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

TL;DR

This paper develops a new valuation measure for the stock market based on a stochastic volatility model incorporating earnings, volatility, and interest rate factors, improving upon traditional P/E ratios.

Contribution

It introduces a novel valuation measure using stochastic volatility and residual analysis, with stability proofs, enhancing market valuation accuracy.

Findings

The valuation measure outperforms traditional P/E ratios.

Residuals are effectively modeled with kernel density estimation.

Long-term stability of the valuation measure is demonstrated.

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.