Cost-of-Carry

Cost‑of‑Carry represents the total expense incurred to hold (or carry) a physical commodity until the delivery date of a futures contract. The expense includes financing the purchase, paying for storage, and any other costs such as insurance, while the benefit of holding the commodity is captured by the convenience yield.

In the Indian context, SEBI’s regulations require participants to disclose storage costs for commodities stored in approved warehouses, and the risk‑free rate is usually proxied by the RBI’s repo rate. The convenience yield reflects the non‑monetary advantage of having immediate physical possession, such as meeting production schedules or avoiding stock‑outs.

Exam questions often ask you to identify which component pushes the futures price above the spot (contango) and which pulls it below (backwardation). Understanding each element prevents common mistakes like ignoring the convenience yield when it is significant for perishable commodities.

• Financing cost – interest on capital tied up in the commodity.
• Storage cost – charges for warehousing, insurance, and handling.
• Convenience yield – implicit return from holding the physical asset.

The financing component (r) is the cost of borrowing funds to purchase the commodity. In India, the risk‑free rate is typically the RBI repo rate, but banks may use a slightly higher rate for corporate borrowers.

Storage cost (u) covers warehousing fees, insurance, and any quality‑preserving expenses. SEBI mandates that storage charges be disclosed in the contract specifications, and they are expressed as an annual percentage of the spot price.

Convenience yield (y) is the implicit benefit of holding the commodity, such as the ability to meet sudden demand spikes. It is not a cash flow, but it is treated as a negative cost in the model because it reduces the overall cost of carry.

When all three are combined, the net cost of carry is (r + u – y). A positive net cost leads to a futures price above spot (contango), while a negative net cost results in a futures price below spot (backwardation).

When the net cost of carry (r + u – y) is positive, the futures price exceeds the spot price, a market condition called contango. This is typical for commodities with ample supply and low convenience yield, such as metals stored in large warehouses.

If the convenience yield outweighs financing and storage costs, the net cost becomes negative, and the futures price falls below the spot price, known as backwardation. Agricultural products during a shortage often exhibit backwardation because the immediate availability of the commodity is highly valuable.

Exam questions may present a scenario and ask you to classify the market. Look at the sign of (r + u – y) and compare the computed futures price with the given spot price.

• Contango: F > S, net cost > 0.
• Backwardation: F < S, net cost < 0.

To visualise how each component influences the futures price, consider a base case where S = 5,000 ₹, T = 0.5 year, r = 8%, u = 2%, y = 1%. Varying the convenience yield from 0% to 5% while keeping other inputs constant shows a clear downward shift in F.

The chart below plots futures prices for convenience yields of 0%, 1%, 3% and 5%. As y increases, the net cost of carry declines, pulling the futures price closer to the spot or even below it.

This type of analysis is frequently asked in the exam: you may be given a table of yields and asked to identify which scenario leads to backwardation.

Assume an Indian investor wants to price a 3‑month gold futures contract. Spot price of gold is 5,20,000 ₹ per 10 grams. The RBI repo rate is 6.5% p.a., storage cost for gold in a SEBI‑approved vault is 0.5% p.a., and the market convenience yield is estimated at 1% p.a. The time to maturity is 0.25 years.

Using the simple‑interest cost‑of‑carry formula, the net cost = 0.065 + 0.005 – 0.01 = 0.06 (6%). Multiplying by T gives 0.06 × 0.25 = 0.015. Adding 1 yields 1.015. Therefore, Futures price = 5,20,000 × 1.015 = 5,28,300 ₹ (rounded).

In the exam, you may be asked to compute the fair futures price or to comment on whether the market is in contango. Since F > S, the market is in contango, indicating that financing and storage costs dominate the convenience yield.

Always write down the three components (r, u, y) before plugging numbers into the formula. This prevents omission of the convenience yield, a frequent source of error.

Check the sign of (r + u – y). A positive sign means you should expect a futures price higher than spot; a negative sign signals backwardation. Many NISM questions ask you to infer market condition without explicit calculation.

When the question provides the futures price and asks for the implied convenience yield, rearrange the formula: y = r + u – ( (F/S – 1) / T ). This algebraic manipulation is allowed and often tested.