Academic research

LLMs for Time Series: an Application for Single Stocks and Statistical Arbitrage

Recently, LLMs (Large Language Models) have been adapted for time series prediction with significant success in pattern recognition. However, the common belief is that these models are not suitable for predicting financial market returns, which are known to be almost random. We aim to challenge this misconception through a counterexample. Specifically, we utilized the Chronos model from Ansari et al.(2024) and tested both pretrained configurations and fine-tuned supervised forecasts on the largest American single stocks using data from Guijarro-Ordonnez et al.(2022). We constructed a long/short portfolio, and the performance simulation indicates that LLMs can in reality handle time series that are nearly indistinguishable from noise, demonstrating an ability to identify inefficiencies amidst randomness and generate alpha. Finally, we compared these results with those of specialized models and smaller deep learning models, highlighting significant room for improvement in LLM performance to further enhance their predictive capabilities.

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Optimal Trend Following Portfolios

This paper derives an optimal portfolio that is based on trend-following signal. Building on an earlier related article, it provides a unifying theoretical setting to introduce an autocorrelation model with the covariance matrix of trends and risk premia. We specify practically relevant models for the covariance matrix of trends. The optimal portfolio is decomposed into four basic components that yield four basic portfolios: Markowitz, risk parity, agnostic risk parity, and trend following on risk parity. The overperformance of the proposed optimal portfolio, applied to cross-asset trading universe, is confirmed by empirical backtests. We provide thus a unifying framework to describe and rationalize earlier developed portfolios.

Journal of Investment Strategies, 2024

Refined Model of the Covariance/Correlation Matrix between Securities

A new methodology has been introduced to clean the correlation matrix of single stocks returns based on a constrained principal component analysis using financial data. Portfolios were introduced, namely “Fundamental Maximum Variance Portfolios”, to capture in an optimal way the risks defined by financial criteria (“Book”, “Capitalization”, etc.). The constrained eigenvectors of the correlation matrix, which are the linear combination of these portfolios, are then analyzed. Thanks to this methodology, several stylized patterns of the matrix were identified: i) the increase of the first eigenvalue with a time scale from 1 minute to several months seems to follow the same law for all the significant eigenvalues with 2 regimes; ii) a universal law seems to govern the weights of all the “Maximum variance” portfolios, so according to that law, the optimal weights should be proportional to the ranking based on the financial studied criteria; iii) the volatility of the volatility of the “Maximum Variance” portfolios, which are not orthogonal, could be enough to explain a large part of the diffusion of the correlation matrix; iv) the leverage effect (increase of the first eigenvalue with the decline of the stock market) occurs only for the first mode and cannot be generalized for other factors of risk. The leverage effect on the beta, which is the sensitivity of stocks with the market mode, makes variable the weights of the first eigenvector.

PhD Discussion, Paris 13 University, 2019

Emergence of Correlation of Securities at Short Time Scales

The correlation matrix is the key element in optimal portfolio allocation and risk management. In particular, the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode, sectors and style factors. We investigate how these eigenvalues depend on the time scale of securities returns in the U.S. market. For this purpose, one-minute returns of the largest 533 U.S. stocks are aggregated at different time scales and used to estimate the correlation matrix and its spectral properties. We reveal the emergence of several dominant eigenvalues as the time scale increases. A simple lead–lag factor model is proposed to capture and reproduce the observed time-scale dependence of eigenvalues. Using this model, the relaxation time of the eigenvalues emergence is estimated to be around one minute for all the dominant eigenmodes, including the market mode. As a consequence, the use of five-minute returns time series for inferring correlations between stocks turns out to be a good compromise between statistical abundance of data points and well-established correlations. Our findings evidence that the underlying economic and financial mechanisms determining the correlation structure of securities depend as well on time scales.

Physica A, 2019

The Reactive Beta Model

We present a reactive beta model that accounts for the leverage effect and beta elasticity. For this purpose, we derive a correlation metric for the leverage effect to identify the relation between the market beta and volatility changes. An empirical test based on the most popular market‐neutral strategies is run from 2000 to 2015 with exhaustive data sets, including 600 U.S. stocks and 600 European stocks. Our findings confirm the ability of the reactive beta model to remove an important part of the bias from the beta estimation and from most popular market‐neutral strategies. To examine the robustness of the reactive beta measurement, we conduct Monte Carlo simulations over seven market scenarios against five alternative methods. The results confirm that the reactive model significantly reduces the bias overall when financial markets are stressed.

Journal of Financial Research, 2019

The Reactive Volatility Model

We present a new volatility model, simple to implement, that includes a leverage effect whose return-volatility correlation function fits to empirical observations. This model is able to capture both the “retarded effect” induced by the specific risk, and the “panic effect”, which occurs whenever systematic risk becomes the dominant factor. Consequently, in contrast to a GARCH model and a standard volatility estimate from the squared returns, this new model is as reactive as the implied volatility: the model adjusts itself in an instantaneous way to each variation of the single stock price or the stock index price and the adjustment is highly correlated to implied volatility changes. We also test the reactivity of our model using extreme events taken from the 470 most liquid European stocks over the last decade. We show that the reactive volatility model is more robust to extreme events, and it allows for the identification of precursors and replicas of extreme events.

Quantitative Finance, 2012