Paper: arXiv 2405.10920

Abstract

We study the data-generating processes for factors expressed in return differences, which the literature on time-series asset pricing seems to have overlooked. For the factors’ data-generating processes or long-short zero-cost portfolios, a meaningful definition of returns is impossible; further, the compounded market factor (MF) significantly underestimates the return difference between the market and the risk-free rate compounded separately. Surprisingly, if MF were treated coercively as periodic-rebalancing long-short (i.e., the same as size and value), Fama-French three-factor (FF3) would be economically unattractive for lacking compounding and irrelevant for suffering from the small “size of an effect.” Otherwise, FF3 might be misspecified if MF were buy-and-hold long-short. Finally, we show that OLS with net returns for single-index models leads to inflated alphas, exaggerated t-values, and overestimated Sharpe ratios (SR); worse, net returns may lead to pathological alphas and SRs. We propose defining factors (and SRs) with non-difference compound returns.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced mathematical concepts like geometric Brownian motions, compounding, and log returns, but it lacks empirical backtesting, datasets, or statistical metrics, focusing instead on theoretical critiques of existing models.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Data-generating process for factors?"] --> B{"Methodology<br>Compare Factor Definitions"}

  B --> C["Define Factor: Net Return Difference<br>Used in FF3 & Size/Value"]
  B --> D["Define Factor: Compounded Return<br>Used for Market Factor"]

  C --> E["Computational Process<br>Standard OLS Analysis"]
  D --> F["Computational Process<br>Compounding Separately<br>vs. Jointly"]

  E --> G["Outcome A: Net Returns<br>Inflated Alphas & SRs<br>Pathological Results"]
  F --> H["Outcome B: Compounded Returns<br>Market Factor Underestimates<br>Return Difference"]

  G --> I["Key Finding<br>Factors require Non-Difference<br>Compound Returns"]
  H --> I