Understand futures contract fundamentals — Stock-Market notes

Core Components of a Futures Contract

WHY standardized? So contracts are fungible (interchangeable) and liquid. You can exit a position by taking the opposite side without finding your original counterparty.

The Economic Logic: Why Futures Prices Differ from Spot Prices

Formula The Cost-of-Carry Model (No-Arbitrage Condition)

For storable assets with no convenience yield: $F_0 = S_0 (empty string – the snippet contains only a backslash with no command)cdot e^{rT}$

Where:

$F_0$ = futures price today
$S_0$ = spot (current market) price
$r$ = risk-free interest rate (continuously compounded)
$T$ = time to maturity (in years) Derivation from first principles:

Strategy A: Buy the asset now at $S_0$ $S_{0}$ , hold until time $T$ $T$
- Cost: $S_0$ upfront
- Opportunity cost: You can't earn interest on that $S_0$ → lose $S_0 \cdot (e^{rT} - 1)$
- Storage cost: Assume negligible for financial assets
- Total cost at time T: $S_0 \cdot e^{rT}$
Strategy B: Enter a long futures contract at $F_0$ $F_{0}$ , pay nothing upfront
- Cost at time T: $F_0$
No-arbitrage principle: Both strategies give you the asset at time $T$ , so their costs must be equal: $F_0 = S_0 \cdot e^{rT}$

WHY this step? If $F_0 > S_0 \cdot e^{rT}$ , arbitrageurs would buy spot, sell futures, and profit risk-free. Market forces push $F_0$ back down. The opposite happens if $F_0$ is too low.

Worked example Example 1: Gold Futures Pricing

Setup:

Gold spot price: $S_0 =$ 2000/oz$
Risk-free rate: $r = 5\%$ per year
Time to expiration: $T = 0.5$ years (6 months) Calculate theoretical futures price:

$F_0 = 2000 \cdot e^{0.05 \times 0.5} = 2000 \cdot e^{0.025}$

$e^{0.025} \approx 1.0253$

$F_0 = 2000 \times 1.0253 = \$2050.60$

WHY this step? The $e^{rT}$ term accounts for the interest you could earn by NOT buying gold now and instead investing $2000 at 5% for 6 months. The futures price must compensate for this opportunity cost.

Interpretation: If the market quotes gold futures at $\$ 2070, that's a $\$ 19.40$ premium over fair value → arbitrage opportunity (buy spot, sell futures).

Worked example Example 2: Wheat Futures with Storage Costs

Setup:

Wheat spot price: $S_0 = \emptyset$ 8.00/bushel$
Storage cost: $u = 2\%$ per year (continuously compounded)
Risk-free rate: $r = 4\%$
Time to expiration: $T = 1$ year

Modified formula (with storage): $F_0 = S_0 \cdot e^{(r+u)T}$ WHY? Storage is a cost you incur by holding the physical asset. Add it to the opportunity cost.

$F_0 = 8.00 \cdot e^{(0.04 + 0.02) \times 1} = 8.00 \cdot e^{0.06}$

$e^{0.06} \approx 1.0618$

$F_0 = 8.00 \times 1.0618 = \$8.49$

Sanity check: The futures price is $6.1\%$ higher than spot. That makes sense: you're paying for1 year of storage (2%) plus foregone interest (4%).

Long vs. Short Positions

The key asymmetry: A long position has limited maximum loss — the asset can only fall to zero, so the worst case for the long is losing $F_0$ per unit — but it has theoretically unlimited upside because prices can rise without bound. A short position is the mirror image: its maximum gain is capped (the asset can only fall to zero) but its loss is theoretically unlimited because if the asset price keeps climbing, the short must still deliver at $F_0$ and buy at ever-higher prices.

Worked example Example 3: Profit/Loss Calculation

You take a long position on 1 crude oil futures contract:

Contract size: 1,000 barrels
Futures price when you enter: $F_0 =$ 75/barrel$
Futures price at expiration: $F_T =$ 82/barrel$ Your profit: $\text{Profit} = (\text{Final price} - \text{Entry price}) \times \text{Contract size}$

$= (82 - 75) \times 1000 = \$7000$

WHY this step? You locked in the right to buy at $75. The market price is now$ 82. You effectively buy at $75 and can immediately sell at$ 82, pocketing the $7 difference per barrel.

If you were short: You'd lose $7000 because you agreed to sell at$ 75 but must now buy at $82 to fulfill your obligation.

Margin and Mark-to-Market

Derivation of margin call logic:

You deposit initial margin: $M_0$
Each day, your position is revalued at the new futures price
Profit/loss is credited/debited from your margin account
If your margin balance falls below maintenance margin $M_m$ , you get a margin call
You must deposit additional funds to bring balance back to $M_0$ , or your position is liquidated

Worked example Example 4: Margin Call Mechanics

Setup:

You go long on S&P 500 futures
Contract multiplier: $50 per index point
Entry price: 4500
Initial margin: $20,000
Maintenance margin: $15,000 Day 1: Index falls to 4450
Loss: $(4450 - 4500) \times 50 = -2500$ 2500$
Your margin: $20,000 - 2500 = 17,500$ 17,500$ (still above maintenance) Day 2: Index falls to 4380
Additional loss: $(4380 - 4450) \times 50 = -3500$ 3500$
Your margin: $17,500 - 3500 = 14,000$ 14,000$ (below maintenance!)

Margin call: You must deposit $\$ 6000$ to restore initial margin.

WHY this step? The clearinghouse protects itself. If the index keeps falling and you can't cover losses, they'll close your position before account goes negative.

Contango and Backwardation

Common Mistakes

Common mistake Mistake 1: "Futures prices predict future spot prices"

Why it feels right: The name "futures" suggests forecasting.

The reality: Futures prices reflect current cost-of-carry, not market expectations. If gold futures are at $2050 and gold spot is$ 2000, that $50 premium isn't a prediction that gold will rise – it's the interest rate compensation.

When curves invert: Contango (futures > spot) is the baseline from cost of carry. Backwardation (futures < spot) arises when the convenience yield exceeds the cost of carry — a real economic benefit of holding the physical asset now, not market sentiment. Storage cost is part of the cost of carry itself, not a deviation from it.

The fix: Use futures for hedging or arbitrage based on the formula, not as a crystal ball.

Common mistake Mistake 4: "Futures and forwards are the same thing"

Why it feels right: Both are agreements to buy/sell in the future at a set price.

Key differences:

Feature	Futures	Forwards
Exchange traded	Yes	No (OTC)
Standardized	Yes	Customized
Counterparty risk	Clearinghouse eliminates it	Direct exposure
Daily settlement	Yes	No (settle at maturity)
The fix: Futures are for liquidity and transparency; forwards are for exact customization (e.g., a specific date, odd contract size).

Active Recall Checkpoints

Recall Explain to a 12-year-old

Imagine you see a PlayStation 5 in a store today for $500, but you don't have the money until next month. You're worried the price might go up because everyone wants one.

So you make a deal with the store manager: "I'll pay you $500 next month, no matter what the price is then. Lock it in for me." The manager agrees and writes it down on paper.

That paper is like a futures contract! You've locked in the price. If PS5s go up to $600, you still only pay$ 500 – you win $100. But if they drop to$ 400, you still have to pay $500 – you lose$ 100.

The manager doesn't care about the price next month because they already agreed to your $500. That's the key: both of you MUST follow through. In the real world, farmers do this with wheat, airlines do it with jet fuel, and investors do it with gold or stock indexes.

Connections

5.1.02-Contango-and-backwardation – Why futures curves slope up or down
5.1.03-Hedging-with-futures – Using futures to lock in prices
5.1.04-Futures-vs-options – Obligation vs. right to buy/sell
2.3.01-Time-value-of-money – Why $e^{rT}$ appears in pricing
4.2.01-Arbitrage-pricing – No-arbitrage keeps futures fair-valued

#flashcards/stock-market

What is a futures contract? :: A legally binding agreement to buy or sell an asset at a predetermined price on a specific future date. Both parties are obligated to fulfill the contract.

What's the difference between long and short futures positions?

Long = agree to BUY at futures price (profit if price rises). Short = agree to SELL at futures price (profit if price falls).

Which futures position has unlimited loss potential, and which has bounded loss?

The short has unlimited loss (asset price can rise without bound). The long has bounded loss — the asset can only fall to zero, so max loss per unit is

F_0

What is the cost-of-carry formula for futures pricing?

F_0 = S_0 \cdot e^{rT}

, where

F_0

is futures price,

S_0

is spot price,

r

is risk-free rate,

T

is time to maturity. This assumes no storage costs or convenience yield.

Why are futures contracts standardized?

Standardization makes them fungible (interchangeable) and liquid. You can exit by taking the opposite position without finding your original counterparty.

What is mark-to-market in futures? :: Daily settlement of gains/losses. Your margin account is credited or debited each day based on the new futures price, preventing default risk.

What happens during a margin call?

If your margin balance falls below the maintenance margin, you must deposit funds to restore the initial margin, or your position gets liquidated.

What's the difference between initial margin and maintenance margin?

Initial margin is the upfront deposit to open a position (5-15% of contract value). Maintenance margin is the minimum balance required to keep the position open (usually 75-80% of initial).

Do futures prices predict future spot prices?

No. Futures prices reflect the current cost-of-carry (interest rates, storage costs, convenience yield), not market forecasts.

What is contango?

When futures prices are higher than the spot price (upward-sloping futures curve). Driven by the cost of carry — interest plus storage costs — for storable commodities.

What causes backwardation in commodities?

A positive convenience yield that exceeds the cost of carry, making the net cost of carry negative. The benefit of physically holding the asset now pushes futures below spot — not market sentiment.

How do you calculate profit on a long futures position?

Profit = (Final futures price - Entry futures price) × Contract size. If final price > entry price, long profits; if final price < entry price, long loses.

What's the key difference between futures and forwards?

Futures are exchange-traded, standardized, with daily mark-to-market and clearinghouse guarantee. Forwards are OTC, customized, with counterparty risk and settlement at maturity only.

What is the full cost-of-carry formula including convenience yield?

F_0 = S_0 \cdot e^{(r + u - y)T}

, where

u

= storage cost and

y

= convenience yield. When

y > r + u

, futures fall below spot (backwardation).

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho yaar, futures contract ka core idea bahut simple hai — ye ek legally binding agreement hai jisme aap aaj hi decide kar lete ho ki kisi asset ko future ki ek fixed date par, ek fixed price par kharidoge ya bechoge. Matlab aaj ki price ko "lock" kar diya tomorrow ke transaction ke liye. Ye exist isliye karta hai kyunki do type ke log hote hain: ek hedgers (jaise farmer ya airline) jo price uncertainty se bachna chahte hain, aur doosre speculators jo bina physical asset owned kiye price movement par bet lagate hain. Sabse important baat — futures mein dono parties obligated hote hain follow karne ke liye, options ki tarah choice nahi hoti. Isi obligation se hi risk aur opportunity dono paida hote hain.

Ab main part — futures price spot price se alag kyun hoti hai? Iska logic hai cost-of-carry model jo no-arbitrage principle par based hai. Formula hai $F_0 = S_0 \cdot e^{rT}$ . Iske peeche intuition ye hai: agar aap asset aaj hi kharid loge $S_0$ par, toh aap us paise par interest kama nahi paoge — ye aapki opportunity cost hai. Toh futures price mein wo interest add ho jaati hai. Agar wheat jaisa storable asset hai jiska storage cost bhi lagta hai, toh formula ban jaata hai $F_0 = S_0 \cdot e^{(r+u)T}$ , kyunki storage bhi ek extra cost hai holding ka. Simple logic — jitna cost lagega asset ko hold karne mein, utna hi futures price zyada hogi.

Ye kyun matter karta hai? Kyunki agar market ki actual futures price is theoretical fair value se hat jaaye — jaise gold example mein fair value $2050.60 thi lekin market$ 2070 quote kar rahi ho — toh wahan ek arbitrage opportunity ban jaati hai. Aap spot par kharid ke futures bech doge aur risk-free profit kama loge. Aur jaise hi log ye karte hain, market forces automatically price ko wapas fair value par push kar dete hain. Isi wajah se ye no-arbitrage condition real markets mein hold karti hai, aur yehi futures pricing ka foundation hai jise samajhna har trader ke liye zaroori hai.

Test yourself — Futures

Connections