DP
Futuresintermediate

Cost of Carry

The cost of carry cc is the net cost of holding the underlying asset from today until the futures delivery date. It bundles financing cost (the risk-free rate rr), storage and insurance for physical commodities, and subtracts any benefit from holding the asset such as dividends or convenience yield qq. Under no-arbitrage the fair futures price is F0=S0e(r−q)TF_0 = S_0 e^{(r - q)T} with continuous compounding, which is the engine behind both pricing and cash-and-carry arbitrage in Hull (2022) §5.4.

Why it matters

If you buy spot today and hold until delivery, you finance the purchase at rate rr and earn back any income qq along the way. To eliminate arbitrage, the price someone pays you later through the futures contract must equal what you paid plus that net carrying cost. Positive carry means the futures price sits above spot, the curve is in contango. Negative carry, common for high-dividend stocks or commodities with tight inventories, pulls the futures price below spot, the backwardation case. The futures curve is not a forecast, it is a financing identity.

Formulas

Cost-of-carry pricing, continuous compounding
F0=S0e(r−q)TF_0 = S_0 e^{(r - q) T}
Risk-free rate rr, income or convenience yield qq, time to maturity TT. Hull (2022) eqs. 5.3 and 5.7.
Cost-of-carry pricing, discrete compounding
F0=S0(1+r−q)TF_0 = S_0 (1 + r - q)^T
Annualised rates compounded once a year.
Commodity with storage cost
F0=S0e(r+u−y)TF_0 = S_0 e^{(r + u - y) T}
Storage cost rate uu added, convenience yield yy subtracted. See Hull (2022) §5.11.

Worked examples

Scenario

Gold spot is US$2,000 per ounce. The continuously compounded six-month USD rate is r=5%r = 5\%, and gold has no storage cost in the model and no income.

Solution

Fair futures price F0=2,000×e0.05×0.5=2,000×1.02532≈F_0 = 2{,}000 \times e^{0.05 \times 0.5} = 2{,}000 \times 1.02532 \approx US$2,050.63 per ounce. The premium of US$50.63 over spot is pure financing carry, since gold pays no dividend and storage is ignored. If COMEX June gold trades above this level, a cash-and-carry arbitrage borrows at $5\%$, buys spot, and sells futures.

Scenario

The S&P/ASX 200 spot index is at 7{,}200. The continuously compounded risk-free rate is r=4.3%r = 4.3\%, and the trailing dividend yield is q=3.6%q = 3.6\%. Time to expiry is three months.

Solution

Net carry =r−q=0.7%= r - q = 0.7\%. Fair futures price F0=7,200×e(0.043−0.036)×0.25=7,200×e0.00175≈7,200×1.001751≈7,212.6F_0 = 7{,}200 \times e^{(0.043 - 0.036) \times 0.25} = 7{,}200 \times e^{0.00175} \approx 7{,}200 \times 1.001751 \approx 7{,}212.6. Because dividend yield almost offsets the funding cost, the SPI 200 futures price is only marginally above spot, a common feature of high-yield equity markets such as Australia.

Common mistakes

  • ✗Cost of carry must be positive. It is not. When the income or convenience yield exceeds funding cost, q>rq > r, the futures price falls below spot. This is the textbook explanation of backwardation in commodities like oil during supply squeezes.
  • ✗Cost of carry is a market forecast. It is a no-arbitrage identity, not a prediction. Even when traders expect the spot to rally, the futures curve is pinned by financing and income, otherwise cash-and-carry arbitrage would eliminate the gap.
  • ✗Storage cost only matters for grains and metals. Holding currency requires no warehouse but earns or pays the foreign interest rate, and this foreign rate plays the same role as a continuous yield qq in FX futures pricing, F0=S0e(rd−rf)TF_0 = S_0 e^{(r_d - r_f) T}.

Revision bullets

  • •Net carry =r= r + storage −- income −- convenience yield
  • •Continuous form F0=S0e(r−q)TF_0 = S_0 e^{(r-q) T}
  • •Discrete form F0=S0(1+r−q)TF_0 = S_0 (1 + r - q)^T
  • •F0>S0F_0 > S_0 when carry positive, called contango
  • •F0<S0F_0 < S_0 when carry negative, called backwardation
  • •Identity is enforced by cash-and-carry arbitrage, not forecasts

Quick check

If the net cost of carry is positive, the futures price is:

Spot gold is US$2,400, r=4%r = 4\% continuously compounded, no income, no storage. The fair one-year futures price is approximately:

Connected topics

Cont. PricingDiscrete PricingArb Futures

In learning paths

Futures Path

Sources

  1. Hull (2022), §5.4 and §5.11
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Derives cost-of-carry pricing for assets that pay income and for commodities with storage and convenience yield.
  2. Working (1949) Theory of Price of Storage
    Working, Holbrook. The Theory of Price of Storage. American Economic Review, 39(6), 1949, pp. 1254 to 1262.
    Foundational paper for the cost-of-carry concept in commodity markets and the link between storage costs and the futures curve.
  3. CME Group, Cost of Carry
    CME Group. Understanding Contango and Backwardation. CME Group Education, 2024.
    Practitioner-oriented description of how net carry shapes the futures curve, with energy market examples.
  4. ASX Index Derivatives
    Australian Securities Exchange. ASX SPI 200 Index Futures Contract Specifications. ASX, 2024.
    Local equity-index contract used to illustrate the small net-carry case driven by high Australian dividend yields.
How to cite this page
Dr. Phil's Quant Lab. (2026). Cost of Carry. Derivatives Atlas. https://phucnguyenvan.com/concept/cost-of-carry
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