feat: add bias statistics

src/fpm_risk_model/accuracy/bias.py

@@ -1,3 +1,5 @@
+from typing import Optional
+
 from numpy import ndarray, sqrt, sum
 from pandas import Series
 
@@ -39,3 +41,47 @@ def compute_standardized_returns(
         b_t[index] = returns / vol
 
     return b_t
+
+
+def compute_bias_statistics(
+    X: ndarray,
+    weights: ndarray,
+    rolling_risk_model: RollingFactorRiskModel,
+    rolling_timeframe: int,
+    min_periods: Optional[int] = None,
+) -> Series:
+    """
+    Compute the bias statistics.
+
+    Standardized return is defined as
+
+     .. math::
+        b_t = \\frac{r_t}{\\sigma_t}
+
+    and the bias statistic is expressed as
+
+     ..math::
+        B_T(t) = \\sqrt{\\frac{1}{T} \\sigma_{\\tau}(b_{\\tau} - \bar{b})^2
+
+    Parameters
+    ----------
+    X: ndarray
+        The instrument forecast returns.
+    weights: ndarray
+        Weights of the instruments.
+    rolling_risk_model: RollingFactorRiskModel
+        The rolling risk model.
+
+    Returns
+    -------
+    Series
+        A timeseries of bias statistic.
+    """
+    standardized_returns = compute_standardized_returns(
+        X=X,
+        weights=weights,
+        rolling_risk_model=rolling_risk_model,
+    )
+    return standardized_returns.rolling(
+        rolling_timeframe, min_periods=min_periods
+    ).std()

tests/accuracy/test_bias.py

@@ -2,7 +2,10 @@
 from pandas import Series
 from pandas.testing import assert_series_equal
 
-from fpm_risk_model.accuracy.bias import compute_standardized_returns
+from fpm_risk_model.accuracy.bias import (
+    compute_bias_statistics,
+    compute_standardized_returns,
+)
 
 
 def test_compute_standardized_returns(
@@ -18,3 +21,18 @@ def test_compute_standardized_returns(
         index=list(rolling_factor_risk_model.keys()),
     )
     assert_series_equal(standardized_returns, expected_standardized_returns)
+
+
+def test_compute_bias_statistics(daily_returns, weights, rolling_factor_risk_model):
+    bias_statistics = compute_bias_statistics(
+        X=daily_returns,
+        weights=weights,
+        rolling_risk_model=rolling_factor_risk_model,
+        rolling_timeframe=5,
+        min_periods=0,
+    )
+    expected_bias_statistics = Series(
+        array([nan, nan, 1.8305485, 1.47255984, 1.31524515]),
+        index=list(rolling_factor_risk_model.keys()),
+    )
+    assert_series_equal(expected_bias_statistics, bias_statistics)