Month: December 2024

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.

Option Pricing Models and Strategies for Crude Oil Markets

Financial models and strategies are usually universal and can be applied across different asset classes. However, in some cases, they must be adapted to the unique characteristics of the underlying asset. In this post, I’m going to discuss option pricing models and trading strategies in commodities, specifically in the crude oil market.

Volatility Smile in the Commodity Market

Paper [1] investigates the volatility smile in the crude oil market and demonstrates how it differs from the smile observed in the equity market.  It proposes to use the new method developed by Carr and Wu in order to study the volatility smile of commodities. Specifically, the authors examine the volatility smile of the United States Oil ETF, USO.

Findings

– This paper examines the information derived from the no-arbitrage Carr and Wu formula within a new option pricing framework in the USO (United States Oil Fund) options market.

– The study investigates the predictability of this information in forecasting future USO returns.

– Using the no-arbitrage formula, risk-neutral variance, and covariance estimates are obtained under the new framework.

– The research identifies the term structure and dynamics of these risk-neutral estimates.

– The findings reveal a “U”-shaped implied volatility smile with a positive curvature in the USO options market.

Usually, an equity index such S&P 500 exhibits a downward-sloping implied volatility pattern, i.e. a negative implied volatility skew. Oil, on the other hand, possesses a different volatility smile. This is because while equities are typically associated with crash risks, oil prices exhibit both sharp spikes and crashes, leading to a different implied volatility pattern. This highlights the importance of considering the specific characteristics and dynamics of different asset classes when analyzing and interpreting implied volatility patterns.

Reference

[1] Xiaolan Jia, Xinfeng Ruan, Jin E. Zhang, Carr and Wu’s (2020) framework in the oil ETF option market, Journal of Commodity Markets, Volume 31, September 2023, 100334

Statistical Arbitrage in the Crude Oil Markets

Reference [2] directly applies statistical arbitrage techniques, commonly used in equity markets, to the crude oil market.  It utilizes cointegration to construct a statistical arbitrage portfolio. Various methods are then used to test for stationarity and mean reversion: the Quandt likelihood ratio (QLR), augmented Dickey-Fuller (ADF) test, autocorrelations, and the variance ratio. The constructed strategy performed well both in- and out-of-sample.

Findings

– This paper introduces the concept of statistical arbitrage through a trading strategy known as the mispricing portfolio.

– It focuses specifically on mean-reverting strategies designed to exploit persistent anomalies observed in financial markets.

– Empirical evidence is presented to demonstrate the effectiveness of statistical arbitrage in the crude oil markets.

– The mispricing portfolio is constructed using cointegration regression, establishing long-term pricing relationships between WTI crude oil futures and a replication portfolio composed of Brent and Dubai crude oils.

-Mispricing dynamics revert to equilibrium with predictable behaviour. Trading rules, which are commonly used in equity markets, are then applied to the crude oil market to exploit this pattern.

Reference

[2] Viviana Fanelli, Mean-Reverting Statistical Arbitrage Strategies in Crude Oil Markets, Risks 2024, 12, 106.

Closing Thoughts

As we’ve seen, techniques and models utilized in the equity market can sometimes be applied directly to the crude oil market, while other times they need to be adapted to the unique characteristics of the crude oil market. In any case, strong domain knowledge is essential.

Educational Video

In this webinar, Quantitative Trading in the Oil Market, Dr Ilia Bouchouev delivers an interesting and insightful presentation on algorithmic trading in the oil market. He also encourages viewers to apply the techniques discussed for the oil market to other markets, such as equities.

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.