Crypto Market Arbitrage: Profitability and Risk Management

Cryptocurrencies are becoming mainstream. In this post, I feature some strategies for trading and managing risks in cryptocurrencies.

Arbitrage Trading in the Cryptocurrency Market

Arbitrage trading takes advantage of price differences in different markets and/or instruments. Reference [1] examined some common and unique arbitrage trading opportunities in cryptocurrency exchanges that are not discussed often in the literature. They are,

-Exchange futures contract funding rate arbitrage

-Exchange futures contract intertemporal arbitrage

-Triangular arbitrage

-Pairs trading

-Order book spread prediction arbitrage

I provide details about the funding rate arbitrage below. Other arbitrage strategies are described in the paper.

Cryptocurrency exchanges use the funding rate to ensure perpetual futures prices align with spot prices, improving liquidity and narrowing bid-ask spreads. This mechanism periodically compensates long or short traders based on price differences. For example, Binance settles funding payments every 8 hours to balance demand between buyers and sellers.

When the perpetual contract trades above the spot price, longs pay shorts, discouraging further price increases and encouraging shorts to push it back down. An arbitrage strategy involves shorting Bitcoin in the perpetual market while holding an equal amount in the spot market, earning funding payments with minimal exposure to price fluctuations—excluding exchange and market risks.

When the perpetual contract trades below the spot price, shorts pay longs, so we buy the futures and short the spot.

Findings

– Research on cryptocurrency price prediction focuses on both time-series and cross-sectional analysis.

– This paper explores arbitrage opportunities in cryptocurrency exchanges that are often overlooked in academic literature.

– These arbitrage strategies can generate high returns with minimal risk.

– However, real market conditions and exchange constraints can reduce their effectiveness in live trading compared to backtesting.

– Incorporating these arbitrage strategies into a portfolio can improve the Sharpe ratio compared to simply holding cryptocurrencies.

In short, arbitrage trading is possible and profitable in the crypto market. However, we note that,

-These trading strategies are not riskless. Drawdown can happen

-Diversification helps smooth out the equity curves greatly

Reference

[1] Tianyu Zhou, Semi Risk-free Arbitrages with Cryptocurrency, 2022 5th International Conference on Financial Management, Education and Social Science (FMESS 2022)

Detecting Trends and Risks in Crypto Using the Hurst Exponent

The Hurst exponent is a statistical measure used to assess the long-term memory and persistence of a time series. It quantifies the tendency of a system to revert to the mean, follow a random walk, or exhibit a trending behavior. A Hurst exponent (H) value between 0 and 0.5 indicates mean-reverting behavior, H = 0.5 suggests a purely random process, and H between 0.5 and 1 signals persistent, trending behavior.

Reference [2] utilized the Detrended Fluctuation Analysis technique to study the Hurst exponent of the five major cryptocurrencies. Its main novelty is the calculation of a weekly time series of the Hurst exponent and its usage.

Findings

-This study examines long-range correlations in the cryptocurrency market using Hurst exponents across multiple time scales. It analyzes the log-returns of the top five cryptocurrencies, covering over 70% of market capitalization from 2017 to 2023.

-Four out of five cryptocurrencies exhibit persistent long-range correlations, while XRP follows a random walk.

-Trend Monitoring: The Hurst exponent (H) can help detect trend continuation or reversal. Cryptocurrencies like XRP showed transitions from short-term persistence to long-term anti-persistence, which could signal trend changes.

-Dynamic Strategy Adjustments: Rolling-window DFA estimates can track shifts in market behavior, aiding in strategy adjustments by identifying when a market moves from trend-following (H>0.5) to mean-reverting (H<0.5).

-Asset-Specific Behavior: Different cryptocurrencies exhibit unique behavioral patterns, suggesting that H-based analysis can inform tailored trading strategies.

-Systemic Risk Monitoring: Synchronization of H values across multiple cryptocurrencies during extreme market events may indicate rising volatility or instability, helping traders implement defensive measures like diversification.

In short, the findings suggest opportunities for using Hurst exponents as tools to monitor trend continuation or reversal, develop asset-specific strategies, and detect systemic risks during extreme market conditions, offering valuable insights for traders and policymakers navigating the cryptocurrency market’s inherent volatility.

Reference

[2] Huy Quoc Bui, Christophe Schinckus and Hamdan Amer Ali Al-Jaifi, Long-Range Correlations in Cryptocurrency Markets: A Multi-Scale DFA Approach, Physica A: Statistical Mechanics and its Applications, (2025), j.physa.2025.130417

Closing Thoughts

We have shown that arbitrage strategies in the crypto market are both possible and profitable. Additionally, risk management, trend detection, and reversal identification can be improved using the Hurst exponent, offering traders a valuable tool to navigate market volatility more effectively.

Optimizing Portfolios: Simple vs. Sophisticated Allocation Strategies

Portfolio allocation is an important research area. In this issue, we explore not only asset allocation but also the allocation of strategies. Specifically, I discuss tactical asset and trend-following strategy allocation.

Tactical Asset Allocation: From Simple to Advanced Strategies

Tactical Asset Allocation (TAA) is an active investment strategy that involves adjusting the allocation of assets in a portfolio to take advantage of short- to medium-term market opportunities. Unlike strategic asset allocation, which focuses on long-term asset allocation based on a fixed mix, TAA seeks to exploit market inefficiencies by overweighting or underweighting certain asset classes depending on market conditions, economic outlooks, or valuation anomalies. This approach allows investors to be more flexible and responsive to changing market environments, potentially improving returns while managing risk.

Reference [1] examines five approaches to tactical asset allocation. They are,

  1. The SMA 200-day strategy, which uses the price of an asset relative to its 200-day moving average.
  2. The SMA Plus strategy, which builds on the SMA 200-day by adding a volatility signal to the trend signal, dynamically adjusting allocations between risky assets and cash.
  3. The Dynamic Tactical Asset Allocation (DTAA) strategy, which applies the same trend and volatility signals as SMA Plus but across the entire portfolio, rather than on individual assets.
  4. The Risk Parity method, popularized by Ray Dalio’s All Weather Portfolio, equalizes the risk contributions of different asset classes.
  5. The Maximum Diversification method, which aims to maximize the diversification ratio by balancing individual asset volatilities against overall portfolio volatility.

Findings

– The SMA strategy provides strong risk-adjusted returns by shifting to cash during downturns, though it may miss early recovery phases.

– SMA Plus builds on SMA by adding a more dynamic allocation approach, achieving higher returns but at a slightly increased risk level.

– The DTAA strategy yields the highest returns but experiences significant drawdowns due to aggressive equity exposure and limited risk management.

– Risk Parity and Maximum Diversification focus on stability, offering lower returns with minimal volatility, making them suitable for conservative investors.

In short, TAA based on a simple moving average still delivers the best risk-adjusted return.

This is an interesting and surprising result. Does this prove once again that simpler is better?

Reference

[1] Mohamed Aziz Zardi, Quantitative Methods of Dynamic Tactical Asset Allocation, HEC – Faculty of Business and Economics, University of Lausanne, 2024

Using Trends and Risk Premia in Portfolio Allocation

Trend-following strategies play a crucial role in portfolio management, but constructing an optimal portfolio based on these signals requires a solid theoretical foundation. Reference [2] builds on previous research to develop a unified framework that integrates an autocorrelation model with the covariance structure of trends and risk premia.

Findings

– The paper develops a theoretical framework to derive implementable solutions for trend-following portfolio allocation.

– The optimal portfolio is determined by the covariance matrix of returns, the covariance matrix of trends, and the risk premia.

– The study evaluates five well-established portfolio strategies: Agnostic Risk Parity (ARP), Markowitz, Equally Weighted, Risk Parity (RP), and Trend on Risk Parity (ToRP).

– Using daily futures market data from 1985 to 2020, covering 24 stock indexes, 14 bond indexes, and 9 FX pairs, the authors assess the performance of these portfolios.

– The optimal combination of the three best portfolios—ARP (19.5%), RP (51%), and ToRP (30%)—achieves a Sharpe ratio of 1.37, balancing traditional and alternative approaches.

– The RP portfolio, representing a traditional diversified approach, is a key driver of performance, aligning with recent literature.

– The combination of ARP and ToRP offers the best Sharpe ratio for trend-following strategies, as it minimizes asset correlation.

In the context of a portfolio optimization problem, the article solved the optimal allocation amongst a set of trend-following strategies. It utilized the covariance matrix of returns, trends, and risk premia in its optimization algorithm. The allocation scheme combined both traditional and alternative approaches, offering a better Sharpe ratio than each of the previous methods individually.

Reference

[2] Sébastien Valeyre, Optimal trend following portfolios, (2021), arXiv:2201.06635

Closing Thoughts

We have discussed both asset and strategy allocation, one advocating a relatively simple approach, while the other is more sophisticated. Each method has its advantages, depending on the investor’s objectives and risk tolerance. A well-balanced portfolio may benefit from integrating both approaches to achieve optimal performance and diversification.

Capturing Volatility Risk Premium Using Butterfly Option Strategies

The volatility risk premium is a well-researched topic in the literature. However, less attention has been given to specific techniques for capturing it. In this post, I’ll highlight strategies for harvesting the volatility risk premium.

Long-Term Strategies for Harvesting Volatility Risk Premium

Reference [1] discusses long-term trading strategies for harvesting the volatility risk premium in financial markets. The authors emphasize the unique characteristics of the volatility risk premium factor and propose trading strategies to exploit it, specifically for long-term investors.

Findings

– Volatility risk premium is a well-known phenomenon in financial markets.

– Strategies designed for volatility risk premium harvesting exhibit similar risk/return characteristics. They lead to a steady rise in equity but may suffer occasional significant losses. They’re not suitable for long-term investors or investment funds with less frequent trading.

– The paper examines various volatility risk premium strategies, including straddles, butterfly spreads, strangles, condors, delta-hedged calls, delta-hedged puts, and variance swaps.

– Empirical study focuses on the S&P 500 index options market. Variance strategies show substantial differences in risk and return compared to other factor strategies.

– They are positively correlated with the market and consistently earn premiums over the study period. They are vulnerable to extreme stock market crashes but have the potential for quick recovery.

– The authors conclude that volatility risk premium is distinct from other factors, making it worthwhile to implement trading strategies to harvest it.

Reference

[1] Dörries, Julian and Korn, Olaf and Power, Gabriel, How Should the Long-term Investor Harvest Variance Risk Premiums? The Journal of Portfolio Management   50 (6) 122 – 142, 2024

Trading Butterfly Option Positions: a Long/Short Approach

A butterfly option position is an option structure that requires a combination of calls and/or puts with three different strike prices of the same maturity. Reference [2] proposes a novel trading scheme based on butterflies’ premium.

Findings

– The study calculates the rolling correlation between the Cboe Volatility Index (VIX) and butterfly options prices across different strikes for each S&P 500 stock.

– The butterfly option exhibiting the strongest positive correlation with the VIX is identified as the butterfly implied return (BIR), indicating the stock’s expected return during a future market crash.

– Implementing a long-short strategy based on BIR allows for hedging against market downturns while generating an annualized alpha ranging from 3.4% to 4.7%.

-Analysis using the demand system approach shows that hedge funds favor stocks with a high BIR, while households typically take the opposite position.

-The strategy experiences negative returns at the bottom of a market crash, making it highly correlated with the pricing kernel of a representative household.

-The value-weighted average BIR across all stocks represents the butterfly implied return of the market (BIRM), which gauges the severity of a future market crash.

-BIRM has a strong impact on both the theory-based equity risk premium (negatively) and the survey-based expected return (positively).

This paper offers an interesting perspective on volatility trading. Usually, in a relative-value volatility arbitrage strategy, implied volatilities are used to assess the rich/cheapness of options positions. Here the authors utilized directly the option positions premium to evaluate their relative values.

Reference

[2] Wu, Di and Yang, Lihai, Butterfly Implied Returns, SSRN 3880815

Closing Thoughts

In summary, both papers explore strategies for capturing the volatility risk premium. The first paper highlights the distinct characteristics of the volatility risk premium and outlines trading strategies tailored for long-term investors. The second paper introduces an innovative trading scheme centered around butterfly option structures. Together, these studies contribute valuable insights into optimizing risk-adjusted returns through strategic volatility trading.

Understanding Mean Reversion to Enhance Portfolio Performance

In a previous newsletter, I discussed momentum strategies. In this edition, I’ll explore mean-reverting strategies.

Mean reversion is a natural force observed in various areas of life, including sports performance, portfolio performance, volatility, asset prices, etc. In this issue, I specifically examine the mean reversion characteristics of individual stocks and indices.

Long-Run Variances of Trending and Mean-Reverting Assets

Trading strategies are often loosely divided into two categories: trend-following and mean-reverting. They’re designed to exploit the mean-reverting or trending properties of asset prices. Reference [1] provides a different perspective and approach for studying the mean-reverting and trending properties of assets. It compares the long-run variances of mean-reverting and trending assets to that of a random-walk process.

Findings

-The paper provides an alternative perspective on studying mean-reverting and trending properties of assets.

– Long-run variances of mean-reverting and trending assets are compared to a random-walk process. The paper highlights a probabilistic model for investment styles.

– Theoretical analysis indicates the variance’s direct dependence on the probability of consecutive directional movements.

– It suggests that variance may be reduced through mean reverting strategies, capturing instances of assets moving in opposing directions.

-The model is applied to US stock data. It is found that in 97 of the largest stocks, a regime of mean-reversion is prevalent.

-The paper demonstrated that relative to a random walk, the variance of these stocks is reduced due to this behavior.

-It concluded that most large-cap US stocks exhibit mean-reverting behavior.

-Mean-reverting asset prices are deemed more predictable than a random walk.

In short, the paper concluded that most large-cap US stocks are mean-reverting, and the mean reversion resulted in a reduction of the variances of the assets. This means that mean-reverting asset prices are more predictable as compared to a random walk. The opposite is true for trending assets: larger variances and less predictability.

Reference

[1] L. Middleton, J. Dodd, S. Rijavec, Trading styles and long-run variance of asset prices, arXiv:2109.08242

Mean-Reverting Trading Strategies Across Developed Markets

Reference [2] studies the mean reversion strategy of individual stocks across developed markets. It shows that the mean-reversion strategy is not profitable in all markets. However, when we apply filters for stock characteristics, the strategy becomes profitable.

Findings

-This study examined the reversal strategy in the five largest developed markets using portfolio analysis and the Fama–Macbeth (FM) regression method.

-Portfolio analysis revealed that the unconditional reversal strategy is persistent only in Germany and Japan.

-When applied to firms with higher expected liquidity provision costs, the reversal returns became stronger across all markets.

-The FM regression method provided the strongest support for the reversal strategy while accounting for key firm-related characteristics.

-Reversal returns were significantly linked to market volatility, indicating that they are more pronounced during periods of higher market liquidity costs.

-The lack of liquidity in smaller, high book-to-market, high volatility stocks contributes to their higher reversal effect.

-Small, high book-to-market ratio and volatile stocks exhibit a prominent reversal effect based on portfolio analysis.

-Traditional asset pricing models like CAPM, FF-3, and CF-4 fail to explain the observed reversal returns.

Reference

[2] Hilal Anwar Butt and Mohsin Sadaqat, When Is Reversal Strong? Evidence From Developed Markets, The Journal of Portfolio Management, June 2024

Closing Thoughts

We have examined the mean reversion characteristics of stocks and indices in both U.S. and international markets. Gaining insights into this dynamic can lead to better risk-adjusted returns for your portfolio.

Volatility Risk Premium: The Growing Importance of Overnight and Intraday Dynamics

The breakdown of the volatility risk premium into overnight and intraday sessions is an active and emerging area of research. It holds not only academic interest but also practical implications. ETF issuers are launching new ETFs to capitalize on the overnight risk premium, and the shift toward around-the-clock trading could impact the VRP and popular strategies such as covered call writing. In this post, I’ll discuss the VRP breakdown, its implications, impact, and more.

Volatility Risk Premium is a Reward for Bearing Overnight Risk

The volatility risk premium (VRP) represents the difference between the implied volatility of options and the realized volatility of the underlying asset. Reference [1] examines the asymmetry in the VRP. Specifically, it investigates the VRP during the day and overnight sessions. The research was conducted in the Nifty options market, but previous studies in the S&P 500 market reached the same conclusion.

Findings

– There is a significant difference in returns between overnight and intraday short option positions, unrelated to a weekend effect.

– The return asymmetry decreases as option moneyness and maturity increase.

– A systematic relationship exists between day-night option returns and the option Greeks.

– Average post-noon returns are significantly negative for short call positions and positive for short put positions, while pre-noon returns are largely insignificant, indicating that the VRP varies throughout the trading day for calls and puts.

– A significant jump in the underlying index reduces the day-night disparity in option returns due to increased implied volatilities, which boost both intraday and overnight returns.

– Strong positive overnight returns suggest that the VRP in Nifty options prices mainly compensates for overnight risk.

– A strategy of selling index options at the end of the trading day and covering them at the beginning of the next day yields positive returns before transaction costs but is not profitable after accounting for transaction costs.

Reference

[1] Aparna Bhat, Piyush Pandey, S. V. D. Nageswara Rao, The asymmetry in day and night option returns: Evidence from an emerging market, J Futures Markets, 2024, 1–18

Inventory Risk and Its Impact on the Volatility Risk Premium

The previous paper suggests that the VRP is specifically a reward for bearing overnight risk. Reference [2] goes further by attempting to answer why this is the case. It provides an explanation in terms of market makers’ inventory risks, as they hold a net-short position in put options.

Findings

-Put option risk premia are significantly negative overnight when equity exchanges are closed and continuous delta-hedging is not feasible.

-Intraday, when markets are liquid and delta-hedging is possible, put option risk premia align with the risk-free rate.

-Call options show no significant risk premia during the sample period.

-Market makers’ short positions in puts expose them to overnight equity price “gap” risks, while their call option positions are more balanced between long and short, resulting in minimal exposure to gap risk.

-Increased overnight liquidity reduces option risk premia. Regulatory changes and the acquisition of major electronic communication networks in 2006 boosted overnight equity trade volumes from Monday to Friday, reducing the magnitude of weekday option risk premia compared to weekend risk premia.

-The study concludes that the S&P 500 option risk premium arises from a combination of options demand and overnight equity illiquidity.

An interesting implication of this research is that the introduction of around-the-clock trading could potentially reduce the VRP.

Reference

[2] J Terstegge, Intermediary Option Pricing, 2024, Copenhagen Business School

Closing Thoughts

Understanding the breakdown of the volatility risk premium into overnight and intraday components is crucial for both researchers and practitioners. As ETF issuers develop products to leverage the overnight risk premium and markets move toward 24-hour trading, these dynamics could significantly impact volatility strategies. Recognizing these shifts can help investors refine their approaches and adapt to evolving market conditions.

Exploring Credit Risk: Its Influence on Equity Strategies and Risk Management

Credit risk, also known as default risk, is the likelihood of loss when a borrower or counterparty fails to meet its obligations. A lot of research has been conducted on credit risk, and an emerging line of study explores the connection between the equity and credit markets. In this post, we’ll discuss how credit risk impacts investment strategies in the equity market and how equity options can be used to hedge credit risk.

Understanding Credit Risk and Its Impact on Investment Strategies

Credit risk, also known as default risk, is the likelihood of loss from a borrower or counterparty not meeting its obligations. The Merton model, developed by Robert Merton, is a widely used model to measure a company’s credit risk, utilizing quantitative parameters. Reference [1] examined how credit risk impacts momentum and contrarian strategies in the equity markets.

Findings

-Credit risk is measured using default risk, specifically the distance to default (DD) from the Kealhofer, McQuown, and Vasicek (KMV) model.

– High credit risk firms, when subjected to momentum and contrarian strategies, can generate excess returns.

– Medium credit risk firms also offer opportunities for excessive returns with these strategies.

– Low credit risk firms do not show significant relationships with momentum and contrarian returns.

– Investors should consider credit risk when implementing momentum and contrarian investment strategies.

– The applicability of these findings to the US and other developed markets is suggested for further research.

Reference

[1] Ahmed Imran Hunjra, Tahar Tayachi, Rashid Mehmood, Sidra Malik and Zoya Malik, Impact of Credit Risk on Momentum and Contrarian Strategies: Evidence from South Asian Markets, Risks 2020, 8(2), 37

Using Equity Options to Hedge Credit Risks

Using credit derivatives, such as credit default swaps, to manage credit risks is a common practice in the financial industry. Reference [2] proposed an approach that uses equity derivatives to partially hedge credit risks.

The author generalized the Merton structural model, where a company’s equity is viewed as a call option on its assets. However, instead of using the total debt level as the default trigger, the author proposed an alternative default threshold where default is determined by the stock price’s initial crossing of a predefined level. The credit loss then resembles the payoff of a digital put option.

Findings

– Building on Merton’s model, the paper defines default as the event where the stock price ST falls below a set barrier, B.

– By establishing a link between this default model and the probability P(ST < B) at time T, the study shows that hedging with a European put option can reduce the capital required for projected losses.

– An optimization problem is formulated to find the optimal strike price for the put option, minimizing risk based on a specific measure.

– Numerical analysis indicates that this method reduces the Solvency Capital Requirement (SCR) in both jump and non-jump markets, providing insurance companies with an effective way to reduce losses within their existing risk management structures.

Reference

[2] Constantin Siggelkow, Partial hedging in credit markets with structured derivatives: a quantitative approach using put options, Journal of Derivatives and Quantitative Studies, 2024

Closing Thoughts

Credit risk remains a critical component shaping financial markets, with significant implications for equity investments. The growing research linking credit and equity markets highlights the importance of integrating credit risk considerations into investment strategies. Utilizing equity options for hedging provides a valuable approach to managing these risks effectively. As research in this area evolves, leveraging credit risk insights can enhance portfolio resilience and improve risk-adjusted returns.

Hedging Efficiently: How Optimization Improves Tail Risk Protection

Tail risk hedging aims to protect portfolios from extreme market downturns by using strategies such as out-of-the-money options or volatility products. While effective in mitigating large losses, the challenge lies in balancing cost and long-term returns. In this post, we’ll discuss tail risk hedging and whether it can be done at a reasonable cost.

Tail Risk Hedging Strategies: Are They Effective?

Tail risk hedging involves purchasing put options to protect the portfolio either partially or fully. Reference [1] presents a study of different tail risk hedging strategies. It explores the effectiveness of put option monetization strategies in protecting equity portfolios and enhancing returns.

Findings

– Eight different monetization strategies were applied using S&P 500 put options and the S&P 500 Total Return index from 1996 to 2020.

– Results compared against an unhedged index position and a constant volatility strategy on the same underlying index.

– Tail risk hedging, in this study, yielded inferior results in terms of risk-adjusted and total returns compared to an unhedged index position.

– Over a 25-year period, all strategies’ total returns and Sharpe ratios were worse than the unhedged position.

– Buying puts involves paying for the volatility risk premium, contributing to less favorable results.

– The results are sensitive to choices of time to expiry and moneyness of purchased options in tested strategies.

– The authors suggest the possibility of minimizing hedging costs by optimizing for strikes and maturities.

Reference:

[1] C.V. Bendiksby, MOJ. Eriksson, Tail-Risk Hedging An Empirical Study, Copenhagen Business School

How Can Put Options Be Used in Tail Risk Hedging?

The effectiveness of using put options to hedge the tail risks depends on the cost of acquiring put options, which can eat into investment returns. Reference [2] proposes a mixed risk-return optimization framework for selecting long put options to hedge S&P 500 tail risk. It constructs hypothetical portfolios that continuously roll put options for a tractable formulation.

Findings

– The article discusses the effectiveness of tail risk hedging. It highlights that the premium paid for put options can be substantial, especially when continuously renewing them to maintain protection. This cost can significantly impact investment returns and overall portfolio performance.

– The article introduces an optimization-based approach to tail-risk hedging, using dynamic programming with variance and CVaR as risk measures. This approach involves constructing portfolios that constantly roll over put options, providing protection without losing significant long-term returns.

– Contrary to previous research, the article suggests that an effective tail-risk hedging strategy can be designed using this optimization-based approach, potentially overcoming the drawbacks of traditional protective put strategies.

-The proposed hedging strategy overcame traditional drawbacks of protective put strategies. It outperforms both direct investments in the S&P 500 and static long put option positions.

Reference

[2] Yuehuan He and Roy Kwon, Optimization-based tail risk hedging of the S&P 500 index, THE ENGINEERING ECONOMIST, 2023

Closing Thoughts

Tail risk hedging is expensive. While the first paper demonstrated that tail risk hedging leads to inferior returns, it suggested that results could be improved by optimizing strike prices and maturities. The second paper built on this idea and proposed a hedging scheme based on optimization. The proposed strategy outperforms both direct investments in the S&P 500 and static long put option positions.

Momentum Strategies: Profitability, Predictability, and Risk Management

Momentum strategies have long been a cornerstone of investing, relying on the premise that past winners continue to outperform in the near future. This post explores the effectiveness of momentum strategies, analyzing their ability to generate abnormal returns and assessing their viability in different markets. While previous research has demonstrated the profitability of momentum strategies, recent evidence suggests a decline in return predictability. We then examine how incorporating drawdown control as a risk management tool can enhance performance.

Momentum Trading Strategies Across Capital Markets

Momentum trading is a popular investment strategy. Reference [1] reviewed momentum trading across various markets, from developing to developed countries.

Findings

– The momentum strategy involves investors buying stocks that have shown strong performance, anticipating continued positive performance.

– According to the study, most capital market investors employ the momentum strategy, although its implementation varies.

– This variability suggests inefficiencies in several capital markets’ development.

– The literature review reveals various interpretations and implementations of the momentum strategy.

– Overall, the findings indicate that momentum strategies are prevalent across global capital markets, including both developed and developing countries.

– These strategies typically manifest over the short term, often observed and tested over periods of at least twelve months.

Reference

[1] G. Syamni, Wardhia, D.P. Sari, B. Nafis, A Review of Momentum Strategy in Capital Market, Advances in Social Science, Education and Humanities Research, volume 495, 2021

Is the Momentum Anomaly Still Present in the Financial Markets?

Reference [2] examined whether the momentum anomaly still exists in the financial markets these days. Specifically, it analyzed the performance of a momentum trading strategy where we determined each asset’s excess return over the past 12 months. If the return is positive, the financial instrument is bought, and if negative, the financial instrument is sold.

Findings

– This paper expands on existing research on trend-following strategies.

– The study confirms the presence of the momentum anomaly during the sample period, showing statistically significant evidence.

– A time series momentum strategy, using the methodology of Moskowitz et al. yields a Sharpe ratio of 0.75, slightly higher than the 0.73 Sharpe ratio from a passive long investment in the same instruments.

– Evidence suggests a decline in return predictability over the past decade, with negative alpha from January 2009 to December 2021 when dividing the sample into three subperiods.

– The decline in return predictability indicates a weakening momentum anomaly.

– Incorporating drawdown control as a risk management measure significantly improves strategy performance, increasing the Sharpe ratio to 1.07 compared to 0.75 without drawdown control.

Reference

[2] David S. Hammerstad and Alf K. Pettersen, The Momentum Anomaly: Can It Still Outperform the Market?, 2022, Department of Finance, BI Norwegian Business School

Closing Thoughts

These studies confirm the relevance of momentum strategies but highlight their declining effectiveness since 2009, suggesting increased market efficiency. While time-series momentum still generates returns, its predictive power has weakened. However, incorporating drawdown control significantly improves performance, making risk management essential for sustaining profitability in evolving market conditions.

The Predictive Power of Dividend Yield in Equity Markets

Dividend yield has long been a cornerstone of equity valuation. In this post, we explore how dividend yield predicts stock returns, its impact on stock volatility, and why it holds unique significance for mature, dividend-paying firms.

Relationship Between Implied Volatility and Dividend Yield

Reference [1] explores the relationship between implied volatility (IV) and dividend yield. It investigates how the dividend yield impacts the implied volatility. The study supports the bird-in-hand theory rather than the dividend irrelevance theory. Results show that there exists a negative relationship between dividend yield and IV, and this relationship is stronger for puts than calls.

Findings

– This thesis examines the link between implied volatility and dividend yield in the options market, comparing the Bird-in-Hand theory and the Dividend Irrelevancy theory.

– Results show that dividend yield significantly impacts implied volatility, with a stronger and consistent negative relationship observed in put options, aligning with the Bird-in-Hand theory.

– The relationship in put options suggests a stronger and more consistent impact of dividend yield, aligning with the Bird-in-hand theory.

– The findings support the hypothesis that an increase in a firm’s dividend yield tends to decrease future volatility.

– This effect was particularly pronounced in put option models but also observed in call option models.

– The study emphasizes the need for alternative methodologies, larger sample sizes, and additional variables to deepen the understanding of option pricing dynamics.

Reference

[1] Jonathan Nestenborg, Gustav Sjöberg, Option Implied Volatility and Dividend Yields, Linnaeus University, 2024

The Impact of Dividend Yield on Stock Performance

Dividend yield is a reliable predictor of future stock returns, particularly during periods of heightened volatility. This article [2] explores the connection between dividend yield, stock volatility, and expected returns.

Findings

– This study shows that dividend yield predicts returns for dividend-paying firms more effectively than alternative pricing factors, challenging previous research.

– Using the most recent declaration date to calculate dividend yield significantly improves return predictability compared to using the trailing yield.

– Asset pricing strategies tend to underperform within mature, profitable firms that pay dividends, highlighting a unique pattern.

– Cross-sectional tests suggest dividend yield predicts returns because investors value receiving dividends rather than as an indicator of future earnings.

– Dividend yield is concluded to be a valuable valuation metric for mature, easier-to-value firms that typically pay dividends.

– Volatility, measured as the trailing twelve-month average of monthly high and low prices, impacts return predictability.

– Excessively volatile prices drive predictability, with dividend yield strategies generating around 1.5% per month.

– During heightened volatility periods, dividend yield strategies yield significant returns.

– Cross-sectionally, dividend yield is a more accurate predictor for returns in volatile firms.

Reference:

[2] Ahn, Seong Jin and Ham, Charles and Kaplan, Zachary and Milbourn, Todd T., Volatility, dividend yield and stock returns (2023). SSRN

Closing Thoughts

Dividend yield is shown to be a useful valuation metric, particularly for mature and easily valued firms that consistently pay dividends. Furthermore, the research emphasizes that investors prioritize the receipt of dividends over their informational value regarding future earnings. These insights reaffirm the importance of dividend yield in understanding market dynamics and developing effective investment strategies.

Monte Carlo Simulations: Pricing Weather Derivatives and Convertible Bonds

Monte Carlo simulations are widely used in science, engineering, and finance. They are an effective method capable of addressing a wide range of problems. In finance, they are applied to derivative pricing, risk management, and strategy design. In this post, we discuss the use of Monte Carlo simulations in pricing complex derivatives.

Pricing of Weather Derivatives Using Monte Carlo Simulations

Weather derivatives are a particular class of financial instruments that individuals or companies can use in support of risk management in relation to unpredictable or adverse weather conditions. There is no standard model for valuing weather derivatives similar to the Black–Scholes formula. This is primarily due to the non-tradeable nature of the underlying asset, which violates several assumptions of the Black–Scholes model.

Reference [1] presented a valuation method for pricing an exotic wind power option using Monte Carlo simulations.

Findings

– Wind power generators are exposed to risks stemming from fluctuations in market prices and variability in power production, primarily influenced by their dependency on wind speed.

– The research focuses on designing and pricing an up-and-in European wind put barrier option using Monte Carlo simulation.

– In the presence of a structured weather market, wind producers can mitigate fluctuations by purchasing this option, thereby safeguarding their investments and optimizing profits.

– The wind speed index serves as the underlying asset for the barrier option, effectively capturing the risks associated with wind power generation.

– Autoregressive Fractionally Integrated Moving Average (ARFIMA) is utilized to model wind speed dynamics.

– The study applies this methodology within the Colombian electricity market context, which is vulnerable to phenomena like El Niño.

– During El Niño events, wind generators find it advantageous to sell energy to the system because their costs, including the put option, are lower than prevailing power prices.

– The research aims to advocate for policy initiatives promoting renewable energy sources and the establishment of a financial market for trading options, thereby enhancing resilience against climate-induced uncertainties in the electrical grid.

Reference

[1] Y.E. Rodríguez, M.A. Pérez-Uribe, J. Contreras, Wind Put Barrier Options Pricing Based on the Nordix Index, Energies 2021, 14, 1177

Pricing Convertible Bonds Using Monte Carlo Simulations

The Chinese convertible bonds (CCB) have a special feature, which is a downward adjustment clause. Essentially, this clause states that when the underlying stock price remains below a pre-set level for a pre-defined number of days over the past consecutive trading days, issuers can lower the conversion price to make the conversion value higher and more attractive to investors.

Reference [2] utilized the Monte Carlo simulation approach to account for this feature and to price the convertible bond.

Findings

– The downward adjustment provision presents a significant challenge in pricing Chinese Convertible Bonds (CCBs).

– The triggering of the downward adjustment is treated as a probabilistic event related to the activation of the put option.

– The Least Squares method is employed to regress the continuation value at each exercise time, demonstrating the existence of a unique solution.

– The downward adjustment clause is integrated with the put provision as a probabilistic event to simplify the model.

-When the condition for the put provision is met, the downward adjustment occurs with 80% probability, and the conversion price is adjusted to the maximum of the average of the underlying stock prices over the previous 20 trading days and the last trading day.

Reference

[2] Yu Liu, Gongqiu Zhang, Valuation Model of Chinese Convertible Bonds Based on Monte Carlo Simulation, arXiv:2409.06496

Closing Thoughts

We have explored advanced applications of Monte Carlo simulations in pricing weather derivatives and complex convertible bonds. This versatile method demonstrates its broad applicability across various areas of finance and trading.