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Futures and Forward Contracts

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Present Value and DiscountingOptions: Calls, Puts, and Basic Payoffs→→Forward Pricing and Cost of CarryHedging with Derivatives+2 more
derivatives futures forwards

Core Idea

Futures are standardized exchange-traded contracts obligating delivery of an asset at a future date at an agreed-upon price. Forwards are OTC equivalents. Both lock in prices but differ in standardization, liquidity, and margin requirements. Futures enable hedging, speculation, and arbitrage in commodity, stock, and interest rate markets.

Explainer

Start with the simplest version of the problem. Imagine you are a wheat farmer who will harvest 10,000 bushels in six months. The current price is $5 per bushel, but you don't know what the price will be at harvest. If prices fall to $3, your revenue collapses. You want certainty. A grain elevator operator faces the opposite risk: they need to buy wheat at harvest but worry prices will rise. Both parties have a problem that the other can solve. A forward contract is the bilateral agreement that resolves this: you agree today to sell 10,000 bushels in six months at $4.80 — a price you both can live with. No money changes hands now; the obligation is settled at delivery. You have locked in revenue; they have locked in cost.

A futures contract achieves the same economic goal but is engineered for liquidity and scale. Futures are standardized by exchanges: the contract specifies exact quantity, quality, delivery location, and settlement date. Because contracts are identical, they are tradeable — a farmer can exit their position before harvest by selling the contract to someone else, without negotiating with the original counterparty. The exchange also interposes itself as buyer to every seller and seller to every buyer, eliminating counterparty credit risk. To enforce this guarantee, both parties post initial margin (a good-faith deposit) and daily mark-to-market settlement transfers gains and losses between accounts as prices move. This daily cash flow is the key mechanical difference from forwards, which settle only at maturity.

Your prerequisite — present value and discounting — underlies the pricing of both instruments. The cost-of-carry model says the fair forward price F is approximately F = S × (1 + r)T, where S is today's spot price and r is the risk-free rate over the period T. The intuition: if you could buy the asset today and store it until the delivery date, your total cost would be the spot price plus financing costs (and storage, insurance, etc.). The forward price must equal that cost-to-carry; otherwise arbitrage profits would be available. If F > S(1+r)T, you buy the asset spot, sell a forward, and pocket the difference. Competitive arbitrage drives the price back to fair value.

The three uses of futures follow naturally from this framework. Hedgers like our farmer take positions that offset existing price exposure. Speculators take positions without offsetting exposure — they are betting on directional price moves and provide the liquidity that hedgers need. Arbitrageurs enforce the cost-of-carry relationship by exploiting mispricings. All three are necessary: hedgers transfer risk they don't want, speculators absorb it for expected profit, and arbitrageurs keep prices aligned across time. Understanding which role a participant is playing — and what their position looks like at expiration — is the core analytical skill in derivatives markets.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Center of Mass → Conservation of Linear Momentum → Elastic Collisions → Inelastic Collisions → Coefficient of Restitution → Collision Analysis and Real-World Applications → Two-Body Collisions in the Center-of-Mass Frame → Reduced Mass and Two-Body Problems → Kinematics in Two Dimensions → Projectile Motion → Circular Motion: Kinematics → Simple Harmonic Motion → Introduction to Differential Equations → Solow Growth Model → Capital Accumulation and the Golden Rule → Investment Demand and Capital Formation → Aggregate Demand → The AS-AD Model → Business Cycles → Monetary Policy Tools → Term Structure of Interest Rates → Risk and Return Tradeoff → Options: Calls, Puts, and Basic Payoffs → Futures and Forward Contracts

Longest path: 114 steps · 799 total prerequisite topics

Prerequisites (2)

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