volatility arbitrage – Relative Value Arbitrage

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.

Profitability of Dispersion Trading in Liquid and Less Liquid Environments

Dispersion trading is an investment strategy used to capitalize on discrepancies in volatilities between an index and its constituents. In this issue, I will feature dispersion trading strategies and discuss their profitability.

Profitability of a Dispersion Trading Strategy

Reference [1] provided an empirical analysis of a dispersion trading strategy to verify its profitability. The return of the dispersion trading strategy was 23.51% per year compared to the 9.71% return of the S&P 100 index during the same period. The Sharpe ratio of the dispersion trading strategy was 2.47, and the portfolio PnL had a low correlation (0.0372) with the S&P 100 index.

Findings

-The article reviews the theoretical foundation of dispersion trading and frames it as an arbitrage strategy based on the mispricing of index options due to overestimated implied correlations among the index’s constituents.

-The overpricing phenomenon is attributed to the correlation risk premium hypothesis and the market inefficiency hypothesis.

-Empirical evidence shows that a basic dispersion trading strategy—using at-the-money straddles on the S&P 100 and a representative subset of its stocks—has significantly outperformed the broader stock market.

-The performance of the dispersion strategy demonstrated a very low correlation to the S&P 100 index, highlighting its diversification potential.

-This study reinforces the idea that sophisticated options strategies can uncover persistent market inefficiencies.

This article proved the viability of the dispersion trading strategy. However, there exist two issues related to execution,

-The analysis assumes no transaction costs, which is a key limitation; in practice, only market makers might replicate the back-tested performance due to the absence of slippage.

-Another limitation is the simplified delta hedging method used, which was based on daily rebalancing.

-A more optimized hedging approach could potentially yield higher returns and partially offset transaction costs.

Reference

[1] P. Ferrari, G. Poy, and G. Abate, Dispersion trading: an empirical analysis on the S&P 100 options, Investment Management and Financial Innovations, Volume 16, Issue 1, 2019

Dispersion Trading in a Less Liquid Market

The previous paper highlights some limitations of the dispersion strategy. Reference [2] further explores issues regarding liquidity. It investigates the profitability of dispersion trading in the Swedish market.

Findings

-Dispersion trading offers a precise and potentially profitable approach to hedging vega risk, which relates to volatility exposure.

-The strategy tested involves shorting OMXS30 index volatility and taking a long volatility position in a tracking portfolio to maintain a net vega of zero.

-The backtesting results show that vega risk can be accurately hedged using dispersion trading.

– Without transaction costs, the strategy yields positive results.

-However, after accounting for the bid-ask spread, the strategy did not prove to be profitable over the simulated period.

– High returns are offset by substantial transaction costs due to daily recalibration of tracking portfolio weights.

– Less frequent rebalancing reduces transaction costs but may result in a worse hedge and lower correlation to the index.

In short, the study concluded that if we use the mid-price, then dispersion trading is profitable. However, when considering transaction costs and the B/A spreads, the strategy becomes less profitable.

I agree with the author that the strategy can be improved by hedging less frequently. However, this will lead to an increase in PnL variance. But we note that this does not necessarily result in a smaller expected return.

Reference

[2] Albin Irell Fridlund and Johanna Heberlei, Dispersion Trading: A Way to Hedge Vega Risk in Index Options, 2023, KTH Royal Institute of Technology

Closing Thoughts

I have discussed the profitability of dispersion strategies in both liquid and illiquid markets. There exist “inefficiencies” that can be exploited, but doing so requires a more developed hedging approach and solid infrastructure. The “edge” is apparent, but consistently extracting it demands a high level of skill, discipline, and operational capability. In reality, it is this latter part, i.e. the ability to build and maintain the necessary infrastructure, that represents the true edge.

Breaking Down Volatility: Diffusive vs. Jump Components

Implied volatility is an important concept in finance and trading. In this post, I further discuss its breakdown into diffusive volatility and jump risk components.

Decomposing Implied Volatility: Diffusive and Jump Risks

Implied volatility is an estimation of the future volatility of a security’s price. It is calculated using an option-pricing model, such as the Black-Scholes-Merton model.

Reference [1] proposed a method for decomposing implied volatility into two components: a volatility component and a jump component. The volatility component is the price of a portfolio only bearing volatility risks and the jump component is the price of a portfolio only bearing jump risks. The decomposition is made by constructing two option portfolios: a delta- and gamma-neutral but vega-positive portfolio and a delta- and vega-neutral but gamma-positive portfolio. These portfolios bear volatility and jump risks respectively.

Findings

– The study examines the return patterns of straddles and their component portfolios, focusing on jump risk and volatility risk around earnings announcements.

– The findings show that straddle returns closely resemble those of the jump risk portfolio, suggesting that the options market prioritizes earnings jump risk during these events.

– The research highlights the significant role of earnings jump risk in financial markets, as it is substantially priced into straddles and influences both options and stock market behavior.

– A proposed straddle price decomposition method and the S-jump measure could be applied to other market events, such as M & A and natural disasters, to assess risk and pricing dynamics.

This paper discussed an important concept in option pricing theory; that is, the implied volatilities, especially those of short-dated options, comprise not only volatility but also jump risks.

Reference

[1] Chen, Bei and Gan, Quan and Vasquez, Aurelio, Anticipating Jumps: Decomposition of Straddle Price (2022). Journal of Banking and Finance, Volume 149, April 2023, 106755

Measuring Jump Risks in Short-Dated Option Volatility

Unlike long-dated options, short-dated options incorporate not only diffusive volatility but also jump risks. One of the earliest works examining the jump risks is by Carr et al [2].

Reference [3] developed a stochastic jump volatility model that includes jumps in the underlying asset. It then constructed a skew index, a so-called crash index.

Findings

-This paper introduces a novel methodology to measure forward-looking crash risk implied by option prices, using a tractable stochastic volatility jump (SVJ) model.

-The approach isolates the jump size component from the stochastic volatility embedded within uncertainty risk, extending beyond the Black-Scholes-Merton framework.

-The methodology parallels the construction of implied volatility surfaces, enabling the development of an option-implied crash-risk curve (CIX).

-The CIX is strongly correlated with non-parametric option-implied skewness but offers a more refined measure of crash risk by adjusting for stochastic volatility (Vt) and emphasizing tail risk dynamics.

-In contrast, option-implied skewness reflects both crash and stochastic volatility risks, presenting smoother characteristics of the risk-neutral density.

-Empirical analysis reveals a notable upward trend in the CIX after the 2008 financial crisis, aligning with narratives on rare-event risks and emphasizing the value of incorporating such beliefs into asset pricing frameworks.

References

[2] P Carr, L Wu, What type of process underlies options? A simple robust test, The Journal of Finance, 2003

[3] Gao, Junxiong and Pan, Jun, Option-Implied Crash Index, 2024. SSRN

Closing Thoughts

In this issue, I discussed the breakdown of volatility into diffusive and jump components. Understanding this distinction is important for trading, and risk management in theory and practice.

Capturing Volatility Risk Premium Using Butterfly Option Strategies

The volatility risk premium is a well-researched topic in the literature. However, less attention has been given to specific techniques for capturing it. In this post, I’ll highlight strategies for harvesting the volatility risk premium.

Long-Term Strategies for Harvesting Volatility Risk Premium

Reference [1] discusses long-term trading strategies for harvesting the volatility risk premium in financial markets. The authors emphasize the unique characteristics of the volatility risk premium factor and propose trading strategies to exploit it, specifically for long-term investors.

Findings

– Volatility risk premium is a well-known phenomenon in financial markets.

– Strategies designed for volatility risk premium harvesting exhibit similar risk/return characteristics. They lead to a steady rise in equity but may suffer occasional significant losses. They’re not suitable for long-term investors or investment funds with less frequent trading.

– The paper examines various volatility risk premium strategies, including straddles, butterfly spreads, strangles, condors, delta-hedged calls, delta-hedged puts, and variance swaps.

– Empirical study focuses on the S&P 500 index options market. Variance strategies show substantial differences in risk and return compared to other factor strategies.

– They are positively correlated with the market and consistently earn premiums over the study period. They are vulnerable to extreme stock market crashes but have the potential for quick recovery.

– The authors conclude that volatility risk premium is distinct from other factors, making it worthwhile to implement trading strategies to harvest it.

Reference

[1] Dörries, Julian and Korn, Olaf and Power, Gabriel, How Should the Long-term Investor Harvest Variance Risk Premiums? The Journal of Portfolio Management 50 (6) 122 – 142, 2024

Trading Butterfly Option Positions: a Long/Short Approach

A butterfly option position is an option structure that requires a combination of calls and/or puts with three different strike prices of the same maturity. Reference [2] proposes a novel trading scheme based on butterflies’ premium.

Findings

– The study calculates the rolling correlation between the Cboe Volatility Index (VIX) and butterfly options prices across different strikes for each S&P 500 stock.

– The butterfly option exhibiting the strongest positive correlation with the VIX is identified as the butterfly implied return (BIR), indicating the stock’s expected return during a future market crash.

– Implementing a long-short strategy based on BIR allows for hedging against market downturns while generating an annualized alpha ranging from 3.4% to 4.7%.

-Analysis using the demand system approach shows that hedge funds favor stocks with a high BIR, while households typically take the opposite position.

-The strategy experiences negative returns at the bottom of a market crash, making it highly correlated with the pricing kernel of a representative household.

-The value-weighted average BIR across all stocks represents the butterfly implied return of the market (BIRM), which gauges the severity of a future market crash.

-BIRM has a strong impact on both the theory-based equity risk premium (negatively) and the survey-based expected return (positively).

This paper offers an interesting perspective on volatility trading. Usually, in a relative-value volatility arbitrage strategy, implied volatilities are used to assess the rich/cheapness of options positions. Here the authors utilized directly the option positions premium to evaluate their relative values.

Reference

[2] Wu, Di and Yang, Lihai, Butterfly Implied Returns, SSRN 3880815

Closing Thoughts

In summary, both papers explore strategies for capturing the volatility risk premium. The first paper highlights the distinct characteristics of the volatility risk premium and outlines trading strategies tailored for long-term investors. The second paper introduces an innovative trading scheme centered around butterfly option structures. Together, these studies contribute valuable insights into optimizing risk-adjusted returns through strategic volatility trading.

Volatility Risk Premium: The Growing Importance of Overnight and Intraday Dynamics

The breakdown of the volatility risk premium into overnight and intraday sessions is an active and emerging area of research. It holds not only academic interest but also practical implications. ETF issuers are launching new ETFs to capitalize on the overnight risk premium, and the shift toward around-the-clock trading could impact the VRP and popular strategies such as covered call writing. In this post, I’ll discuss the VRP breakdown, its implications, impact, and more.

Volatility Risk Premium is a Reward for Bearing Overnight Risk

The volatility risk premium (VRP) represents the difference between the implied volatility of options and the realized volatility of the underlying asset. Reference [1] examines the asymmetry in the VRP. Specifically, it investigates the VRP during the day and overnight sessions. The research was conducted in the Nifty options market, but previous studies in the S&P 500 market reached the same conclusion.

Findings

– There is a significant difference in returns between overnight and intraday short option positions, unrelated to a weekend effect.

– The return asymmetry decreases as option moneyness and maturity increase.

– A systematic relationship exists between day-night option returns and the option Greeks.

– Average post-noon returns are significantly negative for short call positions and positive for short put positions, while pre-noon returns are largely insignificant, indicating that the VRP varies throughout the trading day for calls and puts.

– A significant jump in the underlying index reduces the day-night disparity in option returns due to increased implied volatilities, which boost both intraday and overnight returns.

– Strong positive overnight returns suggest that the VRP in Nifty options prices mainly compensates for overnight risk.

– A strategy of selling index options at the end of the trading day and covering them at the beginning of the next day yields positive returns before transaction costs but is not profitable after accounting for transaction costs.

Reference

[1] Aparna Bhat, Piyush Pandey, S. V. D. Nageswara Rao, The asymmetry in day and night option returns: Evidence from an emerging market, J Futures Markets, 2024, 1–18

Inventory Risk and Its Impact on the Volatility Risk Premium

The previous paper suggests that the VRP is specifically a reward for bearing overnight risk. Reference [2] goes further by attempting to answer why this is the case. It provides an explanation in terms of market makers’ inventory risks, as they hold a net-short position in put options.

Findings

-Put option risk premia are significantly negative overnight when equity exchanges are closed and continuous delta-hedging is not feasible.

-Intraday, when markets are liquid and delta-hedging is possible, put option risk premia align with the risk-free rate.

-Call options show no significant risk premia during the sample period.

-Market makers’ short positions in puts expose them to overnight equity price “gap” risks, while their call option positions are more balanced between long and short, resulting in minimal exposure to gap risk.

-Increased overnight liquidity reduces option risk premia. Regulatory changes and the acquisition of major electronic communication networks in 2006 boosted overnight equity trade volumes from Monday to Friday, reducing the magnitude of weekday option risk premia compared to weekend risk premia.

-The study concludes that the S&P 500 option risk premium arises from a combination of options demand and overnight equity illiquidity.

An interesting implication of this research is that the introduction of around-the-clock trading could potentially reduce the VRP.

Reference

[2] J Terstegge, Intermediary Option Pricing, 2024, Copenhagen Business School

Closing Thoughts

Understanding the breakdown of the volatility risk premium into overnight and intraday components is crucial for both researchers and practitioners. As ETF issuers develop products to leverage the overnight risk premium and markets move toward 24-hour trading, these dynamics could significantly impact volatility strategies. Recognizing these shifts can help investors refine their approaches and adapt to evolving market conditions.

Hedging Efficiently: How Optimization Improves Tail Risk Protection

Tail risk hedging aims to protect portfolios from extreme market downturns by using strategies such as out-of-the-money options or volatility products. While effective in mitigating large losses, the challenge lies in balancing cost and long-term returns. In this post, we’ll discuss tail risk hedging and whether it can be done at a reasonable cost.

Tail Risk Hedging Strategies: Are They Effective?

Tail risk hedging involves purchasing put options to protect the portfolio either partially or fully. Reference [1] presents a study of different tail risk hedging strategies. It explores the effectiveness of put option monetization strategies in protecting equity portfolios and enhancing returns.

Findings

– Eight different monetization strategies were applied using S&P 500 put options and the S&P 500 Total Return index from 1996 to 2020.

– Results compared against an unhedged index position and a constant volatility strategy on the same underlying index.

– Tail risk hedging, in this study, yielded inferior results in terms of risk-adjusted and total returns compared to an unhedged index position.

– Over a 25-year period, all strategies’ total returns and Sharpe ratios were worse than the unhedged position.

– Buying puts involves paying for the volatility risk premium, contributing to less favorable results.

– The results are sensitive to choices of time to expiry and moneyness of purchased options in tested strategies.

– The authors suggest the possibility of minimizing hedging costs by optimizing for strikes and maturities.

Reference:

[1] C.V. Bendiksby, MOJ. Eriksson, Tail-Risk Hedging An Empirical Study, Copenhagen Business School

How Can Put Options Be Used in Tail Risk Hedging?

The effectiveness of using put options to hedge the tail risks depends on the cost of acquiring put options, which can eat into investment returns. Reference [2] proposes a mixed risk-return optimization framework for selecting long put options to hedge S&P 500 tail risk. It constructs hypothetical portfolios that continuously roll put options for a tractable formulation.

Findings

– The article discusses the effectiveness of tail risk hedging. It highlights that the premium paid for put options can be substantial, especially when continuously renewing them to maintain protection. This cost can significantly impact investment returns and overall portfolio performance.

– The article introduces an optimization-based approach to tail-risk hedging, using dynamic programming with variance and CVaR as risk measures. This approach involves constructing portfolios that constantly roll over put options, providing protection without losing significant long-term returns.

– Contrary to previous research, the article suggests that an effective tail-risk hedging strategy can be designed using this optimization-based approach, potentially overcoming the drawbacks of traditional protective put strategies.

-The proposed hedging strategy overcame traditional drawbacks of protective put strategies. It outperforms both direct investments in the S&P 500 and static long put option positions.

Reference

[2] Yuehuan He and Roy Kwon, Optimization-based tail risk hedging of the S&P 500 index, THE ENGINEERING ECONOMIST, 2023

Closing Thoughts

Tail risk hedging is expensive. While the first paper demonstrated that tail risk hedging leads to inferior returns, it suggested that results could be improved by optimizing strike prices and maturities. The second paper built on this idea and proposed a hedging scheme based on optimization. The proposed strategy outperforms both direct investments in the S&P 500 and static long put option positions.

PCA in Action: From Commodity Derivatives to Dispersion Trading

Principal Component Analysis (PCA) is a dimensionality reduction technique used to simplify complex datasets. It transforms the original variables into a smaller set of uncorrelated variables called principal components, ranked in order of their contribution to the dataset’s total variance. In this post, we’ll discuss various applications of PCA.

Pricing Commodity Derivatives Using Principal Component Analysis

Due to the seasonal nature of commodities, pricing models should be able to take into account seasonality and other deterministic factors.

Reference [1] proposed a new, multi-factor pricing method based on Principal Component Analysis (PCA). It introduces a multi-factor model designed to price commodity derivatives, with a particular focus on commodity swaptions.

Findings

– The model calibration process consists of two key steps: offline and online.

– The offline step, conducted infrequently, determines mean reversion rates, the ratio of long and short factor volatilities, and the correlation between the factors using historical data.

– The online step occurs every time the model is used to price an option or simulate price paths.

– Empirical analysis demonstrates that the model is highly accurate in its predictions and applications.

– Swaptions, which are relatively illiquid commodities, present a challenge due to their one-sided natural flow in the market.

– Model calibration strategies are divided into seasonal and non-seasonal categories, considering the asset’s characteristics. For seasonal assets like power or gas, local volatilities are calibrated separately for each contract, while a boot-strapping strategy is employed for non-seasonal assets like oil.

– Currently, the multi-factor model lacks a term structure for volatility ratios and mean reversions. However, it can be easily extended to incorporate a time dependency, which would facilitate fitting market prices of swaptions across various tenors.

Reference

[1] Tim Xiao, Pricing Commodity Derivatives Based on A Factor Model, Philarchive

Dispersion Trading Using Principal Component Analysis

Dispersion trading involves taking positions on the difference in volatility between an index and its constituent stocks.

Reference [2] examined dispersion trading strategies based on a statistical index subsetting procedure and applied it to the S&P 500 constituents

Findings

– This paper introduces a dispersion trading strategy using a statistical index subsetting approach applied to S&P 500 constituents from January 2000 to December 2017.

– The selection process employs principal component analysis (PCA) to determine each stock’s explanatory power within the index and assigns appropriate subset weights.

– In the out-of-sample trading phase, both hedged and unhedged strategies are implemented using the most suitable stocks.

– The strategy delivers significant annualized returns of 14.52% (hedged) and 26.51% (unhedged) after transaction costs, with Sharpe ratios of 0.40 and 0.34, respectively.

– Performance remains robust across different market conditions and outperforms naive subsetting schemes and a buy-and-hold approach in terms of risk-return characteristics.

– A deeper analysis highlights a correlation between the chosen number of principal components and the behavior of the S&P 500 index.

– An index subsetting procedure was developed, considering the explanatory power of individual stocks, allowing a replicating option basket with as few as five securities.

– An analysis of sector exposure, principal components, and robustness checks demonstrated that the trading systems have superior risk-return characteristics compared to other dispersion strategies.

Reference

[2] L. Schneider, and J. Stübinger, Dispersion Trading Based on the Explanatory Power of S&P 500 Stock Returns, Mathematics 2020, 8, 1627

Closing Thoughts

PCA is a powerful tool in quantitative finance. In this issue, we have demonstrated its effectiveness in pricing commodity derivatives and developing dispersion trading strategies. Its versatility extends beyond these applications, making it a valuable technique for tackling a wide range of problems in quantitative finance.