Modeling The VIX Futures Curve

by: The Sociology of Finance

In the last few years, ETPs linked to the VIX have become increasingly popular with both retail and professional investors, including the iPath S&P 500 VIX Short-Term Futures ETN (NYSEARCA:VXX), ProShares VIX Short-Term Futures ETF (NYSEARCA:VIXY), VelocityShares Daily 2X VIX Short-Term ETN (NASDAQ:TVIX), and ProShares Ultra VIX Short-Term Futures ETF (NYSEARCA:UVXY). As their names suggest, these products are linked to VIX futures because the VIX is not directly traded.

Confusion between the spot VIX and VIX futures has caused portfolio pain for some, because futures products have their own quirks that investors ignore at their peril. The key issue is that a futures contract is a time-limited instrument based on the price of the underlying asset at some future settlement date. So while the current price of an asset (in this case the VIX) is relevant to its likely future value and can serve as a sort of anchor to the prices of futures contracts, investor sentiment about what will happen in the intervening time also plays a role.

This investor sentiment about the time until settlement is key for VIX futures, which tend to trade at a premium to the spot VIX price, a situation known as contango. This means that if the VIX remains at a constant level while in contango, VIX longs will eventually owe VIX shorts the spread between the futures contract and the spot price because they must converge by the settlement date. Similarly, roll costs from contango go a long way in explaining the terrible performance of long VIX products such as VXX since their inception.

Conceptual Model

The goal of this article is to add a little theoretical and quantitative rigor to the study of the VIX futures curve beyond the banal claims that it is shaped by "investor sentiment" or "supply and demand". True to my value investing roots, I'd like to develop a sense of the intrinsic value of a given VIX futures contract to see whether it is overpriced or underpriced.

Theoretically, I believe that there are two fundamental determinants of the price of a given VIX futures contract. 1.) The anticipated spot price of the VIX at settlement. 2.) The risk premium demanded by VIX shorts as a compensation for tail risk. The value (v) can thus be expressed as a function of expected VIX at settlement (e) and the risk premium for shorts (r):

v = e + r

Including the expected value of the VIX at settlement in any valuation model clearly makes sense, because VIX futures contracts are ultimately settled according to this metric. The risk premium for shorts is a more abstract idea, but its necessity becomes clear when we consider the asymmetric characteristics of returns. When shorts win, they tend to pocket nickels and dimes, but when longs win, they can hit the jackpot. This is because the VIX spikes upwards every now and then during a "black swan" event, so shorts should rationally demand some sort of compensation for the small-but-real risk of being carried out to sea.

Statistical Model

While expected value of VIX at settlement (e) and risk premium for shorts (r) are theoretical concepts and therefore not directly observable, in this section I will attempt to estimate them in the current market.

The first step is to arrive at an estimate of the value of the VIX at settlement. To do this, I built a model using the entire publicly available history of the VIX going back to 1/1/1990 through 5/29/2013. I included indicators for the return of the VIX over the following prior periods: 1 day, 5 day, 22 day (1 month), 44 day (2 month), and 66 day (3 month). I also included starting values of the VIX for each of these periods. The rationale for including these indicators was that they would capture both the momentum and mean reversion characteristics of the VIX. Next, I calculated historical returns of the VIX for the days currently remaining in the existing futures contracts: 19 days (front month contract), 47 days (second month), 82 days, 110 days, 138 days, 173 days, 201 days, and 236 days. Using these models as a baseline, I plugged in the specific values of prior VIX returns and values for each period as of close on 5/30/2013. Although the models are pretty simplistic, they do a pretty good job of estimating the 5,700 or so days of rolling returns in the sample. Here's the results:

Projected VIX performance going Forward


19 day return



47 day return



82 day return



110 day return



138 day return



173 day return



201 day return



236 day return



As the table above reveals, the r-squared for the models is usually pretty high, especially with the 2nd-5th month contacts. So while I will probably want to tweak the models a bit going forward, it appears that past information does a decent job of predicting future VIX performance. For the sake of argument, let's say that these models accurately estimate expected VIX values at settlement. Here's how the expected values stack up compared to the current VIX futures curve:

(Click to enlarge)

The June contract is spot on with the estimated settlement value, but the others have a predicted settlement value lower than the futures contract closing price as of 5/30/2013.

What does this mean? A simple interpretation would suggest that the gap between the two lines is the risk premium demanded by shorts (r). So what sort of premiums are the shorts demanding right now? According to my model, it looks like the shorts are demanding essentially no risk premium in the front month contract, a 5.4% premium in the second month, 6.1% in the third month, 12% in the fourth month, and 24% in the fifth month (October contract).

Trading Implications for Shorts

I think that the fifth month contract is the sweet spot of risk-reward for shorts right now because it commands the largest premium relative to the time to settlement. Unfortunately, this position cannot be directly expressed using an ETP, but is available for those with futures accounts. The bigger take-away for shorts is that the front month does not really offer much of a premium right now, so fans of Proshares Short VIX Short-Term Futures ETF (NYSEARCA:SVXY) like myself should be careful. Personally, I closed out my SVXY position and am sitting on cash right now.

Trading Implications for Longs

I can't believe I'm saying this, but it actually looks like the front month contract is reasonably priced for the longs. Now I would not rush headlong into a product like VXX, because it also includes the second month contract, and by nature I'm allergic to a long VIX position. But I have to follow wherever the evidence leads me. And the evidence suggests that a long position is not such a bad idea right now. So while I would not take a such a position myself, I can understand where the longs are coming from.

Disclosure: I have no positions in any stocks mentioned, but may initiate a long position in SVXY over the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

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