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.
Trading with the Momentum Transformer: An Intelligent and Interpretable Architecture#
We introduce the Momentum Transformer, an attention-based deep-learning architecture, which out- performs benchmark time-series momentum and mean- reversion trading strategies. Unlike state-of-the-art Long Short-Term Memory (LSTM) architectures, which are sequential in nature and tailored to local processing, an attention mechanism provides our architecture with a direct connection to all previous time-steps. Our archi- tecture, an attention-LSTM hybrid, enables us to learn longer-term dependencies, improves performance when considering returns net of transaction costs and naturally adapts to new market regimes, such as during the SARS- CoV-2 crisis. Via the introduction of multiple attention heads, we can capture concurrent regimes, or temporal dynamics, which are occurring at different timescales. The Momentum Transformer is inherently interpretable, providing us with greater insights into our deep-learning momentum trading strategy, including the importance of different factors over time and the past time-steps which are of the greatest significance to the model.
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.
Following a Trend with an Exponential Moving Average: Analytical Results for a Gaussian Model#
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.
On covariance estimation of non-synchronously observed diffusion processes#
We consider the problem of estimating the covariance of two diffusion processes when they are observed only at discrete times in a non-synchronous manner. The modern, popular approach in the literature, the realized covariance estimator, which is based on (regularly spaced) synchronous data, is problematic because the choice of regular interval size and data interpolation scheme may lead to unreliable estimation. We propose a new estimator which is free of any ‘synchronization’ processing of the original data, hence free of bias or other problems caused by it.
Optimizing the Persistence of Price Momentum: Which Trends Are Your Friends?#
The traditional wisdom that price momentum which ranks stocks’ raw trailing returns is crash-prone fails to differentiate the various drivers of stocks’ past performances. As such, we compare the persistence of different sources of stocks’ price momentum discerned from applying factor-based performance attribution to their trailing 12-month returns. Our empirical analysis shows that beta- and country-driven price trends were not robust while style and industry momentum persisted both over the intermediate and, more strongly, short-term. Stock-specific momentum persisted over the intermediate term but strongly reverted over the short term; it was subsumed as a stand-alone strategy by both industry and style momentum and should be downweighed when optimizing a momentum signal for persistence. Our results suggest that style momentum is mostly a proxy for static factor tilts while industry and stock-specific momentum appear a separate anomaly that is strongest conditional on low-volatility market regimes. Their premium may reflect investor underreaction to economic shifts to which stocks’ exposures are imperfectly captured by binary industry classifications. Our results corroborate a strand of the extant literature through the novel lens of exactly decomposing the cross-section of stocks’ price momentum; contradicting findings are explained by methodological differences.
Clustering Market Regimes Using the Wasserstein Distance#
The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm for clustering financial time-series into a suitable number of temporal segments (market regimes). As a special case of the above, we develop a robust algorithm that automates the process of classifying market regimes. The method is robust in the sense that it does not depend on modelling assumptions of the underlying time series as our experiments with real datasets show. This method – dubbed the Wasserstein $k$-means algorithm – frames such a problem as one on the space of probability measures with finite $p^text{th}$ moment, in terms of the $p$-Wasserstein distance between (empirical) distributions. We compare our WK-means approach with a more traditional clustering algorithms by studying the so-called maximum mean discrepancy scores between, and within clusters. In both cases it is shown that the WK-means algorithm vastly outperforms all considered competitor approaches. We demonstrate the performance of all approaches both in a controlled environment on synthetic data, and on real data.
Nonlinear Time Series Momentum#
We document a persistent nonlinear relationship between price trends and risk-adjusted returns across markets and asset classes that is consistent with asset pricing theory. Nonlinearities in time series momentum are consistent with past returns reflecting information about conditional expected returns, in line with investors using conditioning information to form efficient portfolios. Machine learning techniques are useful in uncovering these relationships and yield economically and statistically significant out-of-sample improvements in time series momentum strategies.
Building Diversified Portfolios that Outperform Out-of-Sample#
This paper introduces the Hierarchical Risk Parity (HRP) approach. HRP portfolios address three major concerns of quadratic optimizers in general and Markowitz’s CLA in particular: Instability, concentration and underperformance.
HRP applies modern mathematics (graph theory and machine learning techniques) to build a diversified portfolio based on the information contained in the covariance matrix. However, unlike quadratic optimizers, HRP does not require the invertibility of the covariance matrix. In fact, HRP can compute a portfolio on an ill-degenerated or even a singular covariance matrix, an impossible feat for quadratic optimizers. Monte Carlo experiments show that HRP delivers lower out-of-sample variance than CLA, even though minimum-variance is CLA’s optimization objective. HRP also produces less risky portfolios out-of-sample compared to traditional risk parity methods.
The CoinAlg Bind: Profitability-Fairness Tradeoffs in Collective Investment Algorithms#
Collective In vestment Algorithms (CoinAlgs) are increas- ingly popular systems that deploy shared trading strate- gies for investor communities. Their goal is to democratize sophisticated—often AI-based—investing tools. We identify and demonstrate a fundamental profitability- fairness tradeoff in CoinAlgs that we call the CoinAlg Bind: CoinAlgs cannot ensure economic fairness without losing profit to arbitrage. We present a formal model of CoinAlgs, with definitions of privacy (incomplete algorithm disclosure) and economic fair- ness (value extraction by an adversarial insider). We prove two complementary results that together demonstrate the CoinAlg Bind. First, privacy in a CoinAlg is a precondition for insider attacks on economic fairness. Conversely, in a game-theoretic model, lack of privacy, i.e., transparency, enables arbitrageurs to erode the profitability of a CoinAlg. Using data from Uniswap, a decentralized exchange, we empirically study both sides of the CoinAlg Bind. We quantify the impact of arbitrage against transparent CoinAlgs. We show the risks posed by a private CoinAlg: Even low-bandwidth covert-channel information leakage enables unfair value ex- traction.
E#
This paper introduces a model-free Reinforcement Learning (RL) framework for portfolio allocation across Foreign Exchange (FX) assets, with a particular focus on carry trade strategies. The study examines whether RL-based approaches can yield distinct outcomes compared to traditional portfolio allocation techniques, such as Mean-Variance Optimization (MVO). The objective is to evaluate the performance of an RL agent in constructing a portfolio driven by FX carry signals and benchmark it against MVO. This work contributes to the literature by demonstrating the adaptability of RL to dynamic FX environments and its potential to outperform static optimization methods under varying market conditions.
Risk Beyond Volatility: A Conditional Framework for Downside Harm and Capital Loss#
Volatility remains the dominant operational proxy for risk in portfolio theory, asset pricing, and performance evaluation. Despite its widespread adoption, volatility treats upside and downside deviations symmetrically and abstracts away from the temporal and path-dependent nature of capital loss. This paper argues that these properties reflect not an economic definition of risk, but a modeling convenience rooted in early mean-variance theory.
The authors propose a conditional framework in which risk is defined as cumulative downside exposure relative to an explicit evaluation horizon and constraint set. This formulation captures both the magnitude and persistence of losses while preserving the asymmetry inherent in capital impairment. The paper shows that volatility-based metrics can misrank risk across strategies and assets exhibiting similar dispersion but substantially different drawdown dynamics.
By Ryan Nelson (The University of Tampa).
Mentioned by Ralph Sueppel in this discussion: “Paper proposes an alternative to volatility where risk is defined as cumulative downside exposure relative to an explicit evaluation horizon… It captures both the magnitude and persistence of losses while preserving the asymmetry inherent in capital impairment.”
Optimizing Liquidity Provision on Uniswap v3: A Comparative Analysis of Adaptive Strategies#
A comprehensive six-month backtesting study (April-September 2024) comparing multiple liquidity provision strategies on ETH/USDC pools in Uniswap v3. Tested approaches include constant intervals, moving averages, and dual-range allocations. The study examines capital efficiency, range width effects, and market volatility impacts, with parameter optimization across different strategy configurations. Results highlight the challenges of active liquidity management in volatile market conditions. By Zelos Research.
How Demeter Improves the Calculation of Liquidity Fees in Uniswap V3#
This post addresses the problem of fee calculation accuracy when prices cross liquidity position boundaries within a single minute. The enhanced algorithm assumes uniform price movement within one-minute intervals and allocates fees proportionally based on how many ticks the price has passed within the market-making range. This boundary crossing detection and linear price interpolation significantly improves backtesting precision for Uniswap V3 liquidity positions. By Zelos Research.
Pricing Uniswap V3 with Stochastic Process, Part 4#
A technical exposition of mathematical tools needed for pricing Uniswap V3 positions, including optimal stopping theorems, Laplace transforms, and Chapman-Kolmogorov equations. The authors establish foundations for deriving stopping time formulas that determine when liquidity positions reach price boundaries, covering martingale stopping theorem, two-boundary stopping problems, and exponential martingales. By Zelos Research.
Delta Neutral Strategy and Optimization of Uniswap V3#
Explores hedging strategies for Uniswap V3 liquidity provision using delta neutrality via AAVE borrowing. The approach divides the initial capital into two parts and uses borrowed assets to offset directional exposure while capturing fee income. The study performs backtesting to identify optimal market-making ranges through volatility-linked parameters, covering Greeks analysis, leveraged liquidity, capital allocation formulas, and volatility-adjusted range selection using the Demeter backtesting framework. By Zelos Research.
Pricing Uniswap V3 with Stochastic Process, Part 5#
Presents pricing models for Uniswap V3 positions using stochastic calculus. The work assumes geometric Brownian motion price dynamics and derives both European-style (exit only at boundaries) and American-style (exit anytime) valuation formulas. Fee collection models transition from boundary-only to continuous collection scenarios, covering optimal stopping strategies and boundary crossing problems. By Zelos Research.
An LVR Approach Proof of Guillaume Lambert’s Uniswap V3 Implied Volatility#
Demonstrates that LVR-based and Guillaume Lambert’s approaches produce identical implied volatility formulas for Uniswap V3 positions. The authors prove mathematical consistency between the two methodologies, showing both rely on similar assumptions about risk-free rates and instantaneous liquidity conditions. The proof covers LVR instantaneous loss calculations, Lambert’s IV formula, normalization approaches, and fee acquisition rates. By Zelos Research.
Implied Volatility from Uniswap V3 Liquidity Positions#
Presents methodology for calculating implied volatility in Uniswap V3 by deriving volatility perspectives from liquidity provider behaviors. The approach uses bisection methods to align theoretical option pricing with real market conditions, enabling a distribution of volatility views weighted by their liquidity’s dollar value. Covers option pricing formulas, position-level IV analysis, time series IV tracking, and weighted averaging methodology. Part 6 in the Uniswap V3 pricing series. By Zelos Research.
Uniswap v4: Insights on Performance#
A comparative performance analysis of Uniswap v4 versus v3, examining trading execution and liquidity provision metrics. The research shows that v4 trading participation has been gradually increasing and overtaking v3, and for small-to-mid size trades, v4 achieves lower levels of slippage. However, v4 maintains lower overall liquidity than v3, though fee returns are more stable. Covers hook features, trading participation metrics, slippage analysis, and fee generation stability. By Zelos Research.
Stochastic Processes and the Pricing of Uniswap V2#
Analyzes Uniswap V2 liquidity provider positions through stochastic processes, examining impermanent loss (IL) and loss versus rebalancing (LVR). The authors apply martingale stopping methods to derive pricing formulas for V2 positions, treating them as exotic options. Key findings include that the value of the V2 position is independent of volatility in their model, though they acknowledge this oversimplifies by ignoring position reconstruction costs during price swings. Covers geometric Brownian motion modeling, American perpetual option pricing, and Jensen’s inequality applications. By Zelos Research.
Are Simple Technical Trading Rules Profitable in Bitcoin Markets?#
This paper examines the profitability of simple technical trading rules in bitcoin markets comprehensively, taking into account realistic investor behavior. The study investigates whether classic technical analysis strategies such as moving average rules can generate excess returns in cryptocurrency markets, contributing to the ongoing debate about market efficiency in digital asset markets.
By Michael Frömmel and Niek Deprez, published in the International Review of Economics & Finance (2024).
Mentioned by Jungle Rock in this discussion.
Quality Minus Junk#
This paper provides a tractable valuation model that shows how stock prices should increase in their quality characteristics: profitability, growth, and safety. A “quality” security is defined as one that is safe, profitable, growing, and well managed. Empirically, the authors find that high-quality stocks do have higher prices on average but not by a large margin, and high-quality stocks have high risk-adjusted returns. A quality-minus-junk (QMJ) factor that goes long high-quality stocks and shorts low-quality stocks earns significant risk-adjusted returns in the United States and across 24 countries.
By Clifford S. Asness, Andrea Frazzini, and Lasse Heje Pedersen.
Mentioned by Kurtis The Quant in this discussion.
Episodic Factor Pricing#
This paper challenges conventional factor models by showing that factor pricing power is time varying and frequently switches between active and inactive states. The authors propose a real-time method to identify factor pricing states, showing that conditioning on these states materially improves out-of-sample multifactor portfolio performance, even after transaction costs. A conditional stochastic discount factor with state-dependent risk prices provides a better description of the investment opportunity set. Across a broad set of factors, pricing power is concentrated in active states and largely absent otherwise, implying that factor premia and risk prices are inherently episodic rather than persistent.
By Sophia Zhengzi Li, Peixuan Yuan, and Guofu Zhou.
Mentioned by Ivan Blanco in this discussion.
All Days Are Not Created Equal: Understanding Momentum by Learning to Weight Past Returns#
By flexibly weighting the information contained in past realized returns, the authors construct a momentum strategy that outperforms and subsumes the performance of traditional stock momentum. The strategy performs well in crises and continues to work in recent decades, circumventing the issue of momentum crashes. The authors show that the way past returns are weighted is consistent with the strategy exploiting an underreaction to information contained in realized returns. Earnings announcements, market-wide jumps, and large individual returns realized during the formation period are found to be most informative about future stock returns.
By Heiner Beckmeyer and Timo Wiedemann, published in the Journal of Banking and Finance (2025).
Mentioned by Ivan Blanco in this discussion.
Beat the Market: An Effective Intraday Momentum Strategy for S&P500 ETF (SPY)#
This paper investigates the profitability of a simple yet effective intraday momentum strategy applied to SPY, one of the most liquid ETFs tracking the S&P 500. Unlike academic literature that typically limits trading to the last 30 minutes of the trading session, this model initiates trend-following positions as soon as there is an indication of abnormal demand/supply imbalance in the intraday price action. The strategy introduces dynamic trailing stops to mitigate downside risks while allowing for unlimited upside potential. From 2007 to early 2024, the resulting intraday momentum portfolio achieved a total return of 1,985% (net of costs), an annualized return of 19.6%, and a Sharpe Ratio of 1.33.
By Carlo Zarattini, Andrew Aziz, and Andrea Barbon.
Mentioned by Pasta Capital in this discussion.
A Unified Framework for Anomalies based on Daily Returns#
Numerous cross-sectional equity anomalies draw on the same underlying information: the sequence of daily returns over the previous month. Using a data-driven approach, the authors estimate the empirical mapping from the distribution of last month’s daily returns to future performance without imposing functional forms. The resulting Daily Return Information Factor (DRIF) earns economically large premia, holds across subsamples and research designs, and remains significant after controlling for the modern factor zoo. DRIF subsumes most short-horizon and lottery-style anomalies and emerges as a key factor in asset pricing tests.
By Nusret Cakici, Christian Fieberg, Gabor Neszveda, Robert J. Bianchi, and Adam Zaremba.
Mentioned by Quantitativo in this discussion: “The factor zoo isn’t crowded. It’s redundant. Daily returns already contain the signal — we just kept slicing them the wrong way.”
ASRI: An Aggregated Systemic Risk Index for Cryptocurrency Markets#
This paper introduces the Aggregated Systemic Risk Index (ASRI), a composite measure comprising four weighted sub-indices: Stablecoin Concentration Risk (30%), DeFi Liquidity Risk (25%), Contagion Risk (25%), and Regulatory Opacity Risk (20%).
The framework incorporates data from DeFi Llama, Federal Reserve FRED, and on-chain analytics, and was validated against historical crises including Terra/Luna (May 2022), Celsius/3AC (June 2022), FTX (November 2022), and SVB (March 2023). Event study analysis detected statistically significant signals for all four crises with an average lead time of 18 days. A three-regime Hidden Markov Model identifies distinct Low Risk, Moderate, and Elevated states with regime persistence exceeding 94%, and out-of-sample testing on 2024-2025 data confirmed zero false positives.
The ASRI framework addresses a critical gap in risk monitoring by capturing DeFi-specific vulnerabilities—composability risk, flash loan exposure, and tokenized real-world asset linkages—that traditional systemic risk measures cannot accommodate.
By Murad Farzulla and Andrew Maksakov.
Mentioned by Saeed in this discussion.
R&D Alpha: Investment Intensity and Long-Term Stock Returns#
This paper tests whether high research and development (R&D) intensity predicts higher subsequent equity returns in a large-cap U.S. universe using methodology designed for portfolio implementability. Each year, S&P 500 stocks are sorted into quintiles by R&D intensity (R&D expense divided by revenue) and subsequent returns are evaluated with timing designed to mitigate look-ahead bias.
The high-minus-low R&D factor averages 3.73% per year, with monthly factor spanning tests confirming a statistically distinct premium (FF5 alpha = 4.37%, p < 0.01). The investable RD20 strategy, a simple long-only portfolio holding the top 20 stocks by R&D intensity equal-weighted, delivers 7.52% annual excess return versus SPY after transaction costs. The paper documents sector tilts, factor exposures, and regime dependence, noting that much of the value comes from sector tilts and regime dependence rather than a clean textbook factor.
By Abhishek Sehgal.
Mentioned by Ivan Blanco in this discussion: “Worth a read for anyone thinking seriously about intangible capital, innovation exposure, and practical factor implementation.”
Magnificent, but Not Extraordinary: Market Concentration in the US and Beyond#
This paper examines equity market concentration in the US since 1926 and in several developed markets. The authors find that current index weights of the largest firms align with historical and international patterns, and that valuation concentration moves with earnings concentration. A geometric Brownian motion benchmark with firm-specific shocks reproduces observed concentration, with idiosyncratic volatility identified as the key driver.
The central finding is that high concentration alone does not justify deviations from market weights or policy conclusions about firm breakups. The market portfolio remains optimal in the authors’ benchmark framework. Their evidence constrains pure multiple-expansion narratives and behavioral channels by linking valuations to fundamentals, pushing back on the popular narrative that the Magnificent 7 represent an unprecedented anomaly.
By Per Bye, Jens Soerlie Kvaerner, and Bas J.M. Werker.
Mentioned by Ivan Blanco in this discussion: “If you believe today’s US equity market is uniquely concentrated because of the Magnificent 7, history may disagree.”
Credit Spread News and Financial Market Risk#
This paper shows that credit spread news, defined by changes and absolute changes in corporate bond credit spreads, predict a substantial share of future variation in financial market risk. The author first documents a strong and robust predictive relationship between credit spread news and financial market risk, then investigates the economic mechanism underlying this relationship.
Both theoretical and empirical evidence highlight a central role for financial intermediaries’ risk expectations in driving the predictive power of credit spread changes. The findings establish credit spread news as statistically significant and economically meaningful predictors of financial market risk, offering a practical signal for macro-oriented systematic traders.
By Fabrizio Ghezzi.
Mentioned by Ralph Sueppel in this discussion.
Trend Following in Strategic Asset Allocation: A Long-Horizon Analysis and Retail-Oriented Implementation#
Traditional portfolio construction frameworks rely on static asset allocation and cross-asset diversification to manage risk and improve long-term outcomes. This paper investigates the role of trend following as a structural component of strategic asset allocation, rather than as a standalone return-seeking strategy. Using long-horizon historical data from 1979 to 2025, the authors examine whether systematic trend-based exposure management can complement traditional diversification by addressing risk from a different dimension: the temporal evolution of market trends.
The results suggest that incorporating trend following as a structural overlay can provide a complementary form of diversification — one based on time and regime dynamics rather than asset classes alone — potentially improving portfolio efficiency and resilience without relying on return forecasting or discretionary market timing. Simple equity trend filters such as 10-month moving averages or 12-1 momentum signals deliver comparable returns to buy-and-hold while substantially reducing maximum drawdown and improving risk-adjusted performance.
By Gabriele Galletta (Investimento Custodito).
Mentioned by Ivan Blanco in this discussion: “Trend following is not about alpha. It’s about risk control.”
A Quantitative Trading Strategy Based on A Position Management Model#
This paper establishes a quantitative trading strategy based on a position management model, applied to gold and bitcoin trading. The approach combines ARIMA time-series forecasting for price prediction with a position management framework that governs trade sizing and entry/exit rules. The authors develop differential autoregressive moving average models calibrated at different cycle times, finding that a 60-day data window produces the smallest prediction error, with the relative error of the average prediction value controlled at 0.003016. The position management model then uses these forecasts to determine optimal trade timing and allocation.
The strategy achieves an annualized rate of return of 25%, with accumulated income reaching $223,640.58 USD by September 10, 2021. Profitability and risk resistance are evaluated using Principal Component Analysis, and model validation via parameter variation confirms the solution is locally optimal and consistent with the initial parameterization. Sensitivity analysis shows that as initial commission increases or principal decreases, both trade count and returns decline gradually, confirming the model behaves as expected under parameter perturbation.
Efficient Portfolio Estimation in Large Risky Asset Universes#
This paper addresses the challenge of constructing efficient portfolios within a large investment universe composed exclusively of risky assets. The authors derive a linearly constrained regression representation of the efficient portfolio, which circumvents the need to estimate the mean vector and covariance matrix. Instead, they apply constrained sparse regression techniques (Linearly Constrained LASSO) to estimate portfolio weights directly.
The key insight is that in many real-world settings — such as institutional equity funds, emerging markets with unstable sovereign debt, or decentralized finance — a risk-free asset is unavailable. Traditional approaches like sample-based plug-in estimators, the 1/N rule, or minimum variance portfolios struggle to achieve mean-variance efficiency in large asset pools. By recasting the efficient portfolio problem as a linearly constrained regression, the authors bypass the notoriously difficult estimation of high-dimensional covariance matrices and mean vectors.
Theoretically, the authors establish asymptotic mean-variance efficiency of the estimated portfolio as both the number of assets and the sample size proportionally approach infinity. In extensive simulations and empirical studies using S&P 500 constituents with out-of-sample returns from 1981 to 2024, the method yields portfolios that satisfy specified risk levels, achieve superior Sharpe ratios, and outperform various benchmarks including equally weighted, minimum variance, and other sparse portfolio methods — both net and gross of transaction costs.
By Leheng Chen, Yingying Li, and Xinghua Zheng (Hong Kong University of Science & Technology).
Mentioned by Piotr Pomorski in this discussion.
Multiples for Valuation: Go High, Go Low, Ignore the Middle#
This paper examines whether valuation multiples such as D/P (dividend-to-price), P/E (price-to-earnings), and CAPE (cyclically adjusted P/E) can forecast stock returns, and under what conditions they are most useful. Using US data spanning 1871–2025, the author finds that multiples are far more useful at predicting forward returns when they are at relatively high or low levels than when they sit in the middle of their historical range.
The key finding is that the predictive power of valuation multiples is concentrated at the extremes. When multiples fall into the top or bottom quartile of their historical distribution, the in-sample correlation with subsequent approximately ten-year returns is substantially higher, with R² reaching up to 0.70. Out-of-sample forecasts generated from extreme multiples also significantly outperform those derived from mid-range multiples. The practical implication is that investors should pay close attention to valuations when they are unusually stretched in either direction, but can largely ignore them when they are near the middle of their historical range.
By Javier Estrada (IESE Business School).
Mentioned by Ivan Blanco in this discussion: “Do multiples predict returns? Valuations Only Matter at Extremes.”
Covariance Implied Risk Factors#
This paper examines the role of heteroskedasticity in extracting latent risk factors from asset returns. Standard principal component analysis (PCA) suffers from distortions when assets exhibit heterogeneous idiosyncratic variances, causing estimated factors to reflect clusters of idiosyncratic risk rather than true systematic risk. The author applies heteroskedastic PCA (heteroPCA) to correct for this bias by iteratively replacing the diagonal of the sample covariance matrix with estimates implied by the off-diagonal structure.
HeteroPCA delivers substantially better out-of-sample cross-sectional pricing performance compared to standard PCA across multiple equity portfolio sorts. The identified factors exhibit clearer economic interpretability, and the implied stochastic discount factor achieves lower Hansen-Jagannathan distances. The method trades off slightly worse time-series fit for much stronger cross-sectional pricing power, a tradeoff the author argues is economically favorable.
Key results: On AP-Tree portfolios, heteroPCA achieves out-of-sample Sharpe ratios of 0.46 (Tree10) and 0.55 (Tree40), compared to 0.18 and 0.26 from standard PCA. Across double-sorted portfolios, heteroPCA consistently outperforms: Size & Book-to-Market Sharpe ratio 0.28 vs 0.15, Size & Accruals 0.21 vs 0.13, Size & Investment 0.32 vs 0.20, and Size & Idiosyncratic Volatility 0.35 vs 0.21. Sharpe ratio gains often exceed 50% relative to standard PCA. RMS pricing errors are also lower, with heteroPCA reducing RMS alpha from 0.85-0.90 to 0.72-0.80 on AP-Tree portfolios.
By Mohammed Mehdi Kaebi (Insper Institute of Education and Research).
Mentioned by Ivan Blanco in this discussion: “Your PCA might be lying to you. Standard PCA distorts latent factors when assets have different idiosyncratic variances. The fix? Heteroskedastic PCA.”
Asset Allocation: From Markowitz to Deep Reinforcement Learning#
This paper benchmarks nine asset allocation strategies spanning traditional Modern Portfolio Theory and deep reinforcement learning. The traditional methods include the tangency portfolio, minimum variance, risk parity, and equal weight. The DRL methods include A2C, PPO, DDPG, SAC, and TD3. Each strategy is evaluated across both bullish and bearish market environments using real stock data.
Traditional MPT-based approaches deliver stable, consistent results without requiring a training phase. The tangency portfolio achieves the highest Sharpe and Calmar ratios across scenarios. DRL agents can surpass traditional methods in bull markets at their best (SAC achieved 179% annual return and a 2.58 Sharpe ratio), but exhibit high variance across runs due to stochastic optimization. In their worst runs, DRL agents fail to outperform the simple equal weight baseline. In bear markets the performance gap between traditional and DRL approaches narrows substantially, and DRL results become less reliable. The author suggests that more training data, additional technical indicators, and architectures like transformers could help stabilize DRL performance.
By Ricard Durall (Open University of Catalonia).
Mentioned by Jungle Rock in this discussion.