rvarb – Relative Value Arbitrage

Option Pricing Models and Strategies for Crude Oil Markets

Financial models and strategies are usually universal and can be applied across different asset classes. However, in some cases, they must be adapted to the unique characteristics of the underlying asset. In this post, I’m going to discuss option pricing models and trading strategies in commodities, specifically in the crude oil market.

Volatility Smile in the Commodity Market

Paper [1] investigates the volatility smile in the crude oil market and demonstrates how it differs from the smile observed in the equity market. It proposes to use the new method developed by Carr and Wu in order to study the volatility smile of commodities. Specifically, the authors examine the volatility smile of the United States Oil ETF, USO.

Findings

– This paper examines the information derived from the no-arbitrage Carr and Wu formula within a new option pricing framework in the USO (United States Oil Fund) options market.

– The study investigates the predictability of this information in forecasting future USO returns.

– Using the no-arbitrage formula, risk-neutral variance, and covariance estimates are obtained under the new framework.

– The research identifies the term structure and dynamics of these risk-neutral estimates.

– The findings reveal a “U”-shaped implied volatility smile with a positive curvature in the USO options market.

Usually, an equity index such S&P 500 exhibits a downward-sloping implied volatility pattern, i.e. a negative implied volatility skew. Oil, on the other hand, possesses a different volatility smile. This is because while equities are typically associated with crash risks, oil prices exhibit both sharp spikes and crashes, leading to a different implied volatility pattern. This highlights the importance of considering the specific characteristics and dynamics of different asset classes when analyzing and interpreting implied volatility patterns.

Reference

[1] Xiaolan Jia, Xinfeng Ruan, Jin E. Zhang, Carr and Wu’s (2020) framework in the oil ETF option market, Journal of Commodity Markets, Volume 31, September 2023, 100334

Statistical Arbitrage in the Crude Oil Markets

Reference [2] directly applies statistical arbitrage techniques, commonly used in equity markets, to the crude oil market. It utilizes cointegration to construct a statistical arbitrage portfolio. Various methods are then used to test for stationarity and mean reversion: the Quandt likelihood ratio (QLR), augmented Dickey-Fuller (ADF) test, autocorrelations, and the variance ratio. The constructed strategy performed well both in- and out-of-sample.

Findings

– This paper introduces the concept of statistical arbitrage through a trading strategy known as the mispricing portfolio.

– It focuses specifically on mean-reverting strategies designed to exploit persistent anomalies observed in financial markets.

– Empirical evidence is presented to demonstrate the effectiveness of statistical arbitrage in the crude oil markets.

– The mispricing portfolio is constructed using cointegration regression, establishing long-term pricing relationships between WTI crude oil futures and a replication portfolio composed of Brent and Dubai crude oils.

-Mispricing dynamics revert to equilibrium with predictable behaviour. Trading rules, which are commonly used in equity markets, are then applied to the crude oil market to exploit this pattern.

Reference

[2] Viviana Fanelli, Mean-Reverting Statistical Arbitrage Strategies in Crude Oil Markets, Risks 2024, 12, 106.

Closing Thoughts

As we’ve seen, techniques and models utilized in the equity market can sometimes be applied directly to the crude oil market, while other times they need to be adapted to the unique characteristics of the crude oil market. In any case, strong domain knowledge is essential.

Educational Video

In this webinar, Quantitative Trading in the Oil Market, Dr Ilia Bouchouev delivers an interesting and insightful presentation on algorithmic trading in the oil market. He also encourages viewers to apply the techniques discussed for the oil market to other markets, such as equities.

When Correlations Break or Hold: Strategies for Effective Hedging and Trading

It’s well known that there is a negative relationship between an equity’s price and its volatility. This can be explained by leverage or, alternatively, by volatility feedback effects. In this post, I’ll discuss practical applications to exploit this negative correlation between equity prices and their volatility.

A Trading Strategy Based on the Correlation Between the VIX and S&P500 Indices

This paper [1] examines the strong correlation in the S&P 500 and identifies trading opportunities when this correlation weakens or breaks down.

Findings

-The study covers the period from January 1995 to October 2020, utilizing 6,488 daily observations of the VIX and S&P500 indexes.

– In scenarios where the options market indicates increased drawdown risk with higher implied volatility but negative returns have not yet occurred, consider shorting the market.

– The signal to short the market occurs when the negative correlation between the S&P 500 and VIX is broken, and they start exhibiting a positive correlation.

– The test setup involves identifying one or two consecutive days with positive co-movement between the VIX and S&P 500, then setting the transaction date for the day after or at the close of the chosen date.

– Empirical results show that the strategy outperforms the S&P500 index over the 25-year period, achieving higher returns, lower systematic risk, and reduced volatility.

-The findings provide evidence that excess returns can be generated by timing the market using historical data, even after accounting for trading costs.

Reference

[1] Tuomas Lehtinen, Statistical arbitrage strategy based on VIX-to-market based signal, Hanken School of Economics

Optimal Hedging for Options Using Minimum-Variance Delta

Contrary to the first paper, Reference [2] focuses on the strong correlation between the S&P 500 and its volatility, designing an efficient scheme for hedging an options book.

The authors developed a so-called minimum variance (MV) delta. Essentially, the MV delta is the Black-Scholes delta with an additional adjustment term.

Findings

-Due to the negative relationship between price and volatility for equities, the minimum variance delta is consistently less than the practitioner Black-Scholes delta.

-Traders should under-hedge equity call options and over-hedge equity put options compared to the practitioner Black-Scholes delta.

-The study demonstrates that the minimum variance delta can be accurately estimated using the practitioner Black-Scholes delta and the historical relationship between implied volatilities and asset prices.

-The expected movement in implied volatility for stock index options can be approximated as a quadratic function of the practitioner Black-Scholes delta divided by the square root of time.

-A formula for converting the practitioner Black-Scholes delta to the minimum variance delta is provided, yielding good out-of-sample results for both European and American call options on stock indices.

-For S&P 500 options, the model outperforms stochastic volatility models and models based on the slope of the volatility smile.

-The model works less well for certain ETFs

Reference:

[2] John Hull and Alan White, Optimal Delta Hedging for Options, Journal of Banking and Finance, Vol. 82, Sept 2017: 180-190

Closing Thoughts

These two papers take opposing approaches: one exploits correlation breakdown, while the other capitalizes on the correlation remaining strong. However, they are not mutually exclusive. Combining insights from both can lead to a more efficient trading or hedging strategy.

Educational Video

This seminar by Prof. J. Hull delves into the second paper discussed above.

Abstract

The “practitioner Black-Scholes delta” for hedging equity options is a delta calculated from the Black-Scholes-Merton model with the volatility parameter set equal to the implied volatility. As has been pointed out by a number of researchers, this delta does not minimize the variance of a trader’s position. This is because there is a negative correlation between equity price movements and implied volatility movements. The minimum variance delta takes account of both the impact of price changes and the impact of the expected change in implied volatility conditional on a price change. In this paper, we use ten years of data on options on stock indices and individual stocks to investigate the relationship between the Black-Scholes delta and the minimum variance delta. Our approach is different from earlier research in that it is empirically-based. It does not require a stochastic volatility model to be specified. Joint work with Allan White.

Hurst Exponent Applications: From Regime Analysis to Arbitrage

One of my favourite ways to characterize the market regime is by using the Hurst exponent. However, its applications are not limited to identifying market regimes. There are innovative ways to utilize it. In this post, I will discuss two approaches to applying the Hurst exponent.

Using the Hurst Exponent to Time the Market

The Hurst exponent can be employed to directly time the market. Reference [1] calculated the moving Hurst exponents for rolling windows of 100 and 150 days. The timing signals are subsequently generated by using these calculations.

Findings

-The study suggests that the Moving Hurst (MH) indicator is effective for forecasting and managing volatility in Indian equity markets.

-MH is more effective at capturing profitable trading opportunities than Moving Averages (MA).

-MH is a less lagging indicator than MA, making it more responsive to market changes.

-MH incorporates principles from chaos theory and fractal analysis, offering a unique perspective for market analysis.

-The research was conducted in the Indian stock market. However, it can be readily applied to any stock market.

Reference

[1] Shah, Param, Ankush Raje, and Jigarkumar Shah, Patterns in the Chaos: The Moving Hurst Indicator and Its Role in Indian Market Volatility. Journal of Risk and Financial Management 17: 390, 2024

Using the Hurst Exponent for Pairs Trading

The Hurst method isn’t restricted to single underlying assets; it can also be applied to a pair of stocks to identify pairs trading (statistical arbitrage) opportunities. Reference [2] proposed a new approach to measure the co-movement of two price series through the Hurst exponent of the product.

Findings

– The Hurst exponent of the product series, referred to as HP, can measure the existence of a relationship between two series.

– The HP method is a new way to measure the dependence between two series, detecting various types of relationships, including correlation, cointegration, and non-linear relationships, even when the relationship is weak or given by a copula.

– This method is particularly useful for studying financial series as it gives more weight to high increments than low increments, unlike other correlation measures.

– The efficiency of the HP method was tested through a statistical arbitrage technique for pairs selection and compared with the classical correlation method. Results indicate that the HP method performs better in most cases.

Reference

[2] José Pedro Ramos-Requena, Juan Evangelista Trinidad-Segovia, and Miguel Ángel Sánchez-Granero, An Alternative Approach to Measure Co-Movement between Two Time Series, Mathematics 2020, 8, 261

Educational Video

This seminar by Markis Vogl presents the theory and application of the Hurst exponent.

Abstract

My presentations elaborates on the meaning of Hurst exponents, namely, that instead of long memory, fractal trends are measured instead (contradicting Mandelbrot’s conception). Further, the talk encompasses the generation of rolling window (time varying) Hurst exponent series based upon the cascadic level 12 wavelet filtered (denoised) S&P500 logarithmic return series (2000-2020). The Hurst exponent series are then analysed with a generalizable nonlinear analysis framework, which allows the determination of the underlying empirical data generating process.

Closing thoughts

The Hurst exponent is an effective tool for gaining insights into market dynamics. Whether for timing the market or identifying pairs trading opportunities, it offers traders an edge in strategy development.

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.

The Weekend Effect in The Market Indices

The weekend (or Monday) effect in the stock market refers to the phenomenon where stock returns exhibit different patterns on Mondays compared to the rest of the week. Historically, there has been a tendency for stock prices to be lower on Mondays. Various theories attempt to explain the weekend effect, including investor behaviour, news over the weekend, and the impact of events occurring during the weekend on market sentiment.

In this post, we’ll investigate the weekend effect in the market indices using data from Yahoo Finance spanning January 2001 to December 2023. Specifically we choose SPY, which tracks the SP500, and the volatility index, VIX.

Our strategy involves taking a long position in SPY at Friday’s close and exiting the position at Monday’s close, or the next business day’s close if Monday is a holiday. The figure below depicts the cumulative, non-compounded return of the strategy.

Cumulative return of holding SPY over the weekend

From the figure, we observe that holding SPY over the weekend resulted in negative returns during the GFC, Covid pandemic, and the recent 2022 bear market. The overall return is flat-ish, indicating a low reward/risk ratio for holding the SPY over the weekend.

Next, we analyze the change in the VIX index during the weekend. We compute the change in the VIX index from Friday’s close to the close of the next business day and plot the cumulative difference in the figure below. A noticeable upward trend is observed in the cumulative difference. This result indicates that maintaining a long vega/gamma position over the weekend would offer a favourable reward-to-risk trade.

Cumulative difference of the VIX index over the weekend

It’s important to note, however, that investing directly in the spot VIX is not possible. To confirm and capitalize on the weekend effect in the volatility index, one would have to:

Trade a volatility ETN, or
Trade a delta-hedged option position

Each of these approaches introduces additional risk factors, specifically 1- the roll yield and contango, and 2- PnL originating from gamma and theta. These issues will be addressed in the next installment.

Which System Has The Lowest Risk of Ruin?

Would you rather choose a trading system that wins small amounts most of the time but when it loses, the loss is big? Or would you rather choose a trading system that loses small amounts most of the time but when it wins, the gain is big? In this blog post, we will examine such systems from the risk of ruin perspective.

The risk of ruin is the probability of an investor’s eventual bankruptcy due to a series of losses that exceed his/her capital. It is essential for any trader to understand their risk of ruin, as it will heavily influence the trading system they ultimately develop.

We will use Monte Carlo simulations to perform our analysis. We examine the following 3 trading systems

System	Percent win	Win	Loss	Expectancy
A	10%	$90	$10	0
B	50%	$18	$18	0
C	90%	$10	$90	0

For each system, we generate 1000 trades randomly. If a trade is a win, then we’ll make the amount in the column “Win”, and if it’s a loss, then we’ll lose the amount in the column “Loss”. For example, for system A, if we win, we make $90 and if we lose, we lose $10.

To simplify the analysis, we assume that all 3 systems have zero expectancies. The total winning/losing amounts of each system equal $9000. We start with an initial capital of $1000. The figure below shows the first 100 simulated paths for system A. It’s clear that the system has zero expectancy as the terminal wealth equals the starting capital.

To calculate the probability of ruin, we first count the number of paths that go below $0 at any time in their evolutions. We then divide the number of such paths by the number of iterations which is 10000.

The table below summarizes the results.

System	Risk of Ruin
A	10.22%
B	0.18%
C	9.95%

We can see from the results that system B has the lowest probability of ruin. This confirmed that traders should avoid systems that have high win percentages but suffer occasional large losses. Short volatility trading systems are in this category. Traders should also avoid systems that have low percentage win rates.

Asset Price Dynamics and Trading Strategy’s PnL Volatility

In a previous post, we discussed how the dynamics of assets are priced in the options prices. We recently came across a newly published article [1] that explored the same topic but from a different perspective that does not involve options.

The conclusion of the new article [1] is consistent with the previous one [2]; that is, the volatilities of mean-reverting assets are smaller than those of assets that follow the GBM process. The reverse applies to trending assets.

In this post, we are going to investigate whether the mean-reverting/trending property of an asset has any impact on a trading strategy’s PnL volatility.

To do this, we first generate asset prices using Monte Carlo simulations. We evolve the asset prices in both mean-reverting and trending regimes for 500 days. We then apply a simple trading system to the simulated asset prices. The trading system is as follows,

Go LONG when the Relative Strength Index <40, SHORT when the Relative Strength Index >70

The picture below shows the Autocorrelation Functions (ACF) of the asset returns. Panels (a) and (b) present ACFs of the trending and mean-reverting assets respectively. It’s clear that the assets are trending and mean-reverting at lag 3, respectively.

Autocorrelation Functions of asset returns

The picture below shows the simulated equity curves of the trading strategy applied to the trending (a) and mean-reverting (b) assets. The starting capital is $100 in both cases.

Visually, we do not observe any difference in terms of PnL dispersion. Indeed, the standard deviation of the terminal wealth at day 500 is $18.9 in the case of the trending asset (a), and $17.3 in the case of the mean-reverting asset (b). Is the difference statistically significant? We don’t think so.

This numerical experiment shows that the PnL volatility of a trading strategy has little to do with the underlying asset’ mean-reverting/trending property. Maybe it depends more on the strategy itself? (Note that in this example, we utilize a mean-reverting strategy). What would happen at the portfolio level?

References

[1] L. Middleton, J. Dodd, S. Rijavec, Trading styles and long-run variance of asset prices, 2021, arXiv:2109.08242

[2] Liao, S.L. and Chen, C.C. (2006), The valuation of European options when asset returns are autocorrelated, Journal of Futures Markets, 26, 85-102.

Correlation Between the VVIX and VIX indices

The VIX index is an important market indicator that everyone is watching. VVIX, on the other hand, receives less attention. In this post, we are going to take a look at the relationship between the VIX and VVIX indices.

While the VIX index measures the volatility risks, VVIX measures the volatility-of-volatility risks. Its calculation methodology is similar to the VIX’s except that instead of using SPX options it uses VIX options.

To study the relationship between these 2 indices, we first calculated the rolling 20-days correlation of the VIX and VVIX returns from January 2007 to March 2020. The median value of correlation is 0.807 and 25% quantile is 0.66

The figure below presents the rolling 20-days VIX/VVIX correlation for the last 2 years. We also superimposed SPY on the chart. We observe that the correlation is usually high but there are periods where it decreases significantly. The current period is one of those.

Correlation Between the VVIX and VIX indices — Correlation between the VVIX and VIX indices

The next figure shows the scatter plot of VVIX returns vs. VIX returns. It’s observed that there is a significant population where VIX and VVIX returns are of opposite signs. We subsequently calculated the number of instances where VIX and VVIX move in the opposite direction. This indeed happens 22% of the time.

Some implications of this study are:

Although the correlation between VIX and VVIX appears to be high, there is a significant number of instances where VIX and VVIX move in the opposite direction. So it’s fair to say that VVIX follows separate price dynamics which is different from the VIX. In other words, VVIX prices in different risks.
Long VIX options or SPX back spreads are not always a good hedge for an equity portfolio. The hedge can break down.
At times it’s cheaper to hedge a long equity portfolio using SPX options; at times it’s cheaper using VIX options.
The speed of VIX mean reversion is greater when VIX is high as compared to when VIX is low.