Author: rvarb

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.

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.