# VIX FUTURES

While the VIX index is not investable, it is possible to invest in VIX futures. This is in part because VIX futures do not continuously roll their valuation period. They always refer to the same window of time regardless of the present date. On expiration, the VIX futures cash settle to the value of the VIX index.

To illustrate this concept, let us look at an example.

- On January 15, the VIX index represents implied volatility from January 15 through February 14. April VIX futures represent implied volatility from April 15 through May
- On January 20, the VIX index represents implied volatility from January 20 through February 19; however, the April VIX futures still represent implied volatility from April 15 through May

NOTE: A VIX futures contract = 1,000 vega.

##### Expiration

An investor can manage VIX expiration much like SPX options expiration. Recall that for SPX expiration, an investor must trade a basket of 500 stocks that represents the index on the opening print. The transaction replicates both the risk and the price level of the investor’s expiring options or futures.

Similarly, if an investor is long (or short) VIX futures, they can trade a basket of SPX options on the CBOE to offset the expiring VIX exposure.

An investor is long 1000 December VIX futures contracts, representing 1 mm SPX vega. These futures expire December 21 to the value of the January SPX options.

NOTE: **VIX futures and options settle 30 days prior to the next month’s SPX expiration. At expiration, the index is composed of only one month’s SPX option prices. It is precisely at this time that the exact price level of the VIX can be replicated by trading this basket of options.**

To offset the expiring position, the investor needs to buy a basket of SPX options on the opening print. The basket is constructed to replace the 1 mm expiring vega.

It is important to remember that by exchanging the VIX futures for a strip of SPX options, the portfolio’s risk exposure changes sporadically. The investor receives exposure to gamma and theta, which the position did not have before trading the basket of options. It is similar to the difference between being long a forward starting variance swap and being long a realized variance swap.

##### Term Structure

Since every VIX future refers to a specific time period, the CBOE has listed contracts with multiple expiration dates.

While the VIX settles to the price of variance on expiration, the VIX future represents the value of forward starting variance. In an upward-sloping term structure, the VIX futures will generally trade at a higher price than a variance swap with the same expiration.

While the VIX settles to the price of variance on expiration, the VIX future represents the value of forward starting variance. In an upward-sloping term structure, the VIX futures will generally trade at a higher price than a variance swap with the same expiration.

When there is stress in the equity markets, the near-term futures often react by appreciating value more than the long-term futures. This creates a downward-sloping term structure, which implies that the market expects Implied volatility to revert to its long-term average over time.

In a downward-sloping volatility environment, VIX futures will usually trade at prices lower than that of a variance swap with the same expiration.

##### Vega-Beta

Short-term volatility reacts more dramatically to market events t1an long-term volatility. Short-term VIX futures behave likewise. For every change in the VIX index, the nearest-term VIX future’s price moves more than the longer-term future’s price. We refer to this as the ** vega-beta **of the futures contract.

Vega-beta is approximated with a weighting system that uses a combination of historical data and a square root of time.

When choosing which VIX future to trade, an investor should take into account the vega-beta of each futures contract in order to properly size the position. A small amount of short-dated contracts has the same vega-beta risk exposure as a large amount of long-dated contracts.

*An investor is long 500 one-month VIX futures contracts with a vega-beta of0.75. The risk exposure is equivalent to 2,000 five-month VIX futures contracts with a vega-beta of 0.1875.*

*500 X 0.75 = 375*

*2,000 X 0.1875 = 375*

*Both positions have equivalent VIX vega-betas of 375,000 vega of 30-day volatility.*

Because of the difference in vega-beta among the VIX futures contracts, each term hedges against a different type of risk.

Type of Futures Contract | Helps Hedge Against |

Short-term Futures | Cash Risk
Short-term Catalysts |

Mid-term Futures | Event-driven risk of an in determinant time horizon |

Long-term Futures | Changes in risk regimes |

##### Roll Yield

In a normal market environment, short-term futures are more expensive to hold than long-dated futures. This holds because an investor has to buy the next future on the curve when the near-term future expires.

In a stressed market with a downward- sloping volatility term structure, roll decay is positive.

This term structure is upward-sloping. To maintain constant vega exposure, an investor must sell the lower-priced future and buy a higher-priced one. This is known as ** roll yield **or

*roll decay.*##### Convexity

VIX futures are the expected value of the VIX index at a future date. They are also the expected value of the price of a one-month variance swap on this same date.

The risk profile of a VIX futures position is similar to a one-month forward starting variance swap with a start date of the VIX expiration. However, the two positions differ in a fundamental way. The VIX futures payout is linear with respect to volatility, while forward variance payout is convex.

VIX Futures Payout vs. Forward Variance Swap Payout

When implied volatility increases, a forward variance swap generates a higher payout than a VIX future. If volatility decreases, a forward variance swap does not lose as ·much as a VIX future.

# VIX OPTIONS

VIX options. like VIX futures, settle to the value of the VIX index on expiration. Each VIX options contract represents 100 vega.

*An investor buys 1,000 Dec 25 calls on VIX for $2.00.*

*On Dec 27, the VIX expires at 29. Fees and Commissions = $0.*

*P&L = ((Spot – Strike) -Premium paid) x vega per contract x # of contracts*

*= ((29-25)-2) X 100 X 1,OOQ*

*= $200,000*

### Volatility of Volatility

NOTE: VIX options settle to the value of the VIX at the corresponding option’s expiration. To hedge a December VIX option, an investor should use December VIX futures.

VIX options derive their value from the volatility of volatility of the SPX. The implied volatility of VIX options reflects the expected volatility of the corresponding VIX future.

The beta of VIX futures is greatest for short dated contracts. Therefore. the implied volatility of short- dated options is higher than that of long-dated options. The implied volatility of VIX options is downward sloping with respect to term.

The daily returns of VIX spot are skewed. The VIX index goes down by small amounts more frequently than it moves higher. However, when the VIX moves up, it tends to move up significantly. The implied volatility of out-of-the-money calls on the VIX should be higher than the implied volatility of out-of-the- money puts. This is similar to equity options where out-of-the-money puts trade at a higher implied volatility to reflect the possibility of a crash.

**Trading Strategies**

VIX-based products give investors access to unique trading opportunities. The trading strategies are similar to those used with equity derivatives and bucketed typically as either hedging or carry trades.

**Hedging**

VIX-based products have two important characteristics that make them attractive hedging vehicles:

- They have a negative beta to equity prices, and
- There beta increases with larger market

##### Carry Trades

Implied volatility on the SPX tends to trade over realized volatility. As a result, selling volatility is a popular yield-enhancing carry trade. VIX products and options are particularly attractive trading vehicles for this strategy.

- When the implied volatility term structure Is upward-sloping, forward-starting volatility VIX trades higher than term volatility and decay over
- While volatility is normally mean reverting, it can exhibit large gap moves. Options on the VIX may limit portfolio losses during crash