**Background**

In recent articles, I looked at the relationship between contango in VIX futures and subsequent VelocityShares Daily Inverse VIX Short-Term ETN (NASDAQ:XIV) price movement. I found that contango has some predictive value, but not all that much.

Predictive signals are hard to come by. Despite the small signal-to-noise ratio I think contango-based XIV trading strategies have great potential. I recently proposed a contango-based pair trading strategy, where you buy XIV and hedge a beta-matched inverse SPDR S&P 500 Trust ETF (NYSEARCA:SPY) when contango is high, and buy the iPath S&P 500 VIX Short-Term Futures ETN (NYSEARCA:VXX) and hedge a beta-matched SPY when contango is low or VIX futures are in backwardation.

**Longer holding period = stronger signal**

While working more on contango-based pair trading, I recently discovered that the predictive value of contango is much more pronounced for longer holding periods.

For example, historically, change in SPY explains 69.7% of the variability in 1-day XIV price movement, change in VIX an additional 11.5%, and baseline contango an additional **1.4%**.

For a 10-day holding period, change in SPY explains 63.1% of the variability in XIV growth, change in VIX an additional 8.6%, and baseline contango an additional **7.8%**.

The figure below shows the relationship between contango and subsequent XIV growth, for holding periods ranging from 1 day to 100 days. Pearson correlation coefficients and p-values are shown on each plot.

First of all, notice that the signal isn't very strong in general. For a 1-day holding period, the correlation is only borderline significant.

But notice how much stronger the correlation gets when you look at longer holding periods. Moving to a 5-day holding periods renders the predictive value of contango highly significant, and it remains so for 10-day, 25-day, and 50-day holding periods.

I bet a lot of readers are thinking to themselves "well, there still isn't much there." Luckily, as I've discussed in prior articles, the predictive power of contango improves drastically when you look at relative growth vs. a beta-matched SPY fund.

In the first figure, we saw that moving from a 1-day holding period to a 10-day holding period increased the correlation from 0.05 to 0.12. In this SPY-hedged analysis, the correlation increases from 0.17 to 0.34.

I was pretty excited when I realized hedging on beta-matched SPY could increase the predictive power of contango from a correlation of 0.05 to 0.17. It turns out we can boost the correlation all the way up to about 0.36 by working with longer holding periods.

**Other Measures of Contango**

In line with prior articles, I defined contango as what percent higher the second-month VIX futures are compared to the first-month futures, i.e. using the formula (M2 / M1 - 1) x 100.

You could alternatively define contango as the difference M2 - M1. Or, you could incorporate the spot VIX price and define contango as the difference or percent difference between spot VIX and M1, or spot VIX and M2.

I did experiment with various measures of contango, and wanted to mention that the difference (M2 - spot VIX) seemed to be the most predictive version. Also, the difference (M2 - M1) was somewhat more predictive than the percent difference (M2 / M1 - 1) x 100.

**Conclusions**

I previously showed that hedging on a beta-matched SPY fund is a great way to increase the signal-to-noise ratio for contango-based volatility trades. Here, I report that modeling longer-term XIV price movement, say 10-day or 25-day growth, boosts the predictive power of contango even more.

Moving from unhedged to hedged XIV trades increases the predictive power of contango from borderline significant to a modest correlation of 0.17. Moving from 1-day to 10-day predictions brings the correlation all the way up to 0.34.

A stronger signal means more potential for the development of profitable volatility trading strategies.

**Data Source**

Historical contango data are from The Intelligent Investor Blog, and historical prices for various securities are from Yahoo! Finance. I used R to analyze data and generate figures. All results are for data from Nov. 30, 2010, to March 18, 2016.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within 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.

**Additional disclosure: **Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.