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# Colin Bennett on volatility trading. Part 2: Volatility Futures as an alternative to equity and puts

## Colin Bennett on volatility trading. Part 2: Volatility Futures as an alternative to equity and puts

*In part 2 of our 3 part series on volatility, **Volatility Futures are examined in depth both as an alternative to equity and as an alternative to puts. The key characteristics of trading volatility in practice are demonstrated, and the differences between **Volatility Futures and Variance Swaps analyzed.*

**Volatility Futures were first listed in Europe**

The DTB (now Eurex) was the first exchange to list Volatility Futures. These VOLAX® Futures were based on ATM 3 month implied on the DAX®, and they were listed in 1998 (and subsequently delisted later the same year). Six years later in 2004 Volatility Futures were listed on the VIX, which was swiftly followed a year later by the launch of VSTOXX® (and VDAX® and VSMI®) futures in 2005.

**Volatility has negative correlation to equity**

As volatility tends to rise when equities decline, a long Volatility Futures position can be taken as a hedge. For short periods of time (e.g. over 1 day or 1 week) there appears to be a linear negative relationship between volatility and equity returns, as can be seen in the chart below (we note this hedge has a certain amount of noise).

**Volatility can have convex profile vs equities, just like a put**

Returns over relatively short periods of time hide the fact that volatility is floored at a certain level, for example the VSTOXX® never trades below c12%. This means that the loss from a long VSTOXX® Future is floored, hence returns over a longer time period (e.g. 3 months) show a more convex profile than daily returns. A long Volatility Future can therefore be compared against puts, particularly when volatility is low and the impact of the volatility floor is greatest.

**Long ATM SX5E put has similar payout to 5 ****VSTOXX® Volatility Futures**

As a Volatility Future is a future on a 1 month Volatility Index, the implied volatility of a 3 month Volatility Future trades in line with that of a 4 month put. The return of Volatility Future of 3 month expiry until maturity should therefore be compared to the 3 month return of a 4 month put (i.e. the return of a put with 4 month maturity up until it has only 1 month left to expiry). Similarly, the return of a Volatility Future with 1 month until expiry should be compared to the 1 month return of a 2 month put (i.e. return of a put with 2 month maturity until it has only 1 month left to expiry). For both 3 month Volatility Futures (vs 4 month ATM put) and 1 month Volatility Futures (vs 2 month ATM put) the payout of an ATM put is very similar to the payout of 5 VSTOXX® Volatility Futures. Hence 5 VSTOXX® Volatility Futures could be considered an alternative to one SX5E ATM put. It should be remembered that the payout of a Volatility Future is less reliable than that of a put.

**Volatility futures could outperform puts**

While the performance of a SX5E ATM put and 5 VSTOXX® Volatility Futures appears similar, the payout of 5 VSTOXX® Volatility Futures has historically been higher than for SX5E ATM puts. This means using VSTOXX® Volatility Futures for protection could outperform using SX5E ATM puts.

**Volatility Futures trading in practice**

Trading Volatility Futures allow a volatility position to be taken without the overhead of delta hedging an option. Before trading Volatility Futures it is important to take into account the key differences between volatility trading via options, and Volatility Futures.

**VOLATILITY FUTURE TRADING IN PRACTICE**

Upon expiration of a Volatility Futures, the pay-out is based on the underlying Volatility Index. Hence when trading a Volatility Futures, the profit and loss is based on a future on volatility (which is the same as a forward on volatility, as a future is simply a listed forward). While trading a forward on volatility has many similarities with trading volatility itself, there are also important differences.

**Volatility Futures expiration is 30 days prior to normal expiry**

To make it easier for traders to hedge their Volatility Futures position, a Volatility Futures expires 30 days (the maturity of the underlying volatility index) prior to a normal option expiration. As expiration is normally on the 3rd Friday of a month, a Volatility Futures expiration will be on the 3rd or 4th Wednesday of a month (as normal option expirations can be 4-5 weeks apart, i.e. 28-35 days).

**Non-standard expiry (3rd or 4th Wednesday) makes Volatility Futures easier to hedge**

While having a non-standard expiry could be seen to be confusing, it does mean that on the date of expiration, the underlying Volatility Index is calculated using the implied volatility for only one maturity (no interpolation or extrapolation between two expiries is needed). A Volatility Futures that expires in November, will therefore be hedged by trading a strip of options for the December expiry one month later.

**Volatility Futures implied should be compared with underlying index implied one month later**

As Volatility Futures are a based on 1 month forward volatility, they should be compared with the volatility of the underlying index 1 month later than the Volatility Futures expiration. The term structure of Volatility Futures therefore has a 1 month offset to the term structure of the underlying index.

For example, the Volatility Futures for VSTOXX® December expiry should be compared with the SX5E January expiry the following year. This is because the December expiration of the VSTOXX® is based on what the VSTOXX® is on the (3rd or 4th Wednesday) Volatility Futures expiration in December. On the December Volatility Futures expiration, the VSTOXX® 30 day volatility is based on the index (3rd Friday) January expiry (of the following year) of the SX5E options. Due to the large number of public holidays between December and January expirations (Christmas and new year) the SX5E volatility term structure normally has a dip in January. Therefore VSTOXX® volatility term structure normally has a dip in December (due to the 1 month offset).

**Volatility mean reversion dampens returns of far dated futures**

When an unexpected event occurs, volatility normally jumps. As markets digest the news, volatility tends to soften and mean revert over a period of up to 10 months. This mean reversion can be seen by plotting the minimum and maximum implied volatility per maturity (a volatility cone) as can be seen in the chart below. As near dated implieds have a wider min-max range than far dated implieds, this means that when a volatility index spikes near dated Volatility Futures rise more than far dated volatility futures. Far dated Volatility Futures could be seen as a more stable (or less levered) way of gaining volatility exposure.

**Near dated Volatility Futures have highest sesitivity to index, but need to be rolled more frequently**

While near dated Volatility Futures are more sensitive to the underlying Volatility Index, the position needs to be rolled frequently. Before deciding on the maturity of a Volatility Futures, an investor needs to decide how much overhead (i.e. rolling frequency) they are willing to take, and how sensitive to moves in volatility they want the position to be. For example, while the front month Volatility Futures has a very high delta (90%) with the Volatility Index this would require rolling every month.

**Volatility mean reversion reduces delta of far dated futures**

Volatility tends to jump, and then mean revert over a period of time just under 1 year. Near dated Volatility Futures will therefore have a delta (or exposure/sensitivity) to the underlying Volatility Index of nearly 100% (e.g. c90% for 1 month volatility futures). The delta (or exposure/sensitivity) of Volatility Futures will fall as maturity increases, as mean reversion makes it unlikely that the current levels of volatility will remain over the entire life of the Volatility Futures. A plot of the sensitivity (i.e. delta) of Volatility Futures to the underlying Volatility Index is shown above both for rolling every month, and for rolling at expiry. For example, the 3 month data point can either always have a 3 month maturity (i.e. it is rolled when the maturity reduces to 2 months) or can have a maturity between 0 and 3 months (i.e. it is rolled at expiry). The delta when rolling at expiration can be considered a blend of the deltas when 1 month rolling. For example, the delta of a 3 month future rolled at expiry is a blend of the deltas of the 3, 2 and 1 month future rolled after 1 month.

**Using 1 month or 3 month futures is best (when rolled at expiry)**

The diagram above shows the delta of a Volatility Futures rolled at expiry vs the number of times in a year you have to roll the position. Investors seeking the highest delta should always use 1 month futures and roll 12 times per year. Investors seeking a balance between the delta, and the overhead of rolling the position should use 3 month futures and roll at expiry (i.e. roll 4 times a year). While using 2 month futures has a higher delta than 3 month futures, it is not very significantly for the additional overhead of rolling 6 times a year rather than 4. Using 4 month futures only saves 1 roll per year (as you roll 3 times not 4) and has a significantly reduced delta compared to 3 month futures.

**While near dated Volatility Futures are most sensitive to index, they also suffer from being most expensive**

In addition to considering the sensitivity of a Volatility Futures to the underlying index, and the number of times the position has to be rolled, and investor should also consider how expensive the position is to hold. As term structure is on average upward sloping, this means a Volatility Futures should on average decline as maturity approaches. As the slope of term structure is relatively flat at the far end, longer dated Volatility Futures suffer less from time decay than near dated Volatility Futures. This can be seen in the diagram below. To reduce the impact of time decay an investor can use far dated futures, potentially rolling when the position is 2 months or less. This strategy would have a lower delta than using near dated futures. There is in effect a trade-off between the cost of holding the position, and the effectiveness of the position. Should an investor be using Volatility Futures tactically (i.e. not all the time, but only in advance of key events likely to cause high volatility) near dated Volatility Futures are likely to be preferred. If an investor is using volatility strategically (i.e. continuously as part of a diversified portfolio) far dated Volatility Futures (potentially rolled before expiry) is likely to be preferred.

**Volatility Indexes overestimate future volatility **

A variance based estimate includes not only information about future volatility, but also includes a volatility risk premium. As a volatility risk premium lifts the value of a variance based Volatility Index, Volatility Indexes usually overestimate future volatility. This means that selling Volatility Futures is a viable way of earning alpha.

**Volatility Futures settlement can suffer from imbalances**

A Volatility Futures will be hedged with a strip of options of all strikes. As OTM options are typically less liquid than ATM options, Volatility Index providers have rules to exclude OTM options if they are too far OTM or are illiquid. While this improves the reliability of the Volatility Index calculation, it makes it harder for traders to hedge as they are not certain if they need to trade an OTM option or not (a sudden change in spot or liquidity approaching expiry could cause the option to be included or excluded from the calculation). In deciding the methodology, there is a trade-off between how easy it is for liquidity providers (i.e. market makers and traders) to hedge and data reliability. Typically end clients are reluctant to trade an instrument that could expire at a significantly different value to the prints just before and just after expiration. Just as there have been issues with the settlement price of equity indexes (e.g. the FTSE June 2005 expiration) there can be issues with the settlement price of Volatility Futures.

**APPENDIX**

For all the examples in the appendix we shall for simplicity assume that the calculation of the volatility index is identical to a variance swap. This means the difference between forward volatility, Volatility Futures and forward variance is not related to any chopping of OTM tails or any other practicalities of Volatility Futures.

**Volatility Futures fair price is not equal to forward variance**

Despite the fact Volatility Futures use a variance swap based calculation, the fair price of a Volatility Futures is not equal to forward variance. In fact the fair price of a volatility future is below that of forward variance. As maturity (and volatility of volatility) increases the difference between the price of a variance swap and Volatility Futures widens. This can be seen by comparing a Volatility Index such as the VSTOXX® with a forward variance swap. We note that volatility of volatility can be seen in an index such as the VV2X, which is the volatility of options on VSTOXX® Futures.

**Fair price of Volatility Futures is below forward variance**

Volatility Futures tend to trade just below the levels of forward variance. If a Volatility Futures traded at the same level as forward variance an arbitrageur could simply go long forward variance and short Volatility Futures to construct a portfolio that can only earn profits. This can be seen by looking at the pay-out of a VSTOXX® Volatility Futures and a forward 30 day (to match VSTOXX®) variance swap for identical vega. We shall assume the strike of both the VSTOXX® and forward variance is 20. As vega gives the P&L sensitivity to volatility, having identical vega means the pay-out should be identical for small deviations of volatility about the level 20 (i.e. the gradient of the two lines are identical for volatility at 20). The diagram below shows the pay-out of forward variance is always equal to or above the pay-out of the VSTOXX® (if they are the same price), hence a long forward variance short VSTOXX® portfolio only has a positive pay-out.

**Volatility Futures discount to forward variance increases as maturity and volatility of volatility increases**

For reasonable prices (i.e. volatility future price less than forward variance) the profile of a long Volatility Futures and short forward variance swap is similar to short straddle on volatility of volatility. This means the difference between a volatility and forward variance should increase as the maturity increases, and as volatility of volatility increases (just as the premium of a short straddle increases as time increases and volatility increases). While we have used Volatility Futures in this example, volatility swaps (which can be approximated by ATMf volatility) can be substituted for Volatility Futures.

To see this effect graphically we shall first examine the pay-out of a long Volatility Futures and short forward variance swap. We shall assume the forward variance swap is trading at 20 (as before) but this time the VSTOXX® volatility future trades 1 point lower at 19.

The pay-out of a long Volatility Futures short forward variance is then similar to a short straddle on volatility (as can be seen from the below diagram).

**Volatility Futures is short volatility of volatility**

As the volatility (or variance) exposure of a variance swap can be hedged with a static portfolio of options, a variance swap has no volatility of volatility risk. As the pay-out of a Volatility Futures is linear in volatility, this means it is short volatility of volatility.

This can be seen in the diagram above, if volatility remains near 20 (i.e. low volatility of volatility) a Volatility Futures is more profitable than a forward variance swap. If volatility suddenly changes to be very high or very low (i.e. high volatility of volatility) then a Volatility Futures is less profitable than a forward variance swap. As a (forward) variance swap is neither long nor short volatility of volatility risk, this means a Volatility Futures is short volatility of volatility risk (as it profits when vol of vol is low, and suffers when vol of vol is high).

**Options on ****Volatility Futures can hedge volatility of volatility position**

Typically Volatility Futures are expensive, which is why many trading desks put on a short Volatility Futures long forward variance position. As a short Volatility Futures position is long volatility of volatility, this means a short Volatility Futures long forward variance position is also long volatility of volatility (an uncapped variance swap has zero volatility of volatility exposure). The value from this position can be extracted by selling (a strip of) options on Volatility Futures, as options on Volatility Futures (like most options) are on average expensive.

**Post credit crunch, many banks prefer to trade ****Volatility Futures / swaps rather than variance swaps**

By some measures the levels of volatility seen post Lehman bankruptcy were higher than during the great depression. As there was a long low volatility bull market between 2003 and 2007, risk departments were not prepared for the extreme pay-outs of convex instruments such as variance swaps. Now there is a preference for non-convex instruments, such as Volatility Futures or volatility swaps, as many banks prefer to take (small) vol of vol risk than (high) convexity risk.

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