Month: September 2025

Volatility Risk Premium Across Different Asset Classes

The volatility risk premium has been studied extensively in the equity space, but less so in other asset classes. In this post, we are going to examine the VRP across different asset classes.

Volatility Risk Premium Across Different Asset Classes

The volatility risk premium (VRP) is the compensation investors receive for bearing the risk associated with fluctuations in market volatility, typically measured as the difference between implied and realized volatility. The VRP in equities has been studied extensively. However, relatively little attention has been paid to the VRP in other asset classes.

Reference [1] examined the VRP in different asset classes. It specifically studied the VRP in 18 different underlyings belonging to the commodity, fixed-income, and equity asset classes.

Findings

-The paper analyzes the use of the volatility risk premium (VRP) for volatility forecasting across 18 distinct markets in two time periods.

-The study introduces RIV models, which adjust current implied volatility for the VRP, and finds that these models produce significantly more accurate forecasts compared to other approaches.

-Multiple methodologies for deriving RIV models are examined, with their strengths and limitations evaluated.

-The findings are consistent across most of the assets analyzed and are supported by various loss functions and statistical tests, reinforcing their robustness.

-The newly introduced RIV models outperform implied volatility (IV) and GARCH-based forecasts in predictive accuracy.

-The study finds that the VRP is generally positive across most markets.

-A link is identified between the magnitude of VRP and the trading volume of underlying futures, with higher volumes associated with positive VRP.

-Negative VRP is observed in a few low-volume markets, suggesting that insufficient depth in these markets prevents efficient option pricing.

In short, the VRP is positive in most markets and is positively correlated with trading volume. Additionally, the VRP can be used to predict future realized volatility.

This is an interesting look at the VRP in different markets. We note, however, that just because the VRP is positive in a given market, it does not necessarily mean that P&L can be easily extracted without taking on too much risk. To earn a respectable risk-adjusted return in a given market, a sophisticated system must be developed.

Reference

[1] Štěpán Havel, Volatility Risk Premium Across Multiple Asset Classes, Charles University, 2024

Illiquidity Premium in the Bitcoin Options Market

The previous article explored the VRP across asset classes, primarily commodities. Reference [2] examines the illiquidity risk premium in the crypto market, which is indirectly related to the VRP. Specifically, it studies the role of liquidity risks in the returns of bitcoin options.

In the bitcoin options market, market makers face significant challenges in hedging inventory risk due to price jump risks and lower liquidity. As a result, they charge a higher risk premium.

Findings

-The paper examines the economic drivers of illiquidity in cryptocurrency options markets and their impact on option returns.

-It uses transaction-level data for Bitcoin (BTC) options on Deribit from January 2020 to July 2024 to compute intraday measures of option illiquidity.

-The results show that when market makers hold net-long positions, they demand a positive illiquidity premium to offset hedging and rebalancing costs.

-A one standard deviation increase in option illiquidity raises daily delta-hedged returns by about 0.07% for calls and 0.06% for puts.

-A factor model based on latent instruments derived from option characteristics confirms that illiquidity is a distinct pricing factor in the cross-section of option returns.

-The Bitcoin options market remains illiquid, with this structure leading to a significant illiquidity premium where higher illiquidity predicts higher subsequent returns.

-Investors on average tend to sell options, though the net sell imbalance has declined with increased participation from small retail investors.

-Both panel OLS and IPCA factor models show a robust and positive relationship between illiquidity and expected option returns, consistent across different proxies and model specifications.

-The illiquidity premium compensates market makers for risks and costs associated with delta-hedging, rebalancing, and inventory management.

-Regression analyses indicate that relative spreads are driven by hedging costs, inventory costs, and asymmetric information, and remain an important determinant of expected returns, especially for options with negative order imbalances.

In short, Bitcoin options market makers and active traders earn excess returns, partly driven by the illiquidity premium.

Reference

[2] C Atanasova, T Miao, I Segarra, TT Sha, F Willeboordse, Illiquidity Premium and Crypto Option Returns, Working paper, 2024

Closing Thoughts

Together, these studies expand the understanding of risk premia beyond traditional equity markets. While the first paper demonstrates the existence of the VRP across asset classes, the second highlights the presence of an illiquidity risk premium in cryptocurrency options, reflecting unique market frictions. For traders and researchers alike, the results underscore the importance of adapting models and expectations to the characteristics of each market.

When Trading Systems Break Down: Causes of Decay and Stop Criteria

A key challenge in system development is that trading performance often deteriorates after going live. In this post, we look at why this happens by examining the post-publication decay of stock anomalies, and we address a practical question faced by every trader: when a system is losing money, is it simply in a drawdown or has it stopped working altogether?

Why and How Systematic Trading Strategies Decay After Going Live

Testing and validating a trading strategy is an important step in trading system development. It’s a commonly known fact that a well-optimized trading strategy’s performance often deteriorates after it goes live. Thus, developing a robust strategy that performs well out-of-sample is quite a challenge.

Reference [1] attempts to answer the question: why a strategy’s performance decays after going live.

Findings

-The paper investigates which ex-ante characteristics can predict the out-of-sample decline in risk-adjusted performance of published stock anomalies.

-The analysis covers a broad cross-section of anomalies documented in finance and academic journals, with the post-publication period defined as out-of-sample.

-Predictors of performance decay are based on two hypotheses: (1) arbitrage capital flowing into newly published strategies, and (2) in-sample overfitting due to multiple hypothesis testing.

-Publication year alone accounts for 30% of the variance in Sharpe ratio decay, with Sharpe decay increasing by 5 percentage points annually for newly published factors.

-Three overfitting-related variables—signal complexity (measured by the number of operations required) and two measures of in-sample sensitivity to outliers—add another 15% of explanatory power.

-Arbitrage-related variables are statistically significant but contribute little additional predictive power.

-The study tests both hypotheses using explanatory variables and univariate regressions, finding significant coefficients from both sets.

In short, the results indicate that performance decay is driven jointly by overfitting and arbitrage effects.

Reference

[1] Falck, Antoine Rej, Adam and Thesmar, David, Why and How Systematic Strategies Decay, SSRN 3845928

When to Stop Trading a Strategy?

When a trading system is losing money, an important question one should ask is: Are we in a drawdown, or has the system stopped working? The distinction is crucial because the two situations require different solutions. If we are in a drawdown, it means that our system is still working and we just have to ride out the losing streak. On the other hand, if our system has stopped working, we need to take action and find a new system.

Reference [2] attempted to answer this question.

Findings

-The paper examines how to distinguish between normal unlucky streaks and genuine degradation in trading strategies.

-It argues that excessively long or deep drawdowns should trigger a downward revision of the strategy’s assumed Sharpe ratio.

-A quantitative framework is developed using exact probability distributions for the length and depth of the last drawdown in upward-drifting Brownian motions.

-The analysis shows that both managers and investors systematically underestimate the expected length and depth of drawdowns implied by a given Sharpe ratio.

I found that the authors have some good points. But I don’t think that the assumption that the log P&L of a strategy follows a drifted Brownian process is realistic.

Note that a trading strategy’s P&L can often exhibit serial correlation. This is in contradiction with the assumption above.

Reference

[2] Adam Rej, Philip Seager, Jean-Philippe Bouchaud, You are in a drawdown. When should you start worrying? arxiv.org/abs/1707.01457v2

Closing Thoughts

Both papers address the critical issue of strategy persistence and performance decay, though from different perspectives. The first highlights how published anomalies tend to lose risk-adjusted returns over time, with evidence pointing to both overfitting in backtests and arbitrage capital crowding as drivers of performance decay. The second provides a quantitative framework for assessing when drawdowns signal genuine deterioration rather than normal variance, showing that investors often underestimate the length and depth of drawdowns implied by a given Sharpe ratio. Taken together, these studies underscore the need for investors to treat historical performance with caution, monitor strategies rigorously, and account for both statistical fragility and realistic drawdown expectations in portfolio management.

Volatility Targeting Across Asset Pricing Factors and Industry Portfolios

Position sizing is an important aspect of portfolio management, as it directly influences both risk and return. While investors can choose from a number of position sizing techniques, one approach that has gained traction is volatility targeting. In this post, I explore how volatility targeting can be applied to manage portfolio exposure and improve risk-adjusted returns.

Volatility Timing in Portfolio Management

Volatility of an asset is the measure of how much its price changes over time. The higher the volatility, the greater the price swings.  Volatility is important because it can have a big impact on the value of your investments. For example, if you’re holding an asset that has high volatility, the value of your investment will be more volatile as well.

Reference [1] proposed a volatility timing technique to manage an investment portfolio.

Findings

-The study shows that volatility-managed portfolios generate large alphas, higher factor Sharpe ratios, and significant utility gains for mean-variance investors.

-Evidence is provided across equity factors (market, value, momentum, profitability, return on equity, and investment) as well as the currency carry trade.

-Volatility timing enhances Sharpe ratios because factor volatilities change more than expected returns, creating inefficiencies to exploit.

-The strategy runs contrary to conventional wisdom: it reduces risk in recessions and crises but still delivers high average returns.

-These findings challenge traditional risk-based explanations and structural models of time-varying expected returns.

-Volatility-managed portfolios are straightforward to implement in real time and provide consistently high risk-adjusted returns.

-Because volatility does not strongly predict future returns, reducing exposure when volatility is high and increasing it when volatility is low improves performance.

-Utility gains from volatility timing for mean-variance investors are estimated at around 65%, which far exceeds the gains from timing expected returns.

-The strategy also sheds light on the dynamics of effective risk aversion, which is central to theories of time-varying risk premia.

In short, the authors advocated lowering risk exposure when volatility is high and increasing risk exposure when volatility is low. The technique relies on the idea that volatility is autocorrelated but only weakly correlated with future returns. It has been widely adopted by industry practitioners.

Reference

[1] Moreira, Alan and Muir, Tyler, Volatility-Managed Portfolios, Journal of Finance, 72(4), 1611–1644

Applying Volatility Management Across Industries

Based on the previous paper, Reference [2] continues this line of research by applying volatility-managed techniques to U.S. industry portfolios. It uses four measures of volatility: one-month realized variance, one-month realized volatility, six-month exponentially weighted moving average (EWMA) of realized volatility, and GARCH-forecasted one-month volatility.

Findings

-Four volatility-management techniques are tested: one-month realized variance, one-month realized volatility, six-month EWMA volatility, and GARCH-forecasted one-month volatility.

-Volatility-managed portfolios show statistically and economically significant improvements in Sharpe and Sortino ratios compared to unmanaged portfolios.

-The EWMA-based strategy is the most robust after accounting for transaction costs and leverage constraints.

-Technology, telecom, and utilities benefit the most, with Sharpe ratio improvements of 27.6%, 30.5%, and 25.5%, respectively.

-Results show that volatility management is practical and enhances investor welfare for both mean-variance and benchmark-aware investors.

-The technology sector emerges as the most favorable for implementing volatility-management strategies due to consistent performance gains.

-Strategy effectiveness varies across subperiods, with negative skewness and kurtosis disrupting traditional volatility patterns.

-Statistical significance weakens during recessionary periods, suggesting caution when applying strategies in stressed market environments.

In short, the article concluded that,

-Volatility management using a six-month EWMA volatility measure is the most consistent,

-The strategy improves Sharpe ratios in the technology, telecom, and utilities sectors, though not all sectors benefit equally. Technology performs best due to the persistence of its volatility,

-The statistical significance of volatility-managed strategies weakens when tested over selected subperiods and recessionary periods.

Reference

[2] Ryan Enney, Sector-Specific Volatility Management: Evidence from U.S. Equity Industry Portfolios, Claremont McKenna College, 2025

Closing Thoughts

These two studies highlight the effectiveness of volatility management across both factor-based and industry-specific portfolios. Evidence shows that scaling risk exposure inversely with volatility can significantly enhance Sharpe ratios, utility gains, and investor welfare. While factor-level strategies demonstrate robustness across market regimes, sector-level analysis points to particularly strong improvements in technology, telecom, and utilities. Collectively, the findings confirm that volatility management is not only theoretically sound but also practically implementable, offering investors a disciplined framework to improve risk-adjusted returns across diverse applications.

Tail Risk Hedging Using Option Signals and Bond ETFs

Tail risk hedging plays a critical role in portfolio management. I discussed this topic in a previous article. In this post, I continue the discussion by presenting different techniques for managing tail risks.

Hedging with Puts: Do Volatility and Skew Signals Work?

Portfolio hedging remains a complex and challenging task. A straightforward method to hedge an equity portfolio is to buy put options. However, this approach comes at a cost—the option premiums—leading to performance drag. As a result, many research studies are focused on designing effective hedging strategies that offer protection while minimizing costs.

Reference [1] presents the latest research in this area. It examines hedging schemes for equity portfolios using several signals, including MOM (momentum), TREND, HVOL (historical volatility), IVOL (implied volatility), and SKEW. The study also introduces a more refined rehedging strategy for put options:

-If, during the investment period, a put option’s delta falls to −0.9 or lower, the option is sold to lock in profits and avoid losing them in case of a sudden price reversal.

-Put options are bought when implied volatility is below 10%, as they are considered cheap. No position is taken if implied volatility is above 30%, to avoid overpaying for expensive options.

Findings

-The study investigates how option strategies can be integrated into equity portfolios to improve performance under risk constraints. It highlights weaknesses in traditional equity and fixed-income diversification for institutional investors.

-The research tests backward-looking signals from equity markets and forward-looking signals from options markets in covered call and protective put strategies.

-The TREND signal is found to be the most valuable, reducing portfolio risk without reducing returns compared to equity-only portfolios.

-The SKEW signal has a positive impact on GMV allocation but is less effective under EW allocation.

-Adding extra trading rules (TR1, TR2) does not enhance performance and is often negative.

-Backtests of long-put strategies confirm that the TREND signal offers the best balance between downside protection and performance preservation.

-Bootstrapped results diverge from backtests, showing that HVOL and IVOL signals outperform the BASE portfolio in risk-adjusted terms.

-The differences between bootstrap and backtest results suggest that the effectiveness of signals depends on the prevailing market regime.

In short, buying put options using the TREND signal appears to improve portfolio risk-adjusted returns. While SKEW and IVOL add little in backtests, they perform better in bootstrapped results, suggesting that the effectiveness of put protection strategies is regime-dependent.

This study offers a comprehensive evaluation of various hedging rules. There is no conclusive answer yet, implying that designing an efficient hedging strategy is complex and requires ongoing effort. Still, the article is a strong step in the right direction.

Reference

[1] Sylvestre Blanc, Emmanuel Fragnière, Francesc Naya, and Nils S. Tuchschmid, Option Strategies and Market Signals: Do They Add Value to Equity Portfolios?, FinTech 2025, 4(2), 25

Tail Risk Hedging with Corporate Bond ETFs

Reference [2] proposed a tail risk hedging scheme by shorting corporate bonds. Specifically, it constructed three signals—Momentum, Liquidity, and Credit—that can be used in combination to signal entries and exits into short high-yield ETF positions to hedge a bond portfolio.

Findings

-Investment Grade (IG) bonds in the US typically trade at modest spreads over Treasuries, reflecting corporate default risk.

-During market crises, IG spreads widen and liquidity decreases due to rising credit risk and forced selling by asset holders such as mutual funds.

-This non-linear widening of spreads during drawdowns is referred to as downside convexity, which can be captured through short positions in IG ETFs.

-The study develops three signals—Momentum, Liquidity, and Credit—to time entry and exit for short IG positions as a dynamic hedge.

-The dynamic hedge effectively protects high-carry bond funds like PIMIX and avoids drawdowns for funds such as DODIX, even after considering trading and funding costs.

-Each signal captures different aspects of the IG bond market, and their combination provides the strongest results, improving the Sortino ratio by at least 0.7.

-The hedge model performs consistently well across a broad range of tested parameters, showing robustness.

-Shorting IG (LQD) and HY (HYG) ETFs is found to be more cost-effective than shorting individual IG bonds, due to liquidity and low bid-ask spreads.

-IG and HY CDXs, despite larger volumes, lack the downside convexity of ETFs and are less effective for hedging.

Overall, ETF-based hedging delivers both cost efficiency and strong downside protection, making it a practical approach for institutional investors.

An interesting insight from this paper is that it points out how using corporate ETFs benefits from downside convexity, while using credit default swaps, such as IG CDXs, does not.

Reference

[2] Travis Cable, Amir Mani, Wei Qi, Georgios Sotiropoulos and Yiyuan Xiong, On the Efficacy of Shorting Corporate Bonds as a Tail Risk Hedging Solution, arXiv:2504.06289

Closing Thoughts

Both studies highlight the importance of adapting traditional portfolio strategies by incorporating alternative approaches to better manage risk and improve performance. The first paper shows how option-based overlays, particularly when guided by signals such as trend, can enhance equity portfolios by providing downside protection without materially reducing returns. The second paper demonstrates that credit and liquidity risks in investment-grade bonds can be more effectively managed through dynamic hedging with liquid bond ETFs. Together, these findings underscore that integrating derivative-based strategies offers investors practical tools to navigate market volatility, reduce drawdowns, and achieve more resilient portfolio outcomes.

Stochastic Volatility Models for Capturing ETF Dynamics and Option Term Structures

The standard Black-Scholes-Merton model is valuable in both theory and practice. However, in certain situations, more advanced models are preferable. In this post, I explore stochastic volatility models.

Stock and Volatility Simulation: A Comparative Study of Stochastic Models

Stochastic volatility models, unlike constant volatility models, which assume a fixed level of volatility, allow volatility to change. By incorporating factors like mean reversion and volatility of volatility, stochastic volatility models offer a robust framework for pricing derivatives, managing risks, and improving investment strategies.

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).

Findings

-The paper compares several stochastic models for simulating leveraged ETF (LETF) price paths, using TQQQ as the case study.

-The MSVJ model captures both fast and slow volatility components and demonstrates superior performance in modeling volatility dynamics and price range estimation.

-The evaluation framework tests price and volatility characteristics against actual TQQQ data under different market conditions, including the COVID-19 crash and the 2022 drawdown.

-GBM and Heston models are most effective in simulating market crashes, as they reproduce historical drawdowns and capture tail risk well.

-The MSVJ model is the most suitable for option pricing because it provides the best fit for both price and volatility, as measured by its highest WMCR.

-The SVJD model performs best in generating realistic price and volatility paths, as it incorporates both stochastic volatility and jump processes.

-SVJD’s realism makes it useful for portfolio managers in backtesting trading strategies and assessing portfolio risk across different market conditions.

In short, each model has distinct strengths, so the optimal choice depends on whether the goal is risk management, option pricing, or portfolio simulation.

Reference

[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

Modeling Short-term Implied Volatilities in Heston Model

Despite their advantages, stochastic volatility models have difficulty in accurately characterizing both the flatness of long-term implied volatility (IV) curves and the steep curvature of short-term ones. Reference [2] addresses this issue by introducing a term-structure-based correction to the volatility of volatility (vol-vol) term in the classical Heston stochastic volatility model.

Findings

-Existing financial models struggle to capture implied volatility (IV) shapes across all option maturities simultaneously. This paper introduces a term-structure-based correction to the volatility of volatility (vol-vol) term in the classical Heston stochastic volatility model.

-The correction is modeled as an exponential increase function of the option expiry.

-An approximate formula for IV is derived using the perturbation method and applied to Shanghai Stock Exchange 50 ETF options.

-Numerical and empirical results show that the correction significantly improves the Heston model’s ability to capture short-term IVs.

-The corrected model enhances both IV forecasting and option quoting performance compared to the classical Heston model.

-While demonstrated on the Heston model, the method can be extended to other stochastic volatility models.

-Future research could include embedding strike into the correction function to better capture the entire implied volatility surface.

In brief, both short- and long-term IVs are accurately modeled in the new Heston variant.

This paper improves the existing Heston model. Thus, it helps portfolio managers and risk managers to better manage the risks of investment portfolios.

Reference

[2] Youfa Sun, Yishan Gong, Xinyuan Wang & Caiyan Liu, A novel term-structure-based Heston model for implied volatility surface, International Journal of Computer Mathematics, 1–24.

Closing Thoughts

Both studies advance volatility modeling in financial markets. The first highlights how different stochastic models, including a novel multi-scale volatility with jumps framework, can better simulate leveraged ETF dynamics under varying conditions, with specific strengths depending on the application. The second shows that enhancing the Heston model with a term-structure correction improves the fit of implied volatility surfaces across maturities, especially for short-dated options. Together, these findings underscore the importance of refining volatility models to capture market complexity and improve applications in risk management, option pricing, and forecasting.