Equity Value and Volatility

As shown by continuous-time mathematics, a current stock price is the sum of the mean or equity value and the residual volatility of the current stock price. The residual volatility is a fraction of the volatility of the current stock price. Equity value is derived from the valuation of corporate and economic events. In a continuous-time first-order autoregressive process for a current demeaned stock price, valuation is completed when a lagged demeaned stock price is discounted. Volatility is present in a lagged demeaned stock price. Discounting a nominal lagged demeaned stock price converts it to equity value. A discounted model is a valuation model. The equity value from the valuation model is the sum of the mean stock price and the discounted lagged demeaned stock price. The valuation process starts from the process of mean reversion and ends at the process of autoregression. During mean reversion, the current demeaned stock price reacts to corporate and economic events. At autoregression, the lagged demeaned stock price is discounted completing valuation. My objective is to derive and test a valuation model under uncertainty. The residual volatility is produced by speculation. The residual volatility is a measure of stock market inefficiency, which is of topical interest. First-order autoregression of current demeaned stock prices was noticeably demonstrated at the start of the COVID-19 pandemic. The daily equity value represented 98.46% of the current S&P 500 in 2019. The proportion of daily equity value to the current S&P 500 was high. The inefficiency of a stock market is measured by the daily residual volatility of the current stock price. At the start of the COVID-19 pandemic, the S&P 500 market was 3.17% inefficient. The inefficiency was small in a stock market under great uncertainty.