously, at the start of the year, to create exposure over the entire 12-month period. We are able to do this because, although each contract has a RVP of only three months, all such contracts are listed a full year before their RVPs begin and thus can be traded well in advance of the actual RVP.

Therefore, it would suffice, in order to capture a year’s worth of realized volatility, for a trader to purchase, on January 1, four 3Vols whose expirations are in March, June, September, and December, respectively. This strip of 3Vols provides the desired exposure to the realized volatility achieved by the underlying over the entire year. Or does it? In theory, the strategy would appear altogether equivalent to the purchase of a single VolContract futures with a RVP of the full year. In fact, such is not necessarily the case.

Mathematicians will understand the problem. Whereas variances (the squares of volatility) can be added and then averaged in linear fashion (three-month variance of 400 plus next-three-month variance of 900 equals six-month variance of 1,300/2, or 650), it is not possible to aggregate volatilities in similar fashion (three-month volatility of 20 plus next-three-month volatility of 30 does not equal six-month volatility of 50/2, or 25. In fact, the six-month volatility turns out to be, in this case, 25.5). Thus, cumulative, discrete volatilities must be calculated using the root-mean-square methodology outlined above, and cannot simply be added and averaged.

For this reason, the resultant volatility captured from a strip of four consecutive 3Vols may be close to the actual one-year realized volatility, but it would be merely a rare coincidence for the two to coincide exactly. What’s more, although two sets of four three-month volatilities might both average linearly to the same value, producing identical payoffs, at year-end, for the strip buyer, the more the individual quarterly volatilities vary from that yearly mean, the more the actual annual volatility will differ from the strips’ values. Consider the following examples.

Suppose, in year one, the consecutive quarterly vols achieved are: 25, 30, 35, and 40. Averaged, they are 32.5, but the root-mean-square method tells us that actual annual vol is 32.98. Again, the two values may be relatively close to each other, but they are not identical. Now, consider a much “wilder” year, whose discrete quarterly volatilities nonetheless still average linearly to 32.5: 15, 20, 45, and 50. In such a case, the payoffs from four 3Vols might have been similar to those of our first year, or not. But, the realized annual volatility for this second, somewhat schizophrenic, year turns out to be a considerably larger 34.60.

In short, longer-term investors must understand that buying a strip of 3Vols is not the mathematical equivalent of buying a contract that directly calculates the volatility of the entire period covered by the strip, and that this may result in a payoff that could be better or worse than that achieved by, say, a longer-term vol swap.

Finally, there is a third manner in which a volatility investor can gain exposure over a longer time frame, and that is through an at-the-money options straddle (long call, long put) that is hedged on a frequent (usually daily) basis, to be kept delta-neutral (deltas of the calls plus deltas of the puts, plus any other hedge, such as futures contracts, are as close to zero as possible). Indeed, traditionally, before the advent of either vol swaps or VolContract futures, buying or selling ATM straddles was actually the only way for an investor to trade volatility.

Suppose there exist one-year options on an underlying whose volatility the investor believes will be high (say 40) for the coming year. And suppose that a current ATM straddle can be bought at implied volatilities of the options of, say, 32. Theory tells us that by judiciously hedging the cumulative deltas of the puts (negative) and calls (positive) that comprise the straddle with, say, futures contracts on the underlying, one can “capture” the actual realized volatility displayed by the underlying asset over the holding period. Thus, the theory continues, should 40 volatility be so displayed, the straddle buyer will have achieved a profit of eight volatility points, representing the differential between the purchase “price” of 32 (implied) vol and the vol of 40, realized by the delta-neutral hedging of the straddle throughout the year.

But, the technique is not without problems of its own. We shall enumerate three of the primary obstacles to capturing volatility in the above-proposed manner. First, there are considerable transaction costs associated with daily hedging. Whether one chooses to adjust the straddle’s delta using options or futures, each such contract’s price has a bid-offer spread, and, often, one may have to buy on the offer or sell on the bid, thereby incurring an implicit fee associated with trading. For the vol-swap investor, there is but one such initial spread. For the VolContract futures strip investor, there would be four such transactions for a one-year period. For the straddle hedger, there are 252 daily adjustments, each, potentially, subject to the bid-offer spread! It isn’t hard to imagine a good portion of the available profits from our trade, above, being eroded by the ongoing “tax” of the ubiquitous bid-offer spread.

Next, consider that markets move. And sometimes, they do so in one direction for long periods of time. When this happens, it’s possible for the deltas of our puts and calls to become, in absolute value, so large or so small that, for all intents and purposes, our original straddle is such in name only; that is, our options have lost most of their option-like characteristics and no longer are sensitive to the very changes in the volatility of the underlying that we set out to capture. In this event, the trader is forced to “roll” his position to a different strike-price level, whose options’ deltas are more suitable for such volatility trading. And, yes, there is often a “price” involved in effecting such an adjustment to the original position.

Finally, and this point is considerably more subtle, from a mathematical point of view, successful delta-neutral straddle trading is, itself, as was the case for the VolContract futures strip, path dependent. This is true because the sensitivity of the options’ deltas to changes in the price of the underlying (the options’ gamma) is dependent not only upon the relationship of the current underlying price to the options strike price, but also to the time period during which the price movement may occur. For these reasons, not all yearly volatilities of, say, 40 are created equal from the point of view of the straddle trader. And, therein lies the problem. We can never be assured of capturing any particular overall volatility for a given time period, via a straddle, for success in so doing depends, to a large extent, not just on what the volatility was but also on how it was actually achieved.

To summarize: The single most efficient way to capture long-term realized volatility is via the volatility swap. Such OTC agreements are, however, available primarily to large institutional traders and are subject to counterparty risk. An alternative to such a yearly contract is a series, or strip, of four consecutive three-month VolContract futures. While such an investment might often produce annual returns similar to those of the swap, there is no guarantee that the cumulative payoffs will be identical to that of the one-year vol swap, and, therefore, the strategy may prove to be more ― or less ― profitable. Finally, capturing long-term volatility through delta-neutral hedging of ATM options straddles may be the most challenging of the three methods considered. Considerable transaction costs, as well as the path dependency of the trade, make it difficult to predict if profits will actually accrue, and to what extent, even if the investor’s forecast turns out to be correct.

Inter-Market Spreads

As the name suggests, an inter-market spread is achieved when a trader buys a contract on one asset or commodity while simultaneously selling a similar contract on a different asset. There need not be any correlation between the two assets, but there may be. The idea is to buy a VolContract futures on Asset A, with the expectation of rising volatility, while selling a VolContract futures on Asset B, whose volatility one expects to decline. Alternatively, one might expect both volatilities to move in the same direction, but with the vol of Asset A exceeding that of Asset B. In either scenario, profits accrue from an accurate forecast.

If there is volatility correlation between the two assets, or markets, then there is less likelihood that both sides of the trade will go against the investor; conversely, if there is no such correlation, there is a greater risk of loss to both sides of the trade.

Conclusion

While the above ideas are not intended to be exhaustive of all the possibilities for trading VolContract futures, we hope to have given the reader ample food for thought as to how realized volatility might be traded, in a variety of manners, through the use of VolContract futures. As further such opportunities arise, we shall be sure to discuss them on our web site, so please check here frequently for any such subsequent additions.