Natural Resources: formula sheet

Key formulas

Land-based asset return

Total return ≈ income yield + biological growth + change in land or asset price

Mainly for timberland and farmland. Income comes from harvest or crop sales and lease payments.

Commodity futures return

Total return = spot price return + roll yield + collateral return

Roll yield is positive when futures are in backwardation and negative in contango. It is a different topic page, but you need the link.

Real return (approximate)

Real return ≈ nominal return − inflation rate

Use it to judge an inflation hedge claim.

Futures price by cost of carry (no-arbitrage)

F₀ = S₀ × (1 + r)^T + FV(storage costs) − FV(convenience yield), with storage costs and convenience yield as currency amounts. Continuous-compounding version, with c and y as annual rates: F₀ = S₀ × e^((r + c − y)T)

In the discrete formula, FV means the currency amount valued at the contract's expiry (time T). In the continuous version, c is the storage cost rate and y is the convenience yield rate. Higher storage and financing costs raise futures above spot. Convenience yield, the benefit of holding the physical good, lowers it.

Contango

Futures price > spot price

Occurs when carry costs (financing and storage) exceed convenience yield. Futures curve slopes upward.

Backwardation

Futures price < spot price

Occurs when convenience yield exceeds carry costs, for example when supply is scarce.

Daily futures gain or loss (long)

(Settlement price today − settlement price yesterday) × contract size × number of contracts

A short position has the opposite sign.

Total return on a commodity futures position

Total return = spot price return + roll yield + collateral yield

Collateral yield is the interest earned on the cash or T-bills posted as margin.

Roll yield (per unit)

Roll yield = near-term futures price − farther-term futures price

Positive in backwardation, negative in contango. Divide by the near price for a percentage.

Futures price with carry (cost of carry)

F = S × (1 + r) + storage costs − convenience yield

A simple form, stated per period. Higher convenience yield lowers F relative to S. Backwardation (F < S) occurs when the convenience yield exceeds interest plus storage costs. Contango (F > S) occurs when it does not.

Curve shape rule

Contango: F > S. Backwardation: F < S

Compare the futures price with the spot price, or a far contract with a near contract.

Timberland return sources

Total return ≈ biological growth + change in timber price + change in land value

Growth comes from added volume and higher-value log sizes. Land value is the third driver.

Farmland return sources

Total return ≈ income (crop sales or rent) + land price appreciation

Income yield is often a large share of farmland return; appreciation adds to it.

Income approach (direct capitalisation)

Value = Net operating income ÷ Capitalisation rate

Use stabilised net income. A higher cap rate gives a lower value.

Income approach (DCF)

Value = Σ [CFt ÷ (1 + r)^t] + terminal value ÷ (1 + r)^n

For timber, cash flows are harvest revenue less costs, and timing depends on harvest decisions.

Commodity futures return

Total return = spot return + roll yield + collateral return

A futures investor earns the spot return, plus the roll yield, plus interest on the cash collateral. Equivalently, futures return = change in futures price, plus collateral return. Both forms give the same total.

Roll yield sign rule

Backwardation (futures < spot): roll yield positive | Contango (futures > spot): roll yield negative

This applies to a long position that rolls to a new contract. It describes the typical effect, not a guarantee of total return.

Exposure ranking by closeness to commodity price

Direct / futures > commodity funds and ETFs > producer equities

A general guide. Equities carry company and equity market risk, so they track commodity prices least closely.

Quick revision

• Natural resources are real assets: commodities, timberland and farmland.
• Investors use them for diversification, inflation sensitivity and return potential.
• Spot trades settle for immediate delivery; futures fix a price for later delivery.
• Commodity futures return = spot return + roll return + collateral return.
• Backwardation: futures price below spot, so the roll return tends to be positive.
• Contango: futures price above spot, so the roll return tends to be negative.
• Collateral return is the interest earned on the cash that backs the futures position.
• Most futures investors close or roll positions before delivery.
• Timberland returns come from tree growth, timber price changes and land value.
• Farmland returns come from crop income or rent and land value changes.
• Direct land ownership is illiquid and needs specialist management.
• Prices of commodities are driven by supply, demand, weather and global events.

Common mistakes

• Treating natural resources as a guaranteed inflation hedge. Fix: Say they may offer inflation protection, but returns are volatile and the link is not constant.
• Confusing commodities with timberland and farmland. Fix: Commodities are traded raw materials with no cash flow of their own. Timberland and farmland are land assets that generate income and growth.
• Treating futures and forwards as identical. Fix: Remember futures are standardized, exchange-traded, cleared and marked to market daily. Forwards are customized and private.
• Assuming commodity investors usually take physical delivery. Fix: Most positions are closed or rolled before expiry. Many contracts settle in cash.
• Saying contango gives a positive roll yield. Fix: In contango you sell the cheaper near contract and buy the dearer far one, so roll yield is negative.
• Calculating roll yield as far minus near. Fix: Use near minus far. Backwardation then gives a positive number.
• Saying farmland has the same harvest flexibility as timberland. Fix: Timber can wait and keep growing. Crops must be harvested when ripe, so farmland has far less timing flexibility.
• Leaving out land value change as a return source for timber. Fix: Remember all three: growth, timber price and land value.
• Treating producer equities as a pure commodity play. Fix: Remember equities carry management, leverage, hedging and equity market risk, so correlation with the commodity is lower.
• Saying futures-based investors earn only the change in the spot price. Fix: A futures investor earns spot return plus roll yield plus collateral return, not the spot change alone. The roll yield can be positive or negative depending on the shape of the futures curve.

Exam tips

• Expect conceptual three-option questions on drivers and portfolio role more than long calculations.
• Watch absolute words such as always and guaranteed. They usually mark the wrong option.
• Read the stem to see whether it concerns commodities or land assets, since return sources differ.
• When a shock is given, predict the price direction first, then check the options.
• Link this topic with commodity futures returns and the alternative investments chapter, as both can appear together.
• Know the sector lists cold: energy, precious metals, industrial metals, grains, softs, livestock.
• Expect feature-matching questions on forward versus futures. Look for the words standardized, exchange-traded and clearinghouse.
• In margin questions, compute for all contracts and note long or short before choosing an option.