A Mathematical Analysis of Technical Analysis
Matthew Lorig, Zhou Zhou, Bin Zou
TL;DR
This paper provides a mathematical analysis of trading strategies based on exponential moving averages, deriving closed-form solutions for different drift models and evaluating their performance through simulations.
Contribution
It introduces new closed-form solutions for ExpMA-based strategies under Ornstein-Uhlenbeck and Markov chain drift models, with empirical performance analysis.
Findings
Optimal strategies depend on drift model parameters.
Transaction costs impact strategy performance.
Monte Carlo experiments illustrate parameter effects.
Abstract
In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modeled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to investigate how the performance of optimal ExpMA strategies is affected by variations in model parameters and by transaction costs.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Markets and Investment Strategies · Economic theories and models