volatility arbitrage – Relative Value Arbitrage

The Effectiveness of Collar Structures in Equity and Commodity Markets

There are several popular options strategies frequently discussed in the trading and investing literature, as well as on social media. In a previous post, we examined the effectiveness of the covered call strategy, which has gained wide adoption among retail investors. In this edition, we extend our critical evaluation to another widely used approach—the options collar, a strategy employed by both retail traders and institutional investors.

Assessing the Effectiveness of Zero-Cost Collar in Different Markets

The zero-cost collar strategy is an options trading strategy that involves the simultaneous purchase of a put option and the sale of a call option. The options are usually of the same maturity, and the transaction results in a zero or small credit to the trader’s account.

This strategy is often used by investors who are bullish on a stock but want to protect themselves against a potential drop in the price. By buying the put option, they have the right to sell the stock at a predetermined price (the strike price). If the stock price falls below the strike price, they can sell the stock and offset any losses.

The sale of the call option helps to offset the cost of the put option and results in a zero or small credit to the trader’s account. This strategy is sometimes referred to as a “zero cost” collar because the net cost of the trade is zero.

Reference [1] examined the effectiveness of the zero-cost collar strategy in the developed and developing markets.

Findings

-The paper’s objective is to provide investors with a continuously implemented trading strategy that can effectively handle turbulent market periods such as the Dotcom bubble, the 2008–2009 financial crisis, and the COVID-19 pandemic.

-The study analyzes stock indices from six countries across both developed and developing economies to assess how extreme market events affect performance.

-Zero-cost collars are proposed as a costless option-based protection strategy, created by equating the cost of the long and short option components.

-Prior literature has not evaluated zero-cost collars across different rebalancing frequencies or tested their outcomes in both turbulent and stable markets.

-Results show that zero-cost collars generate strong returns when market volatility is moderate, and the underlying indices perform well, especially when the put strike is set at a higher level.

-The strategy performs respectably during severe downturns as well as during trending or declining markets.

– Its effectiveness depends on market conditions and the choice of strike levels.

Overall, the paper contributes a practical trading strategy that helps investors manage turbulent market conditions through the continuous application of zero-cost collars.

Reference

[1] Lj Basson, Suné Ferreira-Schenk and Zandri Dickason-Koekemoer, The performance of zero-cost option derivative strategies during turbulent market conditions in developing and developed countries, Cogent Economics & Finance, Volume 10, 2022 – Issue 1

How the Airlines Hedge Fuel Costs

The recent rise in the cost of airline tickets can be attributed in part to the escalating fuel prices, which significantly affect operating expenses for airlines. To counter the adverse impact of fuel price volatility, airlines often adopt a strategic approach known as fuel hedging. This practice involves entering into financial contracts to secure future fuel purchases at predetermined prices, mitigating the vulnerability to sudden spikes in fuel costs. Fuel hedging provides airlines with a degree of price certainty, offering a measure of stability in budgeting and operational planning while allowing them to better manage the economic challenges posed by fluctuating fuel prices.

Amongst the US airlines, Southwest Airlines distinguishes itself for its efficient execution of the hedging strategy. It has maintained a record of profitability since 1973, an accomplishment that sets it apart in the US airline sector. Expert observers attribute Southwest’s sustained financial success to its proficient utilization of derivatives for the purposes of hedging. An analysis of Southwest Airlines’ financial statements across multiple years reveals a distinct trend: the share of jet fuel expenses is consistently lower compared to the industry norm. This achievement can be directly attributed to the precise implementation of their jet fuel hedging strategy, a practice that effectively shields the airline from fluctuations in fuel prices.

Reference [2] examined the fuel hedging strategy of Southwest Airlines in detail.

Findings

-The paper analyzes why hedging jet fuel is critical for airlines, given the high volatility of oil prices, and highlights how Southwest Airlines’ long-term low-cost strategy is closely tied to its effective fuel-hedging program.

-It examines Southwest’s financial background and stock performance as a foundation for evaluating its hedging approach.

-The study identifies four key hedging strategies used by Southwest Airlines: call options, collar structures, call spreads, and put spreads.

-By combining these four strategies, Southwest effectively mitigated jet-fuel price risk without engaging in speculative derivative positions.

-A comparison with other airlines shows that Southwest’s disciplined, non-speculative approach contributed significantly to its hedging success and cost stability.

-The paper also evaluates how COVID-19 and oil-price movements related to production-cut agreements adversely affected Southwest, leading to over-hedging and substantial losses in 2020.

In short, the paper discussed the intricacies of Southwest Airlines’ hedging strategies and demonstrated their value-added effect. It is apparent that the deployment of hedging by Southwest Airlines yields advantages. However, it is important to underscore the necessity of a well-designed hedging program, one that avoids the potential pitfall of over-hedging.

Reference

[2] Xiao Han, Hedging Strategy Analysis of Southwest Airlines, 2023, Proceedings of the 6th International Conference on Economic Management and Green Development

Closing Thoughts

Taken together, the two studies illustrate how collar-based strategies can play an important role in managing volatile market conditions, whether for broad equity portfolios or for highly fuel-sensitive industries such as airlines. The first study shows that zero-cost collars can deliver respectable risk-adjusted outcomes during major market disruptions, particularly when volatility is moderate, and strike selection is calibrated appropriately. The second study highlights how Southwest Airlines effectively applied options structures, including collars, to hedge jet-fuel exposure, while also underscoring the risks of over-hedging during periods such as COVID-19. Collectively, the evidence reinforces that collar strategies can be valuable risk-management tools, but their effectiveness depends critically on market regime, implementation frequency, and disciplined design.

Volatility vs. Volatility of Volatility: Conceptual and Practical Differences

Volatility and volatility of volatility are highly correlated and share many similar characteristics. However, there are subtle but important differences between them. In this post, we will examine some of these differences and explore an application of volatility of volatility in portfolio management.

Improving Portfolio Management with Volatility of Volatility

Managing portfolios using volatility has proven effective. Reference [1] builds on this research by proposing the use of volatility of volatility for portfolio management. The rationale behind using volatility of volatility is that it represents uncertainty.

Unlike risk, which refers to situations where future returns are unknown but follow a known distribution, uncertainty means that both the outcome and the distribution are unknown. Stocks may exhibit uncertainty when volatility or other return distribution characteristics vary unpredictably over time.

Practically, the author used a stock’s daily high and low prices to derive its volatility of volatility.

Findings

-The study investigates how volatility-managed investment strategies perform under different levels of uncertainty across stocks and over time.

-A new measure of volatility-of-volatility (vol-of-vol) is introduced as a proxy for uncertainty about risk, capturing a unique dimension distinct from traditional volatility.

-Results show that abnormal returns from volatility management are concentrated in stocks with low uncertainty and during periods of low aggregate uncertainty.

-The effectiveness of sentiment-based explanations for volatility-managed returns is conditional on the level of uncertainty.

-Cross-sectional differences in uncertainty help explain why volatility-managed factor portfolios perform unevenly across stocks and time.

-Theoretical analysis extends a biased belief model, showing that higher vol-of-vol reduces volatility predictability and belief persistence, weakening the benefits of volatility timing.

-The study hypothesizes that volatility management is most effective for low-uncertainty stocks and in low-uncertainty market environments.

-Empirical tests use realized vol-of-vol derived from intraday high and low prices as the measure of uncertainty.

-Consistent with prior literature, uncertainty is positively related to future returns and contains unique predictive information not explained by other stock characteristics.

-Volatility management significantly improves risk-adjusted performance in low-uncertainty stocks and during low aggregate uncertainty periods, while uncertainty also helps explain performance variation across asset pricing factor portfolios.

In short, using the volatility of volatility as a filter proves to be effective, particularly for low-uncertainty stocks.

We find it insightful that the author distinguishes between risk and uncertainty and utilizes the volatility of volatility to represent uncertainty.

Reference

[1] Harris, Richard D. F. and Li, Nan and Taylor, Nicholas, The Impact of Uncertainty on Volatility-Managed Investment Strategies (2024), SSRN 4951893

Beyond volatility of volatility

This section is written by Alpha in Academia

The Volatility of Volatility Index (VVIX) is a composite measure, driven by both short-term market panic and long-term risk expectations.

For years, the VVIX, often dubbed the “fear of fear” index, was treated primarily as a measure of the volatility of volatility (VOV), but new research reveals it contains a second, equally critical component: Long-Run Variance (LRV).

Using a sophisticated model and leveraging a novel technique involving risk-neutral cumulant data extracted from VIX options, researchers decomposed the VVIX dynamics. Their analysis reveals that the factors driving the index change dramatically depending on market conditions. Specifically, the short-term panic measure, VOV, significantly contributes only during acute periods of financial distress, which aligns with intuition. However, during stable or bull markets, the VVIX is primarily driven by the LRV component, reflecting persistent, underlying risk expectations.

In fact, when testing the explanatory power on market-neutral straddle portfolios using S&P 500 options, combining LRV and VOV produced an adjusted explanatory power up to three times greater than baseline models. The finding shows that the index provides “a clear answer to the question of the informational content of the VVIX, showing that it reflects not only the VOV but also an additional important component—the LRV”. Investors should thus view the VVIX not just as a fear gauge, but as a dual-sensor monitoring immediate market stress and long-term risk.

Reference

[2] Bacon, Étienne and Bégin, Jean-François and Gauthier, Geneviève, Beyond volatility of volatility: Decomposing the informational content of VVIX, 2025, SSRN 5611090

Closing Thoughts

In summary, both studies emphasize the role of volatility-of-volatility in understanding risk and market behavior. The first shows that volatility management is most effective in low-uncertainty environments, while the second reveals that the VVIX reflects not only short-term market stress but also long-term risk expectations. Together, they suggest that volatility-of-volatility offers deeper insight into both portfolio performance and the broader dynamics of market uncertainty.

Volatility Risk Premium Across Different Asset Classes

The volatility risk premium has been studied extensively in the equity space, but less so in other asset classes. In this post, we are going to examine the VRP across different asset classes.

Volatility Risk Premium Across Different Asset Classes

The volatility risk premium (VRP) is the compensation investors receive for bearing the risk associated with fluctuations in market volatility, typically measured as the difference between implied and realized volatility. The VRP in equities has been studied extensively. However, relatively little attention has been paid to the VRP in other asset classes.

Reference [1] examined the VRP in different asset classes. It specifically studied the VRP in 18 different underlyings belonging to the commodity, fixed-income, and equity asset classes.

Findings

-The paper analyzes the use of the volatility risk premium (VRP) for volatility forecasting across 18 distinct markets in two time periods.

-The study introduces RIV models, which adjust current implied volatility for the VRP, and finds that these models produce significantly more accurate forecasts compared to other approaches.

-Multiple methodologies for deriving RIV models are examined, with their strengths and limitations evaluated.

-The findings are consistent across most of the assets analyzed and are supported by various loss functions and statistical tests, reinforcing their robustness.

-The newly introduced RIV models outperform implied volatility (IV) and GARCH-based forecasts in predictive accuracy.

-The study finds that the VRP is generally positive across most markets.

-A link is identified between the magnitude of VRP and the trading volume of underlying futures, with higher volumes associated with positive VRP.

-Negative VRP is observed in a few low-volume markets, suggesting that insufficient depth in these markets prevents efficient option pricing.

In short, the VRP is positive in most markets and is positively correlated with trading volume. Additionally, the VRP can be used to predict future realized volatility.

This is an interesting look at the VRP in different markets. We note, however, that just because the VRP is positive in a given market, it does not necessarily mean that P&L can be easily extracted without taking on too much risk. To earn a respectable risk-adjusted return in a given market, a sophisticated system must be developed.

Reference

[1] Štěpán Havel, Volatility Risk Premium Across Multiple Asset Classes, Charles University, 2024

Illiquidity Premium in the Bitcoin Options Market

The previous article explored the VRP across asset classes, primarily commodities. Reference [2] examines the illiquidity risk premium in the crypto market, which is indirectly related to the VRP. Specifically, it studies the role of liquidity risks in the returns of bitcoin options.

In the bitcoin options market, market makers face significant challenges in hedging inventory risk due to price jump risks and lower liquidity. As a result, they charge a higher risk premium.

Findings

-The paper examines the economic drivers of illiquidity in cryptocurrency options markets and their impact on option returns.

-It uses transaction-level data for Bitcoin (BTC) options on Deribit from January 2020 to July 2024 to compute intraday measures of option illiquidity.

-The results show that when market makers hold net-long positions, they demand a positive illiquidity premium to offset hedging and rebalancing costs.

-A one standard deviation increase in option illiquidity raises daily delta-hedged returns by about 0.07% for calls and 0.06% for puts.

-A factor model based on latent instruments derived from option characteristics confirms that illiquidity is a distinct pricing factor in the cross-section of option returns.

-The Bitcoin options market remains illiquid, with this structure leading to a significant illiquidity premium where higher illiquidity predicts higher subsequent returns.

-Investors on average tend to sell options, though the net sell imbalance has declined with increased participation from small retail investors.

-Both panel OLS and IPCA factor models show a robust and positive relationship between illiquidity and expected option returns, consistent across different proxies and model specifications.

-The illiquidity premium compensates market makers for risks and costs associated with delta-hedging, rebalancing, and inventory management.

-Regression analyses indicate that relative spreads are driven by hedging costs, inventory costs, and asymmetric information, and remain an important determinant of expected returns, especially for options with negative order imbalances.

In short, Bitcoin options market makers and active traders earn excess returns, partly driven by the illiquidity premium.

Reference

[2] C Atanasova, T Miao, I Segarra, TT Sha, F Willeboordse, Illiquidity Premium and Crypto Option Returns, Working paper, 2024

Closing Thoughts

Together, these studies expand the understanding of risk premia beyond traditional equity markets. While the first paper demonstrates the existence of the VRP across asset classes, the second highlights the presence of an illiquidity risk premium in cryptocurrency options, reflecting unique market frictions. For traders and researchers alike, the results underscore the importance of adapting models and expectations to the characteristics of each market.

Volatility Targeting Across Asset Pricing Factors and Industry Portfolios

Position sizing is an important aspect of portfolio management, as it directly influences both risk and return. While investors can choose from a number of position sizing techniques, one approach that has gained traction is volatility targeting. In this post, I explore how volatility targeting can be applied to manage portfolio exposure and improve risk-adjusted returns.

Volatility Timing in Portfolio Management

Volatility of an asset is the measure of how much its price changes over time. The higher the volatility, the greater the price swings. Volatility is important because it can have a big impact on the value of your investments. For example, if you’re holding an asset that has high volatility, the value of your investment will be more volatile as well.

Reference [1] proposed a volatility timing technique to manage an investment portfolio.

Findings

-The study shows that volatility-managed portfolios generate large alphas, higher factor Sharpe ratios, and significant utility gains for mean-variance investors.

-Evidence is provided across equity factors (market, value, momentum, profitability, return on equity, and investment) as well as the currency carry trade.

-Volatility timing enhances Sharpe ratios because factor volatilities change more than expected returns, creating inefficiencies to exploit.

-The strategy runs contrary to conventional wisdom: it reduces risk in recessions and crises but still delivers high average returns.

-These findings challenge traditional risk-based explanations and structural models of time-varying expected returns.

-Volatility-managed portfolios are straightforward to implement in real time and provide consistently high risk-adjusted returns.

-Because volatility does not strongly predict future returns, reducing exposure when volatility is high and increasing it when volatility is low improves performance.

-Utility gains from volatility timing for mean-variance investors are estimated at around 65%, which far exceeds the gains from timing expected returns.

-The strategy also sheds light on the dynamics of effective risk aversion, which is central to theories of time-varying risk premia.

In short, the authors advocated lowering risk exposure when volatility is high and increasing risk exposure when volatility is low. The technique relies on the idea that volatility is autocorrelated but only weakly correlated with future returns. It has been widely adopted by industry practitioners.

Reference

[1] Moreira, Alan and Muir, Tyler, Volatility-Managed Portfolios, Journal of Finance, 72(4), 1611–1644

Applying Volatility Management Across Industries

Based on the previous paper, Reference [2] continues this line of research by applying volatility-managed techniques to U.S. industry portfolios. It uses four measures of volatility: one-month realized variance, one-month realized volatility, six-month exponentially weighted moving average (EWMA) of realized volatility, and GARCH-forecasted one-month volatility.

Findings

-Four volatility-management techniques are tested: one-month realized variance, one-month realized volatility, six-month EWMA volatility, and GARCH-forecasted one-month volatility.

-Volatility-managed portfolios show statistically and economically significant improvements in Sharpe and Sortino ratios compared to unmanaged portfolios.

-The EWMA-based strategy is the most robust after accounting for transaction costs and leverage constraints.

-Technology, telecom, and utilities benefit the most, with Sharpe ratio improvements of 27.6%, 30.5%, and 25.5%, respectively.

-Results show that volatility management is practical and enhances investor welfare for both mean-variance and benchmark-aware investors.

-The technology sector emerges as the most favorable for implementing volatility-management strategies due to consistent performance gains.

-Strategy effectiveness varies across subperiods, with negative skewness and kurtosis disrupting traditional volatility patterns.

-Statistical significance weakens during recessionary periods, suggesting caution when applying strategies in stressed market environments.

In short, the article concluded that,

-Volatility management using a six-month EWMA volatility measure is the most consistent,

-The strategy improves Sharpe ratios in the technology, telecom, and utilities sectors, though not all sectors benefit equally. Technology performs best due to the persistence of its volatility,

-The statistical significance of volatility-managed strategies weakens when tested over selected subperiods and recessionary periods.

Reference

[2] Ryan Enney, Sector-Specific Volatility Management: Evidence from U.S. Equity Industry Portfolios, Claremont McKenna College, 2025

Closing Thoughts

These two studies highlight the effectiveness of volatility management across both factor-based and industry-specific portfolios. Evidence shows that scaling risk exposure inversely with volatility can significantly enhance Sharpe ratios, utility gains, and investor welfare. While factor-level strategies demonstrate robustness across market regimes, sector-level analysis points to particularly strong improvements in technology, telecom, and utilities. Collectively, the findings confirm that volatility management is not only theoretically sound but also practically implementable, offering investors a disciplined framework to improve risk-adjusted returns across diverse applications.

Tail Risk Hedging Using Option Signals and Bond ETFs

Tail risk hedging plays a critical role in portfolio management. I discussed this topic in a previous article. In this post, I continue the discussion by presenting different techniques for managing tail risks.

Hedging with Puts: Do Volatility and Skew Signals Work?

Portfolio hedging remains a complex and challenging task. A straightforward method to hedge an equity portfolio is to buy put options. However, this approach comes at a cost—the option premiums—leading to performance drag. As a result, many research studies are focused on designing effective hedging strategies that offer protection while minimizing costs.

Reference [1] presents the latest research in this area. It examines hedging schemes for equity portfolios using several signals, including MOM (momentum), TREND, HVOL (historical volatility), IVOL (implied volatility), and SKEW. The study also introduces a more refined rehedging strategy for put options:

-If, during the investment period, a put option’s delta falls to −0.9 or lower, the option is sold to lock in profits and avoid losing them in case of a sudden price reversal.

-Put options are bought when implied volatility is below 10%, as they are considered cheap. No position is taken if implied volatility is above 30%, to avoid overpaying for expensive options.

Findings

-The study investigates how option strategies can be integrated into equity portfolios to improve performance under risk constraints. It highlights weaknesses in traditional equity and fixed-income diversification for institutional investors.

-The research tests backward-looking signals from equity markets and forward-looking signals from options markets in covered call and protective put strategies.

-The TREND signal is found to be the most valuable, reducing portfolio risk without reducing returns compared to equity-only portfolios.

-The SKEW signal has a positive impact on GMV allocation but is less effective under EW allocation.

-Adding extra trading rules (TR1, TR2) does not enhance performance and is often negative.

-Backtests of long-put strategies confirm that the TREND signal offers the best balance between downside protection and performance preservation.

-Bootstrapped results diverge from backtests, showing that HVOL and IVOL signals outperform the BASE portfolio in risk-adjusted terms.

-The differences between bootstrap and backtest results suggest that the effectiveness of signals depends on the prevailing market regime.

In short, buying put options using the TREND signal appears to improve portfolio risk-adjusted returns. While SKEW and IVOL add little in backtests, they perform better in bootstrapped results, suggesting that the effectiveness of put protection strategies is regime-dependent.

This study offers a comprehensive evaluation of various hedging rules. There is no conclusive answer yet, implying that designing an efficient hedging strategy is complex and requires ongoing effort. Still, the article is a strong step in the right direction.

Reference

[1] Sylvestre Blanc, Emmanuel Fragnière, Francesc Naya, and Nils S. Tuchschmid, Option Strategies and Market Signals: Do They Add Value to Equity Portfolios?, FinTech 2025, 4(2), 25

Tail Risk Hedging with Corporate Bond ETFs

Reference [2] proposed a tail risk hedging scheme by shorting corporate bonds. Specifically, it constructed three signals—Momentum, Liquidity, and Credit—that can be used in combination to signal entries and exits into short high-yield ETF positions to hedge a bond portfolio.

Findings

-Investment Grade (IG) bonds in the US typically trade at modest spreads over Treasuries, reflecting corporate default risk.

-During market crises, IG spreads widen and liquidity decreases due to rising credit risk and forced selling by asset holders such as mutual funds.

-This non-linear widening of spreads during drawdowns is referred to as downside convexity, which can be captured through short positions in IG ETFs.

-The study develops three signals—Momentum, Liquidity, and Credit—to time entry and exit for short IG positions as a dynamic hedge.

-The dynamic hedge effectively protects high-carry bond funds like PIMIX and avoids drawdowns for funds such as DODIX, even after considering trading and funding costs.

-Each signal captures different aspects of the IG bond market, and their combination provides the strongest results, improving the Sortino ratio by at least 0.7.

-The hedge model performs consistently well across a broad range of tested parameters, showing robustness.

-Shorting IG (LQD) and HY (HYG) ETFs is found to be more cost-effective than shorting individual IG bonds, due to liquidity and low bid-ask spreads.

-IG and HY CDXs, despite larger volumes, lack the downside convexity of ETFs and are less effective for hedging.

Overall, ETF-based hedging delivers both cost efficiency and strong downside protection, making it a practical approach for institutional investors.

An interesting insight from this paper is that it points out how using corporate ETFs benefits from downside convexity, while using credit default swaps, such as IG CDXs, does not.

Reference

[2] Travis Cable, Amir Mani, Wei Qi, Georgios Sotiropoulos and Yiyuan Xiong, On the Efficacy of Shorting Corporate Bonds as a Tail Risk Hedging Solution, arXiv:2504.06289

Closing Thoughts

Both studies highlight the importance of adapting traditional portfolio strategies by incorporating alternative approaches to better manage risk and improve performance. The first paper shows how option-based overlays, particularly when guided by signals such as trend, can enhance equity portfolios by providing downside protection without materially reducing returns. The second paper demonstrates that credit and liquidity risks in investment-grade bonds can be more effectively managed through dynamic hedging with liquid bond ETFs. Together, these findings underscore that integrating derivative-based strategies offers investors practical tools to navigate market volatility, reduce drawdowns, and achieve more resilient portfolio outcomes.

The Rise of 0DTE Options: Cause for Concern or Business as Usual?

Zero DTE (Days to Expiration) options are contracts that expire on the same day they are traded. They were introduced in 2022 and have been gaining popularity. In this post, I discuss their impact on the market and how options traders use them.

Impact of Zero DTE Options on the Market

Zero DTE (0DTE) options, also known as “same-day expiration” options, are financial derivatives with expiration dates on the same day they are traded. These options offer traders the opportunity to profit from short-term price movements in the underlying asset.

The increase in the trading volume of 0DTE options has sparked various concerns among market participants and prompted intense discussions in the media. The main concern revolves around the potential destabilization of the underlying market due to large open positions in 0DTE and other short-term options.

Reference [1] examines whether 0DTE options significantly impact the market.

Findings

-The study finds no evidence that higher 0DTE options open interest gamma increases underlying index volatility; rather, it is linked to reduced intraday volatility levels.

-Volatility effects associated with 0DTE options do not extend into overnight sessions or impact lagged intraday volatility, suggesting limited temporal propagation.

-Positive shocks in 0DTE trading volume are followed by increased underlying market trading activity, although these effects are short-lived and not economically meaningful.

-Recent structural changes in the market have made underlying returns more sensitive to 0DTE trading volume shocks, yet the overall effect size remains minimal.

-The increased trading volume in 0DTE options does not lead to destabilizing market behaviors, challenging prevailing concerns in financial media and among market participants.

-On average, the difference in market response to 0DTE trading volume between earlier and more recent periods is only 0.1 standard deviations of absolute returns, indicating economic insignificance.

-Aggregate gamma in 0DTE options is inversely correlated with realized intraday volatility, suggesting a stabilizing rather than destabilizing influence on short-term market movements.

-The volatility risk premium associated with 0DTE options is notably high, reflecting the elevated compensation demanded by sellers for bearing short-term option risk.

-Contrary to expectations, 0DTE options do not amplify market moves through delta-hedging activity, despite their high gamma and rapid decay characteristics.

-The findings support the view that 0DTE options trading can coexist with stable market conditions, especially when managed within a robust market infrastructure.

In short, the paper concludes that 0DTE options do not destabilize the market. The increase in volume has an insignificant influence.

Reference

[1] Dim, Chukwuma, and Eraker, Bjorn and Vilkov, Grigory, 0DTEs: Trading, Gamma Risk and Volatility Propagation (2024).

Risk, Timing, and Strategy: Key Differences in 0DTE Options Trading Styles

The previous paper discussed the impact of 0DTE options on the market, drawing from both practitioner insights and academic literature. Both sources point to the conclusion that 0DTE options have little or almost no impact on the market; they do not increase market volatility, contrary to what many investors have argued.

The CBOE recently updated its report [2] with new data, which reconfirmed that 0DTE options have little or no impact,

Findings

-Updated CBOE data confirms that zero-DTE options have minimal impact on market volatility, countering common concerns that high trading volumes lead to destabilization.

-The market risk from zero-DTE options depends on the balance of buying and selling, rather than the notional trading volume, which is typically well-distributed.

-SPX zero-DTE options show balanced flow between puts and calls, keeping the put/call ratio near one, unlike non-0DTE options, which are more skewed toward hedging.

-Due to this balanced flow, net gamma exposure from zero-DTE options remains minimal, reducing concerns about market maker-driven volatility.

-Both institutional and retail investors use zero-DTE options for tactical bets and systematic yield strategies, highlighting their broad appeal and diverse applications.

-Institutional investors prefer vertical spreads and tend to initiate trades earlier in the day, maintaining positions longer, suggesting greater risk capacity or hedging alternatives.

-Retail traders are more active during the market open and close, often engaging in complex strategies like iron condors and butterflies, reflecting hands-on risk management.

-The intraday behavior of retail traders—frequent opening and closing of positions—implies lower risk tolerance and a more active trading style.

-Despite using similar option structures, institutional and retail investors differ significantly in execution timing and approach to managing market exposure.

-The findings underscore that strategy similarity does not equate to identical trading behavior, with risk management practices and timing being key differentiators between investor types.

The report highlights that while the strategies are broadly similar, the approach to timing and risk management differs meaningfully between institutional and retail investors.

Reference

[2] 0DTEs Decoded: Positioning, Trends, and Market Impact, CBOE, May 2025

Closing Thoughts

The research and insights from both academia and CBOE confirm that zero DTE options do not destabilize markets, despite growing volumes and media attention. The key factor is the balanced dynamic of SPX 0DTE flows between buyers and sellers, which minimizes net gamma exposure and reduces market impact. While retail and institutional investors differ in timing and strategy preferences, their overall usage remains systematic and diversified.

Using Skewness and Kurtosis to Enhance Trading and Risk Management

Skewness is a measure of the asymmetry of a return distribution. In this post, I’ll discuss the skewness risk premium and how skewness can be used to forecast realized volatility.

Skewness Risk Premium in the Options Market

Skewness of returns is a statistical measure that captures the asymmetry of the distribution of an asset’s returns over a specified period. It is particularly important in risk management and option pricing, where the skewness of returns can affect the valuation of derivatives and the construction of portfolios.

Reference [1] studies the skewness risk premium in the options market. It decomposes the skewness risk premium into two components: jump skewness and leverage skewness risk premia.

Findings

-The skewness risk premium (SRP) is distinct from the variance risk premium (VRP), and both are independently priced in the options market.

-The study introduces model-free, tradable strategies to replicate realized skewness, decomposed into two components:

Jump Skewness Risk Premium
Leverage Skewness Risk Premium

-These strategies dynamically rebalance option and forward positions to track high-frequency realized jump skewness and leverage.

-The SRP is generally higher during overnight periods than during regular trading hours—mirroring similar behavior observed in the VRP.

-Jump skewness dominates the SRP during market hours, while overnight skewness may capture broader macro or non-U.S. investor risk.

-The SRP exhibits countercyclical behavior, becoming more pronounced during periods of market stress or left-tail events.

-The study confirms that the SRP and VRP are fundamentally different, supporting the need to treat them separately in portfolio and derivative strategies.

-This decomposition provides insights for trading and hedging strategies, offering more granular exposure to tail risk components.

-Findings are based on short-maturity S&P 500 options, analyzed both intraday and overnight to capture time-sensitive skewness behavior.

In short, the authors constructed a tradable basket of options to measure the skewness risk premium. This means that this study is model-free.

They reconfirmed that

-The skewness risk premium is different from the variance risk premium.

-The variance risk premium is compensation for bearing overnight risks.

Reference

[1] Piotr Orłowski , Paul Schneider , Fabio Trojani, On the Nature of (Jump) Skewness Risk Premia, Management Science, Vol 70, No 2

Predicting Realized Volatility Using Skewness and Kurtosis

Realized volatility refers to the actual volatility experienced by a financial asset over a specific period, typically computed using historical price data. By calculating realized volatility, investors and analysts can gain insights into the true level of price variability in the market.

Reference [2] examines whether realized volatility can be forecasted. Specifically, it studies whether realized skewness and kurtosis can be used to forecast realized volatility.

Findings

-The study investigates whether realized skewness and kurtosis can improve the prediction of realized volatility for equity assets.

-Using data from 452 listed firms on the Pakistan Stock Exchange, the research evaluates both in-sample and out-of-sample forecast performance.

-The standard Heterogeneous Autoregressive (HAR) model is extended by incorporating realized skewness and kurtosis into the volatility forecasting framework.

-The extended model predicts future realized volatility as a linear function of:

Yesterday’s realized volatility
Average realized volatility over the past week and month
Yesterday’s realized kurtosis

-Realized kurtosis is found to significantly enhance forecast accuracy, particularly for short- to medium-term horizons (1, 5, and 22 days ahead).

-Realized skewness has less predictive power compared to realized kurtosis but still adds context for modeling tail risk.

-These findings suggest that higher-order moments (like kurtosis) contain valuable information beyond basic volatility measures.

-The approach supports improved asset allocation and risk-adjusted return forecasting in equity portfolios.

While the study is based on Pakistan’s equity market, the methodology can be generalized to other asset classes and global markets. The paper concluded that stocks’ own realized kurtosis carries meaningful information for stocks’ future volatilities.

Reference

[2] Seema Rehman, Role of realized skewness and kurtosis in predicting volatility, Romanian Journal of Economic Forecasting, 27(1) 2024

Closing Thoughts

Both studies show that incorporating skewness and kurtosis adds valuable insight to volatility analysis. The first study reveals that the skewness risk premium is distinct, tradable, and especially driven by jump risk during market hours. The second shows that realized kurtosis improves short-term volatility forecasts. Together, they highlight the importance of using higher-order moments for better risk management, portfolio decisions, and understanding market behavior.

Volatility of Volatility: Insights from VVIX

The volatility of volatility index, VVIX, is a measure of the expected volatility of the VIX index itself. In this post, we will discuss its dynamics, compare it with the VIX index, and explore how it can be used to characterize market regimes.

Dynamics of the Volatility of Volatility Index, VVIX

The VVIX, also known as the Volatility of Volatility Index, is a measure that tracks the expected volatility of the CBOE Volatility Index (VIX). As the VIX reflects market participants’ expectations for future volatility in the S&P 500 index, the VVIX provides insights into the market’s perception of volatility uncertainty in the VIX itself.

Reference [1] studied the dynamics of VVIX and compared it to the VIX.

Findings

-The VVIX tracks the expected volatility of the VIX, providing a direct measure of uncertainty around future changes in market volatility itself.

-It shows strong mean-reverting behavior, indicating that large deviations from its average level tend to reverse over time.

-The VVIX responds asymmetrically to S&P 500 movements, typically increasing more sharply during market downturns than it decreases during upswings.

-It experiences sudden jumps in both directions, reflecting its sensitivity to abrupt changes in market sentiment and conditions.

-A persistent upward trend in the VVIX began well before 2020, driven by factors such as rising VIX volatility and an increasing volatility-of-volatility risk premium (VVRP).

-The growth of the VIX options market from 2006 to 2014 improved liquidity, which likely contributed to the VVIX’s upward trend and closer link to the VIX.

-VVIX and VIX innovations are highly correlated, highlighting their structural connection despite often differing in their responses to specific market events.

-VVIX quickly incorporates new market information, with minimal autocorrelation beyond a single day, showing its responsiveness to real-time market changes.

In summary, this paper analyzes the similarities and differences between the VIX and VVIX, offering key insights for traders and hedgers in the VIX options market. Understanding their relationship helps improve risk management, refine hedging strategies, and better assess market sentiment.

Reference

[1] Stefan Albers, The fear of fear in the US stock market: Changing characteristics of the VVIX, Finance Research Letters, 55

Using Hurst Exponent on the Volatility of Volatility Indices

A market regime refers to a distinct phase or state in financial markets characterized by certain prevailing conditions and dynamics. Two common market regimes are mean-reverting and trending regimes. In a mean-reverting regime, prices tend to fluctuate around a long-term average, with deviations from the mean eventually reverting back to the average. In a trending regime, prices exhibit persistent directional movements, either upwards or downwards, indicating a clear trend.

Reference [2] proposed the use of the Hurst exponent on the volatility of volatility indices in order to characterize the market regime.

Findings

-The study analyzes the volatility of volatility indices using data from five international markets—VIX, VXN, VXD, VHSI, and KSVKOSPI—covering the period from January 2001 to December 2021.

-It employs the Hurst exponent to evaluate long-term memory and persistence in volatility behavior, providing a framework to characterize market regimes over time.

-Different range-based estimators were used to calculate the Hurst exponent on various volatility measures, improving the robustness of the analysis.

-The volatility of volatility indices was estimated through a GARCH(1,1) model, which captures time-varying volatility dynamics effectively.

-The results show that Hurst exponent values derived from volatility of volatility indices reflect market regime shifts more accurately than those from standard volatility indices, supporting the authors’ hypothesis (H1).

-The analysis explores how different trading strategies—momentum, mean-reversion, and random walk—align with the Hurst exponent values, linking theoretical behavior to practical trading outcomes.

-The study highlights the effectiveness of the Hurst exponent as a tool for identifying and interpreting market regimes, which is essential for informed trading and investment decisions.

-Findings are particularly useful for financial analysts and researchers working with volatility indices and market behavior analysis.

-The paper contributes a novel methodological approach by combining Hurst exponent estimation with GARCH modeling and strategy backtesting, offering a comprehensive view of volatility behavior across regimes.

In short, the article highlights the effectiveness of employing the Hurst exponent on the volatility of volatility indices as a suitable method for characterizing the market regime.

Reference

[2] Georgia Zournatzidou and Christos Floros, Hurst Exponent Analysis: Evidence from Volatility Indices and the Volatility of Volatility Indices, J. Risk Financial Manag. 2023, 16(5), 272

Closing Thoughts

In this post, we explored the dynamics of the VVIX index, and how to use the Hurst exponent on it to characterize the market regime, offering a practical lens through which traders can gauge the persistence or randomness in volatility movements. By understanding these dynamics, market participants can better anticipate shifts in sentiment, enhance their hedging strategies, and adapt more effectively to evolving risk conditions in the options market.

Low-Volatility Stocks: Reducing Risk Without Sacrificing Returns

The recent market turbulence highlights the need for improved risk management and strategies to reduce portfolio volatility. In this post, I’ll explore how to enhance portfolio diversification using low-volatility stocks.

Gold and Low-Volatility Stocks as Diversifiers

Gold has long been regarded as a valuable diversification tool in investment portfolios due to its unique characteristics. As an asset class, gold has historically exhibited a low correlation with traditional financial assets such as stocks and bonds.

Reference [1] revisited the role of gold as a diversifier in a traditional stock-bond portfolio. It also proposed adding low-volatility stocks to the portfolio in order to reduce the risks without sacrificing the returns.

Findings

-The primary goal of investing is to avoid capital losses.

-Conservative investors often include gold in their portfolios to reduce downside risk. Although gold is volatile, it serves as a partial safe haven during bear markets.

-The study confirms that modest allocations to gold lower a portfolio’s loss probability, expected loss, and downside volatility.

-However, the downside protection offered by gold comes at the cost of reduced returns.

– In contrast, adding low-volatility stocks enhances a portfolio’s defensiveness without sacrificing returns.

-Low-volatility stocks are more effective than gold in mitigating losses while maintaining performance.

-Portfolios combining stocks, bonds, gold, and low-volatility stocks can be more resilient and allow for a higher equity allocation relative to bonds.

-The effectiveness of defensive multi-asset portfolios increases with a longer investment horizon.

In short, a stock-bond-gold allocation benefits significantly from incorporating low-volatility stocks, and the effectiveness of this defensive multi-asset portfolio grows with the investment horizon.

Reference

[1] van Vliet, Pim and Lohre, Harald, The Golden Rule of Investing, 2023, SSRN 4404688

Blending Low-Volatility with Momentum Anomalies

The low volatility anomaly in the stock market refers to the phenomenon where stocks with lower volatility tend to provide higher risk-adjusted returns compared to their higher volatility counterparts, contrary to traditional financial theories.

The momentum anomaly in the stock market refers to the tendency of assets that have performed well in the past to continue performing well in the future, and those that have performed poorly to continue performing poorly.

Reference [2] combined the low volatility anomaly with the momentum anomaly and examined whether the low volatility anomaly can enhance risk-adjusted returns in momentum-sorted portfolios.

Findings

-This paper analyzes the profitability of combining low-volatility and momentum strategies in the Nordic stock markets between January 1999 and September 2022.

-Both volatility and momentum strategies are found to remain effective as standalone (pure-play) approaches

-The authors evaluate three combination methods: 50/50 allocation, double screening, and ranking strategies.

-Among long-only portfolios, the momentum-first double screening strategy delivers the highest Sharpe ratio, slightly outperforming the ranking method.

-All long-only combination portfolios outperform the market in terms of risk-adjusted returns.

-Long-short combination strategies provide significantly better risk-adjusted returns compared to pure-play strategies.

-However, after adjusting returns using the Fama and French five-factor model, none of the combination long-short strategies outperform the pure momentum strategy.

In summary, the paper shows that incorporating both momentum and low volatility anomalies yields positive exposure to factors like value and profitability. Returns from these strategies are consistent over time and are more pronounced in later subsamples, with higher robust Sharpe Ratios. For long-only investors, the DS (double-sorted) strategy, which sorts stocks by momentum first and then by low volatility, seems superior to other strategies.

Reference

[2] Klaus Grobys, Veda Fatmy and Topias Rajalin, Combining low-volatility and momentum: recent evidence from the Nordic equities, Applied Economics, 2024

Closing Thoughts

In this post, we have seen how incorporating low-volatility stocks into a stock-gold portfolio can enhance risk-adjusted returns. We also discussed how to select stocks based on momentum and low-volatility criteria, highlighting the effectiveness of combining these factors through methods like double screening or ranking. While momentum tends to drive performance, especially in long-short strategies, low volatility adds defensiveness to the portfolio.

The Calendar Effects in Volatility Risk Premium

I recently covered calendar anomalies in the stock markets. Interestingly, patterns over time also appear in the volatility space. In this post, I’ll discuss the seasonality of volatility risk premium (VRP) in more detail.

Breaking Down the Volatility Risk Premium: Overnight vs. Intraday Returns

The decomposition of the volatility risk premium (VRP) into overnight and intraday components is an active area of research. Most studies indicate that the VRP serves as compensation for investors bearing overnight risks.

Reference [1] continues this line of research, with its main contribution being the decomposition of the variance risk premium into overnight and intraday components using a variance swap approach. The study also tests the predictive ability of these components and examines the seasonality (day-of-week effects) of the VRP.

An interesting finding of the paper is the day-of-week seasonality. For instance, going long volatility at the open and closing the position at the close tends to be profitable on most days, except Fridays.

Findings

-The analysis is conducted on implied variance stock indices across the US, Europe, and Asia.

-Results show that the VRP switches signs between overnight and intraday periods—negative overnight and positive intraday.

-The findings suggest that the negative VRP observed in previous studies is primarily driven by the overnight component.

-The study evaluates the predictive power of both intraday and overnight VRP in forecasting future equity returns.

-The intraday VRP component captures short-term risk and demonstrates predictive ability over 1–3-month horizons.

-The overnight VRP component reflects longer-term risk and shows predictive power over 6–12-month horizons.

Reference

[1] Papagelis, Lucas and Dotsis, George, The Variance Risk Premium Over Trading and Non-Trading Periods (2024), SSRN 4954623

Volatility Risk Premium Seasonality Across Calendar Months

Reference [2] examines the VRP in terms of months of the year. It concluded that the VRP is greatest in December and smallest in October.

An explanation for the large VRP in December is that during the holiday season, firms might refrain from releasing material information, leading to low trading volumes. The combination of low trading volume and the absence of important news releases would result in lower realized volatility.

Findings

-The paper identifies a “December effect” in option returns, where delta-hedged returns on stock and S&P 500 index options are significantly lower in December than in other months.

-This effect is attributed to investors overvaluing options at the start of December due to underestimating the typically low volatility that occurs in the second half of the month.

– The reduced volatility is linked to lighter stock trading during the Christmas holiday season.

– A trading strategy that involves shorting straddles at the beginning of December and closing the position at the end of the month yields a hedged return of 13.09%, with a t-value of 6.70.

-This return is much higher than the unconditional sample mean of 0.88%, highlighting the strength of the effect.

The paper is the first in academic literature to document and analyze this specific December anomaly in option markets. It is another important contribution to the understanding of the VRP.

Reference

[2] Wei, Jason and Choy, Siu Kai and Zhang, Huiping, December Effect in Option Returns (2025). SSRN 5121679

Closing Thoughts

In this post, I have discussed volatility patterns in terms of both days of the week and months of the year. Understanding this seasonality is crucial for traders and portfolio managers, as it can inform better timing of volatility trades and risk management strategies.