An Empirical Mean Reversion Test on VIX Futures

VIX mean reversion trade gets popular when the market experiences big ups and downs. You hear a lot of talks about how much money people make from trading VXX, XIV and their leveraged equivalents. However, is VIX truly mean reverting, or it seems more lucrative than it is just because people only like to talk about it when they make money and keep quiet when they lose?

In this post I use daily returns of S&P 500 VIX Short-Term Futures Index from December 2005 to August 2015 (2438 observations) to find if there’s empirical evidence that supports short-term VIX MR. It’s the most suitable vehicle for this test becuase there’s no instrument that tracks VIX spot and it is the benchmark for VXX and XIV.

VIX ST Futures Index holds VIX 1-month and 2-month futures contracts and rolls them on daily basis. Its performance suffers from contango effect like commodity futures ETFs do but it’s an inevitable cost in this case.

To find out if extreme VIX returns lead to strong short-term rebound, I group all daily returns by deciles and summarize the distributions of the accumulative future returns of each group up to 5 trading days (1 week). If VIX is truly ST MR, we should see the future returns following the 1st group (lowest) significantly higher than 0 on average, and the returns following the 10th group (highest) significantly lower than 0 on average. Future returns that go beyond the sample time period are recorded as 0.

Daily_Ret_Deciles

As shown above, group 1 and group 10 are the two groups we want to focus on. If someone can systematically make money by putting in MR trade on VIX, we should see the next day (or next 2, 3, maybe 5 days) returns following these two groups distributed like this:

Theoretical_Dist

The actual data look like this:

Day_1_Ret_Dist Day_5_Ret_Dist

It’s hard to spot any major difference between group 1 and 10 on the next day. However, on the 5th day, accumulated returns in group 1 largely outperform group 10. To better illustrate, I perform t-test on both groups from day 1 to day 5, as reported below (H0 = average return equals 0).

Capture

As it turns out, future returns in Group 1 systematically outperform Group 10 within the next 5 days. The results are not blessed by overwhelmingly strong t-stats and p-values but it’s hard to argue that we are looking at random noises here. Additionally, this test is done by end of day prices. Intraday movements, which possibly constitute the bulk of VIX MR trades, are completely ignored by this test. Therefore the results we see are likely a mitigated version of market reality.

Roy

9 thoughts on “An Empirical Mean Reversion Test on VIX Futures

  1. So you’re looking over a full-sample data history of VIX futures returns. Now what about an online version? Care to take your assertions and create a strategy?

    • Not at this stage. This study found a trace of evidence regarding this subject but there are still too many questions left unanswered to make it worthwhile to launch a paper portfolio or even commit capital on it, such as what if we test on minute by minute data? Does this strategy behave differently in different market regimes? How good is the tracking error of the ETFs that we can actually invest in? How does this strategy behave when the term structure of VIX changes? etc. With limited time, sources of information and capital, trying to answer all of these questions are simply too demanding for me.

      Hope that answers your question.

      Roy

      • Hi Ilya sorry about the confusion. I believe it’s just personal preference then. To me backtest is more suitable for presenting instead of analytical purposes. For me backtests are usually the “final product” when every other aspects has been thoroughly looked into.

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    • Hi that’s because this test solely focuses on extreme movements, recall that I dropped all other groups except 1 and 10. If I used ADF the entire time series would be picked up for MR test and that’s not the intention here, also the results would be harder to interpret.

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