Data-generating process and time-series asset pricing

TL;DR

This paper investigates the overlooked data-generating processes of factors in return differences in time-series asset pricing, revealing issues with traditional return definitions and proposing a new approach using non-difference compound returns.

Contribution

It highlights the limitations of current return definitions for factors and introduces a novel method using non-difference compound returns for more accurate asset pricing analysis.

Findings

Market factor significantly underestimates return differences.

Traditional return definitions can lead to misspecification of models.

Using non-difference compound returns improves model accuracy.

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.