The Reliability of Geometric Brownian Motion Forecasts of S&P 500 Index Values

Abstract

This manuscript extends the literature on the application of geometric Brownian motion. Forecasted drift and diffusion terms estimated separately and recursively are plugged into the framework to forecast S&P 500 index values. Expected index values are estimated from one hundred thousand simulated index values and probabilities. The results of comparing expected index values to actual values, indicate that while reliable predictions of S&P 500 index values can be obtained at monthly, quarterly and annual frequencies, the reliability may decrease in that order.

Keywords: Geometric Brownian motion, Monte Carlo Simulation, Realized volatility, Forecasting, Log normal, Wiener process

JEL Classification: C6, C63, G12, G17