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Roadmap — Five Stages from Zero to Fractal Finance

Principles

This roadmap is divided into five stages, not weeks. You advance only when the previous stage's exit test is passed — not when time runs out. If Stage 1 takes two weeks, good. If it takes two months, also good, as long as it genuinely passes.

Every stage has four elements:

  1. Goal — one sentence about what you possess when you finish
  2. Sources — ordered and prioritized
  3. Concrete output — what must exist in the repository
  4. Exit test — questions you must answer without opening a book

Meta-principles that bind every stage

  • Three-column journaling for every new concept: definition in own words | analogy or formula | numerical example from own data. If all three columns cannot be filled, the concept is not understood.
  • Feynman teach-back at the end of each stage. Write a new section in the living essay explaining the stage to a non-technical friend. The essay grows from ~1500 words (Stage 2) to 30+ pages by Stage 5.
  • Retype code, never copy-paste. For every code example from a book, retype it into Jupyter by hand.
  • Sequence is locked; pace is free. Never skip a stage. Never rush through one either.
  • Rest is part of learning. One full day per week with no learning-screen time.
  • Reference books are opened strictly by stage. The biggest temptation is opening The Fractal Theorem during Stage 1. Resist — you will be overwhelmed and lose motivation.

Stage 1 — Tools & Basics

Goal: Open Python, load stock price data, compute returns, and make a chart without any tutorial assistance. Your high-school math feels stronger than before.

Sources (order is binding)

Mathematical intuition — watch and journal:

  1. 3Blue1Brown — Essence of Calculus (12 videos, YouTube, free). Better intuition for derivatives and integrals than a full semester of calculus lectures.
  2. 3Blue1Brown — Essence of Linear Algebra (15 videos). Vectors, matrices, transformations — geometric intuition over computation.
  3. StatQuest with Josh Starmer — Statistics Fundamentals playlist. Histogram, mean, variance, normal distribution, skewness, kurtosis, p-value.

Python practice — do, don't just read:

  1. Python for Everybody by Charles Severance (py4e.com, free). Chapters 1–6: variables, loops, functions, lists, strings.
  2. Kaggle Learn — Pandas (kaggle.com/learn, free). Complete the course. Focus: read_csv, DataFrame, filtering, groupby, basic plotting.
  3. yfinance library — pip install yfinance. Documentation on the yfinance GitHub repo.

Concrete output

  • Three-column journal entries on each 3Blue1Brown video
  • Notebook 01-python-basics.ipynb — py4e exercises, typed by hand
  • Notebook 02-pandas-basics.ipynb — Kaggle Pandas exercises
  • Stage 1 project — 03-ihsg-first-look.ipynb: download the IDX Composite (^JKSE) from 2005 to today via yfinance, compute daily log-returns, plot price and returns, plot a histogram of returns with a normal-curve overlay, compute mean, std, skewness, and kurtosis. Write a 300-word conclusion in your own words: what is not normal about IHSG returns?

Exit test (answer without opening a book)

  • What is the difference between a derivative and an integral, intuitively?
  • If stock A has std = 2% and stock B has std = 4%, what does that mean for a trader?
  • What is the kurtosis of IHSG in your notebook, and what does that number mean relative to 3?
  • Write five lines of Python that download BBCA.JK and plot its price — from memory, without Google.

Signs you haven't passed

  • You still flinch at sigma, integral, or similar math symbols
  • You still copy-paste Python code from the internet without understanding it
  • You still Google "how to read a CSV in pandas" every day

Stage 2 — Conceptual Intuition (No Heavy Math)

Goal: Terms like butterfly effect, self-similarity, fat tails, Hurst exponent, and strange attractor feel familiar. You understand why markets are not normal systems — even if you can't yet prove it mathematically.

Sources (strict order)

  1. James Gleick — Chaos: Making a New Science — read cover to cover, like a novel. No exercises. One three-column journal entry per new concept.
  2. Monograph — The Scientific Legacy of Harold Edwin Hurst — short; one or two reading sessions. Focus: what Hurst discovered studying the Nile, and why it matters to finance.
  3. Mandelbrot & Hudson — The (Mis)behavior of Markets — Chapters 1–8. Deliberately light on math. Focus: Mandelbrot's critique of Bachelier, Markowitz, and Black-Scholes. What does he propose instead?

Concrete output

  • 20+ three-column journal entries on key concepts from Gleick and Mandelbrot
  • Feynman essay: essays/why-markets-are-not-gaussian.md — ~1500 words, written for a non-technical friend, using the charts from Stage 1 as visual evidence. This is a living document that will grow at every subsequent stage.

Exit test

  • Explain the butterfly effect using a non-weather example
  • Difference between the self-similarity of a Koch snowflake and of stock prices
  • Why did Mandelbrot call Black-Scholes "socially dangerous"?
  • What is the Hurst exponent conceptually? (no formulas yet)
  • Why is Nile flood data relevant to a stock trader?

Honest warning

Stage 2 is the most deceptive stage. The books are easy to read, which tricks you into feeling you've understood everything. You haven't. Gleick plants seeds; the trees grow in Stage 4. If you skip the journal, the seeds will vanish within three weeks.

Stage 3 — Classical Time Series (The Orthodoxy That Will Be Challenged)

Goal: Understand the orthodox language of financial econometrics — ARIMA, stationarity, GARCH, volatility clustering. This matters because Stage 4 will challenge much of it, and you cannot challenge what you do not understand.

Sources

  1. Ruey S. Tsay — Analysis of Financial Time Series — Chapters 1–3. The core of this stage. Read slowly; reproduce every numerical example in Python.
    • Chapter 1: characteristics of financial returns
    • Chapter 2: linear time series, ARMA
    • Chapter 3: conditional heteroscedasticity — GARCH family
  2. Peitgen, Jürgens, Saupe — Chaos and Fractals — Chapters 1–3. Read in parallel with Tsay as visual relief when Tsay feels dense. Focus: iteration, mathematical self-similarity, intuitive fractal dimension. Skip heavy formulas — return in Stage 4.
  3. Python libraries: statsmodels (ARMA, stationarity tests), arch (GARCH — the standard library), scipy.stats.

Concrete output

  • Notebook 04-stationarity-and-arma.ipynb — ADF test on IHSG log-returns, ARMA fit, residual analysis
  • Notebook 05-garch-ihsg.ipynb — GARCH(1,1) fit, conditional volatility plot, volatility clustering during 2008 and COVID 2020
  • New section in the Feynman essay: "What Classical Time Series Offers, and Where It Breaks"

Exit test

  • What is stationarity, and why are prices non-stationary while returns are stationary?
  • Difference between ARMA and GARCH intuitively — when do you use which?
  • On your own GARCH plot, point out volatility clustering
  • Why does GARCH still assume "thin" tails, and why is that a problem?
  • What is the fractal dimension of Britain's coastline according to Mandelbrot, and why is it not 1?

Red flag

If GARCH feels like a brick wall, step back to a 3Blue1Brown probability review and re-read Tsay Chapter 1 twice. This is the most technically difficult material in the entire roadmap — being slow here is normal.

Stage 4 — Fractal Finance Core (The Real Destination)

Goal: Compute the Hurst exponent on your own IHSG data, perform MF-DFA, interpret the result, and use those findings for risk management — not price prediction.

Sources (read in zig-zag, not linearly)

  1. Edgar E. Peters — Chaos and Order in the Capital Markets — full book. The clearest practitioner introduction to the Fractal Market Hypothesis, R/S analysis, and Hurst exponent. Reproduce every numerical example in your own Python — do not trust the book's numbers blindly.
  2. Mandelbrot — The (Mis)behavior of Markets — revisit and continue to the technical chapters (Chapter 9 onward). The formulas will feel much more approachable now that Tsay is in the back of your mind.
  3. Bisette & Van Der Post — The Fractal Theorem: Master Financial Chaos — your Python implementation companion. Retype every code snippet. Do not copy-paste — retype. That is the difference between understanding and not understanding.
  4. Peitgen (revisit) — chapters on fractal dimension, multifractals, L-systems. The math will feel more accessible now.

Python libraries

  • hurst — R/S analysis implementation of the Hurst exponent
  • nolds — nonlinear measures (Hurst, Lyapunov exponent, correlation dimension)
  • MFDFA — multifractal detrended fluctuation analysis
  • everything from Stage 3

Concrete output

  • Notebook 06-hurst-exponent-ihsg.ipynb — compute Hurst three ways (R/S, DFA, periodogram), compare results, interpret persistence / anti-persistence
  • Notebook 07-mfdfa-multi-asset.ipynb — MF-DFA on IHSG, USD/IDR, BBCA, BBRI, TLKM. Plot multifractal spectra. Which asset is the most "multifractal"?
  • Notebook 08-fat-tails-var.ipynb — compute Value-at-Risk three ways (normal, historical, Lévy stable). Which is most accurate during crises?
  • Major addition to the Feynman essay: "What I Learned from Fractals"

Exit test

  • What is the Hurst exponent of IHSG in your data, and what does it mean (>0.5, =0.5, <0.5)?
  • Difference between monofractal and multifractal — why do markets show the latter?
  • Why does Peters call the Fractal Market Hypothesis "more honest" than EMH?
  • Explain MF-DFA in five simple steps
  • If your VaR estimate from the normal distribution is 2% but the historical estimate is 3.5%, what does that 1.5% gap mean for a real trading account?

Stage 5 — Integration & Capstone

Goal: Integrate everything into a personal framework for risk management and decision-making — not prediction. Know when markets are "behaving normally" and when they are not, and how to adjust position sizing accordingly.

Sources

  • Tsay advanced chapters — only the relevant ones: VaR (Ch. 7), high-frequency data (Ch. 5), stochastic volatility (Ch. 12)
  • Tanaka — open only when a formula in Peters or Mandelbrot needs formal proof. Do not read linearly. Use it as a dictionary.
  • SSRN journal articles — discover your own. Search: "fractal market hypothesis empirical"

Capstone project — the peak of this roadmap

Title: A Fractal Risk-Management Framework for a Personal IHSG Portfolio

Minimum contents:

  1. Dataset: 5 assets (IHSG, USD/IDR, 3 LQ45 stocks of your choice), 2005 to present
  2. Classical statistical characterization (mean, std, skew, kurtosis, ADF, GARCH)
  3. Fractal analysis (Hurst, DFA, MF-DFA, multifractal spectrum)
  4. VaR comparison (parametric normal vs historical vs fat-tailed)
  5. Rule-based position sizing conditioned on fractal market state (e.g., reduce position when Hurst approaches 0.5, increase when >0.6 with trend confirmation)
  6. Simple backtest of that rule against buy-and-hold and equal-weight
  7. Honest discussion of limitations — what the framework does NOT promise, what can go wrong, why this is not a holy grail
  8. 15–25 page written report with charts, tables, and conclusions

Final exit test — roadmap graduation

Sit with a friend who is interested in investing, open your laptop, and within one hour:

  • (a) explain why a normal-distribution approach to risk is dangerous
  • (b) show, live, a Hurst exponent calculation on a stock of their choice
  • (c) explain how that finding changes the way they should measure risk

If yes — the roadmap is complete.