There is a large volume of literature that deals with the application of the GARCH model in trading. Reference [1] stood out by bringing a new perspective. It examined the robustness of the GARCH model by asking the following questions,

1. Which rolling GARCH specification produces the most accurate volatility forecast?

2. Does more frequent model refitting improve portfolio Information Ratio?

3. How does the size of the training window affect the strategy performance?

4. Is the base model strategy performance stable with regards to different historical volatility estimators?

After several sensitivity tests, the authors concluded,

Referring to the main hypothesis we can say that we were not able to obtain robust abnormal returns with comparison to the equity benchmark strategies. Further empirical findings support this statement. We found out that (see Table 8) across four GARCH model specifications considered, the strategy based on the threshold GARCH (fGARCH – TGARCH extension) was the most attractive one producing the highest value of Information Ratio, the highest annualized returns and the lowest maximum drawdown. ... The more frequent model refitting did not improve portfolio’s Information Ratio – not as it was initially expected. Regarding the size of the training window, we were unable to conclude that the longer or shorter one necessarily improves or diminishes Information Ratio. In our research based on the data used we obtained that there is no direct relationship – and the optimal training window size is within 126 and 252 trading days range. The performance of strategies under different volatility estimators differ considerably. The poor performance of the Garman-Klass and Parkinson estimators might be partially explained by relatively higher number of long signals generated during the overall seven-year downward volatility trend observed.

In short, the performance of the GARCH model is sensitive to system parameters and the length of historical data.

In our opinion, this article tackled a very important question in trading system design, which is robustness.

References

[1] Oleh Bilyk, Paweł Sakowskia, Robert Ślepaczuka, Investing in VIX futures based on rolling GARCH models forecasts, University of Warsaw, Faculty of Economic Sciences, 2020

The author pointed out,

We examine four main points. First, we test whether investors pay a higher premium for volatility associated with equity price declines than for volatility associated with price increases. By decomposing the variance risk premium into upside and downside components using option prices and high-frequency equity return data, we find that the downside variance risk premium is statistically more pronounced than the aggregate variance risk premium.

Second, we examine whether risk premium associated with downside variance and skewness are related to the required return on equities. Empirically, these premium predict future returns, suggesting that investors view rare, large drawdowns and volatility during market declines as risk, and that compensation for bearing such risks is linked to expected equity returns.

Third, we investigate the relationship between the prediction horizon and predictive power (adjusted R2). Consistent with prior findings, predictive power for variance-related premium peaks around three to five months, while skewness-related premium exhibit relatively stronger predictive power at longer horizons.

Fourth, we evaluate whether the term structure (the difference between longer- and shorter-maturity premium) improves return forecasting. While we find limited evidence of improvement for the variance risk premium, the term structure of the skewness risk premium is statistically significant and suggests that when the longer-maturity skewness risk premium is lower (more negative) than the shorter-maturity premium, long-horizon equity returns subsequently rise, and vice versa. This is consistent with the interpretation that when investors anticipate longer-horizon tail risk, required long-run equity returns increase.

In short, the paper finds that downside VRP is substantially more pronounced than aggregate VRP. It also shows that downside variance and skewness risk premiums predict future equity returns, with variance-related predictive power strongest at medium horizons and skewness-related predictive power stronger at longer horizons. Finally, the study finds that the term structure of skewness risk premium contains forecasting information, suggesting that expectations of longer-horizon tail risk are linked to higher future required equity returns.

We believe this paper largely revisits the framework of the earlier study [1], albeit using more recent data and more extensive robustness tests, while ultimately reaching very similar conclusions.

Let us know what you think in the comments below.

References

[1] Feunou, B., Jahan-Parvar, M. R., & Okou, C. (2016), Downside Variance Risk Premium, Journal of Financial Econometrics 16 (3), 341-383

[2] Akio Ito, Variance Risk Premium, Skewness Risk Premium and Equity Expected Returns, SSRN Working Paper 6712647, 2025

Trading strategies are commonly used approaches for finding buying or selling signals for trading. One type of trading strategy is the pairs trading strategy. In the past, parameters in pairs trading strategies are usually set through experience, which is typically time-consuming. In this paper, negative correlation coefficient trading pairs, genetic algorithms, and Bollinger Bands are considered in AGBCPT, the proposed advanced genetic Bollinger Bands and correlation-coefficient based pairs trading algorithm, to determine the appropriate parameters for the long-short pairs trading strategy. To verify the effectiveness of AGBCPT, experiments were conducted on real datasets, showing that the parameters considered in pairs trading do affect the profitability of the pairs trading strategy; AGBCPT profit is superior to that of BAH and GBCPT for three stock market trends on various training and testing periods; and the fitness function used in AGBCPT also outperforms that of the previous approach in terms of reducing the trading risk of the trained model.

In short, the Genetic Algorithm-based pairs trading strategy produced better risk-adjusted returns. This article demonstrated once again that a complex trading system can be profitable with enough research and practice.

We believe that the key to developing a good trading system is thorough testing of its robustness, especially on out-of-sample data. What do you think? Let us know in the comments below.

References

[1] Chen C.-H., Lai W.-H., Hung S.-T., Hong, T.-P. , An Advanced Optimization Approach for Long-Short Pairs Trading Strategy Based on Correlation Coefficients and Bollinger Bands, Appl. Sci. 2022, 12, 1052. https://doi.org/10.3390/app12031052

1. Implied volatility (VIX/VIXBR),

2. GARCH conditional volatility,

3. Historical volatility.

They then incorporate them into a Hidden Markov Model framework. The paper pointed out,

The empirical evidence supports conditional volatility (GARCH as the superior proxy for regime identification in both the Brazilian and U.S. markets). Unlike implied volatility, which exhibited excessive sensitivity to short-term noise and threshold variations, the GARCH- based specification provided the greatest parameter stability and classification robustness, essential attributes for operationalizing dynamic portfolios.

A key finding of this research is the structural identification of three volatility regimes (low, medium, and high). Contrary to binary specifications often assumed in the literature for interpretability, the Bayesian Information Criterion (BIC) results demonstrated that a three-state model better captures the complex dynamics of financial markets, specifically identifying transitional phases that binary models fail to detect. This granular identification allowed for a more precise assessment of international risk transmission…

From an investment perspective, the results highlight the distinct roles of regime-based strategies. The Dynamic Regime strategy consistently outperformed the traditional Static Mean-Variance (Single Regime) strategy in risk-adjusted metrics, successfully mitigating severe drawdowns, most notably in the U.S. market, where the static strategy suffered structural losses (−18.49%) while the dynamic strategy preserved capital (+1.56%). However, the dynamic strategy did not outperform the Naive (1/N) benchmark in terms of total cumulative return…

In short, the authors conclude that GARCH conditional volatility provides the most stable and operationally reliable regime classification. Implied volatility reacts faster to market changes but produces noisier regime switching. The study also finds that a three-regime framework is superior to a simple low/high volatility classification, as the intermediate regime captures transition periods and uncertainty normalization phases.

Another important point emphasized in the paper is that regime-based strategies are best viewed as risk-management tools rather than universal return-enhancing solutions. Regime-based allocation improves drawdown control and risk-adjusted performance relative to static mean-variance optimization.

Let us know what you think in the comments below.

References

[1] Bitencourt, W. A., & Iquiapaza, R. A. (2026), Comparative analysis of volatility proxies and regime-based asset allocation, International Review of Economics and Finance, 109, 105366.

In this edition, 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.

Web-only posts Recap

Below is a summary of the web-only posts I published during last two weeks.

Delta Hedging Performance Under Different Volatility Measures

Is There an Error in the Black–Scholes-Merton Model?

Network Effects in Social Media Sentiment

The Canadian Brokerage Industry Needs More Competition

From Pinning to Amplification: Evidence from S&P500 Options

VIX Forecasting Using Crypto Overnight Returns

Is Linear Regression Still a Good Prediction Method?

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.

Findings

-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

·Simplicity and interpretability,

·Efficiency with smaller datasets,

·Ability to mitigate excessive overfitting.

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.

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Evaluating a Logistic Regression Trading Framework

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.

Findings

-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,

·Even a basic regression framework can serve as a useful predictive tool within a trading system, although further refinement is necessary.

·There might be structural changes in market dynamics, driven by the increasing prevalence of algorithmic trading and artificial intelligence, implying that traders must adapt accordingly.

Reference

[2] Conrad O. Voigt, Logistic Regression-Based Systematic Trading: Performance on the S&P 500, 2026, github

Closing Thoughts

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.

Additional Reading

For further discussion on the regression technique in trading, please refer to the previous issue:

Use of Machine Learning in Pairs Trading (in Simplicity or Complexity? Rethinking Trading Models in the Age of AI and Machine Learning)

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Educational Video

MIT Lecture: Regression Analysis in Finance by Dr. Peter Kempthorne

In this video, Dr. Peter Kempthorne provides an accessible introduction to linear regression, one of the most widely used statistical tools in finance and many other disciplines. He explains that regression can be used for prediction, causal analysis, approximation, and uncovering relationships between variables. The lecture develops the mathematical foundations of multiple linear regression, including the specification of dependent and explanatory variables, residual errors, and the Ordinary Least Squares (OLS) framework. A key takeaway is that regression is far more flexible than it first appears, as nonlinear relationships can often be incorporated through transformations, polynomial terms, Fourier series, and time-series extensions.

The lecture also emphasizes that building a successful regression model requires much more than estimating coefficients. Model assumptions must be carefully checked, residuals analyzed, and the specification refined when necessary. Dr. Kempthorne discusses the Gauss-Markov theorem, which shows that OLS provides the best linear unbiased estimator under certain assumptions, and explains how the framework can be extended to accommodate correlated errors, unequal variances, and non-normal distributions. A recurring theme throughout the lecture is that statistical modeling is an iterative process: rather than applying regression mechanically, practitioners should adapt the model to the characteristics of the data and the underlying process being studied.

Around the Quantosphere

-Bank of Canada says financial system is in good shape, but vulnerabilities have increased (cbc)

-Beyond the Data: Hedge Fund Algorithmic Usage Shifting From Optimal to Essential (thetradenews)

-Hedge fund superstar does due diligence on his new boss. People are getting protective of their clients (efinancialcareers)

-Prediction Markets Target Hedge Funds for Next Growth Push (hedgeweek)

-Rising hedge fund leverage affects monetary policy implementation (dallasfed)

-Robinhood Is Letting AI Trade for You So You Don’t Have to Keep Checking the Markets (coindesk)

-AI Is Making Even Tech Hedge Funds Look Like the S&P 500 (institutionalinvestor)

-Hedge Funds Are Losing Their Edge in a World of ETFs? (advisorperspectives)

-The Evolution of Quant Finance: A Conversation With Bruno Dupire, 2025 IAQF/Northfield Financial Engineer of the Year (bloomberg)

-The billionaire hedge fund manager whose wife disagreed with self-enrichment. The redemption of Morgan Stanley’s tech team (efinancialcareers-canada)

-The Quiet Revolution in Trading: Why the Future May Reward Patience More Than Prediction (globalbankingandfinance)

Recent Newsletters

Below is a summary of the weekly newsletters I sent out recently

-Volatility Derivatives and VIX Market Dynamics (10 min)

-Overfitting and Parameter Selection in Trading Strategies (10 min)

-Volatility Risk Premium and Clustering: Intraday vs Overnight Dynamics (8 min)

-Large Language Models in Trading: Models and Market Dynamics (9 min)

-Evaluating Option-Based Strategies and Dollar-Cost Averaging (10 min)

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1. Flat ATM implied volatility

2. Stochastic Volatility Inspired (SVI) implied volatility

3. Close-to-close realized volatility

4. Parkinson realized volatility

5. Yang–Zhang realized volatility.

The study uses OptionMetrics SPX options data from 2019 to 2024, including the COVID crash and the 2022 hiking cycle, and analyzes 2000 stratified options across four VIX regimes. The author pointed out,

This thesis provides the first empirical evaluation of SVI-calibrated implied volatility as a delta-hedging input on real S&P 500 index options. The results challenge three common assumptions.

First, more information does not automatically improve hedging. The SVI surface, despite encoding the full implied volatility smile with high calibration quality (median RMSE of 19.5 bps), produces 9.4% higher hedging error variance than flat ATM implied volatility. The calibration noise embedded in the five-parameter SVI fit outweighs the informational benefit of strike-specific volatilities for most option types.

Second, statistical efficiency in volatility estimation does not translate into hedging efficiency. The simple close-to-close realized volatility estimator, which uses only closing prices, outperforms both the Parkinson and Yang–Zhang estimators, which incorporate intraday range information. For hedging purposes, smoothness (low sensitivity to intraday noise) appears more valuable than efficiency (low estimation variance under GBM).

Third, and most importantly, the optimal volatility input is strongly dependent on option moneyness and market regime. SVI surface IV reduces hedging error for out-of-the-money calls by 6–12%, where the smile slope carries genuine hedgeable information. Realized volatility dominates for out-of-the-money puts, where the skew premium makes implied-based deltas biased. No single input wins everywhere, suggesting that a moneyness-conditional hedging strategy, using different volatility inputs for different regions of the option space, would outperform any static approach.

In short, the results show that, contrary to intuition, SVI surface volatility does not improve aggregate delta hedging performance. In fact, SVI increases the standard deviation of hedging errors by 9.4% relative to flat ATM implied volatility. Close-to-close realized volatility performs best overall, reducing hedging error standard deviation by 5.8%, while the Parkinson estimator performs worst. The effectiveness of volatility measures, however, is also found to depend on regime and moneyness.

Another important finding is that higher-order effects, including vanna, volga, jumps, and model misspecification, dominate hedging errors.

This paper provides valuable insights for both traders and risk managers. Let us know what you think in the comments below.

References

[1] Annigeri, Z. (2026), Regime-Dependent Delta Hedging with SVI-Calibrated Volatility Surfaces: An Empirical Analysis of SPX Index Options, Rutgers Business School, SSRN 6465741

Recently, Reference [2] argued that there might have been an error in the derivation of the BSM model,

The hedging argument of Black and Scholes (1973) hinges on the assumption that a continuously rebalanced asset portfolio satisfies the continuous-time self-financing condition. This condition, which is a special case of the continuous-time budget equation of Merton (1971), is believed to mathematically formalize the economic concept of an asset portfolio that is rebalanced continuously without requiring an inflow or outflow of external funds. Although we sometimes find it hard to believe our results, we believe that we show with three alternative mathematical proofs that the continuous-time self-financing condition does not hold for rebalanced portfolios. In addition, we pinpoint the mistake in the derivation that Merton (1971) uses to motivate the continuous-time budget equation. Specifically, by inadvertently equating a deterministic variable to a stochastic one, Merton (1971) implicitly assumes that the portfolio rebalancing does not depend on changes in asset prices. If correct, our results invalidate the continuous-time budget equation of Merton (1971) and the hedging argument and option pricing formula of Black and Scholes (1973).

Our thoughts are the following,

• Regardless of whether the derivation was correct or not, there exist assumptions embedded in the BSM model that are not realistic.

• All models in financial markets are wrong. The BSM model is no exception. It’s just a wrong model that gives correct numbers.

• BSM model, despite the fact that some of its assumptions are unrealistic, has proved to be useful and robust in both theoretical and practical contexts.

Let us know what you think.

References

[1] F. Black, and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81, 639–654, 1973

[2] M. Mink, FJ. de Weert, Black–Scholes Option Pricing Revisited?, 2022, https://doi.org/10.48550/arXiv.2202.05671

To study network effects, the authors construct a daily Reddit interaction graph in which nodes represent users and edges represent direct comment replies. They then compute eigenvector centrality to identify influential users, divide users into centrality quintiles, measure sentiment within each group, and test whether lagged sentiment from high-centrality users predicts future sentiment among lower-centrality users and the broader network. They pointed out,

In this study, we examine the relationship between online social interactions and financial markets, specifically focusing on the sentiment dissemination within a stock market community on Reddit. Our findings demonstrate that highly active users can spread their sentiments to a broader audience. This influence becomes more pronounced under two conditions: (1) when there is reduced disagreement among high-centrality nodes and (2) during periods of high market volatility. Additionally, we find that the COVID-19 pandemic represents a structural shift that enhances the influence of high-centrality nodes as increased online activity and uncertainty reshaped network dynamics…

The practical implications of our findings are twofold. For market participants, sentiment-based trading strategies can provide increased profitability, especially in commission-free trading environments. In addition, network sentiment can be an effective tool for market timing and creating downside protection. From a policy standpoint, while online networks can enhance information dissemination, the ability of a few highly active users to stimulate the beliefs of others can be exploited or, to a certain extent, can inflate the prices of specific assets in the market; one example being the GameStop short squeeze case.

In short, the results show that sentiment from influential users significantly predicts sentiment among regular users, with dissemination effects becoming stronger during the COVID period, high-volatility environments, and periods of low disagreement among influential users. The authors also develop a trading strategy based on these findings. The sentiment-timing strategy materially reduces drawdowns, while the long-only version outperforms buy-and-hold before transaction costs.

Let us know what you think in the comments below.

References

[1] Akarsu, S., & Yılmaz, N. (2026), The dynamics of online social interactions and implications on stock market returns, Journal of Economic Interaction and Coordination.

The universities are flooded with talent in quantitative disciplines, people who are hungry and hard-working. The country also has strong financial centers. From the market-cap perspective, Toronto ranks third in North America, and consistently in the top 20 worldwide. One would then imagine that with this pool of talent, strong education and research culture, and major financial centers, the trading industry would be very developed in Canada.

Wrong.

Both from an institutional and individual perspective, it’s a disappointment. From an institutional point of view, there is no comparable to Citadel or Jane Street. And from an individual point of view, the landscape for active traders is also far from being comparable to its counterpart south of the border. The former point will be a topic for discussion another day. In this article, I want to focus on the latter, i.e., the brokerage industry for active retail traders.

The Canadian brokerage industry has been dominated for decades by the big banks, charging exorbitant commissions. I still remember buying my first stock, it was RIM, i.e., Research In Motion (anyone remember this former bellwether, and what they have become?), and paying $29 for entry and another $29 for exit. Exorbitant prices. The landscape started to change when Interactive Brokers (IB) came to Canada in 2001. The banks lowered commissions, but they were still high.

Interactive Brokers is a good broker, catering to self-directed advanced retail traders and small institutions like hedge funds, family offices, and trusts, with cheap commissions and good execution. But the problem with trading through them is that you put “all your eggs in one basket.” They have been almost the only game in town, so active traders effectively had no choice but to use IB, with no diversification and few alternatives.

Well, actually, in the last decade, there used to be Virtual Brokers, which wanted to become a major broker catering to active traders. Then came ThinkorSwim (TOS) after it was acquired by TD Ameritrade. They offered good platforms for Canadian traders for a while. But both of them disappeared. Virtual Brokers was acquired by CI Financial, TOS by Charles Schwab, and the services became worse or no longer available to Canadians.

So back to square one: IB became the only kid in town with little real competition.

Until recently.

Came Wealthsimple, a new kid in town.

They started out as a robo-advisor about 10 years ago. Then they grew and expanded into a variety of financial services, including brokerage for active traders. I was invited to their Trade Show a few weeks ago, and was quite surprised to learn that Wealthsimple offers commission-free trading, not only for ETFs, but also for options, including complex strategies like four-leg butterflies. I don’t have an account with them, but from talking with their existing customers, I can see that they are quite happy and trade actively with them. Also, after talking with a couple of employees, I could sense that they have ambitions to become a dominant force in the Canadian brokerage landscape.

So, currently IB is still the strongest kid in town, but Wealthsimple has the potential to change the competitive landscape, offering active traders an alternative, while also forcing other Canadian banks to reconsider their offerings.

So I’m hopeful that we may finally have a truly competitive brokerage landscape here, where active traders can thrive.

As for the Trade Show itself, it featured good speakers. You can watch Cem Karsan, a former CBOE market maker, discuss market making, volatility, and macro views here.

Disclosure: I was invited by Wealthsimple to their Trade Show, and corresponded with their staff before and after the event, but did not get paid to write this article.

Reference [1] examines options pinning using data from 2016 to 2025, a period marked by the proliferation of weekly and zero-days-to-expiration (0DTE) options, based on 1.6 million near-expiry SPY contracts. The author pointed out,

We find no evidence of options pinning in S&P 500 expiration dynamics across five tests on 2,294 trading days (2016–2025). The significant finding (p < 0.001) shows the opposite: high near-expiry ATM open interest is associated with wider, not narrower, daily ranges. This is consistent with the gamma amplification mechanism documented by Barbon & Buraschi (2021) and the theoretical predictions of Jeannin et al. (2008) under net short dealer gamma.

We interpret these results as evidence of a possible regime shift in S&P 500 expiration dynamics—from pinning in earlier periods (as documented by Golez & Jackwerth through 2009) to amplification in the modern era, potentially driven by the structural growth of short-dated options and changes in dealer positioning. We offer this interpretation as a hypothesis for further investigation, not as a definitive conclusion.

In short, the paper finds no evidence of pinning. Instead, on days with high open interest, prices exhibit approximately 16% wider ranges, indicating a shift from pinning to amplification. This change is likely driven by the growth of short-dated options and increased retail demand for long options, which leaves dealers short gamma and leads to larger price moves.

An interesting point discussed in the paper is that open interest is more informative than implied volatility, signifying that dealer positioning is important information.

Let us know what you think in the comments below.

References

[1] Elms, N. (2026), From Pinning to Amplification: Evidence of a Regime Shift in S&P 500 Options Expiration Dynamics, 2016–2025, SSRN 6564078

Along similar lines, Reference [1] examines whether cryptocurrency overnight returns, defined as price changes during U.S. equity market closures, can predict the VIX. For this study, the authors use five-minute data of Bitcoin and Ethereum from 2018 to 2025, motivated by the idea that crypto markets are highly sensitive to sentiment, and that overnight returns capture this information. They pointed out,

This study examines the informational content of cryptocurrency returns through a novel temporal decomposition framework that aligns cryptocurrency trading activity with U.S. equity market hours. Our analysis shows that the overnight returns of both Bitcoin and Ethereum capture a distinct dimension of investor sentiment, which significantly improves the predictability of equity market volatility…

We then explore the predictive power of cryptocurrency overnight returns for VIX dynamics. In-sample analysis reveals a significantly negative relationship between cryptocurrency overnight returns and subsequent trading-hour VIX changes, indicating that positive overnight sentiment predicts a reduction in equity market uncertainty during the following trading session. Out-of-sample analysis demonstrates that models incorporating cryptocurrency overnight returns consistently outperform baseline models, with results remaining robust across subperiods and extending to other U.S. implied volatility indices. The economic significance of these findings is further validated through long-short trading strategies in VIX derivatives, where overnight-return-augmented models generate superior performance across different risk-aversion levels.

In short, the results show that crypto overnight returns have a negative predictive relationship with the VIX, with strong in-sample and out-of-sample performance. A trading strategy based on this signal is found to be profitable, and the results hold across different periods, including COVID and non-COVID regimes, and extend to other volatility indices.

Once again, the study reinforces the role of cryptocurrencies as leading indicators for broader market dynamics.

Let us know what you think in the comments below.

References

[1] Gu, M., Lin, J., & Liu, S. (2026), Beyond Conventional Sentiment Indicators: Cryptocurrency’s Hidden Potential in VIX Forecasting, Economic Modelling.

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 today’s issue, 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.

Web-only posts Recap

Below is a summary of the web-only posts I published during last two weeks.

Is Gold Still a Good Diversifier?

Regime-Aware Trading Strategies with Machine Learning

Gamma Exposure and S&P500 Return Predictability

Determining Implied Volatilities of American Options Using the Willow Tree Method

Why Backtests Decay: Regime Dependence and Crowding

Forecasting Earnings and Returns

Lead-Lag Relationship Between the VIX Index and VIX Futures

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.

Findings

-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

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Intraday Elasticity Between VIX Futures and Volatility ETPs

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.

Findings

-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.

Closing Thoughts

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.

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Additional Reading

For further discussion on VIX derivatives, please refer to previous issues:

Making Use of Information Embedded in VIX Futures Term Structure

Examining Contango and Backwardation in VIX Futures

Educational Video

Understanding Volatility: A Practical Guide to VIX Futures

In this video, Jose Blasco provides an educational overview of volatility, the VIX index, and VIX futures, with a focus on practical trading applications and risk management. A key distinction made throughout the presentation is between risk and volatility, emphasizing that they are related but fundamentally different concepts. He explains realized volatility as backward-looking market movement, while implied volatility, embedded in option prices and represented by the VIX, reflects the market’s forward-looking expectations of future uncertainty. Using examples from the S&P 500 options market, the presentation illustrates how implied volatility behaves similarly to insurance pricing, rising when market participants anticipate greater future risks.

The second part of the presentation focuses on VIX futures and their unique market structure. Blasco explains that VIX itself is not directly tradable and that exposure must be obtained through VIX futures contracts. An important concept discussed is contango, where longer-dated VIX futures trade at higher prices than shorter-dated contracts due to expectations of greater uncertainty further into the future. He also explains why long-term buy-and-hold strategies in VIX products tend to perform poorly because futures prices gradually converge toward spot VIX over time, creating structural decay.

The webinar concludes with practical discussions on volatility trading, hedging applications, leverage, margin requirements, and the role of VIX futures as a distinct asset class rather than a traditional equity investment.

Around the Quantosphere

-Hedge fund pay is doing very well after a bumper 2025 (efinancialcareers)

-Tech & Quant Trading Hiring Trends in 2026: What Talent Needs to Know (hunterbond)

-Hedge funds seek an edge by using AI’s speed (ft)

-AI Day Traders Seemed Like the Future. Then the Losses Started (latimes)

-Balyasny’s best quant: “Being an outstanding coder is probably not much of a competitive advantage these days” (efinancialcareers)

-QVR Advisors to Wind Down Hedge Fund After 30% Losses and Investor Redemptions (hedgeweek)

-Citadel tells key researchers to relocate from Hong Kong or quit (ft)

-One London hedge fund cut jobs after March. The rest are wary of making big UK government bond bets (efinancialcareers)

Recent Newsletters

Below is a summary of the weekly newsletters I sent out recently

-Overfitting and Parameter Selection in Trading Strategies (10 min)

-Volatility Risk Premium and Clustering: Intraday vs Overnight Dynamics (8 min)

-Large Language Models in Trading: Models and Market Dynamics (9 min)

-Evaluating Option-Based Strategies and Dollar-Cost Averaging (10 min)

-Machine Learning for Derivative Pricing and Crash Prediction (12 min)

Refer a Friend

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Disclaimer

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Reference [1] examined this question using econometric models. It utilized data from G7 countries because of the existence of deep globally integrated financial markets across different financial assets including Gold. The authors pointed out,

The paper attempts to empirically validate the fundamental axiom that gold is a safe haven instrument and diversifying asset especially in turbulent markets by using the concept of financial cycles. The paper has used Baxter-King technique to filter out the cycles in the key financial markets. These filtered cycles have been used to arrive at the coefficients of the determinants of gold returns through UCM. The results hold significance as they imply that is Gold acts as a hedge to not only to US currency movements but financial market uncertainties as well. It also implies that gold’s role as a currency portfolio diversifier (primarily for USD) is more pronounced and effective than its role as an equity portfolio diversifier. Further, we observe that gold offers the role of diversifying asset and its behavior with stock returns helps to manage risks in bearish cycles as well as generate returns in bullish financial conditions.

In short, the article formally proved that Gold is still a good diversifier and a valuable hedge. In uncertain times, gold can provide stability and peace of mind for investors. We believe that the paper has some merits, but we note that the tests presented were in-sample.

What do you think about investing in gold and/or the validity of the results? Leave us a comment below.

References

[1] Ranjan, Aniket and Kumar, Naveen, Performance of Gold as a Financial Asset During Different Phases of Financial Cycles (2022). Available at SSRN: https://ssrn.com/abstract=3999531

Specifically, the machine learning technique used is LightGBM, a gradient boosting framework that employs histogram-based split finding for efficient training on high-dimensional tabular data. The study utilizes 63 features spanning technical, macro, and cross-asset data. The resulting strategy is compared against baseline approaches, including XGBoost classifier, logistic regression, SMA 50/200 crossover, and time-series momentum.

The author pointed out,

This study addresses the question of whether machine learning can generate statistically validated alpha in equity markets while adapting to changing conditions. The main contribution is a regime-aware LightGBM framework that provides three advances over prior work…

2. Feature importance hierarchy. The ablation study reveals that cross-asset features (Bitcoin) contribute more predictive value than traditional technical indicators, while SHAP analysis shows that macroeconomic features (yield curve, gold/equity ratio) dominate over stock-specific patterns for high-beta technology stocks. This challenges the conventional emphasis on technical indicators in equity forecasting.

3. Regime-adaptive decision logic. The model autonomously learns different strategies for different market conditions: mean reversion logic in bear markets (prioritizing distance from 200-day SMA) versus risk appetite monitoring in bull markets (prioritizing market beta and gold/equity flows). This adaptive behavior, revealed through regime-specific SHAP analysis, demonstrates that ML models can internalize economically sound reasoning.

The framework achieves a portfolio Sharpe ratio of 1.18 (95% CI: [0.53, 1.84]) and outperforms four baseline models (XGBoost, Logistic Regression, SMA crossover, momentum) under identical walk-forward evaluation. The consistent ∼17% alpha-positive rate across both NASDAQ-100 and S&P 500 universes suggests the approach generalizes beyond the specific training universe.

In short, the paper finds that cross-asset features, particularly Bitcoin as a leading indicator, provide the strongest predictive value; macroeconomic indicators outperform traditional technical indicators for high-beta stocks; and the model adapts its decision logic across regimes, shifting from mean reversion in bear markets to risk appetite monitoring in bull markets.

It is somewhat surprising to us that Bitcoin emerges as the strongest leading indicator, while it is less surprising that macro indicators outperform technical indicators.

Let us know what you think in the comments below.

References

[1] Antonio Pagliaro (2026), Regime-Aware LightGBM for Stock Market Forecasting: A Validated Walk-Forward Framework with Statistical Rigor and Explainable AI Analysis, Electronics, 15(6), 1334.

This study set out to answer two central research questions. First, we examined whether changes in aggregated gamma exposure influence future stock market movements. Our results clearly indicate that variations in the derivative of GEX have a statistically significant relationship with subsequent returns on the S&P 500. This effect is robust across both the pre- and post-2020 subperiods, albeit with somewhat diminished strength in the latter. These findings suggest that shifts in gamma positioning among OMMs, likely driven by delta-hedging dynamics, can generate price effects that persist beyond intraday horizons and into the following trading days.

Second, we assessed whether the inclusion of GEX in a predictive modeling framework improves the forecast accuracy of S&P 500 returns. Based on out-of-sample testing, including a model comparison using Diebold-Mariano tests, we find that incorporating GEX significantly enhances the model’s forecasting performance relative to both a GEX-excluding specification and a random walk benchmark. This outcome reinforces the idea that GEX contains forward-looking informational value, which can be utilized to improve predictive modeling in equity markets.

In short, the results show that variations in GEX have a statistically significant relationship with subsequent returns, consistent across both pre- and post-2020 periods, although somewhat weaker in the latter. The paper also demonstrates that GEX contains forward-looking information useful for short-term return prediction.

The authors provide an economic interpretation, showing that dealer hedging creates mechanical directional flows, where positive GEX dampens volatility and supports returns, while negative GEX amplifies moves and is associated with risk-off conditions.

An interesting finding of the paper is that market makers’ net gamma exposure is positive most of the time.

Let us know what you think in the comments.

References

[1] Jonsson, G., & Nyberg, T. (2025). Convexity in Motion: Leveraging Gamma Exposure to Predict Equity Market Returns and Improve Predictive Modeling. Linköping University.

The usual approach for determining the implied volatility using the option’s price is the bisection method, which is a numerical root-finding technique. The implied volatility is the value of the volatility that, when input into the options pricing model, produces a model price that is equal to the observed market price of the option. The drawbacks of this method are that it is slow and it can be applied to European options only.

Reference [1] proposed a new approach for calculating implied volatilities of American options. It utilized the Willow tree method [2] that is more computationally efficient,

One is to increase the efficiency of the implied volatility calibration thanks to no need of reevaluation pⁿ _ij at each iteration. That is, the transition probabilities pⁿ _ij just needs to be calculated once in the calibration. When the volatility is updated, we just need to update the tree nodes in (3.9) and (3.10) by the new value of the volatility, and perform a backward induction for evaluating the option price. It can save about 90% computational time in the option evaluation during the implied volatility calibration. The other is the tree structure can be constructed offline. That is, a basic willow tree structure can be formed in advance and stored in a database. Once the front desk requires to calibrate the implied volatility in real time, they can extract the basic tree structure from the database, adjust the tree nodes to satisfy a specific set of market parameters and calibrate the implied volatilities on the adjusted tree structure in a very short time.

Another advantage of the Willow tree method is that it can be easily extended to two- or three-factor models,

Our method is extendable to the two or three-factor models in [42]. The willow tree method manages to price vanilla and exotic options under various stochastic volatility models, see [34]. However, its efficiency may decrease as the more factors are introduced into the model. One of our future works is to explore the special structure in the two-factor or three-factor in [42] to construct an efficient method for commodity futures option pricing and implied volatilities determination.

References

[1] Wei Xu, Aleksandar Šević, Željko Šević, Implied Volatility Surface Construction for Commodity Futures Options Traded in China, Research in International Business and Finance, 2022, https://doi.org/10.1016/j.ribaf.2022.101676

[2] M. Curran, Willow Power: Optimizing Derivative Pricing Trees, ALGO RESEARCH QUARTERLY, Vol. 4, No. 4, December 2001.

Reference [1] examines this issue by analyzing 1,726 commercially marketed strategies from ten global institutions over the period 2009 to 2025, covering equities, rates, foreign exchange, credit, and commodities. Each strategy is classified into one of seven categories: Carry, Hedging, Momentum, Multi Premia, Factor, Value, or Liquidity. The author pointed out,

This paper examines how institutional allocators should interpret marketed backtests of structured investment strategies. The analysis contributes in three ways. First, it quantifies the gap between pro-forma and live performance on a uniquely large commercial sample of 1,726 strategies from ten global institutions over 2009–2025. Second, it shows that once live performance is measured against a leave-one-out bucket-average peer benchmark, the residual information content of the marketed backtest is economically negligible: what looks like strategy-specific skill is predominantly the common factor regime prevailing at launch. Third, it identifies two structural channels—regime timing at launch and a horizon-dependent launch-density effect—that jointly explain the residual decay, and translates the result into an operational rule: the haircut applied to a marketed backtest should increase with the extremity of the pre-launch factor regime.

In summary, the results show that backtested strategies often experience significant performance decay in live trading, approximately 2% to 3% per year. Most of the backtested performance is driven by factor regimes rather than true skill, with regime timing and crowding identified as the main drivers of decay.

This has important implications for allocators and system developers, as strategies should be benchmarked against peers and adjusted for regime effects, given that backtests often reflect the environment rather than persistent alpha.

Let us know what you think in the comments below.

References

[1] Chang Liu (2026), Evaluating Structured Strategy Backtests: Peer Benchmarks, Regime Timing, and Live Performance, arXiv:2604.18821

In the financial market, however, there are still many uncertainties and risks that the new technology cannot predict. The difficulty in forecasting the financial market is due to the unpredictable nature of financial data, a low signal-to-noise ratio in available variables, and model uncertainty. Specifically, financial time series are notoriously non-stationary, and the model parameters are often unstable.

Reference [1] provided an overview of the current state of research on forecasting earnings and returns. It pointed out,

Following prior research, we highlight three major challenges for a forecaster when working with financial data: unpredictability of earnings and returns, noisy X variables, and model uncertainty. Using these challenges as a way to organize the literature, we discuss recent research that advances our collective ability to understand and predict the cross-sections of earnings and returns.

Here we reiterate some important insights from the literature. First, even with recent advancements, finding new meaningful predictors remains an important effort. Second, new out-of-the-box methods may have limited usefulness, but the thoughtful use of estimation methods and constraints seems to present promising opportunities. Third, it continues to be the case that finding earnings predictors that provide better forecasts than lagged earnings is challenging. Fourth, sorting through, combining, and understanding different models and methods likely has a long way to go before we achieve anything close to recommended best practices.

In short, forecasting the financial market is still a challenging task. In our opinion, most of the new forecasting methodologies that use machine learning were developed without good domain knowledge. It’s not a surprise that they do not perform well.

Let us know what you think in the comments below.

References

[1] Green, Jeremiah and Zhao, Wanjia, Forecasting Earnings and Returns: A Review of Recent Advancements. https://ssrn.com/abstract=4033164

Web-only posts Recap

Below is a summary of the web-only posts I published during last two weeks.

Volatility Risk Premium Dynamics Through the Heston Framework

Multifractal Analysis of Herding and Inefficiency in Precious Metals

Where Do Options Returns Come From

Overnight vs Daytime Returns in Sector ETFs

Dispersion Trading Using Principal Component Analysis

Regime Classification Framework for Mean-Reverting and Trending Markets

Formal Study of Overfitting in Trading System Design

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.

Findings

-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,

1. Keep models as simple as possible,

2. Use the longest sensible backtest period available,

3. Develop systems with high Sharpe ratios, and

4. Rely on fewer signals.

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

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Avoiding Overfitting: Searching for Parameter Plateau

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.

Findings

-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

Closing Thoughts

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.

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Additional Reading

For further discussion on the risk of overfitting, please refer to previous issues:

When Trading Systems Break Down: Causes of Decay and Stop Criteria

The Limits of Out-of-Sample Testing

Educational Video

Bootstrapping for Overfitting Detection in Algorithmic Trading

This video discusses the use of bootstrapping as a statistical tool to improve the reliability of algorithmic trading strategies. The focus is on addressing overfitting, where strategies perform well in backtests but fail in live markets. Bootstrapping is presented as a method to resample historical data and test strategies across different scenarios, allowing practitioners to assess the stability of profitability, risk, and Sharpe ratios. The analysis shows that many seemingly strong strategies deteriorate significantly when subjected to resampling, indicating that part of their performance may be driven by luck rather than skill.

The video also highlights important limitations of bootstrapping in financial applications. In particular, it assumes independence in data, which is often violated in time series, and it cannot capture rare extreme events absent from historical data. Different bootstrap methods may produce varying results, and practical trading frictions such as transaction costs and market impact are not fully incorporated. Overall, the discussion emphasizes that while bootstrapping is a useful tool for detecting overfitting and validating strategy robustness, it is not sufficient on its own and requires further development and integration with real-world considerations.

Around the Quantosphere

-Hedge Fund Collapse Sparks Global Hunt for Almost $600 Million (bloomberg)

-The highly attractive hedge fund manager and the $11m breakup fee. How to use your CFA to get $5m while doing no work (efinancialcareers)

-Man Group, Biggest Listed Hedge-Fund Firm, Tumbles After Client Yanks $6 Billion (wsj)

-The Billionaire Math Geek Who Turned AI Into a Money-Printing Machine (wsj)

-Wall Street Brings Sophisticated Quant Trading to the Masses (wsj)

-The Hot Hedge Fund Strategy Triggering a Pay Bonanza for Traders (bloomberg)

-Hedge Funds Are Becoming Colder, Darker, Less Forgiving (efinancialcareers)

-Trading Places: Meet the Physicists Turned Analysts Driving Finance (physicsworld)

-AI Agents Are Becoming Day Traders, But Gains Are Elusive (bloomberg)

-Podcast: The Quiet AI Trade That’s Raking in Billions (bloomberg)

Recent Newsletters

Below is a summary of the weekly newsletters I sent out recently

-Volatility Risk Premium and Clustering: Intraday vs Overnight Dynamics (8 min)

-Large Language Models in Trading: Models and Market Dynamics (9 min)

-Evaluating Option-Based Strategies and Dollar-Cost Averaging (10 min)

-Machine Learning for Derivative Pricing and Crash Prediction (12 min)

-Do Options Exhibit Momentum? (10 min)

Refer a Friend

If you like this newsletter, then help us grow by referring a friend or two. As a token of appreciation, we’ll send you PDFs that include links to our blog posts about financial derivatives, time series analysis and trading strategies, along with the accompanying Excel files or Python codes.

1 referral:

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Disclaimer

This newsletter is not investment advice. It is provided solely for entertainment and educational purposes. Always consult a financial professional before making any investment decisions.

We are not responsible for any outcomes arising from the use of the content and codes provided in the outbound links. By continuing to read this newsletter, you acknowledge and agree to this disclaimer.

Unlike previous studies, the authors do not rely on a theoretical model to estimate the VRP, but instead use returns from variance-related financial instruments, including variance swaps, VIX futures, and straddles, as proxies, examined over 7- and 30-day horizons. They pointed out,

The economic magnitude is substantial. A one-standard-deviation increase in v0 is associated with approximately 730 basis points lower next-day returns for the 7-day variance swap. This confirms that the current level of market variance is the primary driver of near-term VRP: when variance is elevated, the compensation demanded by investors for bearing variance risk increases, depressing expected returns on long-volatility positions…

This pattern supports Hypothesis 2: greater uncertainty about future variance dynamics leads to larger risk premia and more negative expected returns. The slightly weaker significance for 30-day straddles may reflect the attenuation of uncertainty effects at longer horizons, where the convex payoff structure provides some natural hedging against variance fluctuations…

At the 30-day horizon, the significance of κ diminishes substantially. For variance swaps and straddles, coefficients become statistically indistinguishable from zero. Only for VIX futures does κ retain marginal significance. This differential pattern across maturities—significance at 7 days but not at 30 days—is precisely what Hypothesis 3 predicts and provides validation of the underlying economic mechanism.

In summary, the results show that the initial variance level is a strong negative predictor across all cases, volatility of volatility is also negative and robust, mean reversion is relevant only in the short term, and long-run parameters are largely irrelevant.

These findings suggest that the VRP is primarily driven by current volatility levels and uncertainty rather than long-term factors, providing useful insights for portfolio and risk management.

Let us know what you think in the comments below.

References

[1] Han, C.-H., & Wang, K. (2026), Variance Risk Premia under Volatility Models, Review of Quantitative Finance and Accounting.