Month: October 2025

Gold prices have risen sharply in recent months, prompting renewed debate over whether the market has reached its peak. In this post, we examine quantitative models used to forecast gold prices and evaluate their effectiveness in capturing volatility and market dynamics. However, gold is not only a speculative vehicle, it also functions as an effective hedging instrument. We explore both aspects to provide a comprehensive view of gold’s role in modern portfolio management.

Comparative Analysis of Gold Forecasting Models: Statistical vs. Machine Learning Approaches

Gold is an important asset class, serving as both a store of value and a hedge against inflation and market uncertainty. Therefore, performing predictive analysis of gold prices is essential. Reference [1] evaluated several predictive methods for gold prices. It examined not only classical, statistical approaches but also newer machine learning techniques. The study used data from 2021 to 2025, with 80% as in-sample data and 20% as validation data.

Findings

-The study analyzes gold’s forecasting dynamics, comparing traditional statistical models (ARIMA, ETS, Linear Regression) with machine learning methods (KNN and SVM).

-Daily gold price data from 2021 to 2025 were used for model training, followed by forecasts for 2026.

-Descriptive analysis showed moderate volatility (σ = 501.12) and strong cumulative growth of 85%, confirming gold’s ongoing role as a strategic safe-haven asset.

-Empirical results indicate that Linear Regression (R² = 0.986, RMSE = 35.7) and ETS models achieved superior forecasting accuracy compared to ARIMA, KNN, and SVM.

-Machine learning models (KNN and SVM) underperformed, often misrepresenting volatility and producing higher forecast errors.

-The results challenge the assumption that complex algorithms necessarily outperform traditional methods in financial forecasting.

-Forecasts for 2026 project an average gold price of $4,659, corresponding to a 58.6% potential return.

-The study cautions that these forecasts remain sensitive to macroeconomic shocks and market uncertainties.

-The findings emphasize that simpler, transparent, and interpretable models can outperform more complex machine learning approaches in volatile market conditions.

In short, the paper shows that,

-Linear Regression and ETS outperformed ARIMA, KNN, and SVM, delivering the lowest error and highest explanatory power,

-Machine learning models (KNN, SVM) did not outperform traditional statistical methods, emphasizing the value of interpretability and stability in volatile markets.

Another notable aspect of the study is its autocorrelation analysis, which reveals that, unlike equities, gold does not exhibit clear autocorrelation patterns—its price behavior appears almost random. The paper also suggested improving the forecasting model by incorporating macroeconomic variables.

Reference

[1] Muhammad Ahmad, Shehzad Khan, Rana Waseem Ahmad, Ahmed Abdul Rehman, Roidar Khan, Comparative analysis of statistical and machine learning models for gold price prediction, Journal of Media Horizons, Volume 6, Issue 4, 2025

Using Gold Futures to Hedge Equity Portfolios

Hedging is a risk management strategy used to offset potential losses in one investment by taking an opposing position in a related asset. By using financial instruments such as options, futures, or derivatives, investors can protect their portfolios from adverse price movements. The primary goal of hedging is not to maximize profits but to minimize potential losses and provide stability.

Reference [2] explores hedging basic materials portfolios using gold futures.

Findings

-The study examines commodities as alternative investments, hedging instruments, and diversification tools.

-Metals, in particular, tend to be less sensitive to inflation and exhibit low correlation with traditional financial assets.

-Investors can gain exposure to metals through shares of companies in the basic materials sector, which focus on exploration, development, and processing of raw materials.

-Since not all companies in this sector are directly linked to precious metals, the study suggests including gold futures to enhance portfolio diversification.

-The research compares a portfolio composed of basic materials sector stocks with a similar portfolio hedged using gold futures.

-Findings show that hedging with gold reduces both profits and losses, providing a stabilizing effect suitable for risk-averse investors.

-The analysis used historical data from March 1, 2018, to March 1, 2022, and tested several portfolio construction methods, including equal-weight, Monte Carlo, and mean-variance approaches.

-Between March 2022 and November 2023, most portfolios without gold futures experienced losses, while portfolios with short gold futures positions showed reduced drawdowns and more stable performance.

-The basis trading strategy using gold futures did not change the direction of returns but significantly mitigated volatility and portfolio swings.

In short, the study concludes that hedging base metal equity portfolios with gold futures can effectively reduce PnL volatility and enhance portfolio stability, offering a practical approach for conservative investors and professional asset managers.

Reference

[2] Stasytytė, V., Maknickienė, N., & Martinkutė-Kaulienė, R. (2024), Hedging basic materials equity portfolios using gold futures, Journal of International Studies, 17(2), 132-145.

Closing Thoughts

In summary, gold can serve as an investment, a speculative vehicle, and a hedging instrument. In the first article, simpler models such as Linear Regression and ETS outperformed complex algorithms in forecasting gold prices, emphasizing the importance of interpretability in volatile markets. In the second, incorporating gold futures into base metal portfolios reduced profit and loss volatility, offering stability for risk-averse investors. Together, the studies highlight gold’s dual function as both a return-generating asset and a tool for risk management.

Identifying market regimes is essential for understanding how risk, return, and volatility evolve across financial assets. In this post, we examine two quantitative approaches to regime detection.

Hedge Effectiveness Under a Four-State Regime Switching Model

Identifying market regimes is important for understanding shifts in risk, return, and volatility across financial assets. With the advancement of machine learning, many regime-switching and machine learning methods have been proposed. However, these methods, while promising, often face challenges of interpretability, overfitting, and a lack of robustness in real-world deployment.

Reference [1] proposed a more “classical” regime identification technique. The authors developed a four-state regime switching (PRS) model for FX hedging. Instead of using a simple constant hedge ratio, they classified the market into regimes and optimized hedge ratios accordingly.

Findings

-The study develops a four-state regime-switching model for optimal foreign exchange (FX) hedging using forward contracts.

-Each state corresponds to distinct market conditions based on the direction and magnitude of deviations of the FX spot rate from its long-term trend.

-The model’s performance is evaluated across five currencies against the British pound over multiple investment horizons.

-Empirical results show that the model achieves the highest risk reduction for the US dollar, euro, Japanese yen, and Turkish lira, and the second-best performance for the Indian rupee.

-The model demonstrates particularly strong performance for the Turkish lira, suggesting greater effectiveness in hedging highly volatile currencies.

-The model’s superior results are attributed to its ability to adjust the estimation horizon for the optimal hedge ratio according to current market conditions.

-This flexibility enables the model to capture asymmetry and fat-tail characteristics commonly present in FX return distributions.

-Findings indicate that FX investors use short-term memory during low market conditions and long-term memory during high market conditions relative to the trend.

-The model’s dynamic structure aligns with prior research emphasizing the benefits of updating models with recent data over time.

-Results contribute to understanding investor behavior across market regimes and offer practical implications for mitigating behavioral biases, such as panic during volatile conditions.

In short, the authors built a more efficient hedging model by splitting markets into four conditions instead of two, adjusting hedge ratios and memory length depending on the volatility regime. This significantly improves hedge effectiveness, especially in volatile currencies.

We believe this is an efficient method that can also be applied to other asset classes, such as equities and cryptocurrencies.

Reference

[1] Taehyun Lee, Ioannis C. Moutzouris, Nikos C. Papapostolou, Mahmoud Fatouh, Foreign exchange hedging using regime-switching models: The case of pound sterling, Int J Fin Econ. 2024;29:4813–4835

Using the Gaussian Mixture Models to Identify Market Regimes

Reference [2] proposed an approach that uses the Gaussian Mixture Models to identify market regimes by dividing it into clusters. It divided the market into 4 clusters or regimes,

Cluster 0: a disbelief momentum before the breakout zone,

Cluster 1: a high unpredictability zone or frenzy zone,

Cluster 2: a breakout zone,

Cluster 3: the low instability or the sideways zone.

Findings

-Statistical analysis indicated that the S&P 500 OHLC data followed a Gaussian (Normal) distribution, which motivated the use of Gaussian Mixture Models (GMMs) instead of k-means clustering, since GMMs account for the distributional properties of the data.

-Traditional trading strategies based on the Triple Simple Moving Average (TSMA) and Triple Exponential Moving Average (TEMA) were shown to be ineffective across all market regimes.

-The study identified the most suitable regimes for each strategy to improve portfolio returns, highlighting the importance of regime-based application rather than uniform use.

-This combined approach of clustering with GMM and regime-based trading strategies demonstrated potential for improving profitability and managing risks in the S&P 500 futures market.

In short, the triple moving average trading systems did not perform well. However, the authors managed to pinpoint the market regimes where the trading systems performed better, relatively speaking.

Reference

[2] F. Walugembe, T. Stoica, Evaluating Triple Moving Average Strategy Profitability Under Different Market Regimes, 2021, DOI:10.13140/RG.2.2.36616.96009

Closing Thoughts

Both studies underscore the importance of regime identification and adaptive modeling in financial decision-making. The four-state regime-switching hedging model demonstrates how incorporating changing market conditions enhances risk reduction in foreign exchange markets, while the Gaussian Mixture Model approach illustrates how clustering can effectively capture distinct market phases in equity trading. Together, they highlight the value of data-driven, regime-aware frameworks in improving both risk management and trading performance.

Much emphasis has been placed on developing accurate and robust financial models, whether for pricing, trading, or risk management. However, a crucial yet often overlooked component of any quantitative system is the reliability of the underlying data. In this post, we explore some issues with financial data and how to address them.

How to Deal with Missing Financial Data?

In the financial industry, data plays a critical role in enabling managers to make informed decisions and manage risk effectively. Despite the critical importance of financial data, it is often missing or incomplete. Financial data can be difficult to obtain due to a lack of standardization and regulatory requirements. Incomplete or inaccurate data can lead to flawed analysis, incorrect decision-making, and increased risk.

Reference [1] studied the missing data in firms’ fundamentals and proposed methods for imputing the missing data.

Findings

-Missing financial data affects more than 70% of firms, representing approximately half of total market capitalization.

-The authors find that missing firm fundamentals exhibit complex, systematic patterns rather than occurring randomly, making traditional ad-hoc imputation methods unreliable.

-They propose a novel imputation method that utilizes both time-series and cross-sectional dependencies in the data to estimate missing values.

-The method accommodates general systematic patterns of missingness and generates a fully observed panel of firm fundamentals.

-The paper demonstrates that addressing missing data properly has significant implications for estimating risk premia, identifying cross-sectional anomalies, and improving portfolio construction.

-The issue of missing data extends beyond firm fundamentals to other financial domains such as analyst forecasts (I/B/E/S), ESG ratings, and other large financial datasets.

-The problem is expected to be even more pronounced in international data and with the rapid expansion of Big Data in finance.

-The authors emphasize that as data sources grow in volume and complexity, developing robust imputation methods will become increasingly critical.

In summary, the paper provides foundational principles and general guidelines for handling missing data, offering a framework that can be applied to a wide range of financial research and practical applications.

We think that the proposed data imputation methods can be applied not only to fundamental data but also to financial derivatives data, such as options.

Reference

[1] Bryzgalova, Svetlana and Lerner, Sven and Lettau, Martin and Pelger, Markus, Missing Financial Data SSRN 4106794

Predicting Realized Volatility Using High-Frequency Data: Is More Data Always Better?

A common belief in strategy design is that ‘more data is better.’ But is this always true? Reference [2] examined the impact of the quantity of data in predicting realized volatility. Specifically, it focused on the accuracy of volatility forecasts as a function of data sampling frequency. The study was conducted on crude oil, and it used GARCH as the volatility forecast method.

Findings

-The research explores whether increased data availability through higher-frequency sampling leads to improved forecast precision.

-The study employs several GARCH models using Brent crude oil futures data to assess how sampling frequency influences forecasting performance.

-In-sample results show that higher sampling frequencies improve model fit, indicated by lower AIC/BIC values and higher log-likelihood scores.

-Out-of-sample analysis reveals a more complex picture—higher sampling frequencies do not consistently reduce forecast errors.

-Regression analysis demonstrates that variations in forecast errors are only marginally explained by sampling frequency changes.

-Both linear and polynomial regressions yield similar results, with low adjusted R² values and weak correlations between frequency and error metrics.

-The findings challenge the prevailing assumption that higher-frequency data necessarily enhance forecast precision.

-The study concludes that lower-frequency sampling may sometimes yield better forecasts, depending on model structure and data quality.

-The paper emphasizes the need to balance the benefits and drawbacks of high-frequency data collection in volatility prediction.

-It calls for further research across different assets, markets, and modeling approaches to identify optimal sampling frequencies.

In short, increasing the data sampling frequency improves in-sample prediction accuracy. However, higher sampling frequency actually decreases out-of-sample prediction accuracy.

This result is surprising, and the author provided some explanation for this counterintuitive outcome. In my opinion, financial time series are usually noisy, so using more data isn’t necessarily better because it can amplify the noise.

Another important insight from the article is the importance of performing out-of-sample testing, as the results can differ, sometimes even contradict the in-sample outcomes.

Reference

[2] Hervé N. Mugemana, Evaluating the impact of sampling frequency on volatility forecast accuracy, 2024, Inland Norway University of Applied Sciences

Closing Thoughts

Both studies underscore the central role of high-quality data in financial modeling, trading, and risk management. Whether it is the frequency at which data are sampled or the completeness of firm-level fundamentals, the integrity of input data directly determines the reliability of forecasts, model calibration, and investment decisions. As financial markets become increasingly data-driven, the ability to collect, process, and validate information with precision will remain a defining edge for both researchers and practitioners.