Equity

Endogeneity in Empirical CorporateFinance ArXiv ID: ssrn-1748604 “View on arXiv” Authors: Unknown Abstract This chapter discusses how applied researchers in corporate finance can address endogeneity concerns. We begin by reviewing the sources of endogeneity - omitted Keywords: Endogeneity, Corporate Finance, Instrumental Variables, Quasi-Natural Experiments, Omitted Variables Bias, Equity Complexity vs Empirical Score Math Complexity: 7.0/10 Empirical Rigor: 4.0/10 Quadrant: Lab Rats Why: The paper is highly technical, covering advanced econometric techniques like instrumental variables, panel data methods, and regression discontinuity designs, which places it firmly in high math complexity. However, it is a theoretical survey/review focused on methodology rather than presenting backtest-ready data or specific implementations, leading to low empirical rigor. flowchart TD A["Research Goal<br>Address Endogeneity in Corporate Finance"] --> B["Identify Endogeneity Source<br>e.g., Omitted Variables"] B --> C{"Choose Methodology"} C --> D["Instrumental Variables<br>IV Approach"] C --> E["Quasi-Natural Experiments<br>DID / RD Designs"] D --> F["Data & Inputs<br>Equity Data, Instrument Validity"] E --> F F --> G["Computational Process<br>2SLS / Regression Analysis"] G --> H["Key Findings<br>Validated Causal Inferences<br>Reduced Bias in Equity Studies"]

Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2013 Edition ArXiv ID: ssrn-2238064 “View on arXiv” Authors: Unknown Abstract Equity risk premiums are a central component of every risk and return model in finance and are a key input in estimating costs of equity and capital in both cor Keywords: Equity Risk Premiums, Cost of Equity, Risk and Return Models, Capital Budgeting, Corporate Finance, Equity Complexity vs Empirical Score Math Complexity: 5.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper discusses theoretical risk-return models (like CAPM and multi-factor models) which involve mathematical formulas, but the excerpt shows conceptual explanation rather than dense derivations. Empirical rigor is low as it focuses on conceptual discussions, historical data limitations, and forward-looking estimates without providing backtesting, code, or implementation-heavy datasets. flowchart TD A["Research Goal<br>Determine & estimate the Equity Risk Premium (ERP)<br>for corporate finance & valuation"] --> B["Key Inputs & Data<br>• Historical Market Returns (Equity & Bonds)<br>• Implied ERP from Valuation Models<br>• Macroeconomic Factors (Inflation, Interest Rates)"] B --> C["Methodology<br>1. Historical Approach<br>2. Forward-Looking/Implied ERP<br>3. Macroeconomic Determinants"] C --> D["Computational Process<br>• Estimate Historical ERP<br>• Forecast future ERP<br>• Adjust for risk & macro conditions"] D --> E["Key Findings & Outcomes<br>• ERP varies over time (not constant)<br>• Influenced by macroeconomic factors<br>• Crucial for Cost of Equity & Capital Budgeting"]

Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2015 Edition ArXiv ID: ssrn-2581517 “View on arXiv” Authors: Unknown Abstract Equity risk premiums are a central component of every risk and return model in finance and are a key input in estimating costs of equity and capital in both cor Keywords: Equity Risk Premiums, Cost of Equity, Risk and Return Models, Capital Budgeting, Corporate Finance, Equity Complexity vs Empirical Score Math Complexity: 6.0/10 Empirical Rigor: 4.0/10 Quadrant: Lab Rats Why: The paper introduces advanced financial models like CAPM and multi-factor models with formulas, indicating moderate math complexity. However, it focuses on conceptual frameworks and theoretical estimation approaches (historical, survey, implied) without providing specific backtests, code, or detailed empirical datasets. flowchart TD A["Research Goal: Determine ERP"] --> B{"Methodology & Inputs"}; B --> C["Data: Historical Market Returns<br>Risk-Free Rate<br>Implied ERP from Valuation"]; B --> D["Model: DCF & Risk Models"]; C --> E{"Computational Process"}; D --> E; E --> F["Estimate Base ERP<br>+ Adjust for Risk Factors"]; E --> G["Forward-Looking Analysis<br>vs. Historical Averages"]; F --> H["Key Outcomes"]; G --> H; H --> I["2015 ERP Estimate<br>5.5% - 6.5%"]; H --> J["Implications for:<br>Cost of Equity & Capital"];

In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis ArXiv ID: ssrn-3686935 “View on arXiv” Authors: Unknown Abstract We develop a framework for analyzing stock market fluctuations, both theoretically and empirically. Households allocate capital to institutions with limited fle Keywords: Stock Market Fluctuations, Household Portfolio Allocation, Capital Flows, Institutional Investors, Market Dynamics, Equity Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 7.0/10 Quadrant: Holy Grail Why: The paper employs advanced theoretical modeling and econometrics (GIV) to derive and estimate market elasticity, demonstrating high mathematical sophistication. Empirical analysis uses granular instrumental variables and macro data to quantify a key parameter ($5 impact per $1 invested), making it data-heavy and implementation-ready. flowchart TD A["Research Goal: Investigate origins of stock market fluctuations"] --> B["Key Methodology: Inelastic Markets Hypothesis (IMH) Framework"] B --> C["Data/Inputs: Household capital allocation to institutions, institutional equity holdings"] C --> D["Computational Process: Theoretical modeling & empirical analysis of capital flows"] D --> E["Key Outcomes: Capital flows drive price fluctuations, explains market inelasticity"]

In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis ArXiv ID: ssrn-3875134 “View on arXiv” Authors: Unknown Abstract We develop a framework to theoretically and empirically analyze the fluctuations of the aggregate stock market. Households allocate capital to institutions, whi Keywords: Stock Market Fluctuations, Household Capital Allocation, Institutional Holdings, Financial Markets, Portfolio Choice, Equity Complexity vs Empirical Score Math Complexity: 8.0/10 Empirical Rigor: 7.0/10 Quadrant: Holy Grail Why: The paper introduces a novel theoretical framework with dynamic general equilibrium models and pricing kernels (high math complexity), while rigorously testing its core hypothesis using granular instrumental variables (GIV) on real financial data to estimate a precise price impact multiplier of ~5, including robustness checks (high empirical rigor). flowchart TD A["Research Goal<br>Understand aggregate stock market fluctuations"] --> B["Methodology<br>Develop theoretical & empirical framework"] B --> C["Input Data<br>Household & institutional capital allocation data"] C --> D["Computational Process<br>Estimate supply & demand elasticities"] D --> E["Key Finding<br>Markets are inelastic due to limited arbitrage"] E --> F["Outcome<br>Explains volatility puzzles & asset pricing"]

In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis ArXiv ID: ssrn-3886763 “View on arXiv” Authors: Unknown Abstract Our framework allows us to give a dynamic economic structure to old and recent datasets comprising holdings and flows in various segments of the market. The mys Keywords: Asset Pricing, Market Dynamics, Holding Data Analysis, Flow Analysis, Financial Markets, Equity Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 7.0/10 Quadrant: Holy Grail Why: The paper presents a complex stochastic framework using integrals and non-linear dynamics to model price impact and liquidity, indicating high mathematical density. Empirically, it leverages extensive granular datasets on holdings and flows across various market segments, suggesting strong data backing and backtest potential. flowchart TD A["Research Goal:<br>Determine the origins of financial fluctuations<br>via the Inelastic Markets Hypothesis"] --> B["Methodology:<br>Theoretical framework integrating<br>asset pricing with holdings/flows"] B --> C["Data Inputs:<br>Portfolio holdings & trading flows<br>in various market segments"] C --> D["Computational Process:<br>Dynamic economic structure modeling<br>of supply/demand inelasticity"] D --> E["Key Findings:<br>Price volatility stems from inelastic supply/demand<br>Portfolio adjustments drive financial fluctuations"] E --> F["Outcomes:<br>Unified framework for analyzing<br>old and recent market datasets"]

The Econometrics of Event Studies ArXiv ID: ssrn-608601 “View on arXiv” Authors: Unknown Abstract The number of published event studies exceeds 500, and the literature continues to grow. We provide an overview of event study methods. Short-horizon methods ar Keywords: Event Study, Market Efficiency, Abnormal Returns, Event Study Methodology, Equity Complexity vs Empirical Score Math Complexity: 4.0/10 Empirical Rigor: 6.0/10 Quadrant: Street Traders Why: The paper reviews established econometric methods (like risk-adjusted returns and significance testing) rather than introducing complex new mathematics, scoring moderate math complexity. It emphasizes empirical implementation through statistical properties, data constraints (daily vs. monthly returns), and real-world application guidelines, warranting moderate empirical rigor. flowchart TD A["Research Goal: Assess Market Efficiency & Impact of Equity Events"] --> B["Data Collection: Event Dates, Stock Prices, Market Indices"] B --> C["Methodology: Short-Horizon Event Study"] C --> D["Computation: Abnormal Returns AR_t = R_it - E[R_it|Market Model"]] D --> E["Aggregation: Cumulative Abnormal Returns CAR"] E --> F["Statistical Testing: Significance of CAR"] F --> G["Key Outcome: Evidence of Market Efficiency or Anomalies"]

Switching between states and the COVID-19 turbulence ArXiv ID: 2512.20477 “View on arXiv” Authors: Ilias Aarab Abstract In Aarab (2020), I examine U.S. stock return predictability across economic regimes and document evidence of time-varying expected returns across market states in the long run. The analysis introduces a state-switching specification in which the market state is proxied by the slope of the yield curve, and proposes an Aligned Economic Index built from the popular predictors of Welch and Goyal (2008) (augmented with bond and equity premium measures). The Aligned Economic Index under the state-switching model exhibits statistically and economically meaningful in-sample ($R^2 = 5.9%$) and out-of-sample ($R^2_{"\text{oos"}} = 4.12%$) predictive power across both recessions and expansions, while outperforming a range of widely used predictors. In this work, I examine the added value for professional practitioners by computing the economic gains for a mean-variance investor and find substantial added benefit of using the new index under the state switching model across all market states. The Aligned Economic Index can thus be implemented on a consistent real-time basis. These findings are crucial for both academics and practitioners as expansions are much longer-lived than recessions. Finally, I extend the empirical exercises by incorporating data through September 2020 and document sizable gains from using the Aligned Economic Index, relative to more traditional approaches, during the COVID-19 market turbulence. ...

The Aligned Economic Index & The State Switching Model ArXiv ID: 2512.20460 “View on arXiv” Authors: Ilias Aarab Abstract A growing empirical literature suggests that equity-premium predictability is state dependent, with much of the forecasting power concentrated around recessionary periods (Henkel et al., 2011; Dangl and Halling, 2012; Devpura et al., 2018). I study U.S. stock return predictability across economic regimes and document strong evidence of time-varying expected returns across both expansionary and contractionary states. I contribute in two ways. First, I introduce a state-switching predictive regression in which the market state is defined in real time using the slope of the yield curve. Relative to the standard one-state predictive regression, the state-switching specification increases both in-sample and out-of-sample performance for the set of popular predictors considered by Welch and Goyal (2008), improving the out-of-sample performance of most predictors in economically meaningful ways. Second, I propose a new aggregate predictor, the Aligned Economic Index, constructed via partial least squares (PLS). Under the state-switching model, the Aligned Economic Index exhibits statistically and economically significant predictive power in sample and out of sample, and it outperforms widely used benchmark predictors and alternative predictor-combination methods. ...

Reinforcement Learning in Queue-Reactive Models: Application to Optimal Execution ArXiv ID: 2511.15262 “View on arXiv” Authors: Tomas Espana, Yadh Hafsi, Fabrizio Lillo, Edoardo Vittori Abstract We investigate the use of Reinforcement Learning for the optimal execution of meta-orders, where the objective is to execute incrementally large orders while minimizing implementation shortfall and market impact over an extended period of time. Departing from traditional parametric approaches to price dynamics and impact modeling, we adopt a model-free, data-driven framework. Since policy optimization requires counterfactual feedback that historical data cannot provide, we employ the Queue-Reactive Model to generate realistic and tractable limit order book simulations that encompass transient price impact, and nonlinear and dynamic order flow responses. Methodologically, we train a Double Deep Q-Network agent on a state space comprising time, inventory, price, and depth variables, and evaluate its performance against established benchmarks. Numerical simulation results show that the agent learns a policy that is both strategic and tactical, adapting effectively to order book conditions and outperforming standard approaches across multiple training configurations. These findings provide strong evidence that model-free Reinforcement Learning can yield adaptive and robust solutions to the optimal execution problem. ...