Convergence of Futures Price to Spot Price

1. Introduction

We know that Futures Price differs from Spot Price due to the Cost of Carry (Time Value). But what happens when Time = 0? This leads to the phenomenon of Convergence.

2. The Concept of Convergence

• Logic: On the day of expiry, a Futures Contract effectively becomes a Spot Contract. There is no time left to carry.
• Result: The Cost of Carry becomes Zero.
• Equation: Future Price = Spot Price + 0.
• Phenomenon: As the expiry date gets closer, the gap (Basis) shrinks, and finally, on the last minute of expiry, Spot Price = Future Price.

3. Why must it happen? (Arbitrage Logic)

If they don't converge, there is free money on the table:

• Scenario: On expiry day, Reliance Spot is 2400, Reliance Future is 2410.
• Arbitrage Action: Trader buys Spot @ 2400, Sells Future @ 2410.
• Delivery: He delivers the shares against the future.
• Profit: Risk-free ₹10 profit.
• Effect: Massive selling of Future will push its price down to 2400.

4. Diagram: The Convergence Graph

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5. Exam Notes: Writing the Answer

Question: "Explain the concept of Convergence in Futures Market." (5 Marks)

Answering Structure:

1. Statement: "On the expiry date, Futures Price must equal Spot Price."
2. Reason: "Because the remaining time to maturity is zero, so Cost of Carry is zero."
3. Arbitrage: "If they don't equal, arbitrageurs will force them to equal."

6. Quiz Time! 🎯

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