Use this tool to determine the theoretical Future Price, Spot Price, Annual Cost of Carry Rate, or Time to Maturity for an asset, based on the fundamental Cost of Carry model. Input any three variables to solve for the fourth.
Cost of Carry Calculator
Cost of Carry Formula
Sources: Wikipedia, Investopedia, and proprietary financial modeling.
Variables:
- $F$ (Future Price): The price of the asset at a specified date in the future (the price of the futures contract).
- $P$ (Spot Price): The current market price of the underlying asset.
- $r$ (Annual Cost of Carry Rate): The annual, discrete rate of interest (or net financing cost), expressed as a decimal (e.g., 5% = 0.05).
- $T$ (Time to Maturity): The time remaining until the futures contract expires, measured in years.
What is the Cost of Carry?
The Cost of Carry refers to the net cost of holding an asset, typically a financial asset or commodity, over a period of time. It is a critical concept in futures pricing and plays a major role in determining the theoretical fair value of a futures contract. This cost accounts for the expenses incurred minus any income received from the underlying asset.
For financial assets like stocks or bonds, the primary components of the Cost of Carry are the financing costs (interest paid on borrowed money to buy the asset) minus any dividends or interest received from the asset. For physical commodities like gold or oil, storage costs and insurance are added to the financing cost, while any convenience yield (the benefit of having the physical asset on hand) is subtracted.
In the context of the calculator’s formula, the “Annual Cost of Carry Rate” ($r$) simplifies these factors into a single annual rate, which is typically the risk-free interest rate used to finance the purchase of the spot asset.
How to Calculate Cost of Carry (Example)
Follow these steps to find the Annual Cost of Carry Rate ($r$) if the Spot Price, Future Price, and Time are known:
- Gather Variables: Assume Spot Price ($P$) = $1,000, Future Price ($F$) = $1,050, and Time to Maturity ($T$) = 1 year.
- Rearrange the Formula: Start with $F = P \times (1 + r)^T$ and solve for $r$: $r = (F/P)^{(1/T)} – 1$.
- Calculate the Ratio: Calculate the ratio of Future Price to Spot Price: $F/P = 1,050 / 1,000 = 1.05$.
- Apply the Exponent: Raise the ratio to the power of $(1/T)$. Since $T=1$, $(1/T) = 1$. The result is $1.05$.
- Subtract 1: $r = 1.05 – 1 = 0.05$.
- Convert to Percentage: The Annual Cost of Carry Rate is $5.0\%$.
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Frequently Asked Questions (FAQ)
What happens if the calculated Cost of Carry is negative? A negative Cost of Carry (when $F < P$ and $r$ is solved) is often referred to as an inverted market or "backwardation" in the commodity markets. This suggests that the cost of holding the asset is less than the income/benefit derived, or that the market expects the spot price to decline.
What is the difference between discrete and continuous compounding in this context? The formula used in this calculator employs discrete compounding: $F = P \cdot (1 + r)^T$. Continuous compounding uses the exponential function: $F = P \cdot e^{rT}$. While continuous compounding is often used in theoretical finance, the discrete version is more straightforward for annual interest rate calculations.
What are the components of the Cost of Carry? The components generally include the financing cost (risk-free rate), storage costs, insurance, and dividends or convenience yield (which subtract from the cost). The rate $r$ in the calculator represents the net effect.
Why must I enter exactly three variables? The Cost of Carry model has four inter-dependent variables. To solve the equation $F = P \cdot (1 + r)^T$, you must know the values of three variables to algebraically solve for the unknown fourth variable.