feat(PRICING-001): add GLD expense ratio decay correction

app/domain/instruments.py

@@ -1,11 +1,49 @@
 from __future__ import annotations
 
+import math
 from dataclasses import dataclass
+from datetime import date
 from decimal import Decimal
 
 from app.domain.backtesting_math import AssetQuantity, PricePerAsset
 from app.domain.units import BaseCurrency, PricePerWeight, Weight, WeightUnit
 
+# GLD expense ratio decay parameters (from docs/GLD_BASIS_RESEARCH.md)
+# Formula: ounces_per_share = 0.10 * e^(-0.004 * years_since_2004)
+GLD_INITIAL_OUNCES_PER_SHARE = Decimal("0.10")
+GLD_EXPENSE_DECAY_RATE = Decimal("0.004")  # 0.4% annual decay
+GLD_LAUNCH_YEAR = 2004
+
+
+def gld_ounces_per_share(reference_date: date | None = None) -> Decimal:
+    """
+    Calculate GLD's current gold backing per share based on expense ratio decay.
+
+    GLD's expense ratio (0.40% annually) causes the gold backing per share to
+    decay exponentially from the initial 0.10 oz/share at launch (2004).
+
+    Formula: ounces_per_share = 0.10 * e^(-0.004 * years_since_2004)
+
+    Args:
+        reference_date: Date to calculate backing for. Defaults to today.
+
+    Returns:
+        Decimal representing troy ounces of gold backing per GLD share.
+
+    Examples:
+        >>> # 2026 backing should be ~0.0919 oz/share (8.1% decay)
+        >>> from datetime import date
+        >>> result = gld_ounces_per_share(date(2026, 1, 1))
+        >>> float(result)  # doctest: +SKIP
+        0.0919...
+    """
+    if reference_date is None:
+        reference_date = date.today()
+
+    years_since_launch = Decimal(reference_date.year - GLD_LAUNCH_YEAR)
+    decay_factor = Decimal(str(math.exp(-float(GLD_EXPENSE_DECAY_RATE * years_since_launch))))
+    return GLD_INITIAL_OUNCES_PER_SHARE * decay_factor
+
 
 @dataclass(frozen=True, slots=True)
 class InstrumentMetadata:
@@ -64,7 +102,7 @@ class InstrumentMetadata:
 _GLD = InstrumentMetadata(
     symbol="GLD",
     quote_currency=BaseCurrency.USD,
-    weight_per_share=Weight(amount=Decimal("0.1"), unit=WeightUnit.OUNCE_TROY),
+    weight_per_share=Weight(amount=gld_ounces_per_share(), unit=WeightUnit.OUNCE_TROY),
 )
 
 _INSTRUMENTS: dict[str, InstrumentMetadata] = {