Valuation Measure of the Stock Market using Stochastic Volatility and Stock Earnings

Paper: arXiv 2508.06010

Authors: Andrey Sarantsev, Angel Piotrowski, Ian Anderson

Abstract

We create a time series model for annual returns of three asset classes: the USA Standard & Poor (S&P) stock index, the international stock index, and the USA Bank of America investment-grade corporate bond index. Using this, we made an online financial app simulating wealth process. This includes options for regular withdrawals and contributions. Four factors are: S&P volatility and earnings, corporate BAA rate, and long-short Treasury bond spread. Our valuation measure is an improvement of Shiller’s cyclically adjusted price-earnings ratio. We use classic linear regression models, and make residuals white noise by dividing by annual volatility. We use multivariate kernel density estimation for residuals. We state and prove long-term stability results.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous empirical modification to Shiller’s CAPE ratio using annual stochastic volatility and stock earnings while offering formal proofs of long-term stability. Reproducibility is exceptionally strong due to publicly accessible datasets, code, and a live web application.

Research Flowchart

  flowchart TD
    A[Research Goal: Improved Multi-Asset Valuation & Wealth Simulation] --> B[Data Inputs: S&P 500, Int'l Stocks, BAA Bonds, Treasury Spread, Earnings]
    B --> C[Methodology: Linear Regression with Volatility-Normalized Residuals]
    C --> D[Density Estimation: Multivariate Kernel Density Estimation for Residuals]
    D --> E[Model Verification: Proof of Long-Term Stability Results]
    E --> F[Outcomes: Enhanced CAPE Ratio & Interactive Wealth Simulation App]