From wealth-management
Analyzes commodity markets including futures curve dynamics, roll yield, contango, backwardation, and supply/demand fundamentals for investing and ETF queries.
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Analyze commodity markets including futures curve dynamics, roll yield mechanics, commodity index construction, and supply/demand fundamentals. This skill covers the unique return drivers of commodity investing and the critical distinction between spot returns and futures-based returns.
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Analyze commodity markets including futures curve dynamics, roll yield mechanics, commodity index construction, and supply/demand fundamentals. This skill covers the unique return drivers of commodity investing and the critical distinction between spot returns and futures-based returns.
2 — Asset Classes
both
The futures price is related to the spot price through the cost-of-carry model:
F = S × e^((r + u - y) × t)
where S = spot price, r = risk-free rate, u = storage cost, y = convenience yield, t = time to expiration. The convenience yield represents the benefit of holding the physical commodity (e.g., avoiding production shutdowns).
When F > S, the futures curve is upward-sloping. Storage costs and financing costs exceed the convenience yield. Contango creates negative roll yield because investors must sell cheaper expiring contracts and buy more expensive later contracts. Contango is common in well-supplied markets and for storable commodities like oil and natural gas.
When F < S, the futures curve is downward-sloping. The convenience yield exceeds storage and financing costs, often due to near-term supply scarcity. Backwardation creates positive roll yield because investors sell expensive expiring contracts and buy cheaper later contracts. Backwardation is common in tight supply environments.
Total commodity return has three components:
Total Return = Spot Return + Roll Yield + Collateral Yield
The gain or loss realized when an expiring futures contract is replaced by a longer-dated contract. In contango (upward curve), roll yield is negative. In backwardation (downward curve), roll yield is positive. Roll yield can be a significant drag or boost to total returns — in deep contango, roll yield can eliminate or even exceed spot price gains.
Commodities tend to correlate positively with unexpected inflation, making them a potential hedge. The mechanism is direct: rising commodity prices are a component of inflation. However, the hedge is imperfect and works better for supply-driven inflation than demand-driven or monetary inflation.
Agricultural commodities show harvest-related patterns (supply increases at harvest, depressing prices). Energy shows heating/cooling demand patterns (natural gas peaks in winter, gasoline in summer driving season). Seasonality is well-known and partially priced in, but seasonal patterns can still affect futures curve shape.
| Formula | Expression | Use Case |
|---|---|---|
| Cost of Carry | F = S × e^((r+u-y)×t) | Theoretical futures price |
| Roll Yield (approx) | (F_near - F_far) / F_near | Return from contract rolling |
| Total Return | Spot Return + Roll Yield + Collateral Yield | Complete commodity return |
| Annualized Roll Yield | ((F_near/F_far)^(365/days_between) - 1) | Annualized roll impact |
| Convenience Yield | y = r + u - (1/t) × ln(F/S) | Implied convenience yield |
Given: Front month crude oil futures at $50, next month at $52 (contango), 1-month roll period Calculate: Annualized roll yield Solution: Monthly roll yield = (F_near - F_far) / F_near = ($50 - $52) / $50 = -4.0% This is a 1-month loss of 4.0%. Annualized roll yield ≈ -4.0% × 12 = -48% (simple annualization) More precisely: (50/52)^12 - 1 = (0.9615)^12 - 1 = -38.1%
This illustrates how severe contango can create enormous roll yield drag. In practice, front-to-second-month contango is rarely this steep, but the example shows why curve shape matters enormously for commodity investors.
Given: Over one year, spot crude oil rises from $70 to $77 (+10%). Roll yield = -6%. Collateral yield (T-bill rate) = 5%. Calculate: Total return of a futures-based commodity ETF Solution: Total Return = Spot Return + Roll Yield + Collateral Yield Total Return = 10% + (-6%) + 5% = 9%
Despite a 10% spot price increase, the futures-based investor earned only 9% due to 6% roll yield drag, partially offset by 5% collateral yield. A physical holder (no roll cost, no collateral yield) would have earned 10%.
See scripts/commodities.py for computational helpers.