Section Twelve: Systems and Quantitative

Compare five common trading models

Trend-Following: Buys assets when prices rise and sells when falling. Does not predict price movements but follows existing trends. Generates consistent profits from sustained directional moves.

Mean Reversion: Based on the premise that prices, returns, or financial variables revert to historical averages over time. Profits when assets deviate too far from their mean by betting on convergence back to average levels.

Scalping: High-frequency, short-term strategy profiting from small price changes in liquid markets. Scalpers hold positions for seconds or minutes, making numerous trades daily with typically 80–90% win rates but small per-trade profits.

Pairs Trading: Market-neutral strategy buying one asset while simultaneously selling a correlated asset. Profits from price relationship convergence, betting that relative mispricings correct. One asset is perceived as underpriced or overpriced relative to its pair.

Arbitrage: Exploits price differences of the same or similar instruments across different markets or exchanges. Buys low in one market while simultaneously selling high in another, profiting from brief price inefficiencies with minimal risk.

Outline the go/no-go

Net Profit: The ultimate metric, but varies with strategy type; view alongside drawdowns.

Profit Factor: Gross profit ÷ gross loss. Generally acceptable range: 1.25–10. Most reliable strategies: 3–5. Greater than 10 strongly suggests curve fitting.

Total Number of Trades: Absolute minimum 30; 100 or more ideal. Few trades (<30) lack statistical validity.

Winning Percent: Depends on strategy type. Trend-following: 30–50%. Scalping: 80–90%.

Average Net Profit Per Trade: Varies by strategy type and holding period.

Average Winner ÷ Average Loser: Trend-following models typically >1. Mean reversion models typically <1.

Slippage and Commissions: Often overlooked but crucial, especially for actively traded systems.

Maximum Drawdown: Should be as low as possible. Measures maximum risk during testing and is the primary input for position sizing and leverage.

Calmar Ratio: Annualized return ÷ maximum drawdown. Widely used by active traders. Ideal 300%+; acceptable at 200%+.

Explain the four ways of generating trading signals

Historical Backtesting: Tests on historical data using optimization. Produces the best-looking results—smooth equity curves, modest drawdowns, strongest metrics. However, results cannot be replicated in real trading due to optimization bias. Use for early screening and eliminating poor ideas.

Out-of-Sample Testing: Divides data into in-sample and out-of-sample portions. Optimize parameters on the first portion, then test on the second (untested) portion. Addresses optimization overfitting by validating results on unseen data.

Walk Forward Analysis (WFA): Repeats optimization multiple times, rolling forward the test window. Simulates real-time trading by adapting to changing market conditions. More realistic than optimized backtests. WFA produces better results for swing models (positions held days/weeks/months) than intraday models. Identifies both overfitted strategies and genuinely effective ones.

Real-Time Analysis: Most accurate method but requires weeks, months, or years of live trades to generate meaningful statistics (minimum 30–50 trades; more is always better). Provides definitive performance validation but is time-consuming.

Analyze the seven steps to a consistently profitable trading system

1. Document Trading Objectives: Write specific, measurable goals (e.g., “15–20% annual return”) rather than vague targets. Difficult to accept marginal systems lacking objective alignment.

2. Describe the Trading Idea: Include general description, markets to test, bar intervals, historical test period, entry/exit rules, and risk management. Keep rules simple and testable; minimize parameters.

3. Basic Testing: Use the trading idea’s data with lightly optimized testing and exhaustive/genetic testing depending on variables. This phase eliminates poor ideas early.

4. Walk Forward Testing: The core approach since it adapts to market changes. If results don’t match objectives, discard and restart—they will only worsen.

5. Monte Carlo Analysis: Simulates various scenarios to assess risk and reward under different conditions. Otherwise good systems can fail here through return pressure or expanded drawdowns.

6. Live Simulated Trading: The acid test. Trade in simulated accounts or very small real positions. Results must meet objectives. If met, increase position size incrementally until maximum.

7. Leverage or Deleveraging: Adjust based on maximum drawdown data to achieve target risk/reward balance.

Outline each step of the quantitative process

1. Define Risk Limits: Know personal/client risk tolerance. Allows filtering strategies inappropriate for that tolerance level.

2. Select Universe: Choose securities or markets to analyze (e.g., S&P 500 stocks). Account for survivorship bias in data.

3. Select Data Time Frame: Choose appropriate timeframe (daily, weekly, intraday). Shorter timeframes yield more signals with shorter holding periods; longer timeframes yield fewer signals with longer holds. Consider signal-to-noise ratio—shorter timeframes capture more noise; longer timeframes capture truer trends.

4. Define Rules: Create codified entry triggers, filters to eliminate signals, and value rules for ranking. Keep rules simple and testable.

5. Visualize the Rule: Confirm the rule captures the intended signal before testing.

6. Signal Testing: Test the rule on historical data to measure probability of gain, average return, and consistency. First test uses no filters; subsequent tests add refinements.

7. Define Exit Rules: Specify when to close positions (fixed bars, profit targets, or technical conditions).

8. Define Stops: Establish stop-loss levels to limit risk.

9. Strategy Testing: Test complete strategies including entries, exits, and stops. Measure key metrics (win rate, profit factor, Calmar ratio).

10. Analyze Results: Evaluate walk-forward analysis results against original objectives.

11. Optimization: Refine parameters based on results while avoiding curve fitting. Select robust parameter ranges that work across different market conditions.

Compare the use of trigger rules, filter rules and value rules

Trigger Rules: Return true only on the date when a condition is satisfied—the discrete event generating a signal. Example: “Close() CrossesAbove MA(BARS=200)”. Used to generate entry signals.

Filter Rules: Return true for many consecutive days, used to reject signals that met the trigger rule but should be ignored due to another factor. Example: “Index() IsUp”—only accept signals when the benchmark closed higher. Filters eliminate signals in unfavorable market conditions.

Value Rules: Return numeric values rather than true/false, used for ranking when multiple signals trigger on the same day. Example: “ATR(BARS=14)”—rank securities by average true range in ascending order (lowest volatility first). Determines execution order when quantity constraints exist.

The three rule types serve distinct purposes: triggers generate signals, filters eliminate inappropriate ones, and value rules prioritize execution. Mixing types produces erroneous test results.

Contrast signal test results and select the most appropriate

Signal Test #1 (Initial Test—No Filters): Measures raw signal performance. Results show probability of gain, average return, and standard deviation. If results are poor (low probability of gain, negative returns), the hypothesis may be rejected. However, quantitative analysis is iterative—slight adjustments based on analysis and technical knowledge are applied.

Signal Test #2 (With Environmental Filter): Adds a filter reflecting market conditions. Example: only accept signals when the benchmark is above its moving average. Test whether this environmental condition improves results. If results worsen or don’t improve, the filter hypothesis is rejected.

Signal Test #3 (Refined Filters—Final Iteration): Based on visual inspection and pattern recognition, add refined filters capturing when signals perform best. Example: enter signals only when the security is moving in specific heading directions and at specific distances from a reference point on relative rotation graphs. Results should show substantially improved probability of gain and average return.

Selection Criteria: Choose the iteration with:

1. Highest probability of gain (ideally 55%+)

2. Highest mean/annualized return

3. Lowest standard deviation

4. Positive visual inspection of the profit history bar

5. Positive Monte Carlo plot showing no extreme tail risks

More signals are preferable (1,000+) unless capturing unique high-probability opportunities. The “best” signal test balances high returns with consistency and avoids curve fitting—parameter ranges should work across different market conditions, not just the test period.

Interpret trade measures, performance measures, and accounting measures, including annualized return, annualized volatility, total return, CAGR, maximum drawdown, profit factor, and expected value

Trade Measures:

• Profit Factor: Gross profit ÷ gross loss. Higher is better; 1.25–10 acceptable; 3–5 most reliable; >10 suggests curve fitting.

• Average Trade Return: Total return ÷ number of trades. Indicates per-trade profitability.

• Winning Percent: Winning trades ÷ total trades. Trend-following 30–50%; mean reversion varies; scalping 80–90%.

Performance Measures:

• Total Return: Cumulative profit/loss over the entire period.

• Annualized Return: Total return expressed as an annual percentage.

• Annualized Volatility: Standard deviation of returns on an annualized basis. Measures return variability.

• CAGR (Compound Annual Growth Rate): Smooths returns across periods, showing average annual compounding effect.

• Maximum Drawdown: Peak-to-trough decline. Measures maximum risk realized during testing; inputs position sizing and leverage calculations.

Risk-Adjusted Performance:

• Calmar Ratio: Annualized return ÷ maximum drawdown. Ideal >300%; acceptable >200%. Rewards consistent returns relative to drawdown risk.

• Sharpe Ratio: (Return − risk-free rate) ÷ standard deviation. Rewards excess return per unit of risk.

• Sortino Ratio: (Return − risk-free rate) ÷ downside deviation. Penalizes only downside volatility.

• Information Ratio: (Strategy return − benchmark return) ÷ tracking error. Measures outperformance consistency.

Expected Value: Average profit/loss per trade, considering win rate and average winner/loser sizes. Positive expected value indicates profitability over time; negative indicates losses. Formula: (Win% × Avg Win) − (Loss% × Avg Loss).

Contrast the performance measures (Sharpe ratio, Information ratio, Sortino ratio, and Calmar ratio)

Sharpe Ratio: Measures excess return per unit of total risk (standard deviation). Appropriate when concerned with overall volatility. Formula: (Rp−Rf)/σp​ where Rp is portfolio return, Rf is risk-free rate, σp is standard deviation. Penalizes both upside and downside volatility equally.

Sortino Ratio: Measures excess return per unit of downside risk only (downside deviation). More appropriate for traders focusing on drawdown protection. Formula: (Rp−Rf)/σd where σd is downside deviation (only negative returns). Ignores upside volatility; rewards consistent positive returns with occasional downside.

Information Ratio: Measures outperformance relative to a benchmark per unit of tracking error. Appropriate for strategies designed to beat a specific index. Formula: (Rs−Rb)/σtracking​ where Rs is strategy return, Rb​ is benchmark return. Indicates consistency of outperformance; higher values show the strategy reliably beats its benchmark.

Calmar Ratio: Measures annualized return relative to maximum drawdown. Simple, directly relevant to traders. Formula: Annual Return ÷ Maximum Drawdown. Ideal >300%; acceptable >200%. Directly inputs position sizing and leverage calculations. Most practical for active trading.

Selection: Use Sharpe Ratio for diversified portfolios with normal return distributions. Use Sortino Ratio when downside protection is paramount. Use Information Ratio when comparing to a benchmark. Use Calmar Ratio for trend-following/directional systems where drawdown is the primary risk concern.

Explain the different calculations that can be used for stops

Stop-Loss Calculations:

Fixed Dollar Stop: Subtract a fixed dollar amount from entry price. Example: Buy at $100, stop at $95.

Percentage Stop: Subtract a fixed percentage from entry price. Example: Buy at $100 with 5% stop = $95 stop level.

Average True Range (ATR) Stop: Use ATR(14) or ATR(20)—for example, stop is entry price minus 2× ATR(14). Adapts to volatility; wider stops in volatile markets, tighter in stable markets.

Support/Resistance Stop: Place stops below key support levels or above resistance levels, based on technical levels.

Channel or Envelope Stop: Use moving average envelopes or channel boundaries as stops. Example: stop when price closes below a 20-period moving average minus one standard deviation.

Time-Based Stop: Close if position hasn’t reached profit target within a fixed period (e.g., 5 bars). Limits capital exposure duration.

Trailing Stop: Adjusts upward (for long positions) as price rises, locking in profits while allowing room for volatility. Stop trails by fixed amount, percentage, or ATR-based calculation.

Impact on Performance: Stops rarely improve absolute returns in normal market conditions but can prevent catastrophic losses during extreme moves. Risk-adjusted returns may improve despite lower absolute returns. Choose based on strategy type and volatility environment; systems should be tested with and without stops to measure impact.

Define robustness when selecting parameter values using optimization

Robustness refers to a strategy’s ability to maintain profitability across different parameter values and market conditions, rather than performing optimally on only the tested data. A robust strategy works well across reasonable ranges of parameters, indicating it captures genuine market behavior rather than overfitting to historical quirks.

Definition Indicators: A robust strategy shows similar results when parameters are varied slightly (e.g., 20-period vs. 22-period moving average). Performance doesn’t collapse with small changes. Results are consistent across different in-sample and out-of-sample periods. The strategy adapts to changing market regimes without requiring frequent parameter adjustment.

Identification: In walk-forward analysis, look for relatively stable equity curves across multiple rolling windows. In optimization, examine the parameter optimization surface (a table showing returns for various parameter combinations). Robust strategies show a wide plateau of acceptable results; overfitted strategies show a narrow peak with sharp performance cliffs. Multiple parameter sets should produce similar (though not identical) results.

Selection: Prefer parameter values near the center of robust plateaus rather than at optimization peaks. Conservative selection prevents overfitting. Test the strategy with out-of-sample data and walk-forward analysis to confirm robustness before live trading. A strategy that works across 30–150 period moving averages is more robust than one requiring exactly 47 periods.

Application: Use robust parameter ranges in trading rather than the single “optimal” value. This approach reduces curve-fitting risk and improves real-world performance consistency.