Interest Rate Sensitivity in Low-Volatility Investing

Low-volatility investing is a strategy that focuses on stocks with historically lower price fluctuations, aiming to achieve strong risk-adjusted returns. Despite conventional finance theory suggesting that higher risk should lead to higher returns, research has shown that low-volatility stocks often outperform their high-volatility counterparts on a risk-adjusted basis. By reducing drawdowns and offering a smoother return profile, low-volatility investing appeals to risk-conscious investors, particularly in uncertain market environments.

Given the appeal of low-volatility investing, there are, however, some concerns about its sensitivity to changes in interest rates, particularly its viability in a higher-yield environment. Reference [1] investigates this issue. The authors pointed out,

The results confirm that low-volatility stock deciles do indeed exhibit positive, statistically significant bond betas (that become negative for high-volatility deciles), and this exposure carries over to the most popular low-volatility indexes such as the S&P 500 Low Volatility Index and the MSCI USA Minimum Volatility Index, even after accounting for their exposures to value, quality, and investment factors. The estimated bond betas roughly correspond to a duration of a two-year Treasury bond, but—as our robustness tests show—this sensitivity does not appear to be very stable over time. It can be quite effectively mitigated by applying leverage (especially within the context of long–short strategies) or by carefully avoiding excessive industry tilts, such as overallocating to companies from the utilities or consumer staples sector.

… Even in 2022, one of the worst years on record for US Treasuries, exposure to interest rates failed to materially affect the performance of low-volatility strategies. The negative bond contribution was more than offset by high positive returns on undervalued, high-quality, and conservative stocks overrepresented in low-volatility portfolios. On a more pessimistic note, however, equity style exposures of our sample low-volatility strategies seem to account for much of their raw excess returns generated in the past 30 years, suggesting some skepticism as to how much value added these strategies can bring to an already diversified and quality-tilted portfolio.

In short, the results confirm that long-only low-volatility strategies exhibit positive, statistically significant bond betas, even after controlling for exposures to value, quality, and investment factors. However, this sensitivity is not stable over time and can be effectively mitigated through leverage or by avoiding excessive industry concentrations.

This article sheds new light and provides insights into low-volatility investing. Let us know what you think in the comments below or in the discussion forum.

References

[1] Juliusz Jabłecki, Low-Volatility Equity Strategies and Interest Rates: A Bittersweet Perspective, The Journal of Beta Investment Strategies, Volume 16, Issue 1 Spring 2025

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Variational Autoencoders for Arbitrage-Free Volatility Modeling

Machine learning and AI are transforming investing by enabling data-driven decision-making, uncovering hidden patterns, and automating complex strategies. From algorithmic trading and portfolio optimization to risk management and sentiment analysis, AI-driven models process vast amounts of data with speed and precision, identifying opportunities that traditional methods might miss.

Most ML and AI approaches have been applied to building predictive models. Reference [1], however, suggests using ML techniques in risk management. Specifically, it explores the use of Variational Autoencoders for generating synthetic volatility surfaces for stress testing and scenario analysis.

The paper develops a robust synthetic data generation framework using parameterized Heston models. It implements comprehensive arbitrage validation, ensuring critical no-arbitrage conditions, including calendar spread and butterfly arbitrage constraints, are preserved. The authors pointed out,

First, we have demonstrated that synthetic data generation using carefully parameterized Heston models can effectively overcome the traditional barriers of limited market data in illiquid markets. By generating over 13,500 synthetic surfaces—compared to the typical constraint of fewer than 100 market-observable surfaces, we have significantly enhanced the robustness and reliability of our VAE training process. Our methodology succeeds in preserving critical no-arbitrage conditions, specifically, both calendar spread and butterfly arbitrage constraints validate its practical applicability in real-world trading environments. .. A key innovation of our approach is expanding the idea of latent space optimization which was alluded to by Bergeron et al [2] and its independence from historical market data for training purposes. This characteristic makes our framework particularly valuable for emerging markets, newly introduced derivatives, and other scenarios where historical data is scarce or non-existent. The ability to generate realistic, arbitrage-free synthetic surfaces provides practitioners with a powerful tool for price simulation and risk assessment in illiquid markets...The successful reconstruction of surfaces with significant missing data points (demonstrated through our test case with 100 randomly removed points) showcases the model’s robustness and practical utility. Extending the framework to examine the model’s performance under various market stress scenarios could constitute further research directions.

This is a significant contribution to the advancement of ML and AI in finance, particularly in risk management—an area with much yet to be explored.

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

References

[1] Nteumagne,  B. F.; Donfack,  H. A.; Wafo Soh,  C. Variational Autoencoders for Completing the Volatility Surfaces. Preprints 2025, 2025021482. https://ift.tt/BxHoiVu

Originally Published Here: Variational Autoencoders for Arbitrage-Free Volatility Modeling

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Improving Portfolio Management with Volatility of Volatility

Managing portfolios using volatility as a filter has proven effective. Reference [1] builds on this research by proposing the use of volatility of volatility for portfolio management. The rationale behind using volatility of volatility is that it represents uncertainty.

Unlike risk, which refers to situations where future returns are unknown but follow a known distribution, uncertainty means that both the outcome and the distribution are unknown. Stocks may exhibit uncertainty when volatility or other return distribution characteristics vary unpredictably over time.

Practically, the author used a stock’s daily high and low prices to derive its volatility of volatility. They pointed out,

Specifically, we hypothesise that the benefits of volatility management are more pronounced for low uncertainty stocks and during periods of low aggregate uncertainty. To test these hypotheses, we use a measure of uncertainty based on the realised volatility-of-volatility (vol-of-vol) derived from intraday high and low prices. We first examine the relation between this measure of uncertainty and future returns. Consistent with the extant literature, we find that uncertainty is positively related to returns, and that it contains unique information about future returns not captured by other stock characteristics. We then explore the role of uncertainty in the performance of volatility management, across individual stocks and over time. We show that volatility management yields a significantly larger improvement in risk-adjusted performance for stocks with low uncertainty compared to those with high uncertainty and, for the market portfolio, it yields better performance during periods of low aggregate uncertainty compared to periods of high uncertainty. We also show that uncertainty potentially explains the performance of volatility management when applied to different asset pricing factor portfolios. Furthermore, our findings complement the sentiment-driven explanation of Barroso and Detzel (2021), revealing that the effect of sentiment on volatility management crucially depends on the level of uncertainty.

In short, using the volatility of volatility as a filter proves to be effective, particularly for low-uncertainty stocks.

We find it insightful that the author distinguishes between risk and uncertainty and utilizes the volatility of volatility to represent uncertainty.

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

References

[1] Harris, Richard D. F. and Li, Nan and Taylor, Nicholas, The Impact of Uncertainty on Volatility-Managed Investment Strategies (2024). https://ift.tt/rVJf7iS

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Incorporating Liquidity into Option Pricing: a Stochastic Approach

Liquidity is an overlooked research area, yet it plays a crucial role in financial markets. Trading system developers often use the bid-ask spread as a proxy for liquidity, but this approach is less effective in the options market.

Reference [1] proposes a method for integrating liquidity into the option pricing model. Essentially, it introduces market liquidity as a variable that can change randomly and affects stock prices through a discounting factor and market liquidity levels.

The paper begins by incorporating a stochastic liquidity variable into the SDE for stock price under the P measure. Here the liquidity process is modeled as an Ornstein-Uhlenbeck process. The SDE is then transformed into the Q measure in which European options are analytically evaluated using the derived closed-form characteristic function. The authors pointed out,

We incorporate three main factors, that is, stochastic volatility, economic cycles, and liquidity risks, into one model used for option pricing. A combination of Heston stochastic volatility and regime switching is selected for modeling the price of the underlying stock when there are no liquidity risks. The stock price is then discounted based on the level of market liquidity levels described by a mean reverting stochastic process. The employment of regime switching Esscher transform provides a risk‐neutral measure as well as the corresponding model dynamics, yielding a European option pricing formula in closed form. Significant impacts of the three factors can be seen through the performed numerical experiments. Our analysis with real data also confirm the necessity to consider stochastic liquidity, which has greatly improved model performance. By leveraging the stochastic liquidity component, our proposed model can help investors refine their hedging positions, better responding to liquidity shocks, and thus mitigate risks more effectively.

In short, liquidity is integrated as a discount factor, and the study demonstrates its impact on option prices.

This research provides a framework for incorporating liquidity into options trading, however, we found it less intuitive. Let us know what you think in the comments below or in the discussion forum.

References

[1] Xin-Jiang He, Hang Chen, Sha Lin, A Closed-Form Formula for Pricing European Options With Stochastic Volatility, Regime Switching, and Stochastic Market Liquidity, Journal of Futures Markets, 2025; 1–12

Originally Published Here: Incorporating Liquidity into Option Pricing: a Stochastic Approach

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Stock and Volatility Simulation: A Comparative Study of Stochastic Models

Stress testing and scenario analysis are essential tools in portfolio management, helping portfolio and risk managers assess potential vulnerabilities under extreme market conditions. By simulating adverse scenarios such as financial crises, interest rate shocks, or geopolitical events, these techniques provide insights into how a portfolio might behave under stress and identify potential weaknesses.

Reference [1] investigates several stochastic models for simulating stock and volatility paths that can be used in stress testing and scenario analysis. It also proposes a method for evaluating these stochastic models. The models studied include

• Geometric Brownian Motion (GBM),
• Generalized Autoregressive Conditional Heteroskedasticity (GARCH),
• Heston stochastic volatility,
• Stochastic Volatility with Jumps (SVJD), and a novel
• Multi-Scale Volatility with Jumps (MSVJ).

The authors pointed out,

When the objective is to evaluate and simulate scenarios that reflect market crashes, both short-term events and long-term crises, models such as GBM and the Heston model have been shown to be more effective. These models are better equipped to capture the sudden and severe price movements associated with market crashes, as demonstrated by their performance in reproducing historical drawdowns and their ability to capture tail risk…

If the objective is to generate future scenario simulations for option pricing, the MSVJ model has proven to be the most suitable choice. The MSVJ model’s superior performance in capturing the range of the actual TQQQ price, as evidenced by its highest WMCR for both price and volatility, makes it particularly valuable for option pricing…

When the primary goal is to simulate the most realistic price path and volatility paths for TQQQ, the SVJD model has demonstrated superior performance. By capturing both stochastic volatility and jump processes, the SVJD model can generate price and volatility trajectories that closely resemble the observed dynamics of TQQQ. Portfolio managers can utilize this model for more accurate backtesting of trading strategies and better assessment of portfolio risk under various market conditions.

In short, each model has its strengths and weaknesses and serves a particular purpose.

This study is an important contribution to the advancement of portfolio risk management. Let us know what you think in the comments below or in the discussion forum.

References

[1]  Kartikay Goyle, Comparative analysis of stochastic models for simulating leveraged ETF price paths, Journal of Mathematics and Modeling in Finance (JMMF) Vol. 5, No. 1, Winter & Spring 2025

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Are Weekend Gaps Always Filled? A Look at Stock Indices

The weekend price gap is a well-known phenomenon in financial markets, particularly in assets that trade continuously during the week but pause over the weekend, such as stocks, futures, and options. When markets reopen after the weekend, prices sometimes experience a gap up or down due to news, geopolitical events, or macroeconomic developments that occurred while trading was halted. For investors, weekend gaps present both risks and opportunities.

The prevailing belief among traders is that gaps are usually filled. Reference [1] examines this assumption, specifically studying weekend gap dynamics in the DJIA, NASDAQ  100, and the DAX. The authors pointed out,

While our findings do not support a universal tendency for markets to revert to the prior closing price at short distances, they reveal that more pronounced movements at larger thresholds may indicate a partial gap-filling mechanism…Although our descriptive statistics and Chi-square tests show minimal evidence of a predictable “fill-the-gap” bias within ranges closer to the Monday open, there is suggestive evidence for directional price movements further away from the gap, reflecting possible longer-horizon effects…

Our regression and correlation analyses reveal that larger gaps typically coincide with higher short-term volatility, reinforcing the argument that weekend price discontinuities signal an increased uncertainty or risk (Hull & Basu, 2016; Mandelbrot, 1972; Plastun et al., 2020). This effect is particularly pronounced for the DJIA and NASDAQ, where an expanded gap size correlates with a greater likelihood of hitting the Take Profit and Stop Loss thresholds alike…Meanwhile, the DAX, though hinting at a moderate positive association between gap size and Take Profit rates, presents less robust evidence—highlighting how regional factors, sectoral composition, or liquidity conditions may temper volatility responses to weekend gaps.

In short, small to medium-sized gaps are not necessarily filled; rather, they are indicative of increased volatility. Larger gaps, however, exhibit some directional predictability and can be used to design trading strategies. Additionally, European market dynamics differ from those of the U.S.

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

References

[1] Marnus Janse van Rensburg, and Terence Van Zyl, Price Gaps and Volatility: Do Weekend Gaps Tend to Close?, J. Risk Financial Manag. 2025, 18, 132

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How Bitcoin Options Compare to Equity Index Options: Volatility, Correlation, and Skew

Bitcoin options are derivative contracts that grant investors the right, but not the obligation, to buy or sell Bitcoin at a predetermined price before a specified expiration date. Major cryptocurrency exchanges offer options on Bitcoin and other cryptocurrencies, including select tokens. However, the vast majority of trading takes place on the Deribit options exchange, which alone accounts for over 90% of Bitcoin options trading volume.

With the growing popularity of Bitcoin options, an important question arises: how do Bitcoin options' volatility dynamics behave?

Reference [1] explores this issue. The study first highlights a key difference between Bitcoin and equity markets: in traditional stock markets, volatility tends to decline when stock indices rise. In contrast, cryptocurrency volatility can increase regardless of whether prices are moving up or down. This characteristic is reflected in the dynamics of Bitcoin’s volatility surface.

The article further compares the equity index and Bitcoin options.

• In equity markets, the correlation between an index's price and its implied volatility is typically large and negative. However, for Bitcoin, this correlation appears to be regime-dependent. From August 2019 to November 2020, the correlation between Bitcoin’s price and its 30-day ATM implied volatility was approximately -0.42. During the following five months, it rose sharply to 0.74, and between July and November 2022, the correlation was nearly neutral at 0.08.
• In traditional equity markets, the pronounced and nearly linear skew of the implied volatility curve means that the options that increase the most in price following a market downturn are those with the lowest moneyness. By contrast, Bitcoin’s implied volatility curve was relatively symmetric before the crash on March 12, 2020. At that time, ATM options had the lowest volatility, around 50%, while both OTM puts and calls had roughly equal but higher volatilities of approximately 75% for moneyness levels of 0.7 and 1.3.
• However, a clear asymmetry in the volatility smile emerged after the crash, as risk-averse investors sought protection against another significant price drop. The implied volatility of 30-day deep OTM puts surged to nearly 200%. For the first time, Bitcoin exhibited a pronounced negative skew, though the skew remained flatter than what is typically observed in equity index options.

Despite these differences, Bitcoin's implied volatility dynamics do share some similarities with equity index options.

• First, volatilities at different moneyness levels tend to move in tandem with ATM volatility of the same maturity, showing a high degree of correlation.
• Second, Bitcoin’s implied volatility term structure exhibits cycles of backwardation during high-volatility periods and contango during relatively calm market conditions. Bitcoin’s implied volatilities tend to move in sync, with minimal dispersion, throughout most backwardation periods, similar to equity index volatility term structures.

This article provides valuable insights for investors, portfolio managers, and market makers in the Bitcoin options market, offering a deeper understanding of its volatility patterns and risk dynamics.

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

References

[1] Alexander, C., & Imeraj, A. (2023). Delta hedging bitcoin options with a smile. Quantitative Finance, 23(5), 799–817.

Originally Published Here: How Bitcoin Options Compare to Equity Index Options: Volatility, Correlation, and Skew

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Forecasting Covered Call ETF Performance

A covered call ETF is an exchange-traded fund that employs a covered call strategy to generate income while maintaining exposure to the underlying assets. This strategy involves holding a portfolio of stocks and selling (or "writing") call options on those stocks to collect option premiums. Covered call ETFs are particularly popular among income-seeking investors, as the premiums collected provide an additional source of returns, potentially enhancing yield.

The growing popularity of covered call ETFs not only attracts investor capital but also draws attention from academics. Reference [1] studied predictive models for forecasting the performance of covered call ETFs. Specifically, the authors utilized traditional time series methods, advanced ML techniques, and Deep Learning models. They pointed out,

This study builds on the existing financial literature to comprehensively assess forecasting models for covered call ETFs, offering a comparative analysis of time series, machine learning, and deep learning techniques.

The findings from the study indicate that, for the traditional time series models, the ARIMA model outperforms the HAR model for tickers QYLD and JEPQ, while the HAR model outperforms the ARIMA model with tickers XYLD, JEPI and RYLD. For the ML models, The RF model consistently outperforms the SVR model for all tickers except for JEPQ, where the SVR slightly outperforms the RF model. Similarly, the RF model consistently shows a better fit compared to the SVR model. For the DL models, The RNN model consistently outperforms the CNN model for all the covered call ETFs; however, the CNN model displays a superior fit. Similarly, the RNN model consistently outperforms all the time–series and ML models in the study, making it the most effective at predicting the prices of covered call ETFs.

In short, the results indicate that Deep Learning models are effective at identifying the nonlinear patterns and temporal dependencies in the price movements of covered call ETFs, outperforming both traditional time series and ML techniques.

We find this result interesting, as the returns of these covered call ETFs have the volatility risk premium embedded in them, yet these techniques are still capable of predicting these more sophisticated instruments.

We are closely following research that explores how covered call ETFs are changing market dynamics.

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

References

[1] Chigozie Andy Ngwaba, Forecasting Covered Call Exchange-Traded Funds (ETFs) Using Time Series, Machine Learning, and Deep Learning Models, J. Risk Financial Manag. 2025, 18, 120

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Applying Prospect Theory to Crypto Valuation and Portfolio Diversification

As cryptocurrencies become mainstream and gain acceptance, there is still no coherent investment framework for valuing them. Reference [1] explores the differences between equity and crypto investors and proposes an investment framework for cryptocurrencies based on the prospect theory.

The differences between equity and crypto investors are:

• Stock market investors typically rely on fundamental analysis, examining financial statements, market position, and industry trends to make informed decisions. In contrast, cryptocurrency investors often prioritize technological innovation and potential rapid appreciation, leading to greater volatility and asymmetry in returns compared to equities.
• Stock markets have a longer history and stricter regulations, resulting in more stable investor behavior. Meanwhile, the relatively new and less regulated cryptocurrency market experiences extreme volatility and speculative trading.
• Stock investors tend to have a long-term horizon, seeking steady returns and dividends, whereas cryptocurrency investors are often more focused on short-term gains, driven by high volatility. As a result, cryptocurrency markets exhibit more irrational investor behavior.

The paper then develops an investment framework built on a utility function, where crypto investors remain risk-averse when anticipating gains. However, investor risk attitudes shift during losses; they become risk-seeking in pursuit of recovery. The authors pointed out,

The results in Fig. 2 show the superior ability of our trading strategies to earn abnormal returns. From 2014, each $1 invested in the medium-PL, low-LV portfolio accelerates to $892 at the end of 2022, which is more than four times as in the Fama-French portfolio. While each $1 invested in the low-PL, high-LV portfolio accelerates to $789 at the end of 2022, which is more than three times as in the Fama-French portfolio. The comparison with the S&P 500 index generates similar results; the values of our PL and LV based strategies are much higher than that of the S&P 500.

Similarly, Table 8 shows the average returns, standard deviations, and Sharpe ratios of the portfolios. The medium-PL, low-portfolio and low-PL, high-LV portfolio generate the larger Sharpe ratios (0.411 and 0.396) than those of the equity portfolios, token portfolio, and market benchmarks. The results demonstrate that our trading strategy based on PL and LV with token can also earn superior risk-adjusted returns.

In short, constructing a portfolio that includes both equities and cryptocurrencies using the prospect theory framework results in superior risk-adjusted returns, demonstrating that cryptocurrencies add value to an equity portfolio.

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

References

[1] Zhan Wang, Xiang Gao, Jiahao Gu, Can cryptocurrencies improve portfolio diversification? Evidence from the prospect risk perspective, Research in International Business and Finance, Volume 76, April 2025, 102828

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Measuring Stock Market Dispersion: The Herd Behavior Index Approach

Dispersion in the stock market refers to the degree of variation in individual stock returns within an index or sector. High dispersion indicates significant differences in performance among stocks. Conversely, low dispersion suggests that stocks are moving more uniformly, often driven by broad market trends.

Usually, dispersion is measured by implied correlation. Reference [1] proposed a method to measure dispersion called the Herd Behavior Index (HIX). It is calculated as the ratio of the variance of a stock index to the variance of a hypothetical index that represents the extreme case of comonotonicity or perfect herd behavior. The variance is determined using model-free methods involving options, similar to the calculation of the VIX. The authors pointed out,

In this paper we made a modest contribution to this complicated matter by proposing a measure for the degree of co-movement or herd behavior present in equity markets. This measure compares the currently observed market situation with the comonotonic situation under which the whole system is driven by a single factor. More precisely, it compares an estimate of the variance of the market index with an estimate of the corresponding worst-case or comonotonic variance. In line with the VIX methodology, the estimate for the variance of the market index is based on the full spectrum of current option information on the index. Although the worst-case market situation is not observed, the comonotonic variance can easily be determined from the option prices on the constituents of the market index.

In short, the authors developed the Herd Behavior Index to measure stock market dispersion. They also explained how it differs from the implied correlation index,

Measuring the degree of co-movement with the HIX/CIX has several advantages compared to implied correlation. The HIX/CIX is able to capture all kinds of dependences between stock prices, whereas the implied correlation is a weighted average of pairwise correlations amongst the asset returns and hence, only focuses on linear dependences. Furthermore, making abstraction of the approximations involved in its calculation, the HIX reaches its maximal value of 1 if and only if the underlying random variables are comonotonic. On the other hand, there is no direct link between the degree of herd behavior and the value of the implied correlation.

This is an innovative proposal, but its practical application and effectiveness remain to be seen. One can apply it, for example, to option dispersion trading. A high HIX value suggests buying individual options and selling index options. The position can then be closed when the market stabilizes and the HIX decreases. Further research is needed to assess the profitability of this strategy and the effectiveness of the Herd Behavior Index in general.

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

References

[1] Jan Dhaene, Daniël Lindersy, Wim Schoutensz, David Vyncke, The Herd Behavior Index: A new measure for the implied degree of co-movement in stock markets, Insurance: Mathematics and Economics Volume 50, Issue 3, May 2012, Pages 357-370

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