arXiv subjects

Markus Pelger

Publications and source records attributed to Markus Pelger.

15 recordsLinked to original sources

arXiv2025

Attention Factors for Statistical Arbitrage

Statistical arbitrage exploits temporal price differences between similar assets. We develop a framework to jointly identify similar assets through factors, identify mispricing and form a trading policy that maximizes risk-adjusted performance after trading costs. Our Attention Factors are conditional latent factors that are the most useful for arbitrage trading. They are learned from firm characteristic embeddings that allow for complex interactions. We identify time-series signals from the residual portfolios of our factors with a general sequence model. Estimating factors and the arbitrage trading strategy jointly is crucial to maximize profitability after trading costs. In a comprehensive empirical study we show that our Attention Factor model achieves an out-of-sample Sharpe ratio above 4 on the largest U.S. equities over a 24-year period. Our one-step solution yields an unprecedented Sharpe ratio of 2.3 net of transaction costs. We show that weak factors are important for arbitrage trading.

cs.LG↗

arXiv2024

Automatic Outlier Rectification via Optimal Transport

In this paper, we propose a novel conceptual framework to detect outliers using optimal transport with a concave cost function. Conventional outlier detection approaches typically use a two-stage procedure: first, outliers are detected and removed, and then estimation is performed on the cleaned data. However, this approach does not inform outlier removal with the estimation task, leaving room for improvement. To address this limitation, we propose an automatic outlier rectification mechanism that integrates rectification and estimation within a joint optimization framework. We take the first step to utilize the optimal transport distance with a concave cost function to construct a rectification set in the space of probability distributions. Then, we select the best distribution within the rectification set to perform the estimation task. Notably, the concave cost function we introduced in this paper is the key to making our estimator effectively identify the outlier during the optimization process. We demonstrate the effectiveness of our approach over conventional approaches in simulations and empirical analyses for mean estimation, least absolute regression, and the fitting of option implied volatility surfaces.

stat.ML↗

arXiv2023

Target PCA: Transfer Learning Large Dimensional Panel Data

This paper develops a novel method to estimate a latent factor model for a large target panel with missing observations by optimally using the information from auxiliary panel data sets. We refer to our estimator as target-PCA. Transfer learning from auxiliary panel data allows us to deal with a large fraction of missing observations and weak signals in the target panel. We show that our estimator is more efficient and can consistently estimate weak factors, which are not identifiable with conventional methods. We provide the asymptotic inferential theory for target-PCA under very general assumptions on the approximate factor model and missing patterns. In an empirical study of imputing data in a mixed-frequency macroeconomic panel, we demonstrate that target-PCA significantly outperforms all benchmark methods.

econ.EM↗

arXiv2023

A Simple Method for Predicting Covariance Matrices of Financial Returns

We consider the well-studied problem of predicting the time-varying covariance matrix of a vector of financial returns. Popular methods range from simple predictors like rolling window or exponentially weighted moving average (EWMA) to more sophisticated predictors such as generalized autoregressive conditional heteroscedastic (GARCH) type methods. Building on a specific covariance estimator suggested by Engle in 2002, we propose a relatively simple extension that requires little or no tuning or fitting, is interpretable, and produces results at least as good as MGARCH, a popular extension of GARCH that handles multiple assets. To evaluate predictors we introduce a novel approach, evaluating the regret of the log-likelihood over a time period such as a quarter. This metric allows us to see not only how well a covariance predictor does over all, but also how quickly it reacts to changes in market conditions. Our simple predictor outperforms MGARCH in terms of regret. We also test covariance predictors on downstream applications such as portfolio optimization methods that depend on the covariance matrix. For these applications our simple covariance predictor and MGARCH perform similarly.

econ.EM↗

arXiv2022

Inference for Large Panel Data with Many Covariates

This paper proposes a novel testing procedure for selecting a sparse set of covariates that explains a large dimensional panel. Our selection method provides correct false detection control while having higher power than existing approaches. We develop the inferential theory for large panels with many covariates by combining post-selection inference with a novel multiple testing adjustment. Our data-driven hypotheses are conditional on the sparse covariate selection. We control for family-wise error rates for covariate discovery for large cross-sections. As an easy-to-use and practically relevant procedure, we propose Panel-PoSI, which combines the data-driven adjustment for panel multiple testing with valid post-selection p-values of a generalized LASSO, that allows us to incorporate priors. In an empirical study, we select a small number of asset pricing factors that explain a large cross-section of investment strategies. Our method dominates the benchmarks out-of-sample due to its better size and power.

econ.EM↗

arXiv2022

Bayesian Imputation with Optimal Look-Ahead-Bias and Variance Tradeoff

Missing time-series data is a prevalent problem in many prescriptive analytics models in operations management, healthcare and finance. Imputation methods for time-series data are usually applied to the full panel data with the purpose of training a prescriptive model for a downstream out-of-sample task. For example, the imputation of missing asset returns may be applied before estimating an optimal portfolio allocation. However, this practice can result in a look-ahead-bias in the future performance of the downstream task, and there is an inherent trade-off between the look-ahead-bias of using the entire data set for imputation and the larger variance of using only the training portion of the data set for imputation. By connecting layers of information revealed in time, we propose a Bayesian consensus posterior that fuses an arbitrary number of posteriors to optimize the variance and look-ahead-bias trade-off in the imputation. We derive tractable two-step optimization procedures for finding the optimal consensus posterior, with Kullback-Leibler divergence and Wasserstein distance as the dissimilarity measure between posterior distributions. We demonstrate in simulations and in an empirical study the benefit of our imputation mechanism for portfolio allocation with missing returns.

stat.ME↗

arXiv2021

Deep Learning Statistical Arbitrage

Statistical arbitrage exploits temporal price differences between similar assets. We develop a unifying conceptual framework for statistical arbitrage and a novel data driven solution. First, we construct arbitrage portfolios of similar assets as residual portfolios from conditional latent asset pricing factors. Second, we extract their time series signals with a powerful machine-learning time-series solution, a convolutional transformer. Lastly, we use these signals to form an optimal trading policy, that maximizes risk-adjusted returns under constraints. Our comprehensive empirical study on daily US equities shows a high compensation for arbitrageurs to enforce the law of one price. Our arbitrage strategies obtain consistently high out-of-sample mean returns and Sharpe ratios, and substantially outperform all benchmark approaches.

cs.LG↗

arXiv2021

Time-Series Imputation with Wasserstein Interpolation for Optimal Look-Ahead-Bias and Variance Tradeoff

Missing time-series data is a prevalent practical problem. Imputation methods in time-series data often are applied to the full panel data with the purpose of training a model for a downstream out-of-sample task. For example, in finance, imputation of missing returns may be applied prior to training a portfolio optimization model. Unfortunately, this practice may result in a look-ahead-bias in the future performance on the downstream task. There is an inherent trade-off between the look-ahead-bias of using the full data set for imputation and the larger variance in the imputation from using only the training data. By connecting layers of information revealed in time, we propose a Bayesian posterior consensus distribution which optimally controls the variance and look-ahead-bias trade-off in the imputation. We demonstrate the benefit of our methodology both in synthetic and real financial data.

stat.ML↗

arXiv2021

TextGNN: Improving Text Encoder via Graph Neural Network in Sponsored Search

Text encoders based on C-DSSM or transformers have demonstrated strong performance in many Natural Language Processing (NLP) tasks. Low latency variants of these models have also been developed in recent years in order to apply them in the field of sponsored search which has strict computational constraints. However these models are not the panacea to solve all the Natural Language Understanding (NLU) challenges as the pure semantic information in the data is not sufficient to fully identify the user intents. We propose the TextGNN model that naturally extends the strong twin tower structured encoders with the complementary graph information from user historical behaviors, which serves as a natural guide to help us better understand the intents and hence generate better language representations. The model inherits all the benefits of twin tower models such as C-DSSM and TwinBERT so that it can still be used in the low latency environment while achieving a significant performance gain than the strong encoder-only counterpart baseline models in both offline evaluations and online production system. In offline experiments, the model achieves a 0.14% overall increase in ROC-AUC with a 1% increased accuracy for long-tail low-frequency Ads, and in the online A/B testing, the model shows a 2.03% increase in Revenue Per Mille with a 2.32% decrease in Ad defect rate.

cs.CL↗

arXiv2020

State-Varying Factor Models of Large Dimensions

This paper develops an inferential theory for state-varying factor models of large dimensions. Unlike constant factor models, loadings are general functions of some recurrent state process. We develop an estimator for the latent factors and state-varying loadings under a large cross-section and time dimension. Our estimator combines nonparametric methods with principal component analysis. We derive the rate of convergence and limiting normal distribution for the factors, loadings and common components. In addition, we develop a statistical test for a change in the factor structure in different states. We apply the estimator to U.S. Treasury yields and S&P500 stock returns. The systematic factor structure in treasury yields differs in times of booms and recessions as well as in periods of high market volatility. State-varying factors based on the VIX capture significantly more variation and pricing information in individual stocks than constant factor models.

econ.EM↗

arXiv2020

Interpretable Sparse Proximate Factors for Large Dimensions

This paper proposes sparse and easy-to-interpret proximate factors to approximate statistical latent factors. Latent factors in a large-dimensional factor model can be estimated by principal component analysis (PCA), but are usually hard to interpret. We obtain proximate factors that are easier to interpret by shrinking the PCA factor weights and setting them to zero except for the largest absolute ones. We show that proximate factors constructed with only 5-10% of the data are usually sufficient to almost perfectly replicate the population and PCA factors without actually assuming a sparse structure in the weights or loadings. Using extreme value theory we explain why sparse proximate factors can be substitutes for non-sparse PCA factors. We derive analytical asymptotic bounds for the correlation of appropriately rotated proximate factors with the population factors. These bounds provide guidance on how to construct the proximate factors. In simulations and empirical analyses of financial portfolio and macroeconomic data we illustrate that sparse proximate factors are close substitutes for PCA factors with average correlations of around 97.5% while being interpretable.

stat.ME↗

arXiv2019

Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal component analysis to an adjusted covariance matrix estimated from partially observed panel data. We derive the asymptotic distribution for the estimated factors, loadings and the imputed values under an approximate factor model and general missing patterns. The key application is to estimate counterfactual outcomes in causal inference from panel data. The unobserved control group is modeled as missing values, which are inferred from the latent factor model. The inferential theory for the imputed values allows us to test for individual treatment effects at any time under general adoption patterns where the units can be affected by unobserved factors.

econ.EM↗

arXiv2019

On the existence of sure profits via flash strategies

We introduce and study the notion of sure profit via flash strategy, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction, we prove that there are no sure profits via flash strategies if and only if asset prices do not exhibit predictable jumps. This result relies on the general theory of processes and provides the most general formulation of the well-known fact that, in an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable direction or magnitude at predictable times. We furthermore show that any price process is always right-continuous in the absence of sure profits. Our results are robust under small transaction costs and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.

q-fin.TR↗

arXiv2019

Deep Learning in Asset Pricing

We use deep neural networks to estimate an asset pricing model for individual stock returns that takes advantage of the vast amount of conditioning information, while keeping a fully flexible form and accounting for time-variation. The key innovations are to use the fundamental no-arbitrage condition as criterion function, to construct the most informative test assets with an adversarial approach and to extract the states of the economy from many macroeconomic time series. Our asset pricing model outperforms out-of-sample all benchmark approaches in terms of Sharpe ratio, explained variation and pricing errors and identifies the key factors that drive asset prices.

q-fin.ST↗

arXiv2018

Change-Point Testing for Risk Measures in Time Series

We propose novel methods for change-point testing for nonparametric estimators of expected shortfall and related risk measures in weakly dependent time series. We can detect general multiple structural changes in the tails of marginal distributions of time series under general assumptions. Self-normalization allows us to avoid the issues of standard error estimation. The theoretical foundations for our methods are functional central limit theorems, which we develop under weak assumptions. An empirical study of S&P 500 and US Treasury bond returns illustrates the practical use of our methods in detecting and quantifying instability in the tails of financial time series.

econ.EM↗