The volatility index and what it measures

What it is computed from 

A volatility index is not calculated from share prices. It is calculated from option prices. The published methodology takes the prices at which options on a large equity benchmark are currently trading across a wide range of strike prices, and solves backwards for the amount of movement those prices imply over a horizon of roughly one month. The result is expressed in annualised percentage points and republished continuously through the trading day.

Two words in that description carry most of the meaning. Implied means the number is extracted from what the market is paying rather than measured from what has happened: it is a price, restated in different units. Forward looking means the horizon is ahead rather than behind, which distinguishes it entirely from realised or historical volatility, a backward looking statistic computed from actual past movements. The two are frequently plotted on the same chart and they are answering different questions.

The Volatility Index instrument sits in the indices class in the ledger because it is quoted as an index level, not because it measures a basket of shares. Nothing in it is an equity. It is a summary of the option market's pricing, and the equity benchmark enters only as the thing those options are written on.

How to read the units 

The level is an annualised standard deviation expressed in percentage points. Two conversions turn it into something interpretable. Dividing by the square root of the number of months in a year restates it as a monthly figure; dividing by the square root of the number of trading days in a year restates it as a daily one. The square root appears because variance accumulates with time while standard deviation accumulates with the square root of time, which is a property of the arithmetic rather than an assumption about markets.

The last point in that note is the one most often lost. A standard deviation describes dispersion. A level of any size implies movement of that magnitude upward and downward with equal weight, and the index contains no information about which of the two the market expects. A volatility index cannot be bullish or bearish, because the quantity it measures has no sign.

Why it rises when equities fall 

If the measure is directionless, its well documented tendency to rise sharply on days when equity indices fall requires an explanation, and there is a structural one. Equity markets fall faster than they rise: declines are more compressed in time and larger in daily magnitude than advances of the same total size. Option prices reflect that asymmetry, and the demand for protection against declines is persistently greater than the demand for exposure to advances, so option prices rise most when a decline is under way or is feared. The volatility measure extracted from those prices rises with them.

The relationship is therefore a strong empirical regularity produced by an identifiable mechanism, and not an identity. It has failed in both directions on many occasions: equity indices have declined with the volatility measure barely moving, in slow orderly markets, and the measure has risen while equity indices rose, when protection was being bought ahead of a scheduled event. Describing it as an inverse index of the equity market overstates a relationship that is real, variable and conditional.

Mean reversion, and the term structure 

Volatility behaves differently from a price. A share price has no level it is obliged to return to, but volatility is bounded below by zero and cannot remain extreme indefinitely, because extreme conditions resolve one way or another. Empirically the measure clusters: calm periods follow calm periods, turbulent periods follow turbulent ones, and extreme readings decay back toward a long run average over weeks. This is one of the most robust findings in the study of financial time series, and it holds across markets and across decades.

That expectation of decay is itself priced. Listed futures on the volatility measure exist for a series of forward dates, and in calm conditions the further dated contracts are priced above the spot level, because the market attaches some probability to turbulence arriving before they expire while the present is quiet. When the spot level is extreme, the ordering inverts: the further dated contracts are priced below spot, because the market expects the present turbulence to subside. The upward sloping arrangement is the more common of the two.

Why a tradable contract does not track the published level 

This is the single most consequential fact about the instrument, and it follows from the previous section rather than from anything about brokers. The published spot volatility level is a calculation, not a portfolio. There is no basket of anything that can be held to reproduce it, because it is derived from a continuously changing set of option prices at a fixed forward horizon. Every tradable instrument referencing it therefore references futures contracts rather than the spot calculation.

A futures contract expires, so a position that is to be maintained beyond that date has to be moved into the following contract. Where the further dated contract is priced above the one expiring, that move happens at a higher price, and it recurs on every roll. The cumulative effect over an extended period is a persistent divergence between a rolled futures position and the published spot level, in the direction dictated by the shape of the term structure. It is a mechanical consequence of the roll and not a fee, not a spread and not a broker charge.

A volatility instrument is a leveraged derivative like any other in the class. Its settlement arithmetic runs on the full contract value while only a margin percentage is posted against it, so an adverse movement is not bounded by the margin. The distribution of movements in a volatility measure is also markedly more skewed than that of an equity index: long stretches of small changes are punctuated by very large ones, which means the size of a typical day is a poor guide to the size of an unusual one.