Yukun Liu Publications

We show that the higher-orders and their interactions of the common sparse linear factors can effectively subsume the factor zoo. To this extend, we propose a forward selection Fama-MacBeth procedure as a method to estimate a high-dimensional stochastic discount factor model, isolating the most relevant higher-order factors. Applying this approach to terms derived from six widely used factors (the Fama-French five-factor model and the momentum factor), we show that the resulting higher-order model with only a small number of selected higher-order terms significantly outperforms traditional benchmarks both in-sample and out-of-sample. Moreover, it effectively subsumes a majority of the factors from the extensive factor zoo, suggesting that the pricing power of most zoo factors is attributable to their exposure to higher-order terms of common linear factors.

We study the impact of supply chain disruptions on U.S. firms based on the universe of seaborne shipment-level import transactions from 2013 to 2023. The granularity of the data allows us to build an index of firm-level disruptions of international suppliers and introduce a comprehensive set of stylized facts for supply chain relationships in the cross-section of firms. We build a general equilibrium heterogeneous firms model with two types of capital stocks—physical and international supplier capitals. Accumulation of supplier capital is an important endogenous margin of adjustment, and limiting this ability substantially delays recovery, especially in financially constrained firms.

The European Union Emission Trading System is a prominent market-based mechanism to reduce emissions. While the theory is well-understood, we are the first to study the whole cap-and-trade mechanism as a financial market. Analyzing the universe of transactions in 2005-2020 (more than one million records of granular transaction data), we show that this market features significant inefficiencies undermining its goals. First, about 40% of firms never trade in a given year. Second, many firms only trade during surrendering months, when compliance is immediate and prices are predictably high. Third, a number of operators engage in speculative trading, exploiting private information.

We propose a new non-linear single-factor asset pricing model 𝑟𝑖𝑡 = ℎ( 𝑓𝑡 𝜆𝑖) + 𝜖𝑖𝑡 . Despite its parsimony, this model represents exactly any non-linear model with an arbitrary number of factors and loadings – a consequence of the Kolmogorov-Arnold representation theorem. It features only one pricing component ℎ( 𝑓𝑡 𝜆𝑖), comprising a nonparametric link function of the time-dependent factor and factor loading that we jointly estimate with sieve-based estimators. Using 171 assets across major classes, our model delivers superior cross-sectional performance with a low-dimensional approximation of the link function. Most known finance and macro factors become insignificant controlling for our single-factor.