Understanding the Cost of Carry Model

The Cost of Carry Model is used to determine the fair price of a futures contract based on the relationship between the spot price of the underlying asset, the cost of holding or carrying that asset until the futures contract expiration, and any benefits or costs associated with holding the asset.

Components of the Cost of Carry

1. Spot Price (S): The spot price is the current market price of the underlying asset. It represents the price at which the asset can be bought or sold for immediate delivery.
2. Cost of Carry (C): The cost of carry encompasses two main components:
   • Cost of Financing (r): This is the cost associated with financing the purchase of the asset until the futures contract expires. It includes interest expenses or opportunity costs incurred by holding the asset instead of investing in alternative opportunities.
   • Income Yield (y): This refers to any income generated from holding the asset, such as dividends, interest payments, or other benefits. For commodities, storage costs may also be considered. The cost of carry is calculated as: C = r – y
   • If ( r ) (cost of financing) is greater than ( y ) (income yield), the cost of carry is positive, indicating a net cost to hold the asset.
   • If ( y ) is greater than ( r ), the cost of carry is negative, indicating a net benefit or income from holding the asset.
3. Fair Futures Price (F):
   • According to the Cost of Carry Model, the fair price of a futures contract (F) is determined by adding the cost of carry to the current spot price (S): F = S + C
   • The fair futures price ( F ) reflects what the market expects the spot price to be at the expiration date of the futures contract, considering the cost of carrying the asset until then.

Application in Different Markets

• Commodities: In commodity futures markets, the cost of carry model is extensively used to determine the fair price of futures contracts. It considers storage costs, financing expenses, and income from carrying the commodity (e.g., dividends for stocks).
• Equities: For stock index futures, the model incorporates dividends and interest rates into the cost of carry calculation. Dividends received from stocks reduce the cost of carry, while interest rates affect the financing cost.
• Foreign Exchange (Forex): In currency futures, interest rate differentials between currencies play a significant role in the cost of carry. Traders factor in interest rates to determine fair futures prices relative to spot prices.

Example Scenario:

• Spot Price (S): Assume the spot price of a stock index in INR is 40,000.
• Cost of Financing (r): Assume an annual financing cost (interest rate) of 8%.
• Income Yield (y): Assume no dividends, but consider the cost of storage and other holding costs, which are negligible for this example.

Calculation of Cost of Carry (C):

C = r – y = 0.08 – 0 = 0.08

Calculation of Fair Futures Price (F):

F = S + C = 40,000 + 0.08 * 40,000 = 40,000 + 3,200 = 43,200 ]

Interpretation:

In this example:

• Spot Price (S): 40,000 INR
• Cost of Financing (r): 8% per annum
• Income Yield (y): Negligible for simplicity

The fair futures price (F) using the Cost of Carry Model would be 43,200 INR. This reflects what the market expects the spot price of the stock index to be at the expiration date of the futures contract, considering the cost of carrying the asset until then.

Conclusion:

The Cost of Carry Model is instrumental in determining fair prices for futures contracts across various asset classes, including stocks, commodities, and currencies. By understanding the components of cost of carry and applying them to real-world scenarios, traders and investors can make informed decisions in futures markets, accounting for financing costs and income yields associated with holding assets.