Optimizing Index Arbitrage Through Mean Reversion

Index arbitrage is a well-established trading strategy. In particular, arbitrage between a stock index futures contract and the underlying basket of stocks is a classical approach.

Reference [1] revisits this technique and proposes a new method called the Basis Mean-Reverting Basket (BMRB) for index arbitrage. Essentially, the authors develop an optimization algorithm to maximize the speed of mean reversion of the basis in price space while incorporating constraints specific to index arbitrage, such as long-only spot positions. The algorithm selects stocks and their weights to maximize the speed of mean reversion while keeping tracking error within acceptable limits.

The authors use Japanese TOPIX futures and constituent stocks from January 2016 to January 2026. They employ rolling 504-trading-day windows with monthly portfolio rebalancing. Trading positions are entered when the basis z-score exceeds a specified threshold and exited when the basis approaches its estimated mean, with a stop-loss threshold also applied.

They pointed out,

This paper proposed the Basis Mean-Reverting Basket (BMRB), a new basket construction method for arbitrage between a stock index futures contract and a spot basket. The problem is formulated to directly optimize the mean reversion of the basis series in price space while constraining the tracking error. An empirical analysis on the Japanese TOPIX market demonstrated the effectiveness of BMRB along three dimensions, in-sample stationarity, out-of-sample arbitrage performance, and robustness to hyperparameters.

In short, the results show that BMRB produces a substantially more mean-reverting price difference than conventional index-tracking and portfolio construction methods. In out-of-sample testing from 2021 to 2026, BMRB achieves an annualized return of 3.80%, a Sharpe ratio of 1.00, and a maximum drawdown of 4.78%, outperforming the competing methods in annualized return. The results are also relatively robust to changes in portfolio size and rebalancing frequency.

The study has limitations, notably that transaction costs and slippage are not considered. Nevertheless, it provides a useful illustration of how optimization can be applied in quantitative trading and highlights the importance of walk-forward analysis.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Hirohashi, K., Kubo, K., & Nakagawa, K. (2026), Basis mean-reverting basket: A unified formulation of index tracking and mean-reverting portfolio for index arbitrage, 2026 IEEE Symposium on Computational Intelligence for Financial Engineering and Economics (CIFEr), 300–307.

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Gold and Bitcoin Return Distributions During Market Crises

The normal distribution is widely used in finance, particularly in financial modeling, derivative pricing, and risk management. However, it is well recognized that asset return distributions are often non-normal and exhibit fat tails. Understanding these distributions is therefore important for derivative pricing, risk management, and even the development of trend-following strategies.

In this context, Reference [1] studies the unconditional return distributions of gold and Bitcoin before, during, and after two major crises: COVID-19 and the Russia–Ukraine war. The authors use daily closing prices from Yahoo Finance for COMEX gold futures and Bitcoin, covering selected periods between January 2019 and December 2023. They test ten probability distributions, including Student's t, Laplace, and others.

The authors pointed out,

Gold demonstrates relative stability across all crises: volatility rises modestly during high-stress periods but remains contained relative to Bitcoin. Its return distributions are best captured by heavy-tailed but near-symmetric specifications, most often the Laplace and, in the calmest sub-period, the normal. These results indicate that gold departs from normality mainly through heavier tails and a sharper central peak, with little role for asymmetry, and that the two-parameter Laplace provides a reliable baseline across the sub-periods considered.

Bitcoin exhibits heightened regime sensitivity. Across the COVID-19 and Russia-Ukraine crises, its best-fitting model shifts with market stress, but the leading specifications are predominantly the Laplace and, at the crisis peak, the Student’s t, both of which capture heavy tails without requiring asymmetry. Scale-mixture models such as the ASLSM become competitive only in the single post-crisis Bitcoin sub-period with the most extreme tails, where the additional mixture component is justified. In all sub-periods Bitcoin retains heavier tails than gold, reinforcing its greater susceptibility to regime shifts.

In short, the paper finds that Bitcoin's return distribution changes substantially across crises, whereas gold is relatively stable. Simple heavy-tailed distributions, particularly Laplace and Student's t, generally provide better in-sample fits than the normal distribution, without consistently requiring additional skewness parameters.

The study makes an important contribution, although the analysis itself is not overly complicated. In fact, this type of analysis can and should be performed by portfolio and risk managers, given its significant implications for investment decisions and risk management.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Nagar, P., Gabin, L. A., & Mandona, K. (2027), Distributional properties of gold and Bitcoin returns across crisis regimes: A comparative analysis, Journal of Statistical Theory and Practice.

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Intraday Breakout Trading and Changing Market Regimes

Intraday breakout trading is a long-established strategy dating back to the 1990s. Despite its long history, researchers continue to revisit it. Reference [1] also examines this strategy, this time applying it to Nasdaq futures. The motivation for this research is as follows,

Most of the published evidence on the rule is either dated, drawn from an instrument that is not the one traded, or presented without the costs, roll conventions, and multiple-testing [glossary_exclude]accounting [/glossary_exclude]that determine whether a reported return is real. This paper addresses that gap in three ways.

First, it reports a cost-aware, non-look-ahead test of a thirty-minute, long-only opening range breakout on NQ futures across sixteen years of one-minute data, and finds that the return is regime-dependent: absent from 2010 to 2019, present from 2020 onward.

Second, it subjects the post-2020 result to the three checks that most often expose a spurious intraday result: risk-normalisation across a period in which the index price quadrupled, a further sample split, and a placebo comparison against unconditional exposure on the same days. The placebo decomposition is the paper’s main finding. The return is not afternoon drift. It is the rule’s separation of sessions into those that continue and those that do not, confirmed after more than half the day’s move has already occurred.

Third, the paper reports the complete registry of 144 rules tested on the same archive during the same research programme, with the statistic that rejected each family, following the argument of Harvey et al. (2016) and Bailey et al. (2014) that a reported survivor is uninterpretable without the count of what did not survive.

Using 16 years of intraday data from 2010 to 2026, the study tests a strategy that buys when the price breaks above its highest level during the first 30 minutes of trading, with a predefined stop-loss and profit target. The strategy produced no meaningful profits before 2020 but earned an average of $129 per trade after transaction costs from 2020 onward. The results remained positive after adjusting for risk and dividing the post-2020 period into two smaller samples. Further tests suggest that the profits come from identifying days with sustained upward momentum rather than simply benefiting from a rising market.

An interesting observation from the paper is the regime change following the pandemic, consistent with findings in other markets and trading strategies. The author attributes this regime change to the growth of zero-commission retail trading, expansion of zero-days-to-expiration options, and increasing leveraged ETF rebalancing flows.

The paper has several limitations, the most significant being that it performs only in-sample testing. Nevertheless, it makes a noteworthy contribution to the existing body of research on intraday breakout strategies.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Chuk, J. (2026). Regime-dependent opening range breakout returns in Nasdaq-100 futures: A pre-registered study with a complete negative-result registry. Working paper

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Do Rough Volatility Models Improve Option Pricing?

The Black-Scholes-Merton (BSM) model is the cornerstone of derivatives pricing. However, because of its limitations, several extensions have been developed since its introduction. Reference [1] explores another direction for extending option pricing models by incorporating the roughness of volatility.

Specifically, the authors implement the rough Bergomi and rough Heston models and compare their performance with standard stochastic volatility models, including one with jumps. The study uses KOSPI 200 options data from January 2003 through June 2025, covering 5,571 trading days. Only at-the-money (ATM) and out-of-the-money (OTM) options with maturities of up to 180 days are included. The models are then evaluated both in-sample and out-of-sample.

The author pointed out,

This study compares the pricing performance of the rough volatility models (rBergomi and rHeston) and the classical models (SV; SVJDE ; SVJLN) in the KOSPI 200 index options market, applying the deep surrogate methodology in daily calibration and out-of-sample forecasting experiments over the 22 years from 2003 to 2025. In-sample, the nine-parameter SVJDE model performed best, but the difference from the rBergomi model, which uses only three core parameters, was not large. Out of sample, by contrast, rBergomi performed best at every forecast horizon. We attribute this to a structural limitation of the SVJ models, whose jump parameters overfit the current-day surface and cannot adapt to market conditions that change abruptly in a crisis. rBergomi, in contrast, maintained stable performance even in extreme environments, owing to its parsimony and to the structural flexibility of being able to reestimate the entire forward variance curve.

In short, the paper finds that KOSPI 200 volatility is empirically rough and that the rough Bergomi model delivers the best out-of-sample pricing performance.

It is worth noting that although the rough Bergomi model appears to have fewer parameters (three), its reliance on the forward volatility curve as an input effectively increases the number of parameters required.

While the study demonstrates the usefulness and strong pricing performance of rough volatility models, their effectiveness in hedging and trading remains to be evaluated.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Jang, W. W. (2026). Empirical performance of rough volatility models in the KOSPI 200 options market using deep surrogates, Journal of Derivatives and Quantitative Studies.

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Why Has Trend-Following Profitability Declined?

Trend following is an investment strategy that seeks to profit from sustained price movements across financial markets. It has long been a popular strategy. However, there are signs that its profitability has declined. In a previous post, we discussed the decline of Trend-Following CTAs.

In a similar context, Reference [1] examines why futures trend-following performance has deteriorated since 2008 and explores ways to improve its profitability. The author analyzes 75 futures markets across six asset classes from January 1990 to August 2026, using data from Norgate Data. The study employs a time-series momentum strategy that takes positions based on the sign of the preceding 12-month return and holds them for one month. Positions are volatility-scaled, with equal risk allocation across markets.

The paper pointed out,

The evidence forms a coherent chain. The 12-month continuation opportunity weakened, and the monthly Moskowitz 12/1 benchmark remains profitable after exact delivery-level costs but produces only a 0.42 post-2008 net Sharpe. A 252-day slope offers a complementary trend definition, although its stand-alone advantage is not decisive. The horizon experiment then shows that decay is concentrated in rules that replace the complete signal vintage every month. Combining all 12 lookback and holding-period rules in one equal-weight, internally netted book raises net Sharpe to 0.62 and reduces maximum drawdown to 12.8% without choosing the best cell after observing the data. Correlation-aware weighting does not improve that simple portfolio.

The funded analysis changes the scale of the question but not its economic meaning. After the common liquidity screen, the multi-horizon book produces a 0.64 Sharpe above cash and a 9.1% maximum drawdown; the sign-slope ensemble produces the highest funded CAGR at 6.74%. Both have statistically positive Sharpe advantages over the capped benchmark. Most transaction participation is low, but isolated events between 29% and 38% remain outside what daily data can validate as one-session execution. The recommendation is therefore a portfolio design plus an execution constraint, not an unrestricted capacity claim.

In short, the study concludes that trend following remains profitable, but its profitability has declined due to weaker underlying trend continuation, particularly in equity-index and currency futures. Interest-rate and agricultural futures, however, have shown greater resilience. The paper also finds that correlation-based optimization does not materially improve risk-adjusted returns, whereas diversification across multiple trend horizons does.

An important takeaway is the value of diversification, not only across asset classes but also across trading time frames and trend horizons.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Bang, P. (2026). Trend Following in Modern Futures Markets: Separating Opportunity Decay, Signal Conversion, and Implementation. Working paper.

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Pricing Derivatives with Mean-Reverting Stochastic Strikes

Financial derivatives are an integral part of modern financial markets, serving important roles in risk management, hedging, and speculation. Since the development of the Black-Scholes-Merton (BSM) model for pricing plain vanilla options, increasingly exotic options have emerged, and quantitative analysts have developed pricing formulas for these instruments.

In this context, Reference [1] develops a closed-form pricing formula for a financial contract whose payoff depends on the difference between two stochastic variables rather than a conventional fixed strike. In other words, the fixed strike in a vanilla option's payoff is replaced by a mean-reverting stochastic variable.

The authors argue that the benchmark's mean-reverting dynamics prevent it from being treated as a directly traded asset under their model, making the market incomplete. Consequently, the benchmark's market price of risk must be specified or calibrated, rather than determined solely by no-arbitrage. They pointed out,

This paper has developed an analytically tractable valuation framework for contracts whose payoff depends on the difference between an underlying asset and a non-tradable, mean-reverting benchmark, with applications to the integrated management of financial, operational, and emerging risks. The paper makes several key theoretical contributions.

First, it provides a formal proof that mean-reversion precludes tradability of the benchmark, requiring the specification of a market price of risk. Second, it derives closed-form pricing formulae for contracts that are linked to the Black–Scholes–Merton structure through a risk-neutral expected benchmark and an expanded effective variance. Importantly, these contracts should not be interpreted as standard vanilla options with fixed contractual strikes; the fixed-strike Black–Scholes–Merton case is recovered only when benchmark uncertainty vanishes, or the benchmark becomes effectively deterministic. Third, it provides a systematic analysis of how cost volatility, mean-reversion speed, and cross-process correlation jointly determine investment option value in a real options setting. Fourth, it applies the formulation to three economically important classes of derivatives: weather derivatives, volatility index options, and inflation-linked instruments.

In short, the paper develops a closed-form pricing formula for a financial contract whose payoff contains a strike that is not fixed but is instead a mean-reverting stochastic variable.

This is an interesting contribution to derivatives pricing. As the authors point out, the formula can be applied to real options, volatility, inflation, and weather derivatives.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Carvalho, P. V., Pinheiro, C. M., & Reis, J. M. (2026). Pricing contracts on a tradable asset and a non-tradable mean-reverting benchmark: Closed-form formulae and applications. Cogent Economics & Finance, 14(1), 2740368.

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How AI and Passive Investing Affect Stock Market Behavior

Artificial Intelligence (AI) is increasingly in the spotlight, attracting widespread attention across industries. One question on investors’ minds is how AI will change investment dynamics. In this context, Reference [1] examines whether AI and passive investing weaken the relationship between stock returns and economic fundamentals while increasing return autocorrelation.

The study analyzes 12 Fama-French U.S. industry portfolios using quarterly data from 2002 Q1 to 2025 Q2, comprising 1,128 industry-quarter observations. To measure AI sentiment, the author uses NVIDIA’s excess returns over the S&P 500, detrended and standardized.

The paper pointed out,

Five findings stand out. First, AI intensity exerts a robust negative effect on quarterly industry returns, acting as a sectoral redistributive force that diverts capital from non-AI segments during sentiment spikes – consistent with Danielsson and Uthemann’s (2025) prediction of intensified procyclical, synchronised capital behaviour – without directly severing the informational relationship between prices and economic activity. Second, fundamental anchoring persists over the full 2002–2025 period but is weakening. Industrial production growth retains its role as a positive and significant predictor of industry returns, although rolling-window and split-sample analyses reveal a sustained deterioration from 2015 Q2 that intensifies in the post-COVID era. Third, no evidence of feedback dynamics emerges: the lagged-return coefficient fails to attain statistical significance throughout the sample and across both sub-periods, providing no support for the market-fragility hypothesis and aligning instead with informationally efficient pricing. Fourth, passive investing flows exert no direct effect on returns, suggesting their influence operates through indirect structural channels–factor exposure, amplified comovement, and liquidity transformation– in line with the microstructure mechanisms identified by Ben-David et al. (2018) and Da and Shive (2018). Fifth, aggregate market returns remain the dominant driver of industry variation, a pattern that neither AI sentiment nor passive growth has yet materially altered.

In short, the paper finds that when AI-related stocks perform particularly well, other industries tend to underperform. This suggests that investors may be shifting capital toward AI companies and away from traditional sectors. The study also finds that stock returns have become less closely linked to economic fundamentals since 2015, although the evidence of this weakening is relatively modest.

This paper contributes to an emerging body of research on the impact of AI on investing, although its real-world effects remain to be seen.

An interesting aspect of the study is its use of NVIDIA’s relative performance as a proxy for AI sentiment. Trading system developers could adopt a similar approach by incorporating similar AI-related variables into investment models.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Piscopiello, M. (2026). Artificial Intelligence, Price Anchoring, and Feedback Dynamics in U.S. Equity Markets, Kent Economics Undergraduate Research Journal, Issue 4.

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The Relationship Between Leverage, Investor Behavior, and Returns

Margin lending and borrowing are integral parts of a well-functioning financial system. However, excessive use of margin, or leverage, can create significant risks. In this context, Reference [1] examines the returns and trading behavior of retail investors using margin financing in the Chinese stock market.

The study uses transaction data from nearly five million brokerage accounts between May and July 2015, covering China's equity market bubble and crash. The authors report an average assets-to-equity ratio of 1.4 for brokerage margin accounts and 6.4 for shadow accounts. They then construct a distance-to-margin-call measure (Z), which estimates how many standard deviations of portfolio losses would bring an account to its liquidation threshold.

The paper  pointed out,

We find that margin traders tend to hold stocks with more scope for “informed trading” and lottery-like features, though they do not outperform their unlevered counterparts. Our results thus suggest that lottery preferences, partly driven by overconfidence, can help explain why investors are willing to pay an annual interest rate of up to 25% in order to lever up.

Both shadow and brokerage margin investors heavily sell their holdings when their account-level leverage edges toward their Pingcang Lines (the maximum leverage limit, or maintenance margin), controlling for stock-date and account fixed effects. In other words, we find strong empirical support for both forced and preemptive margin-induced trading. The fact that investors react asymmetrically to positive and negative return shocks suggests a leverage constraint channel in addition to a rebalancing motive. We exploit the discontinuity around the eligibility of brokerage margin trading and the variation in Pingcang Lines across certain shadow accounts to provide unique evidence that leverage constraints induce selling. Moreover, we find that margin investors are relatively more likely to sell non-lottery stocks as the leverage constraint binds in a down market.

Aggregating trading behavior across margin investors, we find a significant return spillover in the near future: a stock’s return can be strongly forecasted by a portfolio of stocks with which it shares common margin-investor ownership. This pattern is subsequently reversed, and is present only in market downturns.

In short, the paper finds that,

• Retail margin borrowing is associated with lottery preferences and possible overconfidence.
• Margin-induced liquidation creates a feedback loop between declining asset prices and forced selling, transmitting shocks across otherwise unrelated stocks.

Although the study focuses on leveraged trading in the Chinese stock market, its conclusions may also be applicable to developed markets. We would be interested to hear from readers who are aware of similar studies in developed markets.

Another interesting contribution is the adaptation of the Merton credit risk model to leveraged trading, providing a framework for analyzing margin-related risks.

Let us know what you think in the comments below or in the discussion forum.

References

[1]  Jiangze Bian, Zhi Da, Zhiguo He, Dong Lou, Kelly Shue, and Hao Zhou, The Drivers and Implications of Retail Margin Trading, Journal of Finance, 2026.

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Revisiting Gambler’s Ruin: Trading Edge, Drawdowns, and Survival

The gambler's ruin problem is a classical probability problem that examines the likelihood of a gambler reaching a specified wealth target or losing all available capital. Reference [1] revisits this problem. Specifically, it seeks to answer the following questions:

Suppose a gambler enters a casino with finite capital,

• What is the probability of reaching a target wealth level or going bankrupt, and
• What is the expected duration of play?

The author first derives analytical formulas to address these questions, then uses Monte Carlo simulations to validate the theoretical results. Finally, the findings are applied to a real-world investment problem using daily S&P 500 data from January 1990 through September 2026.

The author pointed out,

Applied to daily S&P 500 returns, the model estimates a win rate of p = 0.5369 and finds that the sign sequence is statistically distinguishable from an independent one while being, in magnitude, very nearly independent. The more serious failure is elsewhere. When the fixed unit stake is replaced by a bootstrap of the actual return distribution, holding the win rate and the mean absolute move constant, the projected probability of ruin rises from 5.0% to 42.7%. The model’s weakness is not that markets are predictable but that they do not move in equal steps. That is a useful thing to know about a model, and it is the kind of thing that only becomes visible when the mathematics is exact enough that the discrepancy cannot be blamed on the algebra.

A central finding of the paper is that risk models based solely on the frequency of winning/losing days can substantially underestimate the risk of ruin when actual return magnitudes are unequal and heavy-tailed. In other words, the size of losses relative to gains, as well as the presence of fat tails, is critical in determining ruin probabilities.

Another interesting finding is that a relatively small increase in the probability of winning can dramatically reduce the probability of ruin. For example, at a 51% win rate, the probability of ruin is 44.93%, whereas at a 56% win rate, it falls to just 0.8%.

This paper makes an important contribution by formally confirming two principles already familiar to practitioners, namely

• Keeping losses and drawdowns small, and
• Increasing the trading edge whenever possible.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Jasman Mander, Random Walks and the Gambler’s Ruin Problem: Exact Results, Independent Derivations, and an Empirical Application to Equity Index Returns, Working Paper, 2026

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Market Timing Strategies Using the Implied Volatility Surface

Market timing is typically conducted using technical, macroeconomic, and volatility indicators. However, there is a growing trend in the research community toward using options-implied volatility to extract information for constructing market-timing strategies. For example, we have discussed how option-implied distributions can be used to time the market. Along the same line, Reference [1] develops an approach that uses the implied-volatility surface (IVS) to identify market entry points.

Using the IVS, the authors develop two groups of indicators,

1. Directional-expectation indicators: Directional Sentiment Bias (DSB) and Relative Upside Conviction (RUC).
2. Risk-stability indicators: Tail Risk Concentration (TRC) and Intertemporal Uncertainty Spread (IUS).

These indicators are then combined into three bullish structural regimes:

1. Extreme Hedging Reversal: panic/hedging conditions remain elevated, but directional sentiment has already turned bullish.
2. Trend-Stabilizing Correction: short-term stress has subsided relative to longer-term uncertainty while bullish sentiment remains.
3. Persistent Trend Potential: low short-term stress and longer-term uncertainty combined with bullish conviction, interpreted as conditions favorable to continued trends.

The authors test their approach on AAPL, TSLA, NVDA, and SPY. They generate an entry signal when IVS structural indicators cross dynamically calibrated thresholds into a defined regime, using only the first day of each structural transition as the entry point.

The paper pointed out,

The timely identification of effective market entry points is critical for capturing favorable risk-return opportunities while mitigating downside exposure. To address this challenge, the proposed framework leverages the structural information contained in the IVS through an economically motivated segmentation into the Central Sentiment and Peripheral Risk domains. Structural factors extracted from these domains disentangle directional sentiment from extreme risk pricing, while regime-specific thresholds identify distinct structural market regimes. By focusing on IVS state transitions rather than continuous price movements, this approach identifies discrete, effective entry points. Experimental results show that the framework outperforms conventional price-based and volatility-level baselines in directional accuracy and risk-adjusted returns. These findings highlight the practical value of structurally informed IVS analysis for precise, early-phase entry point detection and tactical decision-making in financial markets.

In short, the authors find that the IVS strategy generally delivers higher risk-adjusted performance, although the magnitude varies materially across assets. Their interpretation is that combining directional information with structural risk conditions improves entry timing.

A noteworthy conclusion is that this approach produced more precise and robust early-phase entry points than the technical and sentiment benchmarks tested, particularly because it uses economically interpretable information from different regions of the IV surface rather than continuously forecasting prices. Consequently, the approach can be used as a standalone regime-detection framework.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Yi-Chieh Sung, Shiou-Chi Li, and Jen-Wei Huang, Market Timing via Structural Transition Detection in the Options Implied Volatility Surface, in Advances in Computational Collective Intelligence, Springer 2026

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