Pricing of Futures – Process & Role of Cost of Carry

1. Introduction

One of the most common questions in exams is "How is the price of a Futures contract determined?". The theoretically correct price is called the Fair Value. It is calculated based on the "Cost of Carry" model, which assumes that the Futures price is simply the Spot price plus the cost of holding the asset until expiry.

2. The Cost of Carry Model

A. The Main Concept

If you want to own Gold after 3 months, you have two choices:

1. Choice A: Buy Gold today (Spot) @ ₹50,000. Store it for 3 months.
   • Cost involves: Interest on money borrowed + Storage charges.
2. Choice B: Buy a Futures Contract to take delivery after 3 months.
   • Cost: The seller will charge you the Spot Price + his cost of holding it for you.

B. The Formula

Futures Price (F) = Spot Price (S) + Cost of Carry (C)

Where Cost of Carry (C) includes:

1. Interest Cost: Opportunity cost of funds tied up.
2. Storage Cost: (For commodities).
3. Less: Income/Convenience Yield: (e.g., Dividends for stocks).

C. Continuous Compounding Formula

The mathematical formula used for Stock Index Futures is:

F = S × e^(r-q)t

• S: Spot Price
• r: Risk-free Interest Rate
• q: Dividend Yield
• t: Time to expiry (in years)

3. Pricing Scenarios

1. Fair Value: If Future Price = Spot + Cost of Carry. (Market is efficient).
2. Over-priced: If Actual Future Price > Fair Value. (Arbitrageurs will Sell Future, Buy Spot).
3. Under-priced: If Actual Future Price < Fair Value. (Arbitrageurs will Buy Future, Sell Spot).

4. Exam Notes: Writing the Answer

Question: "Explain the Cost of Carry model for pricing Futures." (10 Marks)

Answering Structure:

1. Definition: "Ideally, the Futures price is the Spot price adjusted for the cost of carrying the asset...".
2. Components: List the 3 components (Interest, Storage, Dividend).
3. Arbitrage: Mention that "Arbitrageurs ensure that the actual price stays close to this theoretical fair price."

5. Quiz Time! 🎯

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