# Trading Ideas for RealVol Instruments

Here we discuss various strategies and hedges using RealVol Instruments:

### 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 RealVol Futures contract, or its synthetic equivalent, using options (long call, short put with the same strike price and expiration) in a direction, long or short, that corresponds to the direction of reversion to the mean volatility of the underlying asset.   (Note:  for all the strategies discussed on this page, whenever the terms “RealVol Futures” or “futures contract” are used, it is assumed that an analogous strategy, using the above structure, often called an option “combo,” or “synthetic futures” may be employed as well.) For example, suppose that the long-term historical mean volatility for Asset A is 30%. And, suppose further that a current RealVol Futures contract, about to begin its RealVol Calculation Period (CP), is trading at 40.00. One might consider selling the contract at 40.00, with the expectation that, over the next month, 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 RealVol Futures’ value to decrease from 40, creating a profitable opportunity for the seller of the contract.

The buyer of RealVol 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. To initiate such a trade, one might also envision the use of a long options combo.  One might, for example, buy a 20-strike call while simultaneously selling the same tenor 20-strike put.  If there were no debit for the resulting transaction, it would be economically equivalent to having bought a one-month RealVol Futures contract (1VOL) at 20, if such a futures contract were indeed available.

### Arbing with Volatility Swaps

Before the advent of listed RealVol Instruments, 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 an 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.

### 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 RealVol Instruments and a variance swap, but, in this instance, no completely riskless arbitrage is possible. Whereas the payout from a vol swap or RealVol 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 RealVol 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 RealVol Futures would remain unchanged.

For all of the above reasons, direct arbitrage between RealVol 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 average 30-day 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 that trade at the Chicago Futures Exchange, as well as options on the index that trade at the Chicago Board Options Exchange, are readily available.  Such contracts, in theory, reflect predictions of future levels of option implied volatilities, which, themselves, are often related to, though are rarely equal to, future levels of the underlying asset’s realized volatility.

It is possible to conceive of spread trading between RealVol Futures or options 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 RealVol 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 RealVol Instruments, when they are expected to trade mostly on sentiment and, therefore, ought to closely match VIX instruments in their pricing, such may not be the case once RealVol Instruments enter the RealVol Calculation Period (CP) of their existence.  For example, RealVol Futures always settle to the past realized volatility over a given CP, 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 RealVol 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 RealVol Instruments 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 RealVol Instruments, 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 RealVol Futures or their synthetic options equivalent, or for the straddle seller to buy RealVol 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 RealVol Instruments 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 RealVol 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 RealVol Instruments 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 RealVol Instruments, are readily available.

### Trading the Decrease in Sensitivity to Changing Volatility through the RealVol Calculation Period (CP)

Once RealVol Instruments reach the RealVol Calculation Period (CP), 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 CP begins, the formula for calculating the final settlement price of any RealVol Instrument 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 that contract.

We might say that, the more days that have been logged into the formula, the less sensitive the RealVol Instrument 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 CP of a RealVol Futures, with six trading days left to expiration. And, further suppose that the PVOL for the first 15 days of the CP 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 RealVol Futures 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 RealVol Futures will be trading at 40.00. Although, in essence, a good part of the RealVol Future contract’s terminal value has already been input into the RealVol Daily Formula, six more trading days remain. As a result, depending on trader sentiment, the RealVol Futures may be trading above or below the PVOL value of 40.00. Suppose, nonetheless, for simplicity, that the RealVol Futures price is, indeed, exactly 40.00. We are forecasting 30% volatility 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 RealVol Futures? We use a calculation referred to as the root mean square.

There are a total of 21 days in the CP. 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 CP, 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 RealVol Futures of √1,400 = 37.42.

Finally, we compare this forecast of the terminal value of the RealVol 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 RealVol Futures to see if a trade is advisable. Clearly, values above 37.42 might induce us to sell the RealVol Futures, or a synthetic equivalent, 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.

### Conclusion

While the above ideas are not intended to be exhaustive of all the possibilities for trading RealVol Instruments, 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 RealVol 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.

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