3. Commodities

Commodities trade as futures curves, not single prices. The curve shape, roll, and storage economics matter as much as spot.

Algo-wide warning. A commodity "price" series is usually a continuous front-month stitched from expiring contracts. The stitching method (back-adjusted vs ratio-adjusted vs raw) changes returns dramatically. Know which one your data vendor uses — back-adjusted prices can go negative and break log returns.

Curve Structure

Contango

Def. Futures price > spot; the curve slopes upward. Formula. $F(t,T)>S(t)$ for later expiry T. Typically $F\approx S\times e^{(r+\text{storage}-\text{convenience})\cdot T}$. Signal. Normal for storable commodities (carry costs). Steep contango → oversupply / weak near-term demand. Algo. Long futures in contango bleeds via negative roll yield (see below) — a major drag on long commodity ETFs (e.g. USO).

Backwardation

Def. Futures price < spot; curve slopes downward. Formula. $F(t,T)<S(t)$. Signal. Near-term scarcity / high convenience yield (you want it now). Bullish structure. Algo. Long futures in backwardation earns positive roll yield — the structural tailwind behind commodity momentum/carry strategies.

Roll Yield

Def. Return from rolling an expiring future into the next contract, independent of spot moves. Formula. $\text{Roll Yield}\approx \frac{F_{\text{near}}-F_{\text{far}}}{F_{\text{far}}}$ annualized. Positive in backwardation, negative in contango. Signal. Dominates long-horizon futures returns; can swamp spot price changes. Algo. Total return = spot return + roll yield + collateral yield. Model all three; ignoring roll is the classic commodity-backtest error.

Convenience Yield

Def. Implicit benefit of holding the physical commodity (e.g. avoiding stockout). Formula. Back out from cost-of-carry: $\text{convenience}=r+\text{storage}-(1/T)\cdot \ln (F/S)$. Signal. High convenience yield → backwardation → tight physical market. Algo. Not directly observable; inferred from the curve.

Spreads

Calendar Spread

Def. Long one expiry, short another of the same commodity. Formula. $\text{Spread}=F(T_1)-F(T_2)$. Signal. Trades the shape of the curve, not the level; lower directional/vol exposure. Algo. Margin-efficient (offsetting legs); watch for expiry/roll discontinuities in the spread series.

Crack Spread (oil)

Def. Refining margin — value of products minus crude. Formula. Common "3-2-1": $(2\times \text{Gasoline}+1\times \text{Heating Oil})-3\times \text{Crude}$, per barrel. Signal. Wide crack → profitable refining → bullish refiners (e.g. VLO), bullish crude demand. Algo. Watch unit consistency (gasoline/heating oil quoted in $/gal × 42 to convert to $/bbl).

Crush Spread (soybeans)

Def. Processing margin — value of soybean meal + oil minus soybeans. Formula. $\text{Crush}=(\text{Meal value}+\text{Oil value})-\text{Soybean cost}$. Signal. Wide crush → profitable crushing → demand for beans. Algo. Each leg has different contract units/sizes — normalize carefully.

Spark / Dark Spread (power)

Def. Power-generation margin: electricity price minus fuel cost (gas = spark, coal = dark). Formula. $\text{Spark}=\text{Power Price}-(\text{Gas Price}\times \text{Heat Rate})$. Signal. Generation profitability; drives dispatch decisions. Algo. Heat rate (efficiency) is the conversion constant — region/plant specific.

Inter-commodity Ratios

Def. Relative value between related commodities. Formula. e.g. $\text{Gold/Silver ratio}=\frac{\text{Gold price}}{\text{Silver price}}$, Gold/Oil; WTI–Brent spread. Signal. Gold/Silver >80 historically → silver cheap; mean-reverting tendencies. Algo. Classic pairs/mean-reversion candidates, but regimes shift — don't assume a fixed long-run mean.

Key Markets (quick reference)

WTI vs Brent (crude oil)

Def. Two crude benchmarks: WTI (US, Cushing OK delivery) vs Brent (seaborne, global). Formula. WTI–Brent spread. Brent usually trades at a premium. Signal. Spread reflects US shale supply, export capacity, transport bottlenecks. Algo. WTI is landlocked (logistics-driven, famously went negative Apr 2020); Brent is the better global-demand proxy.

Natural Gas

Def. Highly seasonal, storage-driven, regionally fragmented (Henry Hub US, TTF Europe). Signal. Extreme seasonality (winter heating, summer cooling) and storage-report sensitivity. Algo. Among the most volatile/contango-prone — roll yield destroys naive long ETFs (e.g. UNG).

Gold

Def. Monetary metal / safe haven; near-zero industrial consumption. Signal. Inverse to real yields and the dollar; rises on risk-off and inflation fear. Algo. Model with real-yield + DXY regressors. Minimal storage/convenience dynamics (curve near-flat).

Industrial Metals (Cu, Al)

Def. Growth-sensitive base metals ("Dr. Copper" reads global activity). Signal. Copper tracks global manufacturing/China demand; leading growth indicator. Algo. LME pricing conventions (cash vs 3-month) differ from US futures — mind the quote basis.

Storage & Seasonality

Storage / Inventory Reports

Def. Scheduled inventory data (EIA crude/gas weekly, USDA agriculture). Signal. Surprise vs consensus moves price sharply (like a macro print for commodities). Algo. Hard-code release times (EIA petroleum Wed 10:30 ET, nat gas Thu 10:30 ET); expect volatility spikes.

Seasonality

Def. Recurring intra-year demand/supply patterns. Formula. Nat gas winter peak; gasoline summer driving season; grain harvest cycles. Signal. Predictable demand windows create tradable seasonal tendencies. Algo. Use month-of-year features; but seasonality is a tendency, not a guarantee — combine with curve/inventory state.

Cost of Carry (storage model)

Def. Fair futures price from holding-cost economics. Formula. $F=S\times e^{(r+\text{storage}-\text{convenience})\cdot T}$. Signal. Links spot, rates, storage, and convenience into the curve shape. Algo. The unifying equation: contango when carry costs dominate, backwardation when convenience yield dominates.