Author: rvarb

How Machine Learning Enhances Market Volatility Forecasting Accuracy

Machine learning has many applications in finance, such as asset pricing, risk management, portfolio optimization, and fraud detection. In this post, I discuss the use of machine learning in forecasting volatility.

Using Machine Learning to Predict Market Volatility

The unpredictability of the markets is a well-known fact. Despite this, many traders and portfolio managers continue to try to predict market volatility and manage their risks accordingly. Usually, econometric models such as GARCH are used to forecast market volatility.

In recent years, machine learning has been shown to be capable of predicting market volatility with accuracy. Reference [1] explored how machine learning can be used in this context.

Findings

-Machine learning models can accurately forecast stock return volatility using a small set of key predictors: realized volatility, idiosyncratic volatility, bid-ask spread, and returns.

-These predictors align with existing empirical findings, reinforcing the traditional risk-return trade-off in finance.

-ML methods effectively capture both the magnitude and direction of predictor impacts, along with their interactions, without requiring pre-specified model assumptions.

-Large current-period volatility values strongly predict higher future volatility; small values have a muted or negative impact.

-LSTM models outperform feedforward neural networks and regression trees by leveraging temporal patterns in historical data.

-An LSTM using only volatility and return history over one year performs comparably to more complex models with additional predictors.

-LSTM models function as distribution-free alternatives to traditional econometric models like GARCH.

-Optimal lag length remains critical in LSTM performance and must be selected through model training.

-The study reports an average predicted realized volatility of 44.1%, closely matching the actual value of 43.8%.

-Out-of-sample R² values achieved are significantly higher than those typically reported in related volatility forecasting literature.

In short, the paper aimed to demonstrate the potential of machine learning for modeling market volatility. In particular, the authors have shown how the LSTM model can be used to predict market volatility and manage risks. The results suggest that this is a promising alternative approach to traditional econometric models like GARCH.

Reference

[1] Filipovic, Damir and Khalilzadeh, Amir, Machine Learning for Predicting Stock Return Volatility (2021). Swiss Finance Institute Research Paper No. 21-95

Machine Learning Models for Predicting Implied Volatility Surfaces

The Implied Volatility Surface (IVS) represents the variation of implied volatility across different strike prices and maturities for options on the same underlying asset. It provides a three-dimensional view where implied volatility is plotted against strike price (moneyness) and time to expiration, capturing market sentiment about expected future volatility.

Reference [2] examines five methods for forecasting the Implied Volatility Surface of short-dated options. These methods are applied to forecast the level, slope, and curvature of the IVS.

Findings

-The study evaluates five methods—OLS, AR(1), Elastic Net, Random Forest, and Neural Network—to forecast the implied volatility surface (IVS) of weekly S&P 500 options.

-Forecasts focus on three IVS characteristics: level, slope, and curvature.

-Random Forest consistently outperforms all other models across these three IVS dimensions.

-Non-learning-based models (OLS, AR(1)) perform comparably to some machine learning methods, highlighting their continued relevance.

-Neural Networks forecast the IVS level reasonably well but perform poorly in predicting slope and curvature.

-Elastic Net, a linear machine learning model, is consistently outperformed by the non-linear models (Random Forest and Neural Network) for the level characteristic.

-The study emphasizes the importance of model selection based on the specific IVS characteristic being forecasted.

-Performance evaluation is supported using the cumulative sum of squared error difference (CSSED) and permutation variable importance (VI) metrics.

-The research highlights the utility of Random Forest in capturing complex, non-linear patterns in IVS dynamics.

-Accurate IVS forecasting is valuable for derivative pricing, hedging, and risk management strategies.

This research highlights the potential of machine learning in forecasting the implied volatility surface, a key element in options pricing and risk management. Among the five methods studied, Random Forest stands out as the most consistent and accurate across multiple IVS features.

Reference

[2] Tim van de Noort, Forecasting the Characteristics of the Implied Volatility Surface for Weekly Options: How do Machine Learning Methods Perform? Erasmus University, 2024

Closing Thoughts

These studies highlight the growing effectiveness of machine learning in financial forecasting, particularly for market volatility and implied volatility surfaces. Models like LSTM and Random Forest demonstrate clear advantages over traditional methods by capturing complex patterns and dependencies. As financial markets evolve, leveraging such tools offers a promising path for enhancing predictive accuracy and risk management.

Predicting Corrections and Economic Slowdowns

Being able to anticipate a market correction or an economic recession is important for managing risk and positioning your portfolio ahead of major shifts. In this post, we feature two articles: one that analyzes indicators signaling a potential market correction, and another that examines recession forecasting models based on macroeconomic data.

Predicting Recessions Using The Volatility Index And The Yield Curve

The yield curve is a graphical representation of the relationship between the yields of bonds with different maturities. The yield curve has been inverted before every recession in the United States since 1971, so it is often used as a predictor of recessions.

A study [1] shows that the co-movement between the yield-curve spread and the VIX index, a measure of implied volatility in S&P500 index options, offers improvements in predicting U.S. recessions over the information in the yield-curve spread alone.

Findings

-The VIX index measures implied volatility in S&P 500 index options and reflects investor sentiment and market uncertainty.

-A counterclockwise pattern (cycle) between the VIX index and the yield-curve spread aligns closely with the business cycle.

-A cycle indicator based on the VIX-yield curve co-movement significantly outperforms the yield-curve spread alone in predicting recessions.

-This improved forecasting performance holds true for both in-sample and out-of-sample data using static and dynamic probit models.

-The predictive strength comes from the interaction between monetary policy and financial market corrections, not from economic policy uncertainty.

-Shadow rate analysis confirms the cycle indicator’s effectiveness, even during periods of unconventional monetary policy and flattened yield curves.

-The findings suggest a new framework for macroeconomic forecasting, with the potential to enhance early detection of financial instability.

-The VIX-yield curve cycle adds value beyond existing leading indicators and may help in anticipating major economic disruptions like the subprime crisis.

In short, the study concludes that the co-movement between the yield curve spread and the VIX index, which is a measure of implied volatility in S&P 500 index options, provides an improved prediction for U.S. recessions over any information available from just considering the yield-curve spreads alone.

This new research will have implications for how macroeconomists forecast future economic conditions and could even change how we predict periods of high financial instability like the subprime crisis.

Reference

[1] Hansen, Anne Lundgaard, Predicting Recessions Using VIX-Yield-Curve Cycles (2021). SSRN 3943982

Can We Predict a Market Correction?

A correction in the equity market refers to a downward movement in stock prices after a sustained period of growth. Market corrections can be triggered by various factors such as economic conditions, changes in investor sentiment, or geopolitical events. During a correction, stock prices may decline by a certain percentage from their recent peak, signaling a temporary pause or reversal in the upward trend.

Reference [2] examines whether a correction in the equity market can be predicted. It defines a correction as a 4% decrease in the SP500 index. It utilizes logistic regression to examine the predictability of several technical and macroeconomic indicators.

Findings

-Eight technical, macroeconomic, and options-based indicators were selected based on prior research.

-Volatility Smirk (skew), Open Interest Difference, and Bond-Stock Earnings Yield Differential (BSEYD) are statistically significant predictors of market corrections.

-These three predictors were significant at the 1% level, indicating strong reliability in forecasting corrections.

-TED Spread, Bid-Offer Spread, Term Spread, Baltic Dry Index, and S&P GSCI Commodity Index did not show consistent predictive power.

-The best-performing model used a 3% correction threshold and achieved 77% accuracy in in-sample prediction.

-Out-of-sample testing showed 59% precision in identifying correction events, offering an advantage over random prediction.

-The results highlight inefficiencies in the market and support the presence of a lead-lag effect between option and equity markets.

-The research provides valuable tools for risk management and identifying early signs of downturns in equity markets.

In short, the following indicators are good predictors of a market correction,

-Volatility Smirk (i.e. skew),

-Open Interest Difference, and

-Bond-Stock Earnings Yield Differential (BSEYD)

The following indicators are not good predictors,

-The TED Spread,

-Bid-Offer Spread,

-Term Spread,

-Baltic Dry Index, and

-S&P GSCI Commodity Index

This is an important research subject, as it allows investors to manage risks effectively and take advantage of market corrections.

Reference

[2] Elias Keskinen, Predicting a Stock Market Correction, Evidence from the S&P 500 Index, University of VAASA

Closing Thoughts

This research underscores the growing value of combining traditional financial indicators with options market metrics to improve market correction and recession forecasts. Tools like the VIX-yield curve cycle, Volatility Smirk, and BSEYD offer a more refined understanding of market risks. As financial markets evolve, integrating diverse data sources will be key to staying ahead of economic and market shifts.

Rethinking Leveraged ETFs and Their Options

A leveraged Exchanged Traded Fund (LETF) is a financial instrument designed to deliver a multiple of the daily return of an underlying index. Despite criticism, LETFs are frequently used by institutional investors. In this post, I discuss the practicality of LETFs and show that they are not as risky as they may seem.

Information Content of Leveraged ETFs Options

Leveraged ETFs, or exchange-traded funds, are investment funds designed to amplify the returns of an underlying index or asset class through the use of financial derivatives and debt. These ETFs aim to achieve returns that are a multiple of the performance of the index they track, typically two or three times (2x, 3x) the daily performance.

There is evidence that 1x ETF options provide an indication of the future return of the underlying 1x ETF. Reference [1] goes further and postulates that options on leveraged ETFs provide an even stronger indication of the 1x ETF future return.

Findings

-Options on leveraged ETFs provide stronger predictive signals for future ETF returns compared to standard ETF options, showing higher economic and statistical significance.

-The study uses unexpected changes in implied volatility from call and put options on leveraged ETFs to identify signals of informed trading activity.

-Leveraged ETF option signals consistently outperform unleveraged signals in predicting future returns of the underlying ETFs across various market conditions.

-Sophisticated investors often trade leveraged ETFs for exposure and rely on their options markets to hedge or speculate based on market expectations.

-A $1 investment in SPY based on leveraged option signals would have generated $27.59 in net returns from 2009 to 2021 after transaction costs.

-The predictive power of leveraged ETF option signals is especially strong during economic downturns, making them useful in volatile or declining markets.

-Inverse leveraged ETFs provide particularly strong predictive signals, especially when markets are trending downward or experiencing negative momentum.

-A trading strategy based on leveraged ETF option signals produced average abnormal returns of 1.13% per month, even after accounting for transaction costs.

-The findings suggest that options on leveraged ETFs play a key role in market efficiency and price discovery by reflecting informed investor activity.

-Both leveraged and unleveraged ETF options contain return-predictive information, but the economic impact is far greater when using leveraged ETF option signals.

In short, by using the difference in implied volatility innovations between calls and puts of leveraged ETFs as a trading signal, one can gain excess returns.

Reference

[1] Collin Gilstrap, Alex Petkevich, Pavel Teterin, Kainan Wang, Lever up! An analysis of options trading in leveraged ETFs, J Futures Markets. 2024, 1–17

Leveraged Exchange Traded Funds Revisited: Enhancing Returns or Adding Risk?

LETFs have received a lot of criticism. Despite the controversy, they remain popular among institutional investors. Reference [2] revisited the use of LETFs in portfolio allocation.

Findings

-LETFs aim to deliver amplified daily returns using derivatives and debt, making them suitable for short-term tactical strategies but requiring careful risk management.

-The study shows LETFs exhibit call option–like payoff characteristics, suggesting they can offer inexpensive leverage with built-in downside protection in certain scenarios.

-Under ideal conditions like continuous rebalancing and no constraints, the authors derived a closed-form information ratio–optimal strategy that followed a contrarian investment approach

-In realistic market conditions, including quarterly trading and margin constraints, a neural network approach was used to identify performance-optimized LETF allocation strategies.

-Results showed that unleveraged strategies using LETFs outperform benchmarks more frequently than leveraged strategies using standard (vanilla) ETFs on the same index.

-These unleveraged LETF strategies also showed partial stochastic dominance over both the benchmark and vanilla ETF-based strategies in terms of terminal wealth outcomes.

-The neural network–based strategy, trained on historical market data, further supports the practical value of including LETFs in actively managed portfolios.

-The findings challenge the common belief that LETFs only serve short-term speculation, revealing potential for long-term, dynamically optimized investment use.

-Overall, incorporating LETFs through informed strategies can enhance risk-adjusted returns, outperform traditional benchmarks, and improve the robustness of portfolio performance.

An interesting finding of this study is that, through a closed-form solution and numerical simulations, the authors demonstrated that LETFs behave like call options. Based on this, it is intuitive that if LETFs are part of a portfolio, they can enhance risk-adjusted returns.

Reference

[2] Pieter van Staden, Peter Forsyth, Yuying Li, Smart leverage? Rethinking the role of Leveraged Exchange Traded Funds in constructing portfolios to beat a benchmark, 2024, arXiv:2412.05431

Closing Thoughts

In conclusion, both studies provide compelling evidence that leveraged ETFs and their options hold significant value beyond short-term speculation. Leveraged ETF options offer strong predictive signals that can enhance trading strategies and market insight, while actively managed LETF allocations can improve long-term portfolio performance. When used thoughtfully, these instruments can deliver meaningful returns, manage risk, and contribute to price discovery.

Using Skewness and Kurtosis to Enhance Trading and Risk Management

Skewness is a measure of the asymmetry of a return distribution. In this post, I’ll discuss the skewness risk premium and how skewness can be used to forecast realized volatility.

Skewness Risk Premium in the Options Market

Skewness of returns is a statistical measure that captures the asymmetry of the distribution of an asset’s returns over a specified period. It is particularly important in risk management and option pricing, where the skewness of returns can affect the valuation of derivatives and the construction of portfolios.

Reference [1] studies the skewness risk premium in the options market. It decomposes the skewness risk premium into two components: jump skewness and leverage skewness risk premia.

Findings

-The skewness risk premium (SRP) is distinct from the variance risk premium (VRP), and both are independently priced in the options market.

-The study introduces model-free, tradable strategies to replicate realized skewness, decomposed into two components:

  1. Jump Skewness Risk Premium
  2. Leverage Skewness Risk Premium

-These strategies dynamically rebalance option and forward positions to track high-frequency realized jump skewness and leverage.

-The SRP is generally higher during overnight periods than during regular trading hours—mirroring similar behavior observed in the VRP.

-Jump skewness dominates the SRP during market hours, while overnight skewness may capture broader macro or non-U.S. investor risk.

-The SRP exhibits countercyclical behavior, becoming more pronounced during periods of market stress or left-tail events.

-The study confirms that the SRP and VRP are fundamentally different, supporting the need to treat them separately in portfolio and derivative strategies.

-This decomposition provides insights for trading and hedging strategies, offering more granular exposure to tail risk components.

-Findings are based on short-maturity S&P 500 options, analyzed both intraday and overnight to capture time-sensitive skewness behavior.

In short, the authors constructed a tradable basket of options to measure the skewness risk premium. This means that this study is model-free.

They reconfirmed that

-The skewness risk premium is different from the variance risk premium.

-The variance risk premium is compensation for bearing overnight risks.

Reference

[1] Piotr Orłowski , Paul Schneider , Fabio Trojani, On the Nature of (Jump) Skewness Risk Premia, Management Science, Vol 70, No 2

Predicting Realized Volatility Using Skewness and Kurtosis

Realized volatility refers to the actual volatility experienced by a financial asset over a specific period, typically computed using historical price data. By calculating realized volatility, investors and analysts can gain insights into the true level of price variability in the market.

Reference [2] examines whether realized volatility can be forecasted. Specifically, it studies whether realized skewness and kurtosis can be used to forecast realized volatility.

Findings

-The study investigates whether realized skewness and kurtosis can improve the prediction of realized volatility for equity assets.

-Using data from 452 listed firms on the Pakistan Stock Exchange, the research evaluates both in-sample and out-of-sample forecast performance.

-The standard Heterogeneous Autoregressive (HAR) model is extended by incorporating realized skewness and kurtosis into the volatility forecasting framework.

-The extended model predicts future realized volatility as a linear function of:

  1. Yesterday’s realized volatility
  2. Average realized volatility over the past week and month
  3. Yesterday’s realized kurtosis

-Realized kurtosis is found to significantly enhance forecast accuracy, particularly for short- to medium-term horizons (1, 5, and 22 days ahead).

-Realized skewness has less predictive power compared to realized kurtosis but still adds context for modeling tail risk.

-These findings suggest that higher-order moments (like kurtosis) contain valuable information beyond basic volatility measures.

-The approach supports improved asset allocation and risk-adjusted return forecasting in equity portfolios.

While the study is based on Pakistan’s equity market, the methodology can be generalized to other asset classes and global markets. The paper concluded that stocks’ own realized kurtosis carries meaningful information for stocks’ future volatilities.

Reference

[2] Seema Rehman, Role of realized skewness and kurtosis in predicting volatility, Romanian Journal of Economic Forecasting, 27(1) 2024

Closing Thoughts

Both studies show that incorporating skewness and kurtosis adds valuable insight to volatility analysis. The first study reveals that the skewness risk premium is distinct, tradable, and especially driven by jump risk during market hours. The second shows that realized kurtosis improves short-term volatility forecasts. Together, they highlight the importance of using higher-order moments for better risk management, portfolio decisions, and understanding market behavior.

Gold Ratios as Stock Market Predictors

The ratio of gold prices to other asset classes has been shown to be a useful predictor of stock market returns. In this post, we discussed several gold-based ratios and how they can be used to forecast equity market performance.

Gold Oil Price Ratio As a Predictor of Stock Market Returns

Analyzing intermarket relationships between assets can help identify trends and predict returns. Traditionally, analysts use commodity, currency, and interest-rate data to predict the direction of the stock market. In this regard, Reference [1] brings a fresh new perspective. It utilizes price ratios of gold over other assets in order to forecast stock market returns.

Findings

-The gold-oil price ratio (GO) is shown to be a strong predictor of future stock market returns.

-Researchers created ten different gold price ratios by comparing gold to various assets like oil, silver, CPI, corn, copper, and several financial indicators.

-They used statistical models (univariate and bivariate regressions) to test how well these ratios could predict U.S. stock returns.

-Among all the ratios tested, the gold-oil ratio (GO) had the highest predictive power.

-A one standard deviation increase in the GO ratio is linked to a 6.60% rise in annual excess stock returns for the following month.

-The GO ratio performs better than traditional forecasting methods, including the historical average model.

-It also offers meaningful economic benefits for investors who use mean-variance strategies.

-The study concludes that the predictive ability of the GO ratio is both statistically reliable and economically useful.

In summary, the gold-oil price ratio is identified as a robust predictor of stock market returns, outperforming traditional predictors and other gold price ratios. A one standard deviation increase in GO is associated with a significant 6.60% increase in annual excess returns for the next month.

Reference

[1] T. Fang, Z. Su, and L Yin, Gold price ratios and aggregate stock returns, SSRN 3950940

The Bitcoin-Gold Ratio as a Predictor of Stock Market Returns

The ratio of gold prices to other asset classes has been shown to be a useful predictor of stock market returns. The previous article discussed how the gold-oil ratio serves as one such indicator.

Continuing this line of inquiry, Reference [2] examines the informational value of the Bitcoin-gold (BG) price ratio. The logic behind this metric is that Bitcoin represents a high-risk asset, whereas gold is traditionally viewed as a safe haven. Therefore, a rising BG ratio may signal increased investor risk appetite. It may also reflect growing optimism and interest in technological innovation, which boosts demand for Bitcoin. As a result, a higher BG ratio can indicate a tech-driven risk appetite that translates into stronger stock returns.

Findings

-The Bitcoin-Gold (BG) ratio is positively linked to U.S. stock market returns, especially during and after the COVID-19 pandemic.

-A rising BG ratio suggests increased investor risk appetite, as Bitcoin is seen as high-risk and gold as a safe haven.

-The effect of the BG ratio on stock returns remains strong even when using Ethereum instead of Bitcoin, showing broader crypto-gold relevance.

-The positive impact of the BG ratio also applies to the European stock market, not just the U.S., indicating global relevance.

-The main channel through which the BG ratio affects stock returns is investor risk aversion or appetite.

-The study uses various economic controls, like volatility, inflation, and liquidity, and still finds the results hold strong.

-There was no significant impact of the BG ratio on stock returns before the pandemic, suggesting this relationship is more recent.

-The BG ratio reflects shifts in market sentiment and offers a new tool for gauging investor behavior.

-Investors can use the BG ratio as a signal to adjust their equity exposure based on prevailing market conditions.

In summary, the paper makes a novel contribution by introducing crypto-gold ratios as reliable indicators of stock market direction across multiple regions.

Reference

[2] Elie Bouri, Ender Demir, Bitcoin-to-gold ratio and stock market returns, Finance Research Letters (2025) 107456

Closing Thoughts

Both studies show that gold price ratios can offer valuable insights into stock market returns. The gold-oil ratio (GO) stands out as a strong, traditional predictor, while the Bitcoin-gold ratio (BG) brings a modern twist by capturing shifts in investor risk appetite. Together, these findings suggest that combining safe-haven and risk assets in a ratio form can help investors better understand and respond to changing market conditions.

Volatility of Volatility: Insights from VVIX

The volatility of volatility index, VVIX, is a measure of the expected volatility of the VIX index itself. In this post, we will discuss its dynamics, compare it with the VIX index, and explore how it can be used to characterize market regimes.

Dynamics of the Volatility of Volatility Index, VVIX

The VVIX, also known as the Volatility of Volatility Index, is a measure that tracks the expected volatility of the CBOE Volatility Index (VIX). As the VIX reflects market participants’ expectations for future volatility in the S&P 500 index, the VVIX provides insights into the market’s perception of volatility uncertainty in the VIX itself.

Reference [1] studied the dynamics of VVIX and compared it to the VIX.

Findings

-The VVIX tracks the expected volatility of the VIX, providing a direct measure of uncertainty around future changes in market volatility itself.

-It shows strong mean-reverting behavior, indicating that large deviations from its average level tend to reverse over time.

-The VVIX responds asymmetrically to S&P 500 movements, typically increasing more sharply during market downturns than it decreases during upswings.

-It experiences sudden jumps in both directions, reflecting its sensitivity to abrupt changes in market sentiment and conditions.

-A persistent upward trend in the VVIX began well before 2020, driven by factors such as rising VIX volatility and an increasing volatility-of-volatility risk premium (VVRP).

-The growth of the VIX options market from 2006 to 2014 improved liquidity, which likely contributed to the VVIX’s upward trend and closer link to the VIX.

-VVIX and VIX innovations are highly correlated, highlighting their structural connection despite often differing in their responses to specific market events.

-VVIX quickly incorporates new market information, with minimal autocorrelation beyond a single day, showing its responsiveness to real-time market changes.

In summary, this paper analyzes the similarities and differences between the VIX and VVIX, offering key insights for traders and hedgers in the VIX options market. Understanding their relationship helps improve risk management, refine hedging strategies, and better assess market sentiment.

Reference

[1]  Stefan Albers, The fear of fear in the US stock market: Changing characteristics of the VVIX, Finance Research Letters, 55

Using Hurst Exponent on the Volatility of Volatility Indices

A market regime refers to a distinct phase or state in financial markets characterized by certain prevailing conditions and dynamics. Two common market regimes are mean-reverting and trending regimes. In a mean-reverting regime, prices tend to fluctuate around a long-term average, with deviations from the mean eventually reverting back to the average. In a trending regime, prices exhibit persistent directional movements, either upwards or downwards, indicating a clear trend.

Reference [2] proposed the use of the Hurst exponent on the volatility of volatility indices in order to characterize the market regime.

Findings

-The study analyzes the volatility of volatility indices using data from five international markets—VIX, VXN, VXD, VHSI, and KSVKOSPI—covering the period from January 2001 to December 2021.

-It employs the Hurst exponent to evaluate long-term memory and persistence in volatility behavior, providing a framework to characterize market regimes over time.

-Different range-based estimators were used to calculate the Hurst exponent on various volatility measures, improving the robustness of the analysis.

-The volatility of volatility indices was estimated through a GARCH(1,1) model, which captures time-varying volatility dynamics effectively.

-The results show that Hurst exponent values derived from volatility of volatility indices reflect market regime shifts more accurately than those from standard volatility indices, supporting the authors’ hypothesis (H1).

-The analysis explores how different trading strategies—momentum, mean-reversion, and random walk—align with the Hurst exponent values, linking theoretical behavior to practical trading outcomes.

-The study highlights the effectiveness of the Hurst exponent as a tool for identifying and interpreting market regimes, which is essential for informed trading and investment decisions.

-Findings are particularly useful for financial analysts and researchers working with volatility indices and market behavior analysis.

-The paper contributes a novel methodological approach by combining Hurst exponent estimation with GARCH modeling and strategy backtesting, offering a comprehensive view of volatility behavior across regimes.

In short, the article highlights the effectiveness of employing the Hurst exponent on the volatility of volatility indices as a suitable method for characterizing the market regime.

Reference

[2] Georgia Zournatzidou and Christos Floros, Hurst Exponent Analysis: Evidence from Volatility Indices and the Volatility of Volatility Indices, J. Risk Financial Manag. 2023, 16(5), 272

Closing Thoughts

In this post, we explored the dynamics of the VVIX index, and how to use the Hurst exponent on it to characterize the market regime, offering a practical lens through which traders can gauge the persistence or randomness in volatility movements. By understanding these dynamics, market participants can better anticipate shifts in sentiment, enhance their hedging strategies, and adapt more effectively to evolving risk conditions in the options market.

Simplicity or Complexity? Rethinking Trading Models in the Age of AI and Machine Learning

When it comes to trading system design, there are two schools of thought: one advocates for simpler rules, while the other favors more complex ones. Which approach is better? This newsletter explores both perspectives through the lens of machine learning.

Use of Machine Learning in Pairs Trading

Machine learning has become an essential tool in modern finance, transforming the way financial institutions and investors approach data analysis and decision-making.

Reference [1] explored the use of machine learning in pairs trading. Specifically, the authors developed an algorithm to trade the classic Pepsi/Cola pair using three predictive methods: (i) fitting a linear model to real datasets of Pepsi and Coca-Cola stocks, (ii) employing a neural network approach to fit non-linear models, and (iii) utilizing an error correction model (ECM).

Findings

-The study investigates the relationship between two correlated stocks, Pepsi and Coca-Cola, using regression modeling and machine learning algorithms.

-The data is split into a training set (75%) and a testing set (25%) to evaluate model performance.

-A simple linear relationship between Pepsi prices (Y) and Coca-Cola prices (X) is modeled using both ordinary least squares (OLS) and a neural network (NN).

– A non-linear model between Y and X was fitted using the neural network (NN) method, and predictions were made for the X series.

-Two co-integrated stationary processes are used to analyze trading performance: the spread (Y − 𝑌^) and the ratio (𝑌^/X).

-The performance of each strategy is evaluated to determine the most effective approach for trading based on the co-movement of Pepsi and Coca-Cola.

– The total profit was computed and compared: the linear model generated a profit of $1.05102, while the neural network model produced $1.049395.

– The NN model’s performance was similar to that of the linear method.

– The NN model can outperform other methods if the optimal number of neurons is used in the hidden layers.

In short, the neural network performs similarly to the linear model method but can be improved by optimizing the number of neurons.

Reference

[1] R. Sivasamy, Dinesh K. Sharma, Sediakgotla, and B. Mokgweetsi, Machine Learning Algorithmic Model for Pairs Trading, in Machine Learning for Real World Applications, Springer 2024.

Can a Complex Trading System Be Profitable

The previous article shows that a more complex system does not lead to higher returns. Reference [2], however, demonstrates that such a complex system can provide better risk-adjusted performance. The authors achieved that by using Machine Learning techniques.

Findings

-Traditional financial literature often relies on simple models with few parameters to predict market returns.

-This study theoretically proves that such simple models significantly understate the potential for return predictability.

-The article provides new theoretical insights into the out-of-sample performance of machine learning portfolios.

-It demonstrates that high-complexity models in machine learning can improve investment strategies, contradicting conventional wisdom.

-Market timing strategies based on ridgeless least squares can generate positive Sharpe ratio improvements, even for highly complex models.

-The study shows that machine learning models can perform better with greater model parameterization, despite having fewer training observations and minimal regularization.

-The findings are supported by random matrix theory and explained through intuitive statistical mechanisms.

-The article argues that out-of-sample R² is a poor measure of a model’s economic value, as models with large negative R² can still generate large economic profits.

-It recommends that the finance profession shift focus from forecast accuracy to evaluating models based on economic metrics, such as Sharpe ratios.

Reference

[2] Kelly, Bryan T., and Malamud, Semyon and Zhou, Kangying, The Virtue of Complexity in Machine Learning Portfolios (2023). Swiss Finance Institute Research Paper No. 21-90

Closing Thoughts

So, should a trading system be simple and intuitive or complex and data-rich? In this edition, we featured research supporting both schools of thought. Perhaps both approaches have merit, depending on the context and objectives. What ultimately matters is not the simplicity or complexity of the model, but whether it has been thoroughly tested, proven robust across different market conditions, and shown to deliver consistent profitability before risking real capital.

Low-Volatility Stocks: Reducing Risk Without Sacrificing Returns

The recent market turbulence highlights the need for improved risk management and strategies to reduce portfolio volatility. In this post, I’ll explore how to enhance portfolio diversification using low-volatility stocks.

Gold and Low-Volatility Stocks as Diversifiers

Gold has long been regarded as a valuable diversification tool in investment portfolios due to its unique characteristics. As an asset class, gold has historically exhibited a low correlation with traditional financial assets such as stocks and bonds.

Reference [1] revisited the role of gold as a diversifier in a traditional stock-bond portfolio. It also proposed adding low-volatility stocks to the portfolio in order to reduce the risks without sacrificing the returns.

Findings

-The primary goal of investing is to avoid capital losses.

-Conservative investors often include gold in their portfolios to reduce downside risk. Although gold is volatile, it serves as a partial safe haven during bear markets.

-The study confirms that modest allocations to gold lower a portfolio’s loss probability, expected loss, and downside volatility.

-However, the downside protection offered by gold comes at the cost of reduced returns.

– In contrast, adding low-volatility stocks enhances a portfolio’s defensiveness without sacrificing returns.

-Low-volatility stocks are more effective than gold in mitigating losses while maintaining performance.

-Portfolios combining stocks, bonds, gold, and low-volatility stocks can be more resilient and allow for a higher equity allocation relative to bonds.

-The effectiveness of defensive multi-asset portfolios increases with a longer investment horizon.

In short, a stock-bond-gold allocation benefits significantly from incorporating low-volatility stocks, and the effectiveness of this defensive multi-asset portfolio grows with the investment horizon.

Reference

[1] van Vliet, Pim and Lohre, Harald, The Golden Rule of Investing, 2023, SSRN 4404688

Blending Low-Volatility with Momentum Anomalies

The low volatility anomaly in the stock market refers to the phenomenon where stocks with lower volatility tend to provide higher risk-adjusted returns compared to their higher volatility counterparts, contrary to traditional financial theories.

The momentum anomaly in the stock market refers to the tendency of assets that have performed well in the past to continue performing well in the future, and those that have performed poorly to continue performing poorly.

Reference [2] combined the low volatility anomaly with the momentum anomaly and examined whether the low volatility anomaly can enhance risk-adjusted returns in momentum-sorted portfolios.

Findings

-This paper analyzes the profitability of combining low-volatility and momentum strategies in the Nordic stock markets between January 1999 and September 2022.

-Both volatility and momentum strategies are found to remain effective as standalone (pure-play) approaches

-The authors evaluate three combination methods: 50/50 allocation, double screening, and ranking strategies.

-Among long-only portfolios, the momentum-first double screening strategy delivers the highest Sharpe ratio, slightly outperforming the ranking method.

-All long-only combination portfolios outperform the market in terms of risk-adjusted returns.

-Long-short combination strategies provide significantly better risk-adjusted returns compared to pure-play strategies.

-However, after adjusting returns using the Fama and French five-factor model, none of the combination long-short strategies outperform the pure momentum strategy.

In summary, the paper shows that incorporating both momentum and low volatility anomalies yields positive exposure to factors like value and profitability. Returns from these strategies are consistent over time and are more pronounced in later subsamples, with higher robust Sharpe Ratios. For long-only investors, the DS (double-sorted) strategy, which sorts stocks by momentum first and then by low volatility, seems superior to other strategies.

Reference

[2] Klaus Grobys, Veda Fatmy and Topias Rajalin, Combining low-volatility and momentum: recent evidence from the Nordic equities, Applied Economics, 2024

Closing Thoughts

In this post, we have seen how incorporating low-volatility stocks into a stock-gold portfolio can enhance risk-adjusted returns. We also discussed how to select stocks based on momentum and low-volatility criteria, highlighting the effectiveness of combining these factors through methods like double screening or ranking. While momentum tends to drive performance, especially in long-short strategies, low volatility adds defensiveness to the portfolio.

The Calendar Effects in Volatility Risk Premium

I recently covered calendar anomalies in the stock markets. Interestingly, patterns over time also appear in the volatility space. In this post, I’ll discuss the seasonality of volatility risk premium (VRP) in more detail.

Breaking Down the Volatility Risk Premium: Overnight vs. Intraday Returns

The decomposition of the volatility risk premium (VRP) into overnight and intraday components is an active area of research. Most studies indicate that the VRP serves as compensation for investors bearing overnight risks.

Reference [1] continues this line of research, with its main contribution being the decomposition of the variance risk premium into overnight and intraday components using a variance swap approach. The study also tests the predictive ability of these components and examines the seasonality (day-of-week effects) of the VRP.

An interesting finding of the paper is the day-of-week seasonality. For instance, going long volatility at the open and closing the position at the close tends to be profitable on most days, except Fridays.

Findings

-The analysis is conducted on implied variance stock indices across the US, Europe, and Asia.

-Results show that the VRP switches signs between overnight and intraday periods—negative overnight and positive intraday.

-The findings suggest that the negative VRP observed in previous studies is primarily driven by the overnight component.

-The study evaluates the predictive power of both intraday and overnight VRP in forecasting future equity returns.

-The intraday VRP component captures short-term risk and demonstrates predictive ability over 1–3-month horizons.

-The overnight VRP component reflects longer-term risk and shows predictive power over 6–12-month horizons.

Reference

[1] Papagelis, Lucas and Dotsis, George, The Variance Risk Premium Over Trading and Non-Trading Periods (2024), SSRN 4954623

Volatility Risk Premium Seasonality Across Calendar Months

Reference [2] examines the VRP in terms of months of the year. It concluded that the VRP is greatest in December and smallest in October.

An explanation for the large VRP in December is that during the holiday season, firms might refrain from releasing material information, leading to low trading volumes. The combination of low trading volume and the absence of important news releases would result in lower realized volatility.

Findings

-The paper identifies a “December effect” in option returns, where delta-hedged returns on stock and S&P 500 index options are significantly lower in December than in other months.

-This effect is attributed to investors overvaluing options at the start of December due to underestimating the typically low volatility that occurs in the second half of the month.

– The reduced volatility is linked to lighter stock trading during the Christmas holiday season.

– A trading strategy that involves shorting straddles at the beginning of December and closing the position at the end of the month yields a hedged return of 13.09%, with a t-value of 6.70.

-This return is much higher than the unconditional sample mean of 0.88%, highlighting the strength of the effect.

The paper is the first in academic literature to document and analyze this specific December anomaly in option markets. It is another important contribution to the understanding of the VRP.

Reference

[2] Wei, Jason and Choy, Siu Kai and Zhang, Huiping, December Effect in Option Returns (2025). SSRN 5121679

Closing Thoughts

In this post, I have discussed volatility patterns in terms of both days of the week and months of the year. Understanding this seasonality is crucial for traders and portfolio managers, as it can inform better timing of volatility trades and risk management strategies.

Stock-Bond Correlation: What Drives It and How to Predict It

The correlation between stocks and bonds plays a crucial role in portfolio allocation and diversification strategies. In this issue, I discuss stock-bond relationships, the factors that influence their correlation, and techniques for forecasting it.

What Influences Stock-Bond Correlation?

Correlation between stocks and bonds is crucial for portfolio allocation and diversification, but this correlation can vary over time due to factors like inflation and real returns on short-term bonds.

Reference [1] conducts a study on stock-bond correlation spanning an extended timeframe. Their findings indicate that contrary to conventional assumptions, stock-bond correlation generally tends to exhibit a positive or near-zero relationship. Exceptions, where the correlation drops below -0.2, were notably observed during the early 1930s, the late 1950s, and most of the 2000s.

Findings

-The correlation between stock and bond returns is a key component in asset allocation decisions. This correlation is not stable and can vary significantly over time, affecting how portfolios should be constructed.

– The recent market environment has shown that stock-bond correlation can turn positive, potentially impacting diversified portfolios negatively.

– The article suggests that contrary to conventional assumptions, stock-bond correlation generally tends to be positive or near-zero.

– Exceptions to positive correlation occurred during the early 1930s, late 1950s, and most of the 2000s.

– Factors such as inflation, real returns on short-term bonds, and uncertainty surrounding inflation play pivotal roles in determining the direction and strength of stock-bond correlation.

– Time variation in stock and bond volatility can also affect the impact of stock-bond correlation.

– Bond risk premia are positively correlated with estimates of the stock-bond correlation.

– The correlation between stocks and bonds can significantly fluctuate over time and across countries.

In short, the correlation between stocks and bonds can significantly fluctuate over time. Factors such as inflation and real returns on short-term bonds, along with the associated uncertainty regarding inflation, play pivotal roles in determining both the direction and strength of the stock-bond correlation.

Reference

[1] Molenaar, Roderick and Senechal, Edouard and Swinkels, Laurens and Wang, Zhenping, Empirical evidence on the stock-bond correlation (2023), SSRN 4514947

Forecasting Short-Term Stock-Bond Correlation

Reference [2] employs a country’s Correlation Outlook, Prospective Inflation Volatility, the Yield Curve Momentum Regime, and the Trailing 3-month stock-bond correlation to build a predictive model.

Findings

-This paper extends a macroeconomic framework that explains long-term changes in stock-bond correlation.

-Prior research explains around 70% of the variation in 10-year rolling stock-bond correlations using the relative volatility and correlation of growth and inflation.

-The authors shift focus to forecasting short-term (three-month) variations in stock-bond correlation.

-Their method uses indicators based on whether individual forecasters expect stock and bond markets to move in the same or opposite directions.

– This approach improves the ability to forecast stock-bond correlations over tactical, short-term horizons.

This paper complements previous work by focusing on short-term horizons, showing that detailed forecast data can help predict high-frequency changes in stock-bond correlation. It also highlights the value of granular forecast data, especially the correlation between responses, which may be missed in standard survey summaries.

Reference

[2] Flannery, Garth and Bergstresser, Daniel, A Changing Stock-Bond Correlation: Explaining Short-term Fluctuations (2023). SSRN 4672744

Closing Thoughts

As we have seen, stock-bond correlation plays a crucial role in portfolio management and asset allocation. We have discussed how this correlation shifts over time, influenced by macroeconomic factors such as inflation and growth volatility, and how it can be forecasted. Accurately anticipating these shifts enables more informed portfolio construction and risk management.