Papers about algorithmic trading#
This section contains various research papers related to algorithmic trading.
Note
AI-related papers have their own AI section.
An Investor’s Guide to Crypto#
We provide practical insights for investors seeking exposure to the growing cryptocurrency space. Today, crypto is much more than just bitcoin, which historically dominated the space but accounted for just a 21% share of total crypto trading volume in 2021. We discuss a wide variety of tokens, highlighting both their functionality and their investment properties. We critically compare popular valuation methods. We contrast buy-and-hold investing with more active styles. We only deem return data from 2017 representative, but the use of intraday data boosts statistical power. Underlying crypto performance has been notoriously volatile, but volatility-targeting methods are effective at controlling risk, and trend-following strategies have performed well. Crypto assets display a low correlation with traditional risky assets in normal times, but the correlation also rises in the left tail of these risky assets. Finally, we detail important custody and regulatory considerations for institutional investors.
Low-volatility strategies for highly liquid cryptocurrencies#
Managing extreme price fluctuations in cryptocurrency markets are of central importance for investors in this market segment. Using a sample of highly liquid cryptocurrencies from January 2017 to June 2021, this paper proposes a dynamic investment strategy that selects cryptocurrencies based on their historical volatility and is complemented by a simple stop-loss rule. Our results reveal that investing in highly concentrated low volatility cryptocurrency portfolios with six to twelve months volatility look-back and holding period generate statistically significant excess returns. By including a simple stop-loss rule, the downside risk of cryptocurrency portfolios is reduced markedly, and the Sharpe ratios are improved significantly.
How to avoid overfitting trading strategies#
Running a lossy trading strategy would be a very costly mistake, so we spend a lot of effort on assessing the expected performance of our strategies. This task gets harder when we have limited data for this evaluation or when we experiment with the strategy for a longer time and risk manually overfitting the strategy on the same out-of-sample data.
An Efficient Algorithm for Optimal Routing Through Constant Function Market Makers#
Constant function market makers (CFMMs) such as Uniswap have facilitated trillions of dollars of digital asset trades and have billions of dollars of liquidity. One natural question is how to optimally route trades across a network of CFMMs in order to ensure the largest possible utility (as specified by a user). We present an efficient algorithm, based on a decomposition method, to solve the problem of optimally executing an order across a network of decentralized exchanges
Automated Market Making and Arbitrage Profits in the Presence of Fees#
We consider the impact of trading fees on the profits of arbitrageurs trading against an automated marker marker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to both introduce fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of time that an arriving arbitrageur finds a profitable trade.
Momentum and trend following trading strategies for currencies and bitcoin#
Momentum trading strategies are thoroughly described in the academic literature and used in many trading strategies by hedge funds, asset managers, and proprietary traders. Baz et al. (2015) describe a momentum strategy for different asset classes in great detail from a practitioner’s point of view. Using a geometric Brownian Motion for the dynamics of the returns of financial instruments, we extensively explain the motivation and background behind each step of a momentum trading strategy. Constants and parameters that are used for the practical implementation are derived in a theoretical setting and deviations from those used in Baz et al. (2015) are shown. The trading signal is computed as a mixture of exponential moving averages with different time horizons. We give a statistical justification for the optimal selection of time horizons. Furthermore, we test our approach on global currency markets, including G10 currencies, emerging market currencies, and cryptocurrencies. Both a time series portfolio and a cross-sectional portfolio are considered. We find that the strategy works best for traditional fiat currencies when considering a time series based momentum strategy. For cryptocurrencies, a cross-sectional approach is more suitable. The momentum strategy exhibits higher Sharpe ratios for more volatile currencies. Thus, emerging market currencies and cryptocurrencies have better performances than the G10 currencies. This is the first comprehensive study showing both the underlying statistical reasons of how such trading strategies are constructed in the industry as well as empirical results using a large universe of currencies, including cryptocurrencies.
Momentum trading in cryptocurrencies: short-term returns and diversification benefits#
We test for the presence of momentum effects in cryptocurrency market and estimate dynamic conditional correlations (DCCs) of returns between momentum portfolios of cryptocurrencies and traditional assets. First, investment portfolios are constructed adherent to the classic J/K momentum strategy, using daily data from twelve cryptocurrencies for over a period of three years. We identify the existence of momentum effect, which is highly significant for short-term portfolios but disappears over the longer term. Second, we show that cross correlations of weekly returns between momentum portfolio of cryptocurrencies and traditional assets are unlike correlations of returns between traditional assets. Third, we find that momentum portfolios of cryptocurrencies not only offer diversification benefits but also can be a hedge and safe haven for traditional assets.
Pure Momentum in Cryptocurrency Markets#
Momentum is one of the most widespread, persistent, and puz- zling phenomenon in asset pricing. The prevailing explanation for momentum is that investors under-react to new information, and thus asset prices tend to drift over time. We use a unique fea- ture of cryptocurrency markets: the fact that they are open 24/7, and report returns over the last 24 hours. Thus, the one-day re- turn is subject to predictable fluctuations based on the removal of lagged information. We show that investors respond positively to changes in reported returns that are unrelated to any new release of information, or change in the asset fundamentals. We call this behavioral anomaly “Pure Momentum”.
Dissecting Investment Strategies in the Cross Section and Time Series#
We contrast the time-series and cross-sectional performance of three popular investment strategies: carry, momentum and value. While considerable research has examined the perfor- mance of these strategies in either a directional or cross-asset settings, we offer some insights on the market conditions that favor the application of a particular setting.
Can Day Trading Really Be Profitable?#
The validity of day trading as a long-term consistent and uncorrelated source of income for traders and investors is a matter of debate. In this paper, we investigate the profitability of the well-known Opening Range Breakout (ORB) strategy during the period of 2016 to 2023. This period encompasses two bear markets and a few events with abnormal volatility. Our results suggest that with the proper use of leverage or leveraged products (such as 3x leveraged ETFs), day trading can empirically produce significant returns when compared to a standard buy and hold strategy on benchmark indexes in the US public equity markets (Nasdaq or NYSE). Without any loss of generality, we studied the results of an ORB strategy implemented in QQQ. By comparing the results of the active day trading approach with a passive exposure in QQQ, we prove that it is possible for the ORB portfolio to significantly outperform the passive investment. In fact, the day trading portfolio produced an annualized alpha of 33% (net of commissions). Nevertheless, due to leverage constraints enforced by brokers, an active trader would have capped the full upside potential given by the ORB strategy. To overcome this issue, we introduced the use of TQQQ, a leveraged ETF of QQQ, which allows day traders to fully exploit the benefit of the active strategy while adhering to leverage constraints. The resulting portfolio would have earned an outstanding return of 1,484% during the same period of 2016 to 2023, while an investment in the QQQ ETF would have earned only 169%.
Multi-source aggregated classification for stock price movement prediction#
Predicting stock price movements is a challenging task. Previous studies mostly used numerical features and news sentiments of target stocks to predict stock price movements. However, their semantics-based sentiment analysis is sub-optimal to represent real market sentiments. Moreover, only considering the information of target companies is insufficient because the stock prices of target companies can be affected by their related companies. Thus, we propose a novel Multi-source Aggregated Classification (MAC) method for stock price movement prediction. MAC incorporates the numerical features and market-driven news sentiments of target stocks, as well as the news sentiments of their related stocks. To better represent real market sentiments from the news, we pre-train an embedding feature generator by fitting the news to real stock price movements. Embeddings given by the pre-trained sentiment classifier can represent the sentiment information in vector space. Moreover, MAC introduces a graph convolutional network to capture the news effects of related companies on the target stock. Finally, MAC can predict stock price movements for the next trading day based on the aforementioned features. Extensive experiments prove that MAC outperforms state-of-the-art baselines in stock price movement prediction, Sharpe Ratio, and backtesting trading incomes
Cryptocurrencies: Stylized Facts and Risk Based Momentum Investing#
The motivation of this research is in two folds, to understand the distributional characteristics of cryptocurrencies by means of stylized facts, and also to assess the feasibility of risk based and trend following approaches to investing in this asset class. Cryptocurrencies are more of a recent phenomenon, unlike the traditional asset classes. This poses an explicit constraint on the availability of longer history and also reliability of investment performance. Acknowledging such constraint, I focus my analysis based on the few years of data that is available.
151 Trading Strategies#
We provide detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured assets, volatility (as an asset class), real estate, distressed assets, cash, cryptocurrencies, miscellany (such as weather, energy, inflation), global macro, infrastructure, and tax arbitrage. Some strategies are based on machine learning algorithms (such as artificial neural networks, Bayes, k-nearest neighbors). We also give: source code for illustrating out-of-sample backtesting with explanatory notes; around 2,000 bibliographic references; and over 900 glossary, acronym and math definitions. The presentation is intended to be descriptive and pedagogical. This is the complete version of the book.
Cryptocurrency trading: A systematic mapping study#
This systematic mapping examines the current state of cryptocurrency trading research.
This study observes a recent increase in high-quality research and international collaboration in cryptocurrency trading.
This study notes a shift towards practical applications in cryptocurrency trading research, particularly in AI-driven prediction and automated trading.
This study highlights the diverse data types and inputs employed in cryptocurrency trading systems, with emphasis on the prevalent use of neural networks and deep learning algorithms.
Clustering in Cardinality-Constrained Portfolio Optimization#
In portfolio optimization, efficiently managing large pools of assets while adhering to car- dinality constraints presents a significant challenge. We propose a novel portfolio optimization framework that combines cardinality constraints with the classical Markowitz mean-variance model, using clustering to reduce dimensionality and achieve an optimal balance of risk and return. We use spectral clustering to group the residual returns of stocks. This method reveals natural groupings of assets based on their returns and correlations, enhancing our understand- ing and categorization of assets, which is crucial for efficiently reducing the optimization space and dimensionality
Regularised jump models for regime identification and feature selection#
A regime modelling framework can be employed to address the complexities of financial markets. Under the framework, market periods are grouped into distinct regimes, each distinguished by similar statistical characteristics. Regimes in financial markets are not directly observable but are often manifested in market and macroeconomic variables. The objective of regime modelling is to accurately identify the active regime from these variables at a point in time, a process known as regime identification.
One way to enhance the accuracy of regime identification is to select features that are most responsible for statistical differences between regimes, a process known as feature selection. Feature selection is also capable of both enhancing the interpretability of outputs from regime models, and substantially reducing the computational time required to calibrate regime models.
Models based on the Jump Model framework have recently been developed to address the joint problem of regime identification and feature selection. In the following work, we propose a new set of models called Regularised Jump Models that are founded upon the Jump Model framework.
These models perform feature selection that is more interpretable than that from the Sparse Jump Model, a model proposed in the literature pertaining to the Jump Model framework. Through a simulation experiment, we find evidence that these new models outperform the Standard and Sparse Jump Models, both in terms of regime identification and feature selection.
Dynamic Asset Allocation with Asset-Specific Regime Forecasts#
This article introduces a novel hybrid regime identification-forecasting framework designed to enhance multi-asset portfolio construction by integrating asset-specific regime forecasts. Unlike traditional approaches that focus on broad economic regimes affecting the entire asset universe, our framework leverages both unsupervised and supervised learning to generate tailored regime forecasts for individual assets. Initially, we use the statistical jump model, a robust unsupervised regime identification model, to derive regime labels for historical periods, classifying them into bullish or bearish states based on features extracted from an asset return series. Following this, a supervised gradient-boosted decision tree classifier is trained to predict these regimes using a combination of asset-specific return features and cross-asset macro-features. We apply this framework individually to each asset in our universe. Subsequently, return and risk forecasts which incorporate these regime predictions are input into Markowitz mean-variance optimization to determine optimal asset allocation weights. We demonstrate the efficacy of our approach through an empirical study on a multi-asset portfolio comprising twelve risky assets, including global equity, bond, real estate, and commodity indexes spanning from 1991 to 2023. The results consistently show outperformance across various portfolio models, including minimum-variance, mean-variance, and naive-diversified portfolios, highlighting the advantages of integrating asset-specific regime forecasts into dynamic asset allocation.
Optimal Factor Timing in a High-Dimensional Setting#
We develop a framework for equity factor timing in a high-dimensional setting when the number of factors and factor return predictors can be large. To ensure good out-of-sample performance, the approach is disciplined by shrinkage that effectively expresses a degree of skepticism about outsized gains from timing. In our empirical application, the predictors include macroeconomic variables and factor-specific characteristics spreads between the long and short legs of the factors. We find sizable gains from timing equity factors, including for factors constructed only from large-cap stocks.
Optimal Allocation to Cryptocurrencies in Diversified Portfolios#
We apply four quantitative methods for optimal allocation to Bitcoin and Ether cryptocurrencies within alternative and balanced portfolios including metrics for portfolio diversification, expected risk-returns, and skewness of returns distribution. Using roll-forward historical simulations, we show that all four allocation methods produce a persistent positive allocation to Bitcoin and Ether in alternative and balanced portfolios with a median allocation of about 2.7%. We conclude that core cryptocurrencies may provide positive contribution to risk-adjusted performances of broad investment portfolios. We emphasize the diversification benefits of cryptocurrencies as an asset class within broad risk-managed portfolios with systematic re-balancing.
Catching Crypto Trends; A Tactical Approach for Bitcoin and Altcoins#
In recent years, cryptocurrencies have attracted significant attention from both retail traders and large institutional investors. As their involvement in digital assets grows, so does their interest in active and risk-aware investment frameworks. This paper applies a well-established trend-following methodology, successfully deployed for decades in traditional asset classes, to Bitcoin, and then extends the analysis to a comprehensive, survivorship bias-free dataset covering all cryptocurrencies traded since 2015, to evaluate whether its robustness persists in the emerging digital asset space. We propose an ensemble approach that aggregates multiple Donchian channel-based trend models, each calibrated with different lookback periods, into a single signal, as well as a volatility-based position sizing method. This model, applied to a rotational portfolio of the top 20 most liquid coins, achieved notable net-of-fees returns, with a Sharpe ratio above 1.5 and an annualized alpha of 10.8% versus Bitcoin. While assessing the impact of transaction costs, we propose a straightforward yet effective portfolio technique to mitigate these expenses. Finally, we investigate correlations between crypto-focused trend-following strategies and those applied to traditional asset classes, concluding with a discussion on how investors can execute the proposed strategy through both on-chain and off-chain implementations.
Does Trend-Following Still Work on Stocks?#
This paper revisits and extends the results presented in 2005 by Wilcox and Crittenden in a white paper titled Does Trend Following Work on Stocks? Leveraging a survivorship-bias-free dataset of all liquid U.S. stocks from 1950 through November 2024, we examine more than 66,000 simulated long-only trend trades. Our results confirm a highly skewed profit distribution, with less than 7% of trades driving the cumulative profitability. These core statistics hold up out-of-sample (2005–2024), maintaining strong returns despite a modest decline in average trade profitability following the original publication. In the second part of this study, we backtest a long-only trend-following portfolio specifically aimed at capturing outlier returns in individual stocks. While the theoretical portfolio exhibits exceptional gross-of-fees performance from 1991 until 2024 (e.g., a CAGR of 15.19% and an annualized alpha of 6.18%), its extensive daily turnover poses a significant challenge once transaction costs are considered. Examining net-of-fee performance across various asset under management (AUM) levels, we find that the base trend-following approach is not viable for smaller portfolios (AUM less than $1M) due to the dampening effect of trading costs. However, by incorporating a Turnover Control algorithm, we substantially mitigate these transaction cost burdens, rendering the strategy attractive across all tested portfolio sizes even after fees.