Price Trends
Overview
The fact that one can identify trends in a chart does not necessarily mean that following the trend will earn more money than a
market index fund would do. In fact,
the
efficient market Hypothesis
postulates that such visible price trends convey no useful information.
From a statistical perspective,
stochastic trends
are expected to develop within random walks, and do not convey any information.
However, there is a behavioural component to market trends which may justify some expectation of
Modeling Price Trends Quantitatively
The standard quantitative model of asset prices is based on the theory of
Brownian Motion and Ito Processes.
{% dX(t,B(t)) = u(t) dt + \sigma(t) dB(t) %}
Within this framework, a trend is usually interpreted to mean some value for {% u(t) %}
When there is a known long term return, (some average annual return over a long time frame),
the Ito model can be extended by using a
Brownian Bridge
Trend following Algorithms and Strategies
Algorithms
