Month: November 2024

Examining Contango and Backwardation in VIX Futures

In this post, I will continue exploring various aspects of the volatility index and the associated volatility futures.

Data

To conduct this study, data is essential. Below are the data sources:

  • Spot VIX: Yahoo Finance provides data but no longer allows direct downloads. With some programming, a workaround can be found, but the most convenient option is to use Barchart.

https://www.barchart.com/stocks/quotes/$VIX/price-history/historical

  • VX Futures: CBOE offers historical data in CSV format.

https://www.cboe.com/us/futures/market_statistics/historical_data/

  • Short-Term Futures Index:

While not directly utilized in this issue, I use this data to validate other ideas. For completeness, here is the download link:

https://www.spglobal.com/spdji/en/indices/indicators/sp-500-vix-short-term-index-mcap/#overview

Statistics for spot VIX and VX Futures

The table below provides statistics for the S&P 500 (tracked by SPY), spot VIX, and VX futures. It shows the percentage of days the S&P 500 index is up and the percentage of days VX futures are in contango, where the front-month futures price is lower than the next-month futures price.

From January 2013 to November 2024, the S&P 500 index was up  54.9% of the time, while VX futures were in contango most of the time (85.2%).

The next table presents the number of days VX futures were in backwardation while the spot VIX was in contango. Spot VIX in contango is defined as the 1M spot VIX being less than the 3M spot VIX.

From  January 2013 to July 2024, this situation was very rare, occurring only 7% of the time.  However, from  August 1 to November 4, 2024, this divergence occurred with much higher frequency, 53% of the time.

This situation presented a high reward/risk trade opportunity. For instance, one could structure a trade to capitalize on the high likelihood of VX futures returning to contango and a decline in the overall volatility level. One potential trade is buying a put option in VXX. We’ll discuss this strategy in an upcoming webinar.

Seasonality of Volatility

With the holiday season approaching, the equity world often discusses the “Santa Rally.” This raises the question: Is there any seasonality in the volatility market?

The graph below shows the average and median monthly implied and historical volatilities. A clear seasonal pattern is observed, with low volatility between April and July and high volatility in October. However, for December, there is no discernable pattern—volatility can be either high or low during this period.

Educational Video

This webinar by Prof Andrew Papanicolaou covers fundamental concepts of VX futures, such as contango, backwardation, and roll yield. It also presents an approach to modeling the VX futures term structure.

Abstract:

We study VSTOXX, VSTOXX futures and VSTOXX exchange-traded notes (ETNs) econometrically. We find that different rates of mean reversion capture fluctuations in the short and long maturities, respectively. We fit an exponential Ornstein-Uhlenbeck (OU) model to the data and find it to capable of simulating ETN time series that have similar properties to the historical observed ETN time series. We compare these results to a similar study performed on ETNs and futures for VIX. We also look at the joint behavior of VIX and VSTOXX futures, and explore portfolio allocation strategies among ETNs for both markets.

Closing Thoughts

The volatility market offers unique insights and opportunities for investors. By understanding concepts like contango, backwardation, and seasonality, we can structure strategies with favorable risk-reward profiles.

Let me know your thoughts in the comments below.

Making Use of Information Embedded in VIX Futures Term Structures

With the U.S. election now over, the VIX futures term structure has normalized. It typically follows the spot VIX term structure. However, before the election, the futures term structure was in backwardation while the spot VIX was in contango most of the time. This is a rare occurrence.  Below is a snapshot of the spot and futures term structures on September 26.

VIX futures term structure

In a future issue, I’ll present statistics and trade opportunities for such situations. In today’s issue, however, I will discuss two papers that develop trading systems for VIX futures.

Trading VIX Futures Using Neural Networks

Reference [1]  explores the use of neural networks, a type of artificial intelligence, to trade VIX futures. The authors assume that the term structure of VIX futures follows a Markov model. An interesting aspect of this paper is that it made use of a utility function to generate trading signals. The authors also performed thorough out-of-sample testing using the k-fold cross-validation technique.

The Model

  • The trading strategy aims to maximize expected utility for a day-ahead horizon considering the current shape and level of the term structure.
  • Computationally, a deep neural network with five hidden layers models the functional dependence between the VIX futures curve, positions, and expected utility.
  • Out-of-sample backtests indicate that this method achieves good portfolio performance.

Validation

  • The standard procedure for training involves dividing the data into two blocks: one for in-sample training and the other for out-of-sample testing.
  • VIX futures curves from April 14th, 2008, to August 7th, 2019, are used for in-sample training, while the remaining curves from August 8th, 2019, to November 5th, 2020, are used for out-of-sample testing.
  • Since the out-of-sample test is based on a single portfolio run, good performance could be attributed to luck. Therefore the method of k-fold cross-validation is applied.

Reference

[1] M. Avellaneda, T. N. Li, A. Papanicolaou, G. Wang, Trading Signals In VIX Futures, Applied Mathematical Finance. 2021;28(3):275–298

Trading VIX Futures Using Machine Learning Techniques

Building on the first paper, Reference [2] investigates machine learning techniques for trading VIX futures. It proposed using Constant Maturity Futures (CMF) to generate trading signals for VIX futures. It applied machine learning models to create these signals.

Findings

  • The experiment results show that term structure features, such as μt and ∆roll, are highly effective in predicting the next-day returns of VIX CMFs and offer potential economic benefits.
  • The C-MVO strategy outperformed the benchmark rank-based long-short strategy in backtesting across most machine learning models, offering valuable insights for trading VIX CMFs.
  • Neural network models, particularly ALSTM, demonstrated the best performance in both prediction and backtesting.
  • Tree-based models showed no clear superiority, while the linear regression model, which only considers linear relationships, outperformed all other models.
  • The findings highlight the predictive power of term structure features for next-day returns in VIX CMFs.

Reference

[2]  Wang S, Li K, Liu Y, Chen Y, Tang X (2024), VIX constant maturity futures trading strategy: A walk-forward machine learning study, PLoS ONE 19(4): e0302289

Closing Thoughts

These papers present trading systems developed using advanced techniques in machine learning and AI. As such, validation is critical. Techniques such as k-fold validation and walk-forward analysis should be carried out rigorously.

The research also suggests that there is valuable information embedded in the VIX futures term structure. In my opinion, “simple”, intuitive systems can be developed using VIX term structure that can provide decent risk-adjusted returns. Additionally, as I’ve discussed in one of my LinkedIn posts, the S&P 500 market generally leads the VIX market. Therefore, signals from the S&P 500 can also be used to trade VIX futures.

Let me know your thoughts in the comments below.

Rethinking Pairs Trading: Can Traditional Methods Still Deliver Returns?

Pairs trading is a market-neutral strategy that involves trading two correlated stocks or assets. The idea is to identify pairs that historically move together, and then take a long position in one and a short position in the other when they diverge, with the expectation that they will eventually revert to their mean relationship.

The popularity of pairs trading has risen over the years. Naturally, this raises the question: is pairs trading still profitable, and is it worth investing time, money, and resources to find profitable pairs trading strategies?

Pairs Trading: No Longer Profitable

There is a perspective among some researchers and traders that pairs trading may have lost its profitability over time due to increased competition and the efficiency of modern markets.

Reference [1] argues that pairs trading is no longer profitable, especially when using basic approaches for pairs selection.

Findings

  • This paper focuses on the German stock market from 2000 to 2023, a market with relatively few analyses in this area.
  • Basic strategies based on spread distance and cointegration barely cover transaction costs and often break even.
  • A copula-based method, especially when combined with simpler strategies, shows stronger performance, yielding an average portfolio return of around 170 basis points (bps) per month after transaction costs.
  • The strategies are designed to be uncorrelated with systemic market risk, and empirical results confirm this.
  • Sensitivity analyses indicate the robustness of the copula-based method and suggest possible refinements for further strategy enhancement.

Reference

[1] Sascha Wilkens, Pairs Trading in the German Stock Market: There’s Life in the Old Dog Yet.

Pairs Trading: Still Profitable

On the other hand, some argue that pairs trading remains profitable. Reference [2] supports this view, showing evidence of profitability even with classical pairs selection methods like the spread distance approach.

Findings

  • The paper replicates Gatev et al.’s [3] pairs trading strategy using twenty years of stock price data, affirming robustness despite transaction costs in the current market.
  • The top strategy achieves a compounded annual excess return of 6.2%, a notable finding given market dynamics.
  • A broader stock pool mitigates outlier effects from events like delistings or stock splits, enhancing strategy performance compared to typical literature.
  • The study examines two profit determinants in pairs trading: medium-term momentum and the default spread, correlating with the investor risk premium.
  • These findings support Gatev et al.’s [3] hypothesis on arbitrage compensation for restoring market efficiency.

References

[2] Xuanchi Zhu, Examining Pairs Trading Profitability, 2024, Yale University

[3] Gatev, E., Rouwenhorst, K. G., and Goetzmann, W. (2006). Pairs trading: Performance of a relative value arbitrage rule.

Closing Thoughts

In my opinion, pairs trading is still profitable. However, it requires using a pairs selection method that isn’t obvious or widely adopted by others. I was somewhat surprised that, in Reference [2], the author still finds pairs trading profitable using a classical selection method.

What’s your experience with pairs trading? Let me know in the comments section.

Pairs selection is a critical step in developing a winning trading system. In a future issue, I’ll cover different pairs selection methods that could enhance profitability.