Wyandanch Library

Overview

Physical and Financial Commodities covers the structure, economics, and trading of commodity markets -- a domain that operates by fundamentally different rules than equity and fixed income markets. Unlike stocks and bonds, commodities are physical goods with storage costs, transportation logistics, seasonal supply and demand patterns, and unique pricing dynamics driven by the term structure of futures curves. This module examines both the physical side (production, grading, storage, transportation, and delivery) and the financial side (futures, options, swaps, and structured products) of commodity markets, with particular attention to the quantitative frameworks used to model, price, and trade commodity derivatives.

Central concepts include the term structure of commodity futures (contango vs. backwardation), the theory of storage (which links spot prices, futures prices, storage costs, and convenience yields), basis trading (exploiting the relationship between cash and futures prices), and the increasingly important role of financial investors in commodity markets. The module also covers advanced topics: commodity curve bootstrapping, the Nelson-Siegel model adapted for commodity term structures, structured commodity products like accumulators and TARFs, and the application of optimal execution models to commodity markets where liquidity can be thin and delivery constraints bind.

Physical Commodity Markets

Commodity markets begin with physical goods, and understanding the physical market is prerequisite to understanding the financial one. Crude oil is not a single commodity -- it is a family of grades differentiated by API gravity (density) and sulfur content. West Texas Intermediate (WTI) is a light, sweet crude (around 39.6 API, 0.24% sulfur) delivered at Cushing, Oklahoma. Brent crude is a benchmark derived from multiple North Sea fields, used as the global reference price. The spread between WTI and Brent reflects transportation costs, refinery configurations, and regional supply-demand imbalances.

Agricultural commodities have their own grading systems. Hard Red Winter wheat (used for bread flour) trades differently from Soft Red Winter wheat (used for cakes and pastries). Coffee is graded by bean size, defect count, and cup quality. These quality differentials create basis risk -- the risk that your hedging instrument does not perfectly match the physical commodity you are exposed to.

The physical market also imposes logistical constraints that do not exist in financial markets. Oil must be stored in tanks or tankers. Grain must be stored in elevators with temperature and moisture control. Natural gas must be transported through pipelines with finite capacity. These constraints create locational basis (the price difference between the same commodity at different delivery points) and temporal basis (the price difference between spot and futures). Both are tradeable.

Term Structure: Contango, Backwardation, and Convenience Yield

The term structure of commodity futures -- the relationship between futures prices at different expirations -- is the central organizing concept of commodity finance. Two states dominate:

Contango occurs when futures prices exceed spot prices: F(T) > S. This is the "normal" state for commodities with significant storage costs. A futures price must compensate the holder for storing the commodity until delivery. The no-arbitrage relationship is:

F(T) = S * e^((r + c - y) * T)

where r is the risk-free rate, c is the storage cost rate, and y is the convenience yield.

Backwardation occurs when spot prices exceed futures prices: S > F(T). This happens when current demand is strong relative to supply, making physical inventory immediately valuable. The convenience yield -- the implicit benefit of holding physical inventory rather than a futures contract -- rises to reflect the option value of having the commodity on hand.

The Theory of Normal Backwardation, attributed to Keynes, argues that futures prices should on average be below expected future spot prices because hedgers (producers) are net short futures and must offer a risk premium to attract speculators to the long side. Empirically, this theory holds in some markets and periods but not others -- the financialization of commodities has introduced large long-only institutional flows that complicate the picture.

Roll yield is the return generated by the term structure when a futures investor rolls from an expiring contract to a later one. In backwardation, roll yield is positive (you sell the expensive near contract and buy the cheaper far contract). In contango, roll yield is negative. For long-only commodity index investors, persistent contango can erode returns significantly -- a reality that became painfully clear with oil ETFs during periods of steep contango.

Basis Trading

Basis trading exploits the relationship between the cash (spot) price and the futures price. The basis is defined as:

Basis = Cash Price - Futures Price

A basis trader who is long the physical commodity and short futures profits when the basis strengthens (cash price rises relative to futures) and loses when it weakens. This is a lower-risk strategy than outright directional trading because the cash and futures prices are highly correlated -- you are trading the spread, not the level.

Commodity merchants like Cargill, Vitol, and Trafigura are essentially basis traders at massive scale. They buy physical commodities at one location and time, sell futures to hedge the price level, and profit from the logistics -- moving the commodity through space (transportation basis) and time (storage basis) to where and when it is most valuable. The "edge" in basis trading comes from superior physical logistics, storage capacity, and information about local supply-demand conditions.

Commodity Derivatives and Structured Products

Beyond standard futures and options, commodity markets feature sophisticated derivative structures:

Commodity swaps exchange a floating commodity price for a fixed price over a series of settlement dates. An airline might enter a jet fuel swap to lock in its fuel costs for the next year, paying a fixed price per gallon and receiving the floating market price (or vice versa). The swap is economically equivalent to a strip of forward contracts.

Accumulators are structured products where the buyer agrees to purchase a fixed quantity of a commodity at a discount to the current price at regular intervals, as long as the price stays within a specified range. If the price drops below a barrier (knock-in), the buyer must purchase double the quantity. If the price rises above another barrier (knock-out), the structure terminates. Accumulators are sometimes called "I kill you later" products because the leveraged downside exposure can be devastating.

Target Accrual Redemption Forwards (TARFs) are similar to accumulators but terminate once the buyer's accumulated profit reaches a target level. The asymmetry is the same: limited upside (capped by the target), leveraged downside (often 2x notional below the barrier). TARFs were widely sold to commodity producers in Asia and Latin America and caused significant losses during commodity price collapses.

Commodity Curve Bootstrapping and the Nelson-Siegel Model

Just as fixed income analysts bootstrap a zero-coupon yield curve from traded bond prices, commodity analysts bootstrap a forward curve from traded futures prices. The challenge is that commodity futures have discrete expirations with gaps between them, requiring interpolation.

The Nelson-Siegel model, originally developed for interest rate term structures, can be adapted for commodity curves:

F(T) = beta_0 + beta_1 * ((1 - e^(-T/tau)) / (T/tau)) + beta_2 * ((1 - e^(-T/tau)) / (T/tau) - e^(-T/tau))

Here beta_0 represents the long-run price level, beta_1 captures the slope (contango/backwardation), beta_2 captures curvature (humps in the term structure), and tau controls the decay rate. This parsimonious three-factor model provides a smooth, continuous forward curve that can be used for pricing and risk management of commodity derivatives with arbitrary maturities.

Financialization of Commodities

The financialization of commodity markets -- the massive inflow of institutional capital through index investing -- has fundamentally altered market dynamics since the early 2000s. Goldman Sachs Commodity Index (GSCI) and Bloomberg Commodity Index (BCOM) tracking created persistent buying pressure in front-month contracts and predictable roll patterns.

Research by Tang and Xiong (2012) documented increased correlation between commodities and equities following financialization, reducing the diversification benefit that originally attracted institutional investors. The "Masters Hypothesis" (named after hedge fund manager Michael Masters) argued that index speculation drove commodity prices above fundamental values, particularly during the 2007-2008 commodity price spike. Academic evidence is mixed, but the structural impact on roll dynamics and term structure is well-documented.

Optimal Execution in Commodity Markets: Almgren-Chriss

The Almgren-Chriss framework for optimal execution, originally developed for equities, applies with modifications to commodity markets. The core problem: how to execute a large trade over time to minimize the combined cost of market impact and timing risk.

The model minimizes a cost function that trades off execution cost against price risk:

min E[Cost] + lambda * Var[Cost]

where lambda is the trader's risk aversion parameter. In commodity markets, the model must account for additional constraints: delivery schedules, storage capacity limits, pipeline nominations, and the discrete nature of physical delivery. Liquidity also varies dramatically across the term structure -- front-month contracts are liquid, but contracts six months out may trade with wide bid-ask spreads and limited depth.

Why This Matters

Commodities are a distinct asset class with return drivers, risk characteristics, and portfolio diversification properties that differ fundamentally from financial assets. Understanding commodity markets is essential for macro investors, multi-asset portfolio managers, and anyone analyzing industries that depend on commodity inputs. The term structure and roll yield dynamics are particularly important for anyone trading commodity futures or evaluating commodity-linked investment products. The structured products section is relevant to anyone in sales, trading, or risk management at an institution that interacts with commodity producers or consumers.

Key Takeaways

Commodity prices are driven by physical supply-demand fundamentals, storage economics, and the convenience yield of holding inventory.
Contango (futures above spot) reflects storage costs net of convenience yield; backwardation (spot above futures) reflects strong immediate demand and high convenience yield.
The no-arbitrage futures pricing formula F(T) = S * e^((r + c - y) * T) links spot prices, storage costs, interest rates, and convenience yields.
Basis trading -- going long physical and short futures (or vice versa) -- is a spread trade that exploits logistics, storage, and local information advantages.
Structured products like accumulators and TARFs offer discounted prices in exchange for leveraged downside exposure -- the asymmetry has caused catastrophic losses.
The Nelson-Siegel model provides a parsimonious framework for fitting smooth commodity forward curves from discrete futures prices.
Financialization has increased commodity-equity correlations and altered term structure dynamics through predictable index roll patterns.
Almgren-Chriss execution optimization applies to commodity markets but must account for physical delivery constraints and term structure liquidity variation.

Physical & Financial Commodities