Systematic strategies and rigorous backtesting.

Statistics and econometrics for trading

• 2.1.1 Hypothesis tests, p-values, bootstrap; multiple regression with robust errors (Newey-West).
• 2.1.2 Stationarity: ADF, KPSS; differencing; fractional differencing.
• 2.1.3 ARMA and ARIMA models; autocorrelation (ACF, PACF).
• 2.1.4 Volatility: ARCH, GARCH, EGARCH, GJR (arch library).
• 2.1.5 Cointegration: Engle-Granger, Johansen; mean-reversion half-life (Ornstein-Uhlenbeck).
• 2.1.6 Kalman filter for dynamic hedge ratios.
• 2.1.7 Regime detection: hidden Markov models (HMM), structural breaks.
• 2.1.8 The multiple testing problem: Bonferroni, FDR, “factor zoo”.

Anatomy of a trading system

• 2.2.1 The edge hypothesis: where it can come from (risk, behaviour, structure, information).
• 2.2.2 Universe, signal, filter, entry, exit, sizing, risk management.
• 2.2.3 Frequencies: intraday, swing, position; strategy capacity.
• 2.2.4 Research journal and experiment log, to keep data snooping under control.

Strategy families

• 2.3.1 Trend following (crossovers, Donchian and Turtle breakouts, time series momentum) and cross-sectional momentum or sector rotation.
• 2.3.2 Mean reversion: RSI and Bollinger, intraday reversion, gaps.
• 2.3.3 Pairs trading and statistical arbitrage: pair selection, distance, cointegration, Kalman.
• 2.3.4 Carry (FX, roll yield in futures, bonds), seasonality and calendar effects.
• 2.3.5 Factors (value, quality, low volatility, size; long-short) and event strategies (earnings, dividends, index rebalances).
• 2.3.6 Introduction to market making: inventory, spread, adverse selection (Avellaneda-Stoikov model).
• 2.3.7 Crypto-specific strategies (introduction): crypto momentum, funding and basis arbitrage (covered in detail in level 3).

Backtesting: engines and paradigms

• 2.4.1 Vectorised backtest with pandas and NumPy from scratch, and its limits.
• 2.4.2 Event-driven backtest from scratch: loop, portfolio, orders, fills.
• 2.4.3 vectorbt: massive parameter sweeps, portfolio simulation.
• 2.4.4 backtesting.py and backtrader (teaching tools; maintenance status).
• 2.4.5 NautilusTrader: architecture (Rust and Python), data, strategies, the same code in backtest and live.
• 2.4.6 LEAN/QuantConnect and Zipline-reloaded; bt for asset allocation.
• 2.4.7 Cost modelling: broker commissions, spread, slippage, impact, financing, securities lending.
• 2.4.8 Fill modelling: limit orders, queue, partial fills, gaps, stops.

Biases and validation

• 2.5.1 Look-ahead, survivorship, selection, data snooping, narrative bias.
• 2.5.2 In-sample and out-of-sample; anchored and rolling walk-forward.
• 2.5.3 Combinatorial purged cross-validation (CPCV) for strategies.
• 2.5.4 Deflated Sharpe Ratio and Probability of Backtest Overfitting (PBO).
• 2.5.5 Monte Carlo: trade resampling, block bootstrap, signal permutations.
• 2.5.6 Parameter sensitivity analysis (plateaus versus peaks); robustness across assets and periods.
• 2.5.7 Synthetic data (GBM, GARCH, bootstrapping) for stress tests.
• 2.5.8 “Honest backtest” checklist before moving to paper trading.

Performance metrics

• 2.6.1 CAGR, volatility, Sharpe, Sortino, Calmar, Omega; maximum drawdown, duration, Ulcer Index.
• 2.6.2 Win rate, payoff, expectancy, profit factor; alpha and beta, information ratio, turnover and capacity.
• 2.6.3 Reports with QuantStats or pyfolio-reloaded; custom tearsheets.