VIX Futures Term Structure

Everyone quotes the VIX. Almost nobody can buy it. The VIX is a number, recomputed every fifteen seconds from a basket of S&P 500 option prices. There is no share certificate, no warehouse, no way to hold it overnight. So when a fund wants to own volatility, or sell it, the trade goes through a futures contract on the VIX instead. There is one contract for each of the next several months, they all trade at different prices, and the price you pay is almost never the VIX level printed on the screen. Why they differ, and what that difference costs you every month you hold on, is most of what volatility trading actually is.

The umbrella shop

On a clear June morning an umbrella is nearly worthless. But a shop taking orders for November delivery still charges real money, because November has storms in it and everyone knows that. Immediate delivery is cheap; later delivery is dear. Now put a hurricane overhead. Umbrellas today are priceless, yet the November order book barely moves, because the storm will be long gone by then, so later delivery suddenly sits below today's price.

VIX futures behave exactly like those umbrella orders. Today's VIX is the cost of protection in today's weather. A VIX future is a price agreed now for a reading months away, and that reading reflects a typical month, not this one.

The one formula, and why it is unusual

Write $V_t$ for the VIX index level today (time $t$), and $F_t(T)$ for the price today of a VIX future that settles at time $T$. Then

$$F_t(T) \;=\; \mathbb{E}^{Q}_t\!\left[\, V_T \,\right].$$

In plain English: today's futures price is the market's best guess of what the VIX will read on settlement day. The symbol $\mathbb{E}$ means "expected value", the superscript $Q$ says we are using the risk-neutral probabilities baked into option prices rather than real-world ones, and the subscript $t$ says we use only information available today.

Compare a gold future: you can buy the metal now, pay storage, and deliver later, so the futures price is chained to spot by the cost of carry. You cannot store the VIX. That missing link is the whole point: VIX futures can sit ten points from spot for months and no arbitrage will drag them together.

Contango, backwardation, and the slide

When later months cost more than nearer ones the curve is in contango. When they cost less it is in backwardation. Contango is the normal state, roughly four days in five historically, because spot VIX spends most of its life pinned near its lows while the market always prices some chance of a shock a few months out.

The slide has a name and a number. For a long holder,

$$\text{monthly roll} \;=\; \frac{F_t(T_1) - F_t(T_2)}{F_t(T_2)},$$

where $T_1$ is the front settlement month and $T_2$ the one behind it. In plain English: if nothing at all happens and the curve keeps its shape, one month from now the contract you own will have slid down to where the front month sits today, and that percentage move is your gain or loss.

Worked example 1: the cost of doing nothing

Spot VIX is 14.0, the front month trades at 15.5, the second month at 17.0. You buy one second-month contract at 17.0 because you want protection.

A month passes. The market never moves; spot VIX is still 14.0 and the curve has exactly the same shape. Your contract is now the front month, so it is worth 15.5. You lost 1.50 on a 17.00 position, a return of $-1.50/17.00 = -8.8\%$, having been right that nothing happened and having paid for the privilege.

Keep doing that for a year: $(1 - 0.088)^{12} = 0.33$. You end with about a third of your money, with the VIX perfectly flat the entire time. Nothing broke; that is simply what the curve charges. And whoever took the other side collected all of it.

Worked example 2: the spike, and the half-payoff

Now the crash arrives. Spot VIX leaps from 14.0 to 45.0. The front month reprices to 38.0 and the second month to 33.0.

The roll flips in your favour. Hold the second month at 33.0 and, with the curve unchanged, a month later it is the front month at 38.0: $+5.00/33.00 = +15.2\%$ a month, now paid to the long. This is why short-volatility strategies collect small amounts for years and then hand it all back at once.

But look at what your hedge actually captured. Spot VIX went from 14.0 to 45.0, up 31 points, a gain of 221%. Your second-month future went 17.0 to 33.0, up 16 points, a gain of 94%. It picked up $16/31 = 0.52$ of the spot move. The front month went 15.5 to 38.0, up 22.5 points, or $22.5/31 = 0.73$ of it. The further out the curve you go, the less of a spike you capture, because a panic today is expected to have faded long before a distant contract settles.

Seeing the term structure move

VIX futures are quotes on the term structure of index volatility, so look at that structure directly. Each row below is a maturity, each column a strike, and the shading is implied volatility. Drag the "term slope" slider. Push it positive and the lower rows darken, longer maturities carrying higher vol, which is the contango picture; pull it negative and the top row goes darkest, which is backwardation.

Worked example 3: why the future sits below the variance number

One wrinkle catches people. The VIX is a square root, taken of a 30-day variance figure. Futures settle on the VIX itself, not on variance, and square root bends downward, so the average of the roots sits below the root of the average.

Concretely: suppose the market thinks 30-day vol in one month will be either 15 or 25, equally likely. The expected variance is $(15^2 + 25^2)/2 = (225 + 625)/2 = 425$, whose square root is $20.6$. But the expected VIX is $(15 + 25)/2 = 20.0$. So the VIX future prints 20.0 while the matching forward variance swap implies 20.6, a 0.6 point convexity gap that widens the more uncertain the outlook. It is why a VIX future cannot be perfectly hedged with a variance swap.

What this means in practice

Three places this bites. Volatility ETPs hold a rolling blend of the first two contracts, so they inherit the decay directly, which is why they reverse-split so often (Volatility ETPs And Roll Decay). Hedging budgets must be quoted as an annual carry cost, not a one-off premium, because buying vol protection is a subscription. And calendar spreads, long one month against short another, trade the shape of the curve while stripping out the level.

Key terms

• Spot VIX — the index level, computed from option prices, not tradable.
• Contango / backwardation — later months priced above / below nearer months.
• Roll yield — the gain or loss from the contract sliding along an unchanged curve.
• Vol beta — the fraction of a spot VIX move a given contract actually captures.
• Convexity adjustment — the gap between a VIX future and the square root of forward variance.