Category: statistical arbitrage

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.

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.

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.

PCA in Action: From Commodity Derivatives to Dispersion Trading

Principal Component Analysis (PCA) is a dimensionality reduction technique used to simplify complex datasets. It transforms the original variables into a smaller set of uncorrelated variables called principal components, ranked in order of their contribution to the dataset’s total variance. In this post, we’ll discuss various applications of PCA.

Pricing Commodity Derivatives Using Principal Component Analysis

Due to the seasonal nature of commodities, pricing models should be able to take into account seasonality and other deterministic factors.

Reference [1] proposed a new, multi-factor pricing method based on Principal Component Analysis (PCA). It introduces a multi-factor model designed to price commodity derivatives, with a particular focus on commodity swaptions.

Findings

– The model calibration process consists of two key steps: offline and online.

– The offline step, conducted infrequently, determines mean reversion rates, the ratio of long and short factor volatilities, and the correlation between the factors using historical data.

– The online step occurs every time the model is used to price an option or simulate price paths.

– Empirical analysis demonstrates that the model is highly accurate in its predictions and applications.

– Swaptions, which are relatively illiquid commodities, present a challenge due to their one-sided natural flow in the market.

– Model calibration strategies are divided into seasonal and non-seasonal categories, considering the asset’s characteristics. For seasonal assets like power or gas, local volatilities are calibrated separately for each contract, while a boot-strapping strategy is employed for non-seasonal assets like oil.

– Currently, the multi-factor model lacks a term structure for volatility ratios and mean reversions. However, it can be easily extended to incorporate a time dependency, which would facilitate fitting market prices of swaptions across various tenors.

Reference

[1]  Tim Xiao, Pricing Commodity Derivatives Based on A Factor Model, Philarchive

Dispersion Trading Using Principal Component Analysis

Dispersion trading involves taking positions on the difference in volatility between an index and its constituent stocks.

Reference [2] examined dispersion trading strategies based on a statistical index subsetting procedure and applied it to the S&P 500 constituents

Findings

– This paper introduces a dispersion trading strategy using a statistical index subsetting approach applied to S&P 500 constituents from January 2000 to December 2017.

– The selection process employs principal component analysis (PCA) to determine each stock’s explanatory power within the index and assigns appropriate subset weights.

– In the out-of-sample trading phase, both hedged and unhedged strategies are implemented using the most suitable stocks.

– The strategy delivers significant annualized returns of 14.52% (hedged) and 26.51% (unhedged) after transaction costs, with Sharpe ratios of 0.40 and 0.34, respectively.

– Performance remains robust across different market conditions and outperforms naive subsetting schemes and a buy-and-hold approach in terms of risk-return characteristics.

– A deeper analysis highlights a correlation between the chosen number of principal components and the behavior of the S&P 500 index.

– An index subsetting procedure was developed, considering the explanatory power of individual stocks, allowing a replicating option basket with as few as five securities.

– An analysis of sector exposure, principal components, and robustness checks demonstrated that the trading systems have superior risk-return characteristics compared to other dispersion strategies.

Reference

[2] L. Schneider, and J. Stübinger, Dispersion Trading Based on the Explanatory Power of S&P 500 Stock Returns, Mathematics 2020, 8, 1627

Closing Thoughts

PCA is a powerful tool in quantitative finance. In this issue, we have demonstrated its effectiveness in pricing commodity derivatives and developing dispersion trading strategies. Its versatility extends beyond these applications, making it a valuable technique for tackling a wide range of problems in quantitative finance.

CAPM, WACC, and Beyond: Beta’s Application in Arbitrage

Beta is a measure of an asset’s sensitivity to market movements, indicating how much its price is expected to change in relation to the overall market. Beta is often used in CAPM and the calculation of WACC. However, it can also be applied in trading, specifically in arbitrage. In this post, I’ll discuss beta arbitrage.

Beta Arbitrage Around Macroeconomic Announcements

The macroeconomic announcement premium refers to the phenomenon where financial markets experience higher-than-usual returns on days when significant macroeconomic announcements are made.

Reference [1] studies the dynamics of high-beta stock returns around macroeconomic announcements.

Findings

– Stocks in the top beta-decile show distinct return patterns: negative returns before announcements (-0.075%), positive on announcement days (0.164%), and negative again after (-0.093%).

– The beta premium experiences significant fluctuations around macroeconomic announcements, with a swing driven by high-beta stock returns.

– A long-short strategy involving betting against beta (BAB) before and after announcements, and betting on beta (BOB) on announcement days, can yield an annualized return of 25.28%.

– Liquidity effects explain pre-announcement high-beta returns, while risk has a weak but consistent pattern around announcements.

– Investor risk aversion shifts significantly explain the variation in beta returns around announcements.

– Liquidity, risk, and investor risk appetite only partially account for variations in high-beta stock returns.

Reference

[1] Jingjing Chen, George J. Jiang, High-beta stock valuation around macroeconomic announcements, Financial Review. 2024;1–26.

Beta Arbitrage: Betting on Stock Comovements

This trading strategy is based on the assumption that stock betas tend to mean regress towards one in the long run, leading to exploitable comovement patterns in stock prices.

Reference [2] discusses a model for S&P 500 index changes, involving two beta-based styles: index trackers and beta arbitrageurs. The comovement effect has two components, influenced by low and high beta stocks in pre-event scenarios.

The paper presents a stylized model for S&P 500 index changes, highlighting the distinct components of comovement effects and the exploitable nature of beta arbitrage.

Findings

-Beta arbitrage is a trading strategy that capitalizes on the belief that betas tend to mean regress towards one over time.

– This paper develops a model for S&P 500 index changes, focusing on two beta-based trading styles: index trackers and beta arbitrageurs.

– Index trackers follow the index, while beta arbitrageurs trade both high and low beta event stocks to exploit mean reversion toward one.

– Arbitrageurs employ common or contrarian trading patterns depending on whether a stock’s historical beta is below or above one.

– The overall comovement effect of index changes has two components:

1- Pre-event low beta stocks experience beta increases due to common demand from both indexers and arbitrageurs.

2- Arbitrageurs short high beta additions, reducing or reversing beta increases caused by indexers.

– Similar patterns are observed for stocks deleted from the index.

Reference

[2] Yixin Liao, Jerry Coakley, Neil Kellard, Index tracking and beta arbitrage effects in comovement, International Review of Financial Analysis, Volume 83, October 2022, 102330

Closing Thoughts

Beta is more than a measure of an asset’s sensitivity to market movements or a key component in financial models like CAPM and WACC. Its application extends to trading strategies, particularly beta arbitrage, where investors exploit discrepancies in beta values to identify profitable opportunities.

From Gold to Bitcoin: Exploring the Oldest and Newest Asset Classes

Gold, one of the oldest and most enduring asset classes, had an exceptional run in 2024, capturing attention across financial markets. Its role in investment portfolios continues to spark interest, acting as a hedge against uncertainty. On the other end of the spectrum, cryptocurrencies represent the newest frontier in finance. While opinions remain divided, some are enthusiastic supporters, while others remain skeptical, one thing is undeniable: Bitcoin has just crossed the remarkable $100,000 USD milestone. In this article, I’ll discuss gold’s role in an investment portfolio and pairs trading within the crypto market.

Is Gold a Hedge or a Safe Haven Asset?

Historically, gold has exhibited a low correlation with other asset classes such as stocks and bonds, making it an effective hedge against market volatility and economic uncertainty.

Reference [1] delves deeper into examining the role of gold as a hedge or safe haven asset. It defines a weak, strong hedge, or safe haven asset as follows,

-A weak hedge is an asset that has a negative conditional correlation with another asset or portfolio on average. A strong hedge is an asset that has both a negative conditional correlation and positive conditional coskewness with another asset or portfolio on average.

– A weak safe haven is an asset that has a negative conditional correlation with another asset or portfolio in times of market stress or turmoil. A strong safe haven is an asset that has both a negative conditional correlation and positive conditional coskewness with another asset or portfolio in times of market stress or turmoil.

Findings

– The study empirically analyzes the performance of gold across 24 countries over a 40-year period.

– Results show that gold acts as a strong hedge in Brazil, India, Indonesia, Italy, Mexico, Russia, South Korea, Thailand, and Turkey, and as a safe haven in Brazil, France, India, Indonesia, Italy, Mexico, Russia, South Korea, and Turkey.

– The study investigates whether gold can enhance overall portfolio performance as a hedge or safe-haven asset.

– The  conditional comoment-based dynamic (CCD) strategy adjusts portfolio allocation to gold based on its properties and adds gold to the stock portfolio during the holding period only if it serves as a hedge or safe haven.

– Findings indicate that the CCD trading strategy outperforms the buy-and-hold strategy, generating higher returns, Sharpe ratio, and skewness when gold is utilized as a hedge or safe-haven asset.

Reference

[1] Lei Ming, Ping Yang, Qianqiu Liu, Is gold a hedge or a safe haven against stock markets? Evidence from conditional comoments, Journal of Empirical Finance, Volume 74, December 2023, 101439

Pairs Trading in the Cryptocurrency Market

Pairs trading is a popular strategy in equity and commodity markets. While successful in equities, limited research exists on pair trading in the cryptocurrency market. Reference [2] examines the application of pairs trading within the cryptocurrency market.

Findings

-The study applied the Distance Method and Cointegration Method to cryptocurrency pairs using both daily and hourly data for formation and trading periods.

-Results showed that the frequency of the selection period (daily or hourly) did not significantly affect the pairs chosen.

-Pairs selected using the Cointegration Method generally outperformed those chosen with the Distance Method.

-Intraday trading proved more profitable than longer-term trading but lost its advantage when a stop-loss was implemented.

-The Cointegration Method performed better than the Distance Method, as the latter incurred higher trading costs due to an increased number of trades.

– Pairs trading outperformed the buy-and-hold long/short strategy in the cryptocurrency market. But it underperformed the traditional Buy and Hold.

Reference

[2] Lesa, Chiara and Hochreiter, Ronald, Cryptocurrency Pair Trading, SSRN, 2023

Closing thoughts

As we navigate an ever-evolving financial landscape, understanding the roles of these two asset classes can help build diversified, forward-looking investment portfolios.

When Correlations Break or Hold: Strategies for Effective Hedging and Trading

It’s well known that there is a negative relationship between an equity’s price and its volatility. This can be explained by leverage or, alternatively, by volatility feedback effects. In this post, I’ll discuss practical applications to exploit this negative correlation between equity prices and their volatility.

A Trading Strategy Based on the Correlation Between the VIX and S&P500 Indices

This paper [1] examines the strong correlation in the S&P 500 and identifies trading opportunities when this correlation weakens or breaks down.

Findings

-The study covers the period from January 1995 to October 2020, utilizing 6,488 daily observations of the VIX and S&P500 indexes.

– In scenarios where the options market indicates increased drawdown risk with higher implied volatility but negative returns have not yet occurred, consider shorting the market.

– The signal to short the market occurs when the negative correlation between the S&P 500 and VIX is broken, and they start exhibiting a positive correlation.

– The test setup involves identifying one or two consecutive days with positive co-movement between the VIX and S&P 500, then setting the transaction date for the day after or at the close of the chosen date.

– Empirical results show that the strategy outperforms the S&P500 index over the 25-year period, achieving higher returns, lower systematic risk, and reduced volatility.

-The findings provide evidence that excess returns can be generated by timing the market using historical data, even after accounting for trading costs.

Reference

[1] Tuomas Lehtinen, Statistical arbitrage strategy based on VIX-to-market based signal, Hanken School of Economics

Optimal Hedging for Options Using Minimum-Variance Delta

Contrary to the first paper, Reference [2] focuses on the strong correlation between the S&P 500 and its volatility, designing an efficient scheme for hedging an options book.

The authors developed a so-called minimum variance (MV) delta. Essentially, the MV delta is the Black-Scholes delta with an additional adjustment term.

Findings

-Due to the negative relationship between price and volatility for equities, the minimum variance delta is consistently less than the practitioner Black-Scholes delta.

-Traders should under-hedge equity call options and over-hedge equity put options compared to the practitioner Black-Scholes delta.

-The study demonstrates that the minimum variance delta can be accurately estimated using the practitioner Black-Scholes delta and the historical relationship between implied volatilities and asset prices.

-The expected movement in implied volatility for stock index options can be approximated as a quadratic function of the practitioner Black-Scholes delta divided by the square root of time.

-A formula for converting the practitioner Black-Scholes delta to the minimum variance delta is provided, yielding good out-of-sample results for both European and American call options on stock indices.

-For S&P 500 options, the model outperforms stochastic volatility models and models based on the slope of the volatility smile.

-The model works less well for certain ETFs

Reference:

[2] John Hull and Alan White, Optimal Delta Hedging for Options, Journal of Banking and Finance, Vol. 82, Sept 2017: 180-190

Closing Thoughts

These two papers take opposing approaches: one exploits correlation breakdown, while the other capitalizes on the correlation remaining strong. However, they are not mutually exclusive. Combining insights from both can lead to a more efficient trading or hedging strategy.

Educational Video

This seminar by Prof. J. Hull delves into the second paper discussed above.

Abstract

The “practitioner Black-Scholes delta” for hedging equity options is a delta calculated from the Black-Scholes-Merton model with the volatility parameter set equal to the implied volatility. As has been pointed out by a number of researchers, this delta does not minimize the variance of a trader’s position. This is because there is a negative correlation between equity price movements and implied volatility movements. The minimum variance delta takes account of both the impact of price changes and the impact of the expected change in implied volatility conditional on a price change. In this paper, we use ten years of data on options on stock indices and individual stocks to investigate the relationship between the Black-Scholes delta and the minimum variance delta. Our approach is different from earlier research in that it is empirically-based. It does not require a stochastic volatility model to be specified. Joint work with Allan White.

Hurst Exponent Applications: From Regime Analysis to Arbitrage

One of my favourite ways to characterize the market regime is by using the Hurst exponent. However, its applications are not limited to identifying market regimes. There are innovative ways to utilize it. In this post, I will discuss two approaches to applying the Hurst exponent.

Using the Hurst Exponent to Time the Market

The Hurst exponent can be employed to directly time the market.  Reference [1] calculated the moving Hurst exponents for rolling windows of 100 and 150 days. The timing signals are subsequently generated by using these calculations.

Findings

-The study suggests that the Moving Hurst (MH) indicator is effective for forecasting and managing volatility in Indian equity markets.

-MH is more effective at capturing profitable trading opportunities than Moving Averages (MA).

-MH is a less lagging indicator than MA, making it more responsive to market changes.

-MH incorporates principles from chaos theory and fractal analysis, offering a unique perspective for market analysis.

-The research was conducted in the Indian stock market. However, it can be readily applied to any stock market.

Reference

[1] Shah, Param, Ankush Raje, and Jigarkumar Shah, Patterns in the Chaos: The Moving Hurst Indicator and Its Role in Indian Market Volatility. Journal of Risk and Financial Management 17: 390, 2024

Using the Hurst Exponent for Pairs Trading

The Hurst method isn’t restricted to single underlying assets; it can also be applied to a pair of stocks to identify pairs trading (statistical arbitrage) opportunities.  Reference [2] proposed a new approach to measure the co-movement of two price series through the Hurst exponent of the product.

Findings

– The Hurst exponent of the product series, referred to as HP, can measure the existence of a relationship between two series.

– The HP method is a new way to measure the dependence between two series, detecting various types of relationships, including correlation, cointegration, and non-linear relationships, even when the relationship is weak or given by a copula.

– This method is particularly useful for studying financial series as it gives more weight to high increments than low increments, unlike other correlation measures.

– The efficiency of the HP method was tested through a statistical arbitrage technique for pairs selection and compared with the classical correlation method.  Results indicate that the HP method performs better in most cases.

Reference

[2] José Pedro Ramos-Requena, Juan Evangelista Trinidad-Segovia, and Miguel Ángel Sánchez-Granero, An Alternative Approach to Measure Co-Movement between Two Time Series, Mathematics 2020, 8, 261

Educational Video

This seminar by Markis Vogl presents the theory and application of the Hurst exponent.

Abstract

My presentations elaborates on the meaning of Hurst exponents, namely, that instead of long memory, fractal trends are measured instead (contradicting Mandelbrot’s conception). Further, the talk encompasses the generation of rolling window (time varying) Hurst exponent series based upon the cascadic level 12 wavelet filtered (denoised) S&P500 logarithmic return series (2000-2020). The Hurst exponent series are then analysed with a generalizable nonlinear analysis framework, which allows the determination of the underlying empirical data generating process.

Closing thoughts

The Hurst exponent is an effective tool for gaining insights into market dynamics. Whether for timing the market or identifying pairs trading opportunities, it offers traders an edge in strategy development.