Forward Price Determination – Cost of Carry Model

If Gold is 50,000 today, why is the 1-year Forward price 53,000?

1. The Logic: Cost of Carry

If I agree to sell you Gold after 1 year, I have two choices:

1. Buy Gold today with borrowed money (Pay Interest). Store it (Pay Storage). Give it to you after 1 year.
2. So, I will charge you: Spot Price + Interest Cost + Storage Cost.

Forward Price = Spot Price + Cost of Carry

2. The Formula (Continuous Compounding)

F = S × e^(rt)

• F: Forward Price.
• S: Spot Price.
• e: Exponential constant (2.718).
• r: Risk-free interest rate.
• t: Time in years.

Simple Interest Version: F = S × (1 + r × t)

3. What if the Asset pays income (Dividend)?

If the asset gives income (like Dividend from shares), holding the asset is beneficial. So we subtract this benefit.

• Cost of Carry = Interest Cost - Dividend Yield.
• Formula: F = S × e^((r-y)t) where y is dividend yield.

4. Exam Notes: Writing the Answer

Question: "Explain the Cost of Carry model for Forward Pricing." (10 Marks)

Answering Strategy:

1. Concept: "Forward Price is nothing but Spot Price adjusted for time value of money."
2. Components: Interest (Add), Storage (Add), Income/Dividend (Subtract).
3. Assumption: "No Arbitrage" is the key assumption.

Summary

• Fair Price: The specialized formula ensures that no risk-free profit (arbitrage) is possible.
• Contango: If F > S (Normal market).
• Backwardation: If F < S (Inverted market).

Quiz Time! 🎯

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