The Limited Virtue of Complexity in a Noisy World

Speaker: Qi Jin (Oxford)

Measurement error in features affects the out-of-sample performance of portfolios and of return predictions. In a high-dimensional feature space, increasing model complexity under proper regularization can enhance the predictability of asset returns; however, the Sharpe ratio of a portfolio of assets and the R-squared of the prediction of the asset returns decrease monotonically and are convex as the noise level in features increases. Furthermore, when only a subset of features is observed, there is an optimal level of complexity beyond which incorporating additional features can degrade portfolio performance due to the effect of noise in the features. Thus, the marginal benefits of increasing model complexity will, at some point, start to diminish as the number of observed features increases. Our findings underscore a limited virtue of complexity in financial forecasting, where the performance of portfolios depends on the noise level in features, and where more complex models do not necessarily lead to better performance when features are not perfectly observed.

Volatility of Drift

Speaker: Per Mykland (University of Chicago) and Lan Zhang (University of Illinois, Chicago)

Sparse Multivariate Autoregressive Conditional Fréchet Models for High-Frequency Extreme Risk Dynamics

Speaker: Zhengjun Zhang (University of the Chinese Academy of Sciences)

We introduce a novel class of multivariate Fr\'echet models designed to incorporate diverse cross-sectional and temporal dependence while effectively capturing each marginal's time-varying characteristics. The classical multivariate maxima of moving maxima (M4) model is revisited for the multivariate structure, and a variant of the sparse M4 random coefficient model (vSM4R) is proposed to address the challenges in estimating the M4 model. For the marginal processes, the autoregressive conditional Fr\'echet (AcF) model that employs time-varying scale and shape parameter for independent Fr\'echet random variables is adapted and extended to $m$-dependent cases. The $m$-dependent AcF (mAcF) allows a richer class of dependence structures compared with the independent AcF, and establishes a straightforward connection with the vSM4R through a simple standardization. Probabilistic properties of the new models are studied, and composite likelihood (CL) methods are suggested for parameter estimations, along with their statistical properties investigated. Simulations demonstrate the robustness and flexibility of the proposed models, and empirical findings based on high-frequency cryptocurrency returns show our models' effectiveness in monitoring tail risks and understanding the co-movements of financial assets.

Big data and market microstructure in farm operations: a Bayesian study of the predictive distribution of corn revenue in the US Midwest

Speaker: Frederi Viens (Rice University) and Gina Pizzo (Michigan State University)

Corn is the dominant cash crop in the US. We study a Midwestern corn farmer’s annual revenue, using a remote-sensed data set covering upwards of a hundred million acres across nine states.  This presentation focuses on the state of Illinois, the largest state in terms of corn production in our massive dataset.  Our purpose is to describe the principle aspect of the farm finance microstructure: the distribution of farm revenue uncertainty. Working from a Bayesian predictive modeling framework which we developed for corn yield and calibrated at the county level, we incorporate yearly corn price uncertainty at the county level as well, via geometric Brownian motion, based on price data from country grain elevators collected via Bloomberg terminal. This allows us to sample our predictive corn revenue distribution for every field across 90 counties in Illinois. In a preliminary analysis where price and yield uncertainties are assumed to be independent, we find that the level of revenue uncertainty attributable only to yield variability represents scarcely more than a third of the total revenue uncertainty, consistent with what agricultural economists believe about uncertainty scales for farm management. We show how to aggregate these results to the farm level by considering what we call "synthetic farms", a notion which can also be labeled as "digital twins", leading to a preliminary result about economy of scale, which will need to be confirmed via a detailed correlation analysis of farm portfolio diversification. However, negative price-yield correlation is a well-documented phenomenon across the entire US cash-crop industry, at the national level. Working from county-level price and yield data, we estimate price-yield correlation coefficients for all Illinois counties in our study, confirming this negative correlation for the vast majority of Illinois counties, though not all of them. Via a careful implementation of a model with these county-level correlations, reassessing the relation between yield-attributable uncertainty and total uncertainty, since it can no longer be based on additivity of variances under an independence assumption, we find that yield variability typically represents about a quarter of the total variability, as measured in dollars per acres, aggregated across all fields in a county.  This entire study uses a corn yield predictive model that incorporates historical local weather uncertainty. Moving forward, we will recalibrate it to use future weather distribution scenarios as climate change starts having a marked effect on weather patterns in the Midwest. More frequent and more extreme dry weather scenarios will inform future farm revenue uncertainty via our methodology.