Prices are the residue of people arguing about value. Fractals, multifractals, sentiment, and topology all say the market is social, fat-tailed, and memory-laden. They describe wildness; they don't forecast it.
A signal can predict well and still lose money. Signal quality grades the prediction; portfolio quality grades the harvested return. Measure both separately, because they fail in different places.
The signal sets direction; construction decides how much of each you own, moving the result as much as the signal. Correlation, costs, and limits enter here, so construction is alpha.
An indicator's scale knows nothing about money. Calibrate the reading to the risk-adjusted return that historically followed it, scale it to a common target, and size on that, not the raw output.
Raw signals live on different scales, so loud names dominate any sort. Z-scoring recenters and rescales into standard-deviation units, keeping the conviction pure ranking throws away.
Ranking assumes more-of-the-metric means more return. When the metric is U-shaped, both extremes are good and a naive rank buys the worst names. Plot the shape, then fold it monotone before you sort.
Econophysics describes markets beautifully but predicts nothing tradable alone. It shows where to look and keeps the tails in mind; reaching profit takes the same testing and costs as any strategy.
Ranked systems churn at the slice boundaries, where names flicker across on noise and you pay for each swap. A no-trade buffer holds them, and only net-of-cost performance tells the truth.
Trading ideas go absurd, familiar, inevitable; the edge is largest at absurd, gone at inevitable. Hunt in uncomfortable places but verify ruthlessly, because most absurd ideas are wrong, not early.
A market is a complex system where crashes emerge from millions of decisions, leaving power-law fingerprints. Fat tails and clustering are permanent; the lens explains markets, it can't time them.
If prices were random they'd diffuse like ink, spreading as the square root of time. Markets diffuse anomalously: faster trending, slower reverting. That exponent is the variance ratio in physics.
Entropy measures how unpredictable a series is, catching nonlinear structure the variance ratio misses. Maximizing it under market constraints produces fat tails: the tails are natural, not a glitch.