Why is the VIX futures market usually in a state of contango?

Question

I'm a VIX newbie and I'm trying to understand why the VIX futures market is usually in a state of contango.

All I can figure is that the sellers of VIX futures contracts demand high "prices" (because the seller is the holder of the short position and makes money when the price falls), and since there are willing buyers, namely ETNs and ETFs that are trying to track the S&P 500 VIX SHORT-TERM FUTURES INDEX (SPVIXSTR) through the purchase and sale of VIX futures, the contracts get sold.

Also, the farther out the futures contract expires, the less certain the seller is about what the value of the VIX and the SPVIXSTR will be at the future's expiration date. The greater uncertainty over a longer term results in the seller demanding higher premiums over a longer term than he would demand over a shorter term.

It seems like a prudent buyer of VIX futures wouldn't buy contracts that are priced so high.

It seems like the VIX futures market should be in a state of contango about as frequently as it is in a state of backwardation.

What causes contango in the VIX futures market, and why is it the usual state of the market?

Answer 1

• Your questions about contango in VIX futures have close analogies in options too. The Black & Scholes model suggests that all time frames and all strikes should have the same implied volatility, but they don't. I think one of the reasons is that the B&S model assumes that stock returns are distributed in a normal (gaussian) distribution, but the actual returns don't match a gaussian distribution all that well. For example the actual occurrence of big crashes / gains is much more likely than a normal distribution would predict. Since crashes do occur people are willing to pay what the B&S considers a premium to have some insurance against downswings. I view it as being an insurance cost, so the longer youwant the insurance for, the more it will cost you. If you look at the term structure of SPX options you'll see a term structure that looks a lot like the VIX futures curve. The VIX futures on settlement will use the SPX options expiring one month later as the prices for settlement (e.g., Nov VIX futures will settle to Dec SPX options).

• The VIX futures tend to go no higher than around 9% above their equivalent SPX option VIX style implied volatility value , so I suspect above that some sort of arbitrage gets attractive, and the price difference is limited.

• One other thought about VIX futures. They are attractive because you don't have to place your bets as specifically as you do if you are buying out of the money puts for insurance against crashes. If you buy puts and the market rallies your puts are left very out of the money, whereas the VIX can spike up regardless of where the value of the SPX index is. Clearly people are willing to pay a premium for VIX futures, and I don't think they are stupid. At lot of them lived through the 2000 and 2008 bear markets--that leaves an impression on you.

Answer 2

Your question is an important one, but I am not aware of any particularly satisfying answer. There are several papers on this issue -- see Luo and Zhang 2009 and Zhang et al 2010, just for example.

One thing to note is that VIX futures are not always in contango -- after large jumps in the VIX, they can even be in rather steep backwardation. I have heard arguments that this behavior indicates that the futures markets expect the VIX level to revert to a historical mean, which is lower after a jump but higher during 'quiet' periods. Therefore, the futures curve perhaps 'points' to the expected mean. Thinking of the VIX as mean reverting is intuitive (though incomplete), so this explanation has some appeal.

I think your explanation regarding uncertainty makes some sense. Certainly, traditional arguments regarding storage costs used to explain other futures markets do not apply to the VIX, as it is simply a calculated value. Then again, I'm not sure even those markets' term structures are perfectly understood.

It's also important to note that VIX futures contango predates VIX ETNs/ETFs, so their trading activity may not be fundamental to the slope of the term structure. If you've ever looked at a volume chart for front month VIX futures, however, you will see plainly that rolling VIX strategies are a huge component of that market's volume.

Which is all a long way of saying: I do not know, and would be very interested in hearing other explanations.

Answer 3

VIX is a measure of volatility -- something that changes explicitly with uncertainty. The chances of uncertainty arising tomorrow, is lower than the chances of uncertainty increasing in the longer term. A long-dated option should therefore have more "potential uncertainty" baked into the price.

When pricing normal futures, the price is a martingale, the expectation being movement at the risk free rate. With the VIX, this seems not to be the case, the expectation is that it will revert to it's historical average, however this mean-reversion isn't grounded in theory.

Finally, because the VIX has a negative correlation with the market in bad times, and little correlation in good times, in a CAPM world, it has a negative beta in the bad state of the world, and a near 0 beta in the good state of the world. This implies that people will want to hold it simply for diversification, even though the return most of the time may be negative.

The intuition that follows, is that longer futures have more "time-value" embedded in them, because the future state of the VIX is not only unknowable, but, really hard to forecast. They are also worth "paying a little more" for, because they will pay off big in the bad state, but not lose too much in the good state.

Answer 4

VIX futures tend to rise when the S&P 500 falls -- the correlation of returns is about -0.7. If there were no contango in VIX futures, everyone would buy them to get free insurance against stock market declines.

Here is a recent working paper making this argument -- note the last sentence of the abstract.

http://skinance.com/documents/EWFS_Eraker_and_Wu.pdf

Explaining the Negative Returns to VIX Futures and ETNs: An Equilibrium Approach

Bjørn Eraker and Yue Wu

Abstract

We study the returns to investing in VIX futures and VIX Exchange Traded Notes (ETNs). We document a substantial negative return premium for both ETNs and the futures. For example, a one month constant maturity portfolio of futures loses about 12BP per day on average. We propose an equilibrium model to explain the negative returns. In this model, increases in volatility endogenously lead to decreasing stock prices. The negative return premium is an equilibrium outcome because long VIX futures positions hedge against low returns/ high volatility states (i.e, financial crisis).

Answer 5

The fact VIX has a very large contango (right now a % carry of 10%/month) has to do with rational risk premium. The net supply of stocks is 1, so on net investors are long the stock market. They want to hedge this risk by going short, so they buy VIX futures (which are correlated -0.7 with the stock market).

On the other hand, VIX futures are in zero net supply (every long has a short), so the fact that everyone wants to go long volatility means that those who short volatility get to harvest a very large risk premium, which precisely leads to the market clearing in equilibrium. Even more, VIX doesn't really exist as a physical product, so you can't execute a "carry" trade like people do with wheat, corn, oil or even stocks, which means that the only thing that governs the VIX curvature has to do with people's perception of the vol risk premium.

Answer 6

I think there are two ways of looking at it, and that they are ultimately equivalent.

As others have said, it's an insurance premium, as simple as that.

There is only one thing which affects the price of VIX futures: supply and demand. You can choose to be the insurer (sell futures), in which case you earn long-term profit from premiums, but take huge losses from time to time. Or choose to be the insured (buy futures) and make long term losses (the insurance premium) in return for protection from unpleasant volatility.

No sane insurer would offer their services if there wasn't a substantial reward for their taking on risk. No reasonable insuree expects to get insurance for free. Nothing but supply and demand cause the value of a rolling contract to decay according to the inferred value of the insurance premium.

The other (ultimately equivalent) way to look at it is this: one can approximately replicate the risk profile of a long VIX position by buying strips of call and put options. Or one (obviously) can roughly replicate the risk profile of a short VIX position by writing strips of calls and puts.

Option pricing (for the same underlying reason... that buying options is like buying insurance and writing them is like selling insurance) is such that in the long term, the option writer (like the Casino) wins. A strategy of continually buying strips of puts ultimately loses money exactly like VIX future decay, and a strategy of continually writing strips of puts ultimately appreciates exactly like a short VIX position.

Thus the presence of an efficient options market (and the existence of arbitrage) determines that VIX futures must exhibit the same behaviour as equivalent options strategies, i.e. decay for the buyer, long term profit for the seller.

Oh, and don't for a minute believe that either options or VIX futures are priced by any mechanism but supply and demand. Black-Scholes and derived models may inform the options market, but at the end of the day it is just a market, priced according to supply and demand. Similarly, the published VIX index informs the buyers and sellers of VIX futures, but supply and demand dictate the price.

And supply and demand, since we are naturally risk averse, ensures that ultimately insurers make long term profits, and insurees make long term losses.