Quant Project – Randomness in FX vs Coin Flips

Goal: Tests whether EUR/USD daily returns behave like a random walk (fair coin) using statistical tests and simulations.

Data

• Asset: EUR/USD exchange rate (Yahoo Finance ticker: EURUSD=X)
• Frequency: Daily closing prices
• Period: January 2010 – January 2025 (~3,900 observations)
• Transformations:
  • Returns calculated as daily percentage changes
  • Converted to binary sequence: 1 = up day, 0 = down day

This preprocessing allows direct comparison with simulated coin flips.

Methods

• Bias test (binomial)
• Runs test (Wald-Wolfowitz)
• Longest streak Monte Carlo
• Markov transition probabilities
• Autocorrelation & Ljung-Box
• Hurst exponent (R/S method)
• Shannon entropy
• Permutation test (toy momentum rule)

Key Results

• No directional bias (49.5% up days, p=0.52)
• Runs and longest streaks consistent with randomness
• No short-term memory (Markov, permutation)
• Volatility clustering in squared returns (p < 1e-70)
• Mild persistence (Hurst ≈ 0.55)
• Entropy ≈ 1.0 bits → near-max unpredictability

Deliverables

• 📑 Research Paper PDF
• 📸 Figures in docs/charts/
• 📂 Notebook
• 🖼️ Summary Slide