Pro Desk
Volatility and the VIX: What It Measures and How It Is Traded
VIX 20 is a statement about a 5.8 percent move over the next month. Turning that statement into a position runs through futures, roll yield and a product that once lost almost everything overnight.
20 / sqrt(12) = 20 / 3.464 = 5.77
That is what a VIX of 20 says. Translate it out of quoting convention and you have something a portfolio can use. The index is an annualized 30 day implied volatility for the S&P 500, so dividing by the square root of twelve gives the one month figure: a one standard deviation move of about 5.8 percent over the next thirty days, and under the usual distributional assumptions roughly two sessions out of three land inside that range.
Run the same scaling on other horizons. 20 / sqrt(252) = 1.26 percent is the implied daily move. 20 / sqrt(52) = 2.77 percent is the week. Every piece of volatility work starts with this conversion, and a surprising amount of commentary about the VIX being high or low never performs it at all. Implied volatility and the Greeks are the single stock version of everything below.
What the index is made of
Cboe computes the VIX from S&P 500 index option prices. The calculation takes out of the money puts and calls across a wide range of strikes, for the two expirations that straddle 30 days, weights each option’s price by the inverse square of its strike, and interpolates the two expirations to a constant 30 day horizon.
Three things follow from that construction. All three get misstated regularly.
The whole strike range matters, so a surge of demand for far out of the money puts lifts the VIX even when at the money implied volatility has not moved. The index reflects the shape of the skew, which is why calling it a fear gauge is defensible.
It measures expected variance under the risk neutral measure. So it carries a risk premium, and sits systematically above the volatility that subsequently gets realized.
And it is backed out of live prices by an arithmetic formula, which means it inherits every quirk of option supply and demand in that moment, including the dealer positioning covered in the options flow guide.
The premium that pays the sellers
Implied volatility has averaged above realized volatility over long samples, and that gap is the variance risk premium, the economic engine under most systematic option selling.
The intuition is insurance underwriting. A seller of index options holds a position that loses catastrophically in a crash and collects small amounts the rest of the time. Buyers pay above the statistically fair price because the payoff arrives precisely when the rest of their book is falling apart, which is worth a premium to them. The gap is the underwriter’s margin.
The caveat sits in the shape of the payoff. A strategy harvesting this premium produces a long sequence of modest gains and occasional losses large enough to erase several years of them. Sharpe ratio flatters it badly, because the risk lives in the tail and not in the standard deviation, which the portfolio risk guide explains at more length, and a high Sharpe with heavy negative skew is a description of a strategy that has not met its worst week yet.
The curve, and what it costs to hold
| Curve shape | Front month against second | Environment | Effect on a long position |
|---|---|---|---|
| Contango | Front below second | Calm, which is most of the time | Negative roll yield, a constant drag |
| Flat | Roughly equal | Transition, rising nervousness | Little either way |
| Backwardation | Front above second | Active selloff | Positive roll yield |
Put numbers on the drag. The word understates it. The front VIX future trades at 19.50 with 21 calendar days to settlement, the second month trades at 21.00, and a product holding a rolling blend continuously sells the cheap contract and buys the expensive one. Daily roll cost is roughly (21.00 - 19.50) / 21 = 0.071 points per day, and against a 19.50 level that is 0.071 / 19.50 = 0.37 percent per day.
Compound that across a month and a long futures position is down about 10 percent with spot VIX exactly where it started, which is the whole explanation for why long volatility products decay the way they do and why short volatility products made money for years on end before they stopped.
Futures are a different animal from the index
A VIX future settles to spot at expiration. Before that it prices where the market expects the index to be on that date, which is a different question, so with VIX at 14 in a calm market the two month future may trade at 18, because everyone knows volatility mean reverts upward from low levels.
The consequence is a beta well below one. Spot VIX can jump 40 percent in a session while the second month future rises 12 percent, because nobody expects the panic to still be running in two months, so anyone sizing a hedge off the spot index will be badly under hedged and anyone sizing off historical futures behaviour will land much closer. Margin and settlement work like any futures contract.
February 2018, and what it demonstrated
Volatility exchange traded products hold futures. The exposure resets daily. That reset is the same mechanism described in the leveraged and inverse ETF guide, with the same consequence: the stated multiple is delivered over one day, and the path decides everything over any longer period.
For inverse volatility products the arithmetic is merciless. A product delivering minus one times the daily return of a VIX futures index goes to approximately zero if that index doubles in a single session, and on 5 February 2018 VIX futures rose enough in one afternoon and evening to do exactly that. XIV, the best known inverse volatility note, lost almost its entire value, an acceleration clause in the note was triggered, and the product was wound up, so holders who had watched it compound impressively for years found out that the return distribution had contained that day the whole time.
Where a level disagrees with the tape
Run the conversion backwards when a VIX level looks wrong: if the index has been moving 2 percent a day, the annualized number consistent with that behaviour is 2 x sqrt(252) = 31.7. A VIX printing 18 against 2 percent daily moves is a disagreement worth investigating, and the resolution is usually that the realized moves are about to slow or that the option market is underpricing something.
Breadth data helps at the index level. A volatility spike with narrow participation behaves differently from one where the entire market is selling, and the term structure has tended to normalize faster in the first case. That is a tendency. The sample of large spikes is small enough that anyone quoting a precise hit rate on it is overreaching.
Options usually beat the products
Most of the time, options on the index give cleaner exposure than a volatility product does, and a long SPX straddle is long vega and long gamma with a known maximum loss and no roll drag beyond theta. A short strangle or iron condor harvests the variance risk premium directly. The loss profile is visible before entry.
The trade off is several exposures at once. A straddle bought for its vega bleeds theta daily. It picks up directional delta the moment the underlying moves. Model it in the options Greeks calculator first, and decide in advance whether you intend to delta hedge, because an unhedged straddle is a bet on the size of a move while an unhedged strangle held to expiry is a bet on a range.
What none of this can tell you
Volatility is mean reverting until it is not. Strategies that harvest the premium work inside the regime they were designed for and hand back several years of gains during the transition out of it. Nothing in the term structure announces that transition in advance, and backtests of short volatility strategies look extraordinary right up to the sample that includes the bad week.
Two rules survive most of the arguments. Do not hold a daily reset volatility product for longer than a few days. And size any short volatility position by its worst plausible single day. That is the reasoning developed in the position sizing guide.
For the dealer positioning side of the same market, read options flow, the put call ratio and gamma exposure, and the volatility indicators guide for the realized volatility measures that belong alongside the implied ones.
Frequently asked questions
What does a VIX of 20 actually mean?
It means the options market is pricing an annualized 30 day implied volatility of 20 percent for the S&P 500. To convert that into a one month expected move, divide by the square root of 12, which gives roughly 5.8 percent. That is a one standard deviation range, so under the usual assumptions the index would be expected to finish within plus or minus 5.8 percent about two thirds of the time.
How is the VIX calculated?
Cboe computes it from the prices of S&P 500 index options across a wide range of strikes, using near term and next term expirations that are interpolated to a constant 30 day horizon. The formula is a variance swap style calculation that weights each out of the money option by the inverse square of its strike. No single option determines the level, and the calculation uses prices rather than any model of the future.
Can you buy the VIX?
No. The VIX is a calculated statistic and there is no basket of assets that replicates it. Exposure is taken through VIX futures, options on those futures, or exchange traded products that hold the futures. Each of those tracks the index imperfectly, and over holding periods longer than a day the tracking difference is usually larger than the move in the index itself.
What is contango in VIX futures?
Contango is when further dated futures trade above nearer dated ones, which is the usual shape of the VIX curve in calm markets. A long position that holds futures has to keep selling the cheaper expiring contract and buying the more expensive next one, which produces a persistent drag known as negative roll yield. Backwardation is the reverse shape and appears during selloffs.
What is the variance risk premium?
It is the tendency for implied volatility to price above the volatility that is subsequently realized. Option sellers are taking on an exposure that loses badly in crashes, and buyers are willing to pay above fair value for protection, so the premium is best understood as an insurance margin. It has been positive on average over long samples and is heavily negative in the periods when selling volatility hurts most.
Why did XIV collapse in February 2018?
XIV was an exchange traded note that delivered the inverse of a daily VIX futures index. On 5 February 2018 VIX futures rose enormously in a single session, the note's daily inverse exposure produced a loss of almost its entire value, an acceleration clause was triggered and the product was wound up. It remains the standard illustration of why a daily reset inverse volatility product carries a risk of near total loss.