Analysis of Exponential Filter Time Series Operators of Geometric Brownian Motion in Trading Strategies

Abstract

Trading strategies based on moving average indicators have been analyzed in the academic literature numerous times using historical data to make statistical inferences about various properties such as expected returns. In this work, a deductive model is assumed where asset price dynamics are driven by a stochastic differential equation (SDE) in a continuous-time setting under the assumption of a frictionless market. A number of properties about the structure of the stochastic processes which result from the application of an exponential time series operator to the solution of the asset price SDE and various algebraic combinations of such processes are proven. A trading strategy is proposed and analyzed in which the size and direction of the market position in the risky asset incorporates the difference of two exponential time-series operators applied to the asset price process. The resulting portfolio SDE is proven to shown a positive expected return under specific assumptions.