Passive investing, particularly through Exchange-Traded Funds (ETFs), has transformed the world of finance. With ETFs, investors can gain exposure to various asset classes, including stocks, bonds, commodities, and more, while maintaining a passive and diversified approach to their portfolios. Unlike actively managed funds, which aim to outperform the market, passive investing with ETFs seeks to replicate the performance of an underlying index. This approach often comes with lower fees and can be an alternative choice for long-term investors looking for broad market exposure and reduced stock-specific risk. The ease of buying and selling ETFs on stock exchanges makes them a flexible tool for building a well-diversified, cost-effective investment portfolio, appealing to both individual investors and institutions.
While ETFs offer various advantages, their impact on the market has raised questions about potential negative effects. Reference [1] delved into this very issue, investigating the market repercussions of ETFs.
-The study finds that higher passive ETF ownership leads to stronger and more persistent return reversals.
-Higher passive ownership is associated with wider bid-ask spreads, greater exposure to aggregate liquidity shocks, higher idiosyncratic volatility, and greater tail risk.
-The results show that passive ETF ownership reduces the importance of firm-specific information in stock returns.
-Higher passive ownership increases the importance of transitory noise and exposure to market-wide sentiment shocks.
-The study finds that increased passive ETF ownership reduces stock price informativeness and potentially weakens market efficiency.
-The findings highlight a potential trade-off between the benefits of passive investing and the costs of reduced price efficiency and market-making capacity.
Briefly, an increase in passive ETF ownership results in stronger and longer-lasting return reversals, greater idiosyncratic volatility, and elevated tail risk. Higher passive ETF ownership reduces the significance of firm-specific information for returns while increasing sensitivity to transitory noise and market-wide sentiment shocks.
Reference
[1] Höfler, Philipp and Schlag, Christian and Schmeling, Maik, Passive Investing and Market Quality (2023). SSRN 4567751
Financial asset fragility refers to the vulnerability of an asset’s price to sudden and disproportionate changes in response to shocks, even if those shocks are relatively small. This fragility often stems from factors like excessive leverage, crowded positioning, liquidity mismatches, or overreliance on certain market assumptions.
Reference [2] utilized the concept of stock price fragility to study the impact of ETFs on the market. Stock fragility is derived from information on an asset’s ownership composition, combined with data on the correlation between owners’ non-fundamentally driven trades.
The paper generalizes mutual fund (MF) fragility to ETF fragility because it argues that ETF flows are indicative of non-fundamental demand shocks. Theoretically, the creation and redemption of ETF shares mimic relative mispricing correction. Therefore, ETF premiums or discounts (i.e., relative mispricing) signal non-fundamentally driven price distortions.
-The study proposes an ETF-based measure of stock price fragility as an alternative to traditional measures based on equity mutual fund flows.
-The ETF-based measure significantly improves the ability of stock price fragility to predict future stock return volatility.
-The study finds that the explanatory power of mutual fund-based fragility has declined.
-The ETF-based measure partially captures the effect of institutional ownership on stock price volatility.
-The predictive power of ETF-based fragility for next-quarter stock price volatility is primarily driven by active ETFs.
-The study notes that the distinction between passive and active investing has become increasingly blurred as the ETF industry has evolved.
-Specialized, industry-specific, and characteristic-based active ETFs may reflect investors’ extrapolative beliefs, speculative demand, and sentiment-driven demand.
In summary, the article developed the concept of ETF fragility and showed that active ETFs have an impact on the market.
This is an interesting article, as it quantifies the concept of fragility. This concept can be further applied to study, for example:
Reference
[2] H. Galindo Gil and R. Lazo-Paz, An ETF-based measure of stock price fragility, Journal of Financial Markets 72 (2025) 100946
Together, these studies highlight how the growth and evolution of ETFs can affect stock prices and market dynamics. Higher passive ETF ownership is associated with reduced price informativeness, greater non-fundamental noise, higher volatility, and increased tail risk, while the second study shows that ETF-based measures of stock price fragility can better capture and predict these effects, particularly through active ETFs.
Overall, the findings suggest that ETF ownership and flows have become increasingly important factors in understanding stock price volatility and market efficiency.
]]>Is this still a rare occurrence? We don’t know. But one thing is clear: regime detection is becoming increasingly important in today’s markets. In this post, we explore a couple of approaches for detecting market regimes.
Regime classification is important in asset and risk management. Traditional approaches classify regimes based on direction, bullish or bearish, and volatility, high or low.
Reference [1] departs from this framework and instead classifies markets as mean-reverting or trending. Specifically, it uses return thresholds of 0.5%, 0.75%, and 1% to define regimes and examines SPY, QQQ, DIA, and IWM over the period 2000 to 2024.
-The study evaluates Random Forest and Neural Network classifiers using macroeconomic announcement indicators and technical features, including VIX, RSI, and ATR.
-It uses 25 years of daily data from 2000–2024 for IWM, SPY, QQQ, and DIA.
-The study frames next-day ETF behavior as a binary classification problem between “oscillating” and “trending” days.
-Oscillating days are defined using intraday movement thresholds of 0.5%, 0.75%, and 1%, with movements exceeding these thresholds classified as trending.
-At the 0.5% threshold, Neural Networks outperform a naive classifier by 13.4% for IWM, 15.4% for SPY, 4.7% for QQQ, and 3.2% for DIA.
-SPY produces the strongest results, with AUC values reaching 0.67–0.74 at the 0.75% and 1% thresholds.
-IWM shows improvements of 5.7%–13.4% across thresholds, with evidence of predictive power at the 0.5% and 0.75% thresholds.
-QQQ shows improvements of 4.7%–6.1%, but its predictive performance is weaker at lower thresholds.
-The results show that predictive performance varies materially across ETFs and oscillation thresholds, with some configurations providing limited discriminatory power.
In summary, the results show that the best case achieves a 15.4% improvement in prediction over a naive strategy for SPY using a neural network with a 0.5% threshold; although in many cases the improvement is more modest, in the range of 1 to 5%, and varies significantly across ETFs.
While the study has several limitations, it points to a more relevant research direction: predicting the magnitude-based regime appears slightly easier than predicting direction, and machine learning is effective as a risk or regime filter rather than as a direct alpha-generating signal.
Reference
[1] Azizi, S. (2026), Leveraging Machine Learning for Financial Forecasting: Distinguishing Market Trends from Oscillations in ETFs, Journal of Risk and Financial Management, 19(4), 262.
Reference [2] proposes an alternative regime classification by distinguishing between “normal” and heavy-tailed regimes. Specifically, the study develops a nonparametric method to detect financial market regimes using differential entropy rather than volatility alone. The underlying idea is that while volatility measures dispersion, entropy captures the full distributional uncertainty, including tail behavior, which becomes particularly important during crisis periods.
The authors estimate entropy using a kernel density estimator with a heavy-tailed kernel in rolling windows and compare entropy with variance. When markets behave approximately Gaussian, i.e., normally, entropy and variance move together; during turbulent periods, the relationship breaks down, revealing heavy-tailed regimes that volatility alone cannot identify.
-The study develops a differential entropy approach to identify financial market regimes through changes in distributional complexity rather than variance alone.
-The method uses a data-adaptive heavy-tailed kernel and combines entropy with tail-index analysis within a moving-window framework.
-Monte Carlo experiments show that the approach is robust and sensitive to changes in tail behavior.
-Applied to the Ibovespa, S&P 500, Nikkei, and SSE Composite from 1998 to 2025, the method identifies heavy-tailed regimes associated with major periods of market turbulence.
-These periods include the Dot-com Bubble, Global Financial Crisis, COVID-19 shock, and the 2025 tariff-related crisis.
-Gaussian regimes correspond to periods of relative stability and market efficiency.
-The results show that variance and entropy do not necessarily move together during crises.
-While volatility measures dispersion, entropy captures broader uncertainty and tail risk, providing a complementary measure of systemic instability.
In short, the paper developed a regime detection method based on entropy, which provides an alternative regime indicator that captures tail risk and structural shifts that standard volatility measures may miss.
This represents an important contribution to the literature, particularly in the context of managing tail risks and risk management more broadly.
Reference
[2] Raul Matsushita, Iuri Nobre, Sergio Da Silva, Beyond volatility: Using differential entropy to detect financial market regimes, Chaos, Solitons and Fractals 202 (2026) 117553
Together, these studies highlight two different approaches to market regime detection. The first uses machine learning to classify next-day ETF behavior as oscillating or trending, while the second uses differential entropy to identify shifts in market uncertainty and tail behavior. Both demonstrate that market regimes can be characterized using information beyond conventional volatility measures, although their effectiveness varies across markets, thresholds, and conditions.
]]>In this post, we discuss two such extensions. The first incorporates a stochastic volatility model and intraday momentum into the option pricing framework. The second applies stochastic volatility models under the real-world measure to portfolio construction and volatility targeting, highlighting their practical use in risk management beyond derivative pricing.
The Black–Scholes–Merton (BSM) model is a cornerstone of derivative pricing; however, it is not without limitations, and researchers continue to extend it. Reference [1] proposes an extension by incorporating intraday momentum into the BSM framework. This is achieved by introducing a drift term that represents intraday momentum, measured using a simple moving average of returns.
The model also adopts a modified Heston-type structure in which volatility follows a mean-reverting square-root process, allowing it to capture volatility clustering and remain consistent with empirical features such as volatility smiles. The momentum-driven drift adjustment influences the expected price path, while the stochastic volatility process models uncertainty around that path.
-The study extends the BSM option pricing framework by incorporating intraday momentum into the drift term of a stochastic volatility-modified model.
-It models time-varying volatility using a Heston-type stochastic volatility model and derives the momentum term from recent relative price changes.
-The study analyzes the impact of intraday momentum on stock prices, volatility, and option valuations, with particular attention to high-momentum scenarios.
-Numerical simulations show that positive momentum increases option valuations, while negative momentum decreases them.
-The study finds that the proposed model converges to the classical Black-Scholes model under low-volatility or low-momentum conditions.
-It concludes that incorporating momentum provides a theoretical framework for evaluating momentum-driven effects in derivative pricing and establishes quantitative metrics for empirical testing.
In short, the paper introduces a momentum term based on recent price changes to dynamically adjust the drift, capturing short-term intraday effects. Numerical results show that strong positive or negative momentum leads to substantial deviations from standard BSM prices, indicating that momentum is an important factor in option pricing.
This represents an interesting and potentially useful extension of the BSM model for traders and risk managers. However, as noted by the authors, the findings are based on simulated results rather than empirical data, and it would be valuable to see the model tested on real market data.
Reference
[1] Hossain, M.S., Yuan, X. & Sultan, S. Momentum-Driven Option Pricing: Integrating Intraday Trends into Financial Derivative Models. Comput Econ (2025).
In the realm of finance, the risk-neutral measure takes precedence in pricing financial derivatives. However, the real-world measure remains valuable and indispensable across various domains. It plays an important role in risk management and asset-liability applications, facilitating comprehensive evaluation and mitigation of risks.
Real-world measures are useful for simulation-based analyses of trading and investment strategies, offering insights into the practical implications of decisions in complex market environments. Reference [2] undertakes the calibration of stochastic volatility models as a means to estimate the real-world measure.
Employing the efficient method of moments (EMM), the authors perform calibration on the Heston and Bates SVJ models. Subsequently, the calibrated models are used to explore and analyze the risk and returns associated with volatility-target strategies.
-The study shows how a real-world stochastic volatility model can be applied to test a simple volatility targeting strategy.
-The results suggest that both stochastic volatility and jumps are required to characterize equity returns.
-The results indicate that volatility targeting reduces the likelihood of extreme returns and lowers the volatility of volatility.
-The study finds that portfolio risk and return both increase as the volatility target increases.
-The 10% volatility target produces the lowest risk, measured by both the mean of volatility and the volatility of volatility, but also the lowest return.
-An equity-only strategy produces the highest risk and the highest expected return.
-The study states that volatility targeting provides an effective way to manage portfolio downside risk while limiting upside potential.
This article serves to exemplify the practical utility of the real-world measure by demonstrating its application in assessing investment strategies. Specifically, the study underscores the effectiveness of volatility targeting as a strategic approach that empowers investors to effectively manage and mitigate the downside risk inherent in portfolio management.
Reference
[2] Alexis Levendis and Eben Mare, On the calibration of stochastic volatility models to estimate the real-world measure used in option pricing, Orion, Volume 39(1), pp. 65 – 91
Both papers highlight the practical importance of stochastic volatility models in real-world applications. While the first study extends the classical Black-Scholes framework by incorporating momentum into a Heston-type stochastic volatility model, the second demonstrates how stochastic volatility models calibrated under the real-world measure can be used to implement a practical volatility targeting strategy. Together, they illustrate how stochastic volatility models continue to evolve beyond theoretical option pricing and provide useful tools for derivative valuation and portfolio risk management.
]]>In this post, we examine research on the impact of algorithmic trading, from its influence on corporate behavior and stock price crash risk to the role of high-frequency trading in liquidity, volatility, and overall market quality.
Algorithmic trading is a method of executing trades using algorithms, or sets of predetermined rules, to make trading decisions. These algorithms are designed to take into account a variety of market conditions, such as price, volume, and timing. Algorithmic trading is often used by large institutional investors, such as hedge funds and investment banks, to execute trades quickly and efficiently. Algorithmic trading is also becoming increasingly popular with individual investors who have access to sophisticated trading software.
Algorithmic trading has a number of advantages over traditional methods of trading. First, algorithms can take into account a wider range of market data and make better-informed decisions. Second, algorithms can execute trades faster than humans, which can be especially important in fast-moving markets. Third, algorithmic trading can help to reduce costs by eliminating the need for human traders.
Algorithmic trading has grown enormously in the last two decades to become the dominant type of trading in the capital markets. Reference [1] studies the impact that algorithmic trading has on the markets.
-The study examines whether algorithmic trading (AT) increases firm-specific stock price crash risk.
-The authors argue that the short-term focus of algorithmic traders encourages managers to prioritize short-term earnings and delay the disclosure of bad news.
-The empirical results show that higher levels of algorithmic trading are associated with greater future stock price crash risk.
-The study finds that firms with more algorithmic trading are more likely to exhibit opportunistic financial reporting and disclosure practices.
-The relationship between algorithmic trading and crash risk is stronger when managers have greater incentives or the ability to withhold bad news.
-The findings suggest that algorithmic trading may reduce monitoring by fundamental investors, allowing bad news to accumulate over time.
-The results are supported by both instrumental-variable analysis and evidence from the SEC’s 2016 Tick Size Pilot Program.
In short, the authors conclude that increased algorithmic trading can contribute to higher firm-specific crash risk, with potentially adverse consequences for shareholders.
Reference
[1] Ahmed, Anwer S. and Li, Yiwen and McMartin, Andrew Stephen and Xu, Nina, The Rise of Machines: Algorithmic Trading and Stock Price Crash Risk, SSRN 4203738
High-frequency trading (HFT) is a type of algorithmic trading that uses computer programs to place orders at very fast speeds. High-frequency traders use sophisticated algorithms to analyze market data and make trades based on their predictions. These traders typically trade in large volumes of shares and use very short-term strategies.
While the previous article examined the broader impact of algorithmic trading on market behavior and stock price crash risk, Reference [2] focuses specifically on high-frequency trading. Rather than analyzing managerial incentives, it investigates how HFT affects market quality, providing direct evidence on its role in liquidity provision, volatility, and overall market efficiency.
-The study investigates the impact of high-frequency trading (HFT) by examining a major exchange infrastructure failure that temporarily prevented low-latency trading.
-The outage provides a natural experiment for assessing the role of HFT in modern financial markets.
-The authors find that the disruption has only a modest effect on trading volume and the number of trades.
-However, liquidity deteriorates significantly when high-frequency traders lose low-latency access.
-Market volatility also increases during the outage, although the effect is less pronounced than the decline in liquidity.
-The results suggest that investments in HFT infrastructure generate positive spillover benefits for all market participants by improving overall market quality.
-The findings support earlier research showing that HFT enhances market liquidity and, to a lesser extent, reduces volatility.
The authors conclude that markets remain functional without HFT, but trading becomes more expensive, and market quality deteriorates when high-frequency traders cannot operate at low latency.
Reference
[2] Benjamin Clapham, Martin Haferkorn and Kai Zimmermann, The Impact of High-Frequency Trading on Modern Securities Markets, Bus Inf Syst Eng, 2022
Taken together, these two papers illustrate that algorithmic trading is neither inherently beneficial nor harmful; its impact depends on the aspect of the market being examined. While algorithmic trading may encourage short-term corporate behavior and increase stock price crash risk, high-frequency trading appears to enhance market quality by improving liquidity and reducing transaction costs. As algorithmic trading continues to evolve, understanding its diverse effects on market efficiency, stability, and price formation remains an important area of research.
]]>Today, retail investors account for a significant share of options market volume and are changing market dynamics. In this post, we examine the characteristics of retail options trading and how it is reshaping the options market.
Options trading is often thought of as a professional’s domain. However, with the advent of online trading platforms, retail traders now have access to the same tools and information as professional traders. This has changed the dynamics of the options market, as retail traders can now trade options on a level playing field with professionals.
However, a question remains to be answered: do retail options traders have the same knowledge, experience, and discipline as the professionals? Reference [1] examined this question
-The paper documents a rapid increase in retail participation in the U.S. options market in recent years.
-It also finds a sharp rise in payment for order flow (PFOF) paid by wholesalers to retail brokerages for executing customer option orders.
-The authors develop a novel measure of retail options trading using transaction-level data and new regulatory reporting requirements.
-The measure closely tracks other proxies for retail trading activity and declines significantly during brokerage outages and trading restrictions.
-The study finds that retail investors strongly prefer inexpensive weekly options.
-These options have very wide quoted bid-ask spreads, averaging approximately 12%, making them costly to trade.
-The paper finds that retail investors frequently fail to exercise call options optimally before ex-dividend dates.
-Market makers and arbitrageurs profit from these mistakes through nearly risk-free “dividend play” arbitrage strategies.
-The study reports that retail trading now accounts for over 60% of total U.S. options trading volume, with nearly 90% of PFOF originating from three major wholesalers.
The findings are very interesting. In the next paper, we’ll look at how retail traders have changed the volatility term structure and dynamics of the option market.
Reference
[1] S. Bryzgalova, A. Pavlova, T. Sikorskaya, Retail Trading in Options and the Rise of the Big Three Wholesalers, SSRN 4065019
Retail options trading is rising rapidly, driven by factors such as the growth of retail brokers, the popularity of social media, and more flexible working hours. Alongside this trend, there has been an increased interest in research on retail options trading behavior.
Reference [2] examines how retail trading reshapes the implied volatility (IV) surface dynamics. The authors utilize OPRA and Nasdaq data for this study. To isolate the effect of retail options trading, they apply a difference-in-differences approach around retail broker outages, 82 events from 2019 to 2021, comparing implied volatility between high-retail and low-retail stocks, during versus pre-outage periods.
-The paper documents a sharp increase in option trading activity driven by retail investors.
-It finds that retail trading is concentrated in call options, short-dated options, and out-of-the-money call options.
-The authors use brokerage outages as exogenous shocks to identify the impact of retail trading on option markets.
-Retail buying volume falls significantly during outages for the option contracts most favored by retail investors.
-In contrast, buying volume for long-dated options increases during outages, consistent with retail investors typically being net sellers of these contracts.
-The study finds that retail demand has a significant impact on option implied volatility.
-Implied volatility declines during brokerage outages, particularly for call, short-dated, and out-of-the-money options.
-Implied volatility increases for long-dated options during outages, reflecting reduced retail option-writing activity.
-The findings suggest that retail demand influences not only the level of implied volatility but also the term structure, moneyness curve, and call-put spread of the implied volatility surface.
-Robustness tests confirm that these effects are specific to brokerage outages and are not driven by a small subset of actively traded options or by the choice of trading dataset.
In short, retail investors systematically buy short-dated, out-of-the-money (especially calls) and sell long-dated options, creating predictable pressure across the surface. When retail trading activity is reduced during brokerage outages, IV falls for short-dated and OTM options but rises for long-dated options.
This paper contributes to a better understanding of retail options trading and shows how retail traders can materially affect the implied volatility surface.
Reference
[2] Eaton, Gregory W., T. Clifton Green, Brian S. Roseman, and Yanbin Wu (2025). Retail Option Traders and the Implied Volatility Surface. SSRN 4104788
Taken together, these two papers show that retail investors have become a major force in the options market, influencing not only trading volume but also option pricing. Their preference for short-dated, out-of-the-money call options has measurable effects on implied volatility, while payment for order flow and trading behavior have reshaped market microstructure. For practitioners, understanding retail option flows is becoming increasingly important, as they now represent a significant driver of option prices and volatility dynamics.
]]>In this post, we discuss several frameworks for trading system validation and examine how researchers assess the reliability of systematic strategies before deploying them in live markets.
With the rapid advancement in computing power, quantitative researchers can now develop trading strategies quickly, employing multiple variables and methodologies. These approaches extend beyond traditional time-series and statistical models to include machine learning and AI-based techniques.
However, such models often deliver impressive in-sample results but fail in live trading, largely due to overfitting. While researchers still seek to exploit increased computing power, the key challenge remains how to address this overfitting problem.
Reference [1] addresses this problem by introducing a framework for evaluating trading strategies in the presence of multiple testing.
-The paper argues that many trading strategies appear profitable simply because researchers test a large number of ideas and select the best-performing results.
-Traditional statistical methods often ignore multiple testing, which can significantly inflate Sharpe ratios, t-statistics, and the perceived profitability of trading strategies.
-The paper discusses several multiple-testing frameworks, including Bonferroni, Holm, and Benjamini-Hochberg-Yekutieli (BHY), to reduce the likelihood of false discoveries.
-The authors show that a seemingly attractive strategy can emerge purely by chance when hundreds of strategies are tested simultaneously.
-To address this problem, they propose “haircutting” Sharpe ratios to account for data mining and multiple testing.
-In an example involving 200 randomly generated strategies, a strategy with a Sharpe ratio of 0.92 becomes statistically insignificant after multiple-testing adjustments.
-Applying the methodology to a database of 484 equity strategies results in substantial reductions in reported Sharpe ratios, suggesting that many apparent alphas are overstated.
-The paper also discusses the trade-off between false discoveries and missed discoveries, concluding that reducing false positives is more important than retaining marginal signals.
-The paper concludes that many published factors, anomalies, and trading strategies are likely false discoveries and that the traditional two-sigma threshold is no longer sufficient for strategy evaluation.
This is a foundational paper that brought the issue of strategy validation to the forefront of quantitative finance. It highlighted the dangers of data mining and multiple testing, and helped raise awareness that many seemingly profitable trading strategies may simply be statistical artifacts rather than genuine sources of alpha.
Reference
[1] Harvey, Campbell R. and Liu, Yan, Evaluating Trading Strategies, SSRN 2474755
Reference [2] proposes what the authors describe as a rigorous walk-forward validation framework. In this approach, trading systems are developed using machine learning techniques and then tested 34 times over a 10-year sample, with each test period independent and trained solely on past data.
-The paper’s primary contribution is a rigorous validation framework for quantitative trading research rather than a new trading strategy.
-The proposed framework is designed to prevent look-ahead bias, incorporate realistic transaction costs, maintain interpretability, and support a wide range of hypothesis-generation methods, including large language models.
-The framework is evaluated through 34 independent out-of-sample tests spanning a 10-year period.
-The tested strategies generate modest but realistic performance, with an annualized return of 0.55% and a Sharpe ratio of 0.33.
-Despite modest returns, the framework exhibits strong downside protection, with a maximum drawdown of only -2.76% compared with -23.8% for SPY.
-The aggregate returns are not statistically significant, and the authors present this result transparently rather than relying on p-hacking or selective reporting.
-The key empirical finding is that market microstructure signals derived from daily OHLCV data are highly regime-dependent.
-These signals perform well during high-volatility periods but perform poorly during stable market environments.
-The results suggest that daily-data trading signals are most effective when information flow and trading activity are elevated.
-The paper emphasizes the importance of robust validation procedures and honest performance reporting in quantitative finance research.
While the initiative is commendable and highlights the need for more research on system validation, several limitations remain. We observe the following,
Reference
[2] Gagan Deep, Akash Deep, William Lamptey, Interpretable Hypothesis-Driven Trading: A Rigorous Walk-Forward Validation Framework for Market Microstructure Signals, arXiv:2512.12924
Taken together, these papers emphasize that rigorous validation is at least as important as model development. The first paper shows that many seemingly successful trading strategies may be false discoveries arising from multiple testing and data mining, while the second demonstrates that even carefully validated signals can be highly regime-dependent and deliver only modest performance out of sample.
The message is clear: robust validation frameworks, realistic assumptions, and transparent reporting are essential for distinguishing genuine alpha from statistical artifacts and for building trading systems that can survive changing market environments.
]]>In this post, we revisit regression-based trading systems and examine whether simple linear and logistic regression models can still generate useful predictive signals in today’s increasingly complex financial markets.
Forecasting stock prices is a challenge due to the non-stationary nature of price time series and the noisy data inherent in these price sequences. Linear regression was a frequently used prediction method, but recent advancements in computing technologies have given rise to more sophisticated approaches like Long Short-Term Memory (LSTM), Artificial Neural Networks (ANN), Recurrent Neural Networks (RNN), etc.
Does the linear regression method still have its place amongst these advanced techniques?
Reference [1] examines the effectiveness of the linear regression method by applying it to a set of US stocks, using it for predicting closing prices and 10-day moving averages.
-The study develops a stock prediction framework based on historical prices, economic indicators, and linear regression techniques.
-The authors construct two models: one for stock price forecasting and another for predicting the 10-day Exponential Moving Average (EMA_10).
-The methodology includes data cleaning, feature selection, model training using Ordinary Least Squares (OLS), and performance evaluation using RMSE and MAE metrics.
-Both models achieve low prediction errors and high explanatory power, as reflected by favorable RMSE, MAE, and R-squared statistics.
-The results suggest that the models provide accurate forecasts of stock prices and short-term trend indicators.
-The proposed trading strategy generates profitable results while also reducing portfolio risk.
-The study concludes that simple linear regression models can provide useful insights into future stock price movements and market trends.
In summary, linear regression is still an effective prediction method. It remains a viable method due to its
Reference
[1] S. Sanapala, V. A. Reddy, S. Sinha Choudhury, V. V. Akshaya and V. Maheedhar Varma, Optimising Trading Strategies using Linear Regression on Stock Prices, 2023 International Conference on Research Methodologies in Knowledge Management, Artificial Intelligence and Telecommunication Engineering (RMKMATE), Chennai, India, 2023, pp. 1-6.
Reference [2] employs logistic regression, which is particularly suited for modeling binary outcomes, to predict stock price movements based on historical returns.
The author uses cumulative returns over the past 20 days and the past 12 months as predictive variables, capturing short-term and long-term momentum effects. Logistic regression is then applied to classify whether a stock’s return in the upcoming month exceeds that month’s median return. The procedure is implemented on S&P 500 stocks from January 1985 to July 2024 using survivorship-bias-free data.
-The paper evaluates a Logistic Regression-Based Systematic Trading (LRST) strategy applied to S&P 500 stocks from 1983 to 2023.
-The strategy uses logistic regression to predict future stock price direction based on historical returns and frames the problem as a binary classification task.
-The model employs a rolling 10-year estimation window, allowing it to adapt to changing market conditions over time.
-Over the full sample, the strategy achieves an annualized return of 24.61%, outperforming the S&P 500 during several periods, particularly in the 1990s and early 2000s.
-Despite strong historical returns, the strategy exhibits substantial risk, with an annualized volatility of 26.11% and a Sharpe ratio of 0.77.
-Recent performance from 2021 to 2024 is notably weak, with the strategy failing to participate in much of the market’s gains.
-The results suggest that structural market changes, including the growth of algorithmic trading and shifting macroeconomic conditions, may have reduced the strategy’s effectiveness.
-The study highlights the importance of adapting systematic trading models to evolving market environments.
-The authors suggest that incorporating machine learning methods, sentiment indicators, and macroeconomic variables could improve robustness and future performance.
In short, the paper shows that the logistic regression-based strategy delivers an annualized return of 24.61%, outperforming the S&P 500, but its high volatility and Sharpe ratio of 0.77 indicate substantial risk and room for improvement in its risk-return profile. Its recent underperformance may reflect structural weaknesses amid the rise of algorithmic trading and shifting macroeconomic conditions, underscoring the need for adaptation.
This article is insightful as it demonstrates that,
Reference
[2] Conrad O. Voigt, Logistic Regression-Based Systematic Trading: Performance on the S&P 500, 2026, github
Taken together, these studies suggest that simple regression techniques, whether linear or logistic, remain useful tools for systematic trading even in the modern era. Despite the rapid growth of machine learning and AI, relatively straightforward models can still generate meaningful predictive signals and attractive historical performance.
However, the papers also highlight that refinement is necessary, as the effectiveness of these models depends on market conditions, structural changes, and the choice of predictive variables. Continuous adaptation and model improvement remain essential for maintaining performance over time.
]]>However, hedging can be done not only through equity index options, but also through volatility derivatives, although the latter are considerably more complex and nuanced. In this post, we discuss the evolving dynamics of VIX futures and volatility ETPs, including lead-lag relationships, price discovery, and how hedging flows can influence volatility markets across different regimes and trading periods.
The volatility index, VIX, is a measure of the stock market’s expectation of volatility over the next 30 days. The VIX index is calculated by taking a weighted average of the prices of put and call options on the S&P 500 index. The VIX is sometimes referred to as the “fear index” because it tends to spike when investors are worried about a sudden drop in the stock market.
VIX futures are derivative contracts that allow investors to bet on the direction of the VIX. They are traded on the Chicago Board Options Exchange (CBOE). VIX futures were first introduced in 2004, and they are now one of the most popular derivatives contracts. VIX futures are traded in monthly contracts, and each contract represents a bet on the direction of the VIX index at the end of the contract month.
Reference [1] examined the lead-lag relationship between the VIX index and VIX futures. It utilized the symmetric thermal optimal path (TOPS) method that can handle non-stationary time series.
-The study examines the dynamic lead-lag relationship between the VIX and VIX futures markets using the symmetric thermal optimal path (TOPS) method.
-The results show that the VIX dominated VIX futures during the early years, particularly before the introduction of VIX options.
-In most periods, the relationship alternates rather than showing persistent dominance by one market.
-During the initial phase, VIX futures typically lagged the VIX by less than five days.
-The weaker role of VIX futures in the early period is attributed to lower trading volume.
-The importance of VIX futures in price discovery increases over time, especially after the launch of VIX options in 2006 and VIX ETPs in 2009.
-Since 2006, the lead-lag relationship has alternated, with the VIX sometimes leading futures and futures sometimes leading the VIX.
-The growth of VIX derivatives markets appears to have increased the informational efficiency of VIX futures.
Briefly, in the early days, the VIX index led its futures. However, the dynamics have changed; VIX futures now sometimes lead the spot market. This could be explained by the launch of VIX options and Exchange-Traded Notes.
Reference
[1] Yan-Hong Yang and Ying-Hui Shao, Time-dependent lead-lag relationships between the VIX and VIX futures markets, 2019, arXiv:1910.13729
Reference [2] analyzes the sensitivity of VIX ETPs to movements in VIX futures. Specifically, the authors investigate the intraday price dynamics of the SPVXSTR, along with three VIX ETNs (VXX, XIV, TVIX) and three ETFs (VIXY, SVXY, UVXY), all linked to that index. Rather than relying on standard OLS regression, the study employs quantile regression, which minimizes a weighted sum of absolute errors and allows for asymmetric penalties on over- and under-predictions.
-The study analyzes the elasticity of VIX futures to volatility ETP prices using decile regressions on the S&P 500 VIX Short-Term Total Return Index (SPVXSTR).
-The results show that elasticity is lower near market close but higher during intraday trading, likely reflecting liquidity differences.
-Elasticity increases at the extreme ends of the return distribution near the close.
-VXX exhibits significantly higher elasticity than VIXY, attributed to its dominant and largely unhedged note structure.
-XIV and SVXY display similar elasticity patterns, while TVIX shows roughly half the elasticity of UVXY due to its lower leverage.
-The findings suggest that intraday liquidity amplifies the responsiveness of VIX futures to ETP price movements.
-VIX futures are found to be more sensitive to VXX than to TVIX or XIV during most trading periods.
-Sensitivity to XIV increases throughout the trading day in higher-return environments, likely reflecting increased hedging demand.
-The study highlights that VIX futures may overreact to ETP flows during stress periods and volatile market closes.
In short, the results show that VIX futures (SPVXSTR) are generally more sensitive to VXX than to TVIX or XIV, with the exception of the late-afternoon window (3:45–4:15 p.m.). Intraday elasticity is elevated—especially near the close and in the tails—implying that VIX futures can overreact to ETP price changes, which creates potential trading opportunities and important considerations for hedging under stress.
Reference
[2] Michael O’Neill, Gulasekaran Rajaguru, Elasticity dynamics between VIX futures and ETPs: a quantile regression analysis of intraday and closing market behavior, Journal of Accounting Literature (2025) 47 (5): 694–701.
Taken together, these studies highlight the evolving dynamics of volatility markets and the growing importance of VIX derivatives and ETPs in price discovery and market behavior. The evidence suggests that lead-lag relationships between the VIX and VIX futures are time-dependent and increasingly influenced by derivative products and hedging flows.
At the same time, the elasticity of VIX futures to ETP activity varies across volatility regimes and intraday periods, implying that liquidity conditions and dealer positioning can materially affect market dynamics. These findings are particularly relevant for volatility traders, portfolio managers, and risk managers operating in increasingly complex derivatives markets.
]]>A serious problem when designing a trading system is the overfitting phenomenon, wherein the system is excessively tuned to historical data. Overfitting occurs when a trading strategy performs exceptionally well on past data but fails to generalize to new, unseen data. This can lead to false positives and inflated expectations, as the system may appear profitable due to chance rather than true predictive power.
Reference [1] formally studied this issue, using analytical approximations for the in-sample and out-of-sample Sharpe ratios of portfolios.
-The paper analyzes how the in-sample performance of trading strategies based on linear predictive models deteriorates out-of-sample due to overfitting.
-It develops closed-form approximations for both in-sample and out-of-sample Sharpe ratios by modeling the means and variances of strategy PnLs.
-The results show that strategies using a large number of assets and weak signals experience a significant decline in out-of-sample performance.
-In contrast, strategies relying on fewer but stronger signals tend to exhibit more stable and replicable results.
-Increasing the size of the training dataset improves the out-of-sample replication ratio and reduces overfitting risk.
-Signals with low true Sharpe ratios are particularly prone to overfitting, leading to inflated in-sample performance that does not persist.
-Simulation and empirical studies, including applications to commodity futures, confirm the magnitude and robustness of these effects.
-The findings also show that incorporating more realistic signal dynamics does not materially alter the main conclusions.
-The replication ratio is largely determined by the true out-of-sample Sharpe ratio rather than specific model assumptions.
-Overall, the study suggests that controlling model complexity and maximizing data usage are key to mitigating overfitting in predictive trading strategies.
In summary, the paper formally demonstrated that to minimize the risk of overfitting, one should,
From our experience, we have reservations about points #3 and #4, while agreeing with points #1 and #2. What do you think?
Reference
[1] Antoine Jacquier, Johannes Muhle-Karbe, Joseph Mulligan, In-Sample and Out-of-Sample Sharpe Ratios for Linear Predictive Models, 2025, arXiv:2501.03938
To mitigate the risk of overfitting, system developers often employ techniques such as cross-validation and out-of-sample testing to ensure that their strategies remain robust across various market conditions and time periods.
Another technique to prevent overfitting involves selecting a parameter region, often referred to as a “plateau,” where the trading system maintains stable performance. Reference [2] introduced a method for quantifying this plateau and utilized particle-swarm optimization to search for it.
-The study highlights that quantitative trading performance depends heavily on parameter selection and is vulnerable to overfitting.
-It introduces the concept of a parameter plateau to identify stable and robust parameter regions rather than single optimal points.
-A plateau score algorithm is developed to replace the conventional approach of selecting the best in-sample parameters.
-The results show that parameters with high plateau scores exhibit more stable and consistent out-of-sample performance.
-The approach helps avoid “parameter islands” that perform well in-sample but fail out-of-sample.
-To improve search efficiency, the study applies particle swarm optimization instead of brute-force methods.
-Particle swarm optimization enables faster exploration of high-dimensional parameter spaces.
-Experiments demonstrate that the combined plateau and optimization approach improves both robustness and profitability.
-The method remains effective as strategy complexity increases from low- to high-dimensional parameter settings.
-The study also proposes suitable hyperparameter ranges for particle swarm optimization in this framework.
In short, the extent of plateau stability is quantified, and an efficient optimization algorithm is utilized to search for it. The out-of-sample test results show promise.
Reference
[2] Jimmy Ming-Tai Wu, Wen-Yu Lin, Ko-Wei Huang, Mu-En Wu, On the design of searching algorithm for parameter plateau in quantitative trading strategies using particle swarm optimization, Knowledge-Based Systems, Volume 293, 7 June 2024, 111630
Taken together, these studies highlight that both model design and parameter selection are key sources of fragility in quantitative strategies. Overfitting arises not only from using too many weak signals but also from selecting unstable parameter configurations that fail to generalize out-of-sample. Approaches such as reducing model complexity, increasing data, and focusing on stable parameter regions through the concept of parameter plateaus offer practical ways to improve robustness. Overall, the evidence suggests that consistent performance depends less on optimizing in-sample results and more on ensuring stability across regimes and datasets.
]]>The decomposition of the volatility risk premium (VRP) into overnight and intraday components is an emerging 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.
-The paper decomposes the variance risk premium into overnight and intraday components across the US, Europe, and Asia.
-It finds that the variance risk premium is significantly negative during the overnight non-trading period.
-During the intraday trading period, the variance risk premium becomes positive and often insignificant.
-The results show that the overall negative variance risk premium documented in prior studies is largely driven by the overnight component.
-The study uses the P&L of a hypothetical variance swap to analyze these components.
-The intraday variance risk premium captures short-term risk and has predictive power over 1 to 3-month horizons.
-The overnight variance risk premium reflects longer-term risk and shows predictive ability over 6 to 12-month horizons.
-The findings highlight the importance of non-trading periods in explaining the behavior of the variance risk premium.
In summary, the study reaffirms that the variance risk premium is significantly negative during the non-trading overnight period, while it becomes positive and often insignificant during the intraday trading period.
An interesting finding 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.
Reference
[1] Papagelis, Lucas and Dotsis, George, The Variance Risk Premium Over Trading and Non-Trading Periods (2024). SSRN 4954623
Volatility clustering is a phenomenon observed in financial markets where periods of high volatility tend to cluster together, followed by periods of low volatility. This pattern suggests that extreme price movements are not randomly distributed over time but rather occur in clusters or groups.
Volatility clustering has undergone extensive study within the daily timeframe. Reference [2] delves into volatility clustering within intraday and overnight timeframes. It specifically investigates clustering within each timeframe and between them.
-The paper studies volatility clustering in intraday and overnight returns across 15 global equity markets.
-It finds that volatility clustering is present in both intraday and overnight returns across multiple time scales, from daily to long-term horizons.
-The results show that volatility clustering is generally stronger in overnight returns than in intraday returns.
-Cross clustering between intraday and overnight volatility is relatively weak within each market, especially at shorter time scales.
-The findings are consistent across both developed and emerging markets, indicating a universal pattern.
-The study highlights the importance of considering both short-term and long-term risks in equity markets.
-The results suggest that volatility dynamics differ between trading and non-trading periods.
-The paper provides implications for trading and risk management strategies based on volatility clustering behavior.
In short, the paper shows that volatility clustering is a universal feature of both intraday and overnight returns across multiple time scales. It also finds that clustering is stronger overnight, while cross-effects between intraday and overnight volatility remain weak, with consistent patterns across global markets.
Reference
[2] Xiaojun Zhao, Na Zhang, Yali Zhang, Chao Xu, Pengjian Shang, Equity markets volatility clustering: A multiscale analysis of intraday and overnight returns, Journal of Empirical Finance 77 (2024) 101487
Taken together, these studies show that volatility dynamics differ significantly between intraday and overnight periods, both in terms of risk pricing and clustering behavior. The variance risk premium is largely driven by the overnight component, while intraday and overnight volatility exhibit distinct clustering patterns with limited interaction. These findings highlight the importance of separating trading and non-trading periods in both forecasting and risk management, as each captures different horizons and sources of risk, offering more refined inputs for portfolio construction and strategy design.
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