A two-price curve is not a storage profit

Start with an invented pair and explicit units

Unlike the three government-data studies, every price and cost in this exercise is hypothetical. Use a near reference of 80 and a far reference of 82 currency units per identical commodity unit, separated by sixty calendar days. No contract month, exchange settlement, storage terminal or executable quote is asserted. CME's educational discussion supplies context for contango and backwardation; the worksheet's numerical assumptions are original teaching inputs rather than market observations borrowed from that source.

The far-minus-near spread is two units, so this two-point curve is upward sloping, commonly described as contango. Both prices are positive, allowing a relative slope of far divided by near minus one: 2.5 percent. Multiplying that percentage by 365 divided by sixty gives a simple annualized slope of 15.208333 percent. This is a scaling of a price difference over a specified interval, not a measured annual return or a compounded forecast.

Build a transparent carrying-cost reference

Assume an annual simple funding rate of five percent, storage of 0.015 currency units per commodity unit per day, and insurance of 0.10 per unit for the entire horizon. Funding is 80 multiplied by 0.05 multiplied by sixty divided by 365, or 0.6575342466. Storage is 0.015 multiplied by sixty, or 0.90. Insurance is already a horizon amount and is added once rather than multiplied by the number of days.

Adding those costs to the near reference gives 81.6575342466 per unit. Subtract that reference from the far price of 82 to obtain a residual of 0.3424657534. The calculation uses linear funding and constant daily storage. It omits convenience benefits, bid-ask spreads, brokerage, collateral timing, delivery expenses, taxes, capacity constraints and default risk. The residual is therefore an unexplained difference under this limited model, not an independently estimated convenience yield or executable arbitrage margin.

Change one assumption and retain the comparison

Increase storage alone to 0.025 per day while preserving the prices and horizon. Storage becomes 1.50, the reference becomes 82.2575342466, and the residual becomes minus 0.2575342466. The observed two-unit spread has not changed. Its interpretation under the selected costs has changed. This sensitivity is useful because it demonstrates exactly which assumed expense matters, without implying that either storage quote is available for a real contract, grade or location.

The worksheet also permits signed prices so that a valid absolute spread is not lost when a price is zero or negative. Percentage slopes require both prices to be positive. The carrying-cost reference requires a positive near value under this particular simple funding model. If those conditions fail, the affected ratio or reference is withheld with a reason. A synthetic minus-five to plus-three pair therefore illustrates validation behavior, not a reconstruction of any historical oil settlement.

Translate the arithmetic into a research question

Before applying a curve calculation to a real commodity, match grade, location, delivery timing, unit and contract terms. A nearer futures contract is not automatically an immediately available physical purchase at the same price. A calendar spread can also change before an investor closes or rolls a position. The realized outcome depends on the contracts held, entry and exit prices, financing, collateral and costs; a static annualized slope contains none of that path information.

Export the input and result after each sensitivity change so another reader can reproduce the same arithmetic. The useful conclusion is conditional: under these invented prices and declared carrying costs, a small positive residual turns negative when daily storage increases by 0.01. That supports a question about costs and implementation feasibility. It does not establish price convergence, a guaranteed roll yield, available physical capacity or a recommendation to enter a commodity position.

Keep in the decision record

• Label invented curve prices and costs before calculating.
• Simple annualized slope is not roll return or investment performance.
• A carrying-cost residual needs implementation evidence before any profit claim.

Source notes

1. CME Group: contango and backwardation concepts
2. CME Group: variable storage rates and financial full carry context

Source dates and scope matter. Historical inventory observations are retained snapshots; forecasts and synthetic curve assumptions are labelled separately. No investment outcome or product coverage is implied.

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