On the Time-Varying Structure of the Arbitrage Pricing Theory using the Japanese Sector Indices

ArXiv ID: 2305.05998 “View on arXiv”

Authors: Unknown

Abstract

This paper is the first study to examine the time instability of the APT in the Japanese stock market. In particular, we measure how changes in each risk factor affect the stock risk premiums to investigate the validity of the APT over time, applying the rolling window method to Fama and MacBeth’s (1973) two-step regression and Kamstra and Shi’s (2023) generalized GRS test. We summarize our empirical results as follows: (1) the changes in monetary policy by major central banks greatly affect the validity of the APT in Japan, and (2) the time-varying estimates of the risk premiums for each factor are also unstable over time, and they are affected by the business cycle and economic crises. Therefore, we conclude that the validity of the APT as an appropriate model to explain the Japanese sector index is not stable over time.

Keywords: Arbitrage Pricing Theory (APT), Rolling Window Method, Fama-MacBeth Regression, Time-Varying Risk Premiums, GRS Test, Equities (Stock Indices)

Complexity vs Empirical Score

• Math Complexity: 4.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Street Traders
• Why: The paper employs standard but well-established econometric methods (rolling window regressions and GRS tests) with explicit data handling (daily sector indices, macroeconomic factors), resulting in moderate empirical rigor for academic research. While it presents standard APT theoretical setup and standard regression formulas, it lacks the advanced stochastic calculus or novel mathematical derivations typically required for high complexity scores.

  flowchart TD
    A["Research Goal: Test time-varying validity<br>of APT in Japanese market"] --> B["Data Collection<br>Japanese Sector Indices & Macroeconomic Factors"]
    B --> C["Methodology: Rolling Window Approach"]
    C --> D["Step 1: Fama-MacBeth Regression<br>Estimate Time-Varying Risk Premiums"]
    C --> E["Step 2: Generalized GRS Test<br>Assess Arbitrage Constraints"]
    D --> F["Computational Process: Factor Analysis<br>Monetary Policy & Business Cycle Effects"]
    E --> F
    F --> G["Key Findings: APT Validity Unstable<br>Risk Premiums Vary by Economic Crisis"]
    F --> H["Key Findings: Major Central Bank<br>Policy Changes Significantly Impact APT"]