Curriculum·S203 Chart Literacy and Evidence·about 30 min
Trendlines and channels
By the end of this lesson you can
- →State a trendline construction rule precise enough that a second person reproduces your line
- →Explain why the only rigorous tests of chart patterns had to replace the human who draws them
- →Count the degrees of freedom in a hand-drawn line, and see what they cost
- →Use a channel as a description of past behavior without importing a prediction
Sophomore · enrolled learners
This lesson opens with Foundations of Technical Analysis, and the problem it had to solve first.
- What happened
- Lo, Mamaysky and Wang published in the Journal of Finance in 2000 an attempt to test technical patterns rigorously across US stocks from 1962 to 1996. Before they could test anything they had to solve a prior problem: pattern identification is performed by eye and is not reproducible, so there was no definition to test. Their solution was to replace the human entirely, smoothing prices with nonparametric kernel regression and defining each pattern as a formal condition on the smoothed series, then comparing the unconditional distribution of returns against the distribution conditioned on each pattern. With the human removed, they found that several technical indicators do provide incremental information.
- The decision point
- The finding is genuinely positive and it is not available to a person drawing lines by hand, because what was tested was an algorithm with fixed parameters, not the activity people perform. A method that must be automated before it can be evaluated is a method whose manual version has no established properties at all, and the gap between those two things is the entire subject of this course.
What you will be able to answer
- →Why did the rigorous test of chart patterns have to automate them?
- →What did Lo, Mamaysky and Wang find?
- →How many degrees of freedom does a hand-drawn trendline have?
- →What is a channel, used honestly?
Orientation and Year One are open: anyone can read them without an account. From Year Two onward the lessons are for enrolled learners, because progress through the later years only means anything if it is tracked against a record.
It is free. We do not sell the list and there is nothing to buy at the end of it.
Sources and review
- https://onlinelibrary.wiley.com/doi/abs/10.1111/0022-1082.00265
- https://www.nber.org/system/files/working_papers/w7613/w7613.pdf
- https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2308659
- https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-6419.2007.00519.x
Confidence medium·Volatility low·Reviewed 2026-08-05·Owner unassigned
Contested
Lo, Mamaysky and Wang report incremental information, which means the conditional return distribution differs from the unconditional one. That is a weaker claim than profitability after transaction costs, which they did not establish. Do not let a revision upgrade it.
The study covers US equities from 1962 to 1996. Whether the result transfers to crypto is unknown, and the honest position is that no comparable work exists for this market.