[huuan26]

Summary

Expands the benchmark-relative performance metrics in app/services/backtest/metrics.py and Strategy API V2:

1. Shared Curve Alignment: Extracts _align_curves_and_returns to unify timestamp inner joining, percentage return computation, non-continuous gap filtering, and exchange-calendar session alignment across all benchmark metrics.
2. Beta ($\beta$) & Systematic Risk: Implements sample covariance over benchmark variance ($\beta = \frac{\text{Cov}(R_p, R_b)}{\text{Var}(R_b)}$). Handles flat/zero benchmark variance safely via status "zero_benchmark_variance".
3. Jensen's Alpha ($\alpha_{\text{ann}}$): Computes annualized risk-adjusted excess return over CAPM expected return:
   $$\alpha_{\text{ann}} = (R_{p, \text{ann}} - R_f) - \beta (R_{b, \text{ann}} - R_f)$$
4. Treynor Ratio: Evaluates excess return per unit of systematic risk:
   $$\text{Treynor} = \frac{R_{p, \text{ann}} - R_f}{\beta}$$
   Safely returns None when $|\beta| \le 10^{-15}$ to prevent division by zero or infinite values.
5. Correlation & $R^2$: Computes Pearson correlation coefficient ($r \in [-1, 1]$) and coefficient of determination ($R^2 \in [0, 1]$), with edge-case clamping and handling of flat portfolio variance.
6. Capture Ratios:
   • upCapture: Compounded portfolio return divided by compounded benchmark return across periods where $R_b > 0$.
   • downCapture: Compounded portfolio return divided by compounded benchmark return across periods where $R_b < 0$.
   • captureRatio: Ratio of upside capture to downside capture ($\frac{\text{Up Capture}}{\text{Down Capture}}$).
   • Also tracks upMarketPeriods and downMarketPeriods for market regime diagnostics.
7. Comprehensive Integration & Full Backward Compatibility:
   • calculate_benchmark_relative_metrics integrates Information Ratio, Beta/Alpha, and Capture metrics in a single structured result.
   • Preserves 100% backward compatibility for all existing callers of calculate_information_ratio and existing fields of result["benchmarkRelativeMetrics"].
   • Wired into StrategyV2BacktestService (app/services/strategy_v2/service.py).
8. Documentation:
   • Updated docs/product/BACKTEST_CENTER.md detailing the new metrics, formulas, and edge cases.

Changes

• backend_api_python/app/services/backtest/metrics.py:
  • Add _align_curves_and_returns helper.
  • Implement calculate_beta_and_alpha.
  • Implement calculate_capture_ratios.
  • Implement calculate_benchmark_relative_metrics.
  • Export new functions in __all__.
• backend_api_python/app/services/strategy_v2/service.py:
  • Import and call calculate_benchmark_relative_metrics for result["benchmarkRelativeMetrics"].
• backend_api_python/tests/test_backtest_metrics.py:
  • Add unit tests for Beta, Jensen's Alpha (with zero and positive risk-free rate), Treynor Ratio, Correlation, R-squared, Capture Ratios (both markets, up-only, down-only), zero benchmark variance, zero beta handling, insufficient history, and input validation.
  • Total 22/22 unit tests passing.
• docs/product/BACKTEST_CENTER.md:
  • Document Beta, Jensen's Alpha, Treynor Ratio, Correlation, $R^2$, and Capture Ratios.

Test plan

• pytest backend_api_python/tests/test_backtest_metrics.py passes (22/22 tests in 0.91s)
• ruff check app/services/backtest/metrics.py tests/test_backtest_metrics.py app/services/strategy_v2/service.py passes with zero violations
• git diff --check passes with zero whitespace/formatting issues
• Verified full backward compatibility with existing calculate_information_ratio contract

API documentation (if routes/schemas changed)

• No routes or OpenAPI schemas changed; expands benchmarkRelativeMetrics dictionary payload in backtest results