Comprehensive Statistics and Metrics

This document describes the comprehensive statistics and metrics now available in ExPostFacto, bringing the library's analytics capabilities to professional trading standards.

Overview

ExPostFacto now calculates over 30 different metrics that provide deep insights into trading strategy performance. These metrics are automatically calculated when you run Result.compile/1 and can be accessed through the Result.comprehensive_summary/1 function.

Comprehensive Metrics Categories

1. Basic Performance Metrics

Purpose: Core profitability and duration metrics

total_return_pct: Total percentage return of the strategy
cagr_pct: Compound Annual Growth Rate
duration_days: Number of days the backtest ran
trades_count: Total number of completed trades

Example Values:

%{
  total_return_pct: 25.42,
  cagr_pct: 16.80,
  duration_days: 365,
  trades_count: 93
}

2. Risk-Adjusted Performance Metrics

Purpose: Measure return quality relative to risk taken

Sharpe Ratio

Formula: (Annual Return - Risk Free Rate) / Annual Volatility
Interpretation:
- 1.0: Excellent risk-adjusted returns
- 0.5-1.0: Good performance
- < 0.5: Poor risk-adjusted returns

Sortino Ratio

Formula: (Annual Return - Risk Free Rate) / Downside Volatility
Advantage: Only considers downside volatility (negative returns)
Interpretation: Higher values indicate better downside risk management

Calmar Ratio

Formula: Annual Return / |Maximum Drawdown|
Interpretation: Measures return relative to worst drawdown
Good Value: > 0.5

Example Values:

%{
  sharpe_ratio: 0.66,
  sortino_ratio: 1.30,
  calmar_ratio: 0.77,
  annual_volatility: 38.43
}

3. Drawdown Analysis

Purpose: Understand the magnitude and duration of losses

max_drawdown_pct: Largest peak-to-trough decline
max_drawdown_duration_days: Longest time to recover from a drawdown
average_drawdown_pct: Average size of all drawdowns
average_drawdown_duration_days: Average time to recover

Example Values:

%{
  max_drawdown_pct: -33.08,
  max_drawdown_duration_days: 688,
  average_drawdown_pct: -5.58,
  average_drawdown_duration_days: 41
}

4. Trading Performance Metrics

Purpose: Analyze the effectiveness of individual trades

Profit Factor

Formula: Gross Profit / |Gross Loss|
Interpretation:
- 2.0: Excellent strategy
- 1.5-2.0: Good strategy
- 1.0-1.5: Marginal strategy
- < 1.0: Losing strategy

Expectancy

Formula: Total P&L / Number of Trades
Purpose: Average expected profit per trade

Win Rate

Formula: Winning Trades / Total Trades * 100
Note: High win rate doesn't guarantee profitability

Example Values:

%{
  profit_factor: 2.13,
  expectancy: 691.50,
  expectancy_pct: 6.91,
  win_rate: 53.76,
  win_count: 50
}

5. Trade Analysis

Purpose: Detailed breakdown of trade characteristics

best_trade_pct: Largest winning trade as percentage
worst_trade_pct: Largest losing trade as percentage
average_trade_pct: Average trade return as percentage
max_trade_duration_days: Longest held position
average_trade_duration_days: Average holding period

Example Values:

%{
  best_trade_pct: 57.12,
  worst_trade_pct: -16.63,
  average_trade_pct: 1.96,
  max_trade_duration_days: 121,
  average_trade_duration_days: 32
}

6. Profit/Loss Breakdown

Purpose: Understand the composition of returns

gross_profit: Total profits from winning trades
gross_loss: Total losses from losing trades
average_winning_trade: Average profit per winning trade
average_losing_trade: Average loss per losing trade
largest_winning_trade: Single largest profit
largest_losing_trade: Single largest loss

7. System Quality Number (SQN)

Purpose: Measure the quality and reliability of the trading system

Formula: (Average Trade Result / Standard Deviation) * √(Number of Trades)

Interpretation:

< 1.6: Poor system
1.6-1.9: Below average but tradeable
2.0-2.4: Average system
2.5-2.9: Good system
3.0-5.0: Excellent system
5.0-6.9: Superb system
7.0: Too good to be true (likely over-fitted)

Example:

%{
  sqn: 1.78,
  sqn_interpretation: "Below average but tradeable"
}

8. Kelly Criterion

Purpose: Optimal position sizing for maximum long-term growth

Formula: (bp - q) / b Where:

b = odds ratio (average win / average loss)
p = probability of winning
q = probability of losing

Interpretation:

Negative: No edge, avoid strategy
0-10%: Weak edge, small positions
10-25%: Moderate edge, reasonable strategy
25-40%: Strong edge, good strategy
40%: Very strong edge, potentially too aggressive

Example:

%{
  kelly_criterion: 0.6134,  # 61.34% - very aggressive!
  kelly_interpretation: "Very strong edge - potentially too aggressive"
}

9. Market Risk Analysis

Purpose: Compare strategy performance to market benchmarks

Alpha

Definition: Excess return over what would be expected given market performance
Positive Alpha: Strategy outperformed the market
Negative Alpha: Strategy underperformed the market

Beta

Definition: Sensitivity to market movements
Beta = 1.0: Same volatility as market
Beta > 1.0: More volatile than market
Beta < 1.0: Less volatile than market

Information Ratio

Formula: Alpha / Tracking Error
Purpose: Risk-adjusted measure of active return

Example Values:

%{
  alpha: 6.8,           # 6.8% excess return vs market
  beta: 0.85,           # 15% less volatile than market
  information_ratio: 0.45,
  tracking_error: 15.2,
  market_correlation: 0.65
}

Usage Examples

Getting Comprehensive Statistics

# Run backtest
{:ok, output} = ExPostFacto.backtest(data, strategy, starting_balance: 100_000)

# Get comprehensive summary (clean map without internal data)
summary = ExPostFacto.Result.comprehensive_summary(output.result)

# Access specific metrics
IO.puts("Sharpe Ratio: #{summary.sharpe_ratio}")
IO.puts("Kelly Criterion: #{summary.kelly_criterion * 100}%")
IO.puts("SQN Rating: #{summary.sqn_interpretation}")

Raw Result Access

# Access raw result struct with all calculated fields
result = output.result

# All comprehensive metrics are available as struct fields
result.total_return_pct
result.sharpe_ratio
result.profit_factor
result.sqn
result.kelly_criterion
# ... and many more

Professional Reporting

def generate_report(summary) do
  """
  STRATEGY PERFORMANCE REPORT
  ===========================
  
  Returns:
  - Total Return: #{summary.total_return_pct}%
  - CAGR: #{summary.cagr_pct}%
  - Sharpe Ratio: #{summary.sharpe_ratio}
  
  Risk:
  - Max Drawdown: #{summary.max_drawdown_pct}%
  - Volatility: #{summary.annual_volatility}%
  
  Quality:
  - SQN: #{summary.sqn} (#{summary.sqn_interpretation})
  - Profit Factor: #{summary.profit_factor}
  
  Position Sizing:
  - Kelly %: #{summary.kelly_criterion * 100}%
  - Recommendation: #{summary.kelly_interpretation}
  """
end

Implementation Notes

Benchmark Assumptions

Default risk-free rate: 2% annually
Default market return: 10% annually (S&P 500 historical average)
Market volatility estimate: 18% annually

These can be customized by calling the underlying calculation functions directly:

alias ExPostFacto.TradeStats.{FinancialRatios, MarketRisk}

# Custom risk-free rate
sharpe = FinancialRatios.sharpe_ratio(result, 0.03)  # 3% risk-free rate

# Custom benchmark
alpha = MarketRisk.alpha(result, 12.0, 0.025)  # 12% benchmark, 2.5% risk-free

Calculation Accuracy

All metrics handle edge cases (zero trades, zero volatility, etc.)
Time-series calculations are approximated when high-frequency data isn't available
For maximum accuracy with Alpha/Beta, provide actual benchmark time series data

Performance Impact

All comprehensive statistics are calculated once during Result.compile/1
No significant performance impact on backtesting speed
Use comprehensive_summary/1 for clean reporting without internal data structures

Professional Standards

These metrics bring ExPostFacto to the same analytical standards as:

Professional trading platforms (MetaTrader, TradeStation)
Institutional risk management systems
Academic finance research
Hedge fund reporting standards

The implementation follows established formulas from:

"Quantitative Trading" by Ernest Chan
"Evidence-Based Technical Analysis" by David Aronson
CFA Institute standards
Academic finance literature

This comprehensive suite of metrics enables thorough strategy evaluation, risk assessment, and performance attribution analysis at a professional level.

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