Month: August 2025

Momentum strategies can be divided into two categories: time series and cross-sectional. In a previous newsletter, I discussed time series momentum. In this post, I focus on cross-sectional momentum strategies.

Cross-Sectional Momentum in the Commodity Market

Momentum trading is often divided into 2 categories: time-series momentum and cross-sectional momentum. Time-series based trading strategies generate trading signals based on the asset’s past returns. A typical time-series trading strategy usually involves buying assets with positive trend signals and selling those with negative trend signals. In contrast, cross-sectional trading strategies generate trading signals based on the relative performance of assets. A typical cross-sectional trading strategy involves buying assets with the highest-ranked trend signals and selling those with the lowest-ranked trend signals. So basically, this is a relative value strategy.

Reference [1] examined trend trading in the commodity market from the cross-sectional momentum perspective. The authors conducted a study on a portfolio of 35 commodity futures.

Findings

-The study introduces a trend factor that uses short-, intermediate-, and long-run moving averages of settlement prices in commodity futures markets.

-The trend factor generates statistically and economically significant returns during the post-financialization period (2004–2020).

-It outperforms the momentum factor by more than nine times in the Sharpe ratio and carries less downside risk.

-Unlike the momentum factor, which delivers insignificant returns in the sample, the trend factor consistently generates large positive returns.

-The trend factor cannot be explained by existing multifactor asset pricing models.

-It also provides a significant positive risk premium, confirming its economic relevance.

-The trend factor is correlated with funding liquidity, as measured by the TED spread.

-Overall, the findings highlight the economic value of using historical price information in commodity futures markets beyond traditional momentum strategies.

In short, cross-sectional momentum exists in the commodity market, and it is possible to construct a profitable trend trading strategy.

Reference

[1] Han, Yufeng and Kong, Lingfei, A Trend Factor in Commodity Futures Markets: Any Economic Gains From Using Information Over Investment Horizons? SSRN 3953845

Profitability of Cross-Sectional Momentum Strategy

Reference [2] examines the profitability of cross-sectional momentum strategies over the past decades

Findings

– The study investigates how different definitions of cross-sectional momentum affect the performance of long-short momentum strategies under varying market conditions.

-A long-short momentum portfolio buys stocks with strong past performance and shorts stocks with weak past performance.

-Standard long-short momentum strategies have delivered declining returns in recent decades, leading researchers and practitioners to search for solutions.

-A key weakness of momentum strategies is their tendency to experience “crashes,” where large gains are followed by sudden and substantial losses.

-The thesis proposes a method to mitigate crash risk, conditional on market states.

-While the literature offers complex methods for constructing long-short portfolios, the study demonstrates that relatively simple adjustments can meaningfully improve outcomes.

-Techniques such as volatility scaling and adjusting long and short positions based on market state enhance performance.

-These adjustments restore the robustness of the momentum premium and improve the risk-return profile of the strategy.

In short, the paper concludes that the profitability of cross-sectional momentum strategies has diminished. The author subsequently proposes an approach to enhance the strategy’s returns.

By applying techniques such as volatility scaling and adjusting long and short positions based on the market state we can significantly enhance the efficacy of the momentum strategy, restoring its former robustness.

Reference

[2] Pyry Pohjantähti, Revisiting (Revitalizing) Momentum, 2024, Aalto University School of Business

Closing Thoughts

In summary, both studies highlight that momentum remains useful but requires refinement. The first shows that a trend factor in commodity futures, built on moving averages, delivers strong returns and outperforms traditional momentum benchmarks. The second finds that cross-sectional momentum, though weakened and crash-prone, can be improved with simple adjustments like volatility scaling and conditioning on market states. Together, they show that momentum strategies are still effective when adapted to market conditions.

Stop loss is a risk management technique. It has been advocated as a way to control portfolio risk, but how effective is it? In this post, I will discuss certain aspects of stop loss.

When Are Stop Losses Effective?

A stop loss serves as a risk management tool, helping investors limit potential losses by automatically triggering the sale of a security when its price reaches a predetermined level. This level is set below the purchase price for long positions and above the purchase price for short positions.

Reference [1] investigates the effectiveness of stop losses by formulating a market model based on fractional Brownian motion to simulate asset price evolution, rather than using the conventional Geometric Brownian motion.

Findings

-In long positions, stop loss levels are placed below purchase prices, while in short positions, they are positioned above to protect invested capital.

-Stop-loss strategies improve buy-and-hold returns when asset prices display long-range dependence, capturing fractal characteristics of financial market behavior over time.

-The Hurst parameter, expected return, and volatility significantly influence stop-loss effectiveness, making their measurement crucial for optimizing strategy performance.

-Simulation results confirm that optimizing stop-loss thresholds for these variables can significantly enhance investment returns and reduce downside risks.

-Polynomial regression models were developed to estimate the optimal relationship between stop-loss thresholds and influencing variables for better trading outcomes.

-In mean-reverting market conditions, stop losses tend to reduce risk-adjusted returns, highlighting the importance of adapting strategies to market regimes.

In short, the paper formulated a market model based on fractional Brownian motion. Using this model, we can formally study the effectiveness of stop losses. It showed that stop losses enhance the risk-adjusted returns of the buy-and-hold investment strategy when the asset price is trending.

We note, however, that when the underlying asset is in the mean-reverting regime, stop losses decrease the risk-adjusted returns.

Reference

[1] Yun Xiang  and Shijie Deng, Optimal stop-loss rules in markets with long-range dependence, Quantitative Finance, Feb 2024

Fixed and Trailing Stop Losses in the Commodity Market

Building on previous discussion of the theoretical foundations of stop-loss strategies, Reference [2] examines their real-world application in the commodity market. It evaluates the performance of fixed and trailing stop losses, uncovering key factors that influence their effectiveness and impact on returns.

Findings

-The study analyzed fixed and trailing stop-loss strategies in commodity factor trading, focusing on their effectiveness in improving returns and reducing risk exposure.

-Results showed unmanaged factors performed poorly after accounting for transaction costs, while applying simple stop-loss rules significantly improved factor performance at the asset level.

-Fixed-stop strategies achieved an average Sharpe ratio of 0.92, whereas trailing-stop strategies delivered a higher average Sharpe ratio of 1.28.

-Both fixed and trailing stop-loss approaches maintained maximum drawdowns below 20 percent, with generally positive return skewness except for the skewness factor.

-The effectiveness of stop-loss strategies was not regime-dependent, but influenced by the quality of trading signals, commodity return volatility, and serial correlations.

-Transaction costs also played a significant role in determining stop-loss strategy performance, highlighting the importance of cost-efficient execution in commodity markets.

-Dynamically adjusting stop-loss thresholds based on realized volatility further enhanced factor performance compared to static fixed thresholds, especially in volatile trading environments.

-Stop-loss strategies were most effective when applied to factors built with high-conviction weighting schemes, maximizing their potential to capture commodity premia.

-Positive return autocorrelation and higher commodity return volatility were key conditions under which stop-loss strategies delivered the most meaningful performance improvements.

In short, in the commodity market, stop losses are effective when the autocorrelation of returns is positive, which is consistent with the findings of Reference [1]. Additionally, the volatility of returns influences how effective stop losses are.

A notable result of this study is that using trailing-stop with dynamic thresholds could enhance factor performance compared to using fixed thresholds.

Reference

[2] John Hua FAN, Tingxi ZHANG, Commodity Premia and Risk Management, 2023

Closing Thoughts

In summary, the first paper formulates a market model based on fractional Brownian motion to formally study the effectiveness of stop losses. It finds that stop losses improve the risk-adjusted returns of a buy-and-hold strategy when the asset price exhibits trending behavior, but reduce returns in mean-reverting regimes. The second paper focuses on the commodity market and shows that stop losses are effective when return autocorrelation is positive, aligning with the first study’s findings. It also highlights that return volatility affects stop loss effectiveness, and notably, that trailing stops with dynamic thresholds can enhance factor performance compared to fixed thresholds.

In trading system design, out-of-sample (OOS) testing is a critical step to assess robustness. It is a necessary step, but not sufficient. In this post, I’ll explore some issues with OOS testing.

How Well Overfitted Trading Systems Perform Out-of-Sample?

In-sample overfitting is a serious problem when designing trading strategies. This is because a strategy that worked well in the past may not work in the future. In other words, the strategy may be too specific to the conditions that existed in the past and may not be able to adapt to changing market conditions.

One way to avoid in-sample overfitting is to use out-of-sample testing. This is where you test your strategy on data that was not used to develop the strategy. Reference [1] examined how well the in-sample optimized trading strategies perform out of sample.

Findings

-In-sample overfitting occurs when trading strategies are tailored too closely to historical data, making them unreliable in adapting to future, changing market conditions and behaviors.

-The study applied support vector machines with 10 technical indicators to forecast stock price directions and explored how different hyperparameter settings impacted performance and profitability.

-Results showed that while models often performed well on training data, their out-of-sample accuracy significantly dropped—hovering around 50%—highlighting the risk of misleading in-sample success.

-Despite low out-of-sample accuracy, about 14% of tested hyperparameter combinations outperformed the traditional buy-and-hold strategy in profitability, revealing some potential value.

-The highest-performing strategies exhibited chaotic behavior; their profitability fluctuated sharply with minor changes in hyperparameters, suggesting a lack of consistency and stability.

-There was no identifiable pattern in hyperparameter configurations that led to consistently superior results, further complicating strategy selection and tuning.

-These findings align with classic financial theories like the Efficient Market Hypothesis and reflect common challenges in machine learning, such as overfitting with complex, high-dimensional data.

-The paper stresses caution in deploying overfitted strategies, as their sensitivity to settings can lead to unpredictable results and unreliable long-term performance in real markets.

The results indicated that most models had a high in-sample accuracy but only around 50% when applied to out-of-sample data. Nonetheless, a significant proportion of the models managed to outperform the buy-and-hold strategy in terms of profitability.

However, it’s noteworthy that the most profitable strategies are sensitive to system parameters. This is a cause for concern.

Reference

[1] Yaohao Penga, Joao Gabriel de Moraes Souza, Chaos, overfitting, and equilibrium: To what extent can machine learning beat the financial market?  International Review of Financial Analysis Volume 95, Part B, October 2024, 103474

How Reliable Is Out-of-Sample Testing?

Out-of-sample testing is a crucial step in designing and evaluating trading systems, allowing traders to make more informed and effective decisions in dynamic and ever-changing financial markets. But is it free of well-known biases such as overfitting, data-snooping, and look-ahead? Reference [2] investigated these issues.

Findings

-Out-of-sample testing plays a vital role in evaluating trading systems by assessing their ability to generalize beyond historical data and perform well under future market conditions.

-Although useful, out-of-sample testing is not immune to biases such as overfitting, data-snooping, and especially look-ahead bias, which can distort the validity of results.

-A common issue arises when models are developed or tuned using insights gained from prior research, creating an indirect dependency between development and test data.

-Researchers found that excessively high Sharpe ratios in popular multifactor models can be largely explained by a subtle form of look-ahead bias in factor selection.

-Many out-of-sample research designs still overlap with datasets used in earlier studies, leading to results that reflect known patterns rather than genuine model performance.

-The ongoing and iterative nature of financial research makes it difficult to construct fully unbiased validation frameworks that truly represent out-of-sample conditions.

-When alternative evaluation methods were applied, Sharpe ratio estimates dropped significantly, indicating the extent to which traditional approaches may inflate performance expectations.

-This reduction in Sharpe ratios is actually encouraging, as it better reflects the realistic outcomes investors can expect when implementing these models in real time.

-Despite these findings, the paper emphasizes that multifactor models still improve on CAPM, though the improvements are smaller than widely claimed.

In short, out-of-sample testing also suffers, albeit subtly, from biases such as overfitting, data-snooping, and look-ahead.

We agree with the authors. We also believe that out-of-sample tests, such as walk-forward analysis, also suffer from selection bias.

Then how do we minimize these biases?

Reference

[2] Easterwood, Sara, and Paye, Bradley S., High on High Sharpe Ratios: Optimistically Biased Factor Model Assessments (2023). SSRN 4360788

Closing Thoughts

The results indicated that most models achieved high in-sample accuracy, but only around 50% when applied to out-of-sample data. While out-of-sample testing is an essential tool for evaluating trading strategies, it is not entirely free from biases such as overfitting and look-ahead. Research shows that these biases can inflate performance metrics like Sharpe ratios, leading to overly optimistic expectations.