NCEL © 2007

How to Price Gold Futures

An NCEL Tutorial

December 2006

NCEL © 2007

Definition

• Futures are the simplest form of Derivative Products

• Future: Contractual Agreement to Buy or Sell something in the future at a price which is agreed today

• Represents an Obligation

• Derivative, because price depends on spot market

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Spot v Future

• Spot– Agree Price Now– Pay Money Now– Get Commodity Now

• Future– Agree Price Now– Pay Money Later– Get Commodity Later

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Futures Pricing Basics

• Futures Pricing Does Not Involve Predicting the Future

• Difference between Spot and Future is in the timing of Payment and Delivery

• Factors involved in analyzing deferred cash/delivery are also used in pricing Futures

• Opportunity Cost, Time Value of Money, Value of Today’s Rupee versus Tomorrow’s

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Futures Pricing Steps

• Futures Pricing Involves comparing two strategies/decisions:

– Buy Now OR Buy Later

• If Buy Now, Must Pay Money Now

• If Buy Later, Can Save Money Now to Pay Later

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No-Arbitrage Principle

• Economic Benefit of Buying Now or Buying Later should be the same

• Eg. Gold Spot is Rs 13,000/10gms• 3 month Deposit Rate is 10% (Risk-Free,

Market Rate of Return)• Strategy A: Buy Gold Now, Pay Rs 13,000.

Give up potential to earn 10% interest• Strategy B: Agree to Buy Gold in 3 months,

Save Rs 13,000 and earn interest for 3 months (Rs 325)

• Everyone would go for Strategy B if Futures Prices did not adjust for opportunity cost

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No-Arbitrage Principle

• Spot Gold Buyer: Loses 10% interest

• Spot Gold Seller: Earns 10% interest

• Futures Gold Buyer: Earns 10% interest

• Futures Gold Seller: Loses 10% interest

• Futures seller needs to be compensated for foregoing 10% interest income. He will only sell at a price which brings him at least the market rate of return

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Fundamental Question

• Need to weigh just one equation:– Cost and Benefit of Buying/Selling Now– Versus– Cost and Benefit of Buying/Selling Later

• Opportunity Cost of Futures Seller is 10%. He will lose money if he sells futures at less than opportunity cost

• Futures Price = Spot Price + Cost of Carry• Spot = 13,000 ; CoC = 10% ; Time = 3 months • Future Price = 13,325• If F > 13,325: Sell Future and Buy Spot and Lock-in

Guaranteed Rate of Return of > 10%• If F < 13,325: Buy Future, Sell Spot and Earn 10% on

Cash plus extra return from buying future cheaply

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How do Prices Move over Time?

Basis

Prices

Present MaturityTime

Cash

Futures

Credible threat of delivery ensures convergence

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Mathematical Representation

• F = S x (1 + r)t

• Does Futures Price Calculation Mean Prediction? NO

• Futures Price depends on three variables:– Spot– Cost of Carry– Time

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International Gold Price

• Continuously traded round the clock globally in OTC, inter-bank, inter-broker/dealer markets

• London AM/PM Fix 10.30(2.30pm PST) am / 3.00 pm (7.00 pm PST)

• Buying Gold in Spot Market results in a Gold Account being credited with Fine Troy Ounces

• If want Physical Delivery, Have to pay Fine Ounces in exchange for Physical Bars of desired weight and Fineness

NCEL © 2007

Gold Futures Pricing

• International Gold Price is in USD/Fine Troy Oz.

• Fine Troy Ounces i.e. Pure Gold• International Price is for London Delivery• All traders have to factor in their specific costs

of delivering to locations other than London• NCEL Contract is for delivery Karachi• Have to include Costs of importing gold into

Pakistan• Have to determine Cost of Carry

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Karachi Landed Price Calculation

• 1: International Gold Price - $/Troy Oz• 2: Convert to PKR using Open Market

Offer Rate• 3: Convert to Grams – 3.11034768• 4: Freight Cost – Average $1• 5: Customs Duty, CAA Charge, Handling• 6: Withholding Tax – 1%• 7: Spot Gold Karachi Landed Price in

Rs/10gm

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NCEL Gold Futures Cost of Carry

• 1: Rupee Landed Price

• 2: Cost of Carry/Time Value of Money/Opportunity Cost/Interest Rate/Market Rate of Return - Kibor

• 3: Time to Expiry

• 4: F = S x (1+r)t

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Gold Futures Sensitivity Analysis

• SPOT: $1 change in USD/Oz price = Rs 20 / 10gms

• FX: Re1 change in PKR/USD FX rate = Rs 220 / 10gms

• INTEREST RATE: 1% change in Kibor rate = Rs 35/10gms for 3-month futures

• TIME: 1 day closer to maturity for 3-month futures = Rs 3 / 10gms

NCEL © 2007

Box Arbitrage Analysis

International Spot Gold $/oz

Can use International Spot or Futures Prices as base to obtain the same Rupee Futures price, but need to be consistent due to No-Arbitrage Principle

US Gold Futures $/oz

Pakistan Spot Gold Rs/10gms (includes landed costs of Rs 180/10gms)

NCEL Gold Futures Rs/10gms (includes landed costs of Rs 180/10gms)

PKR/USD Spot FX Rate PKR/USD Fwd FX Rate

Implied $ Cost of Carry

Calculate Rupee Cost of Carry

61.00 WRONG!

656.85 665.90

13,064

61.00 61.57

5.51%

9.26% 13,363