⚙ モジュール1：メカニズムと理論

💡 起源s: Osaka, 17th century. Rice farmers faced a problem: the crop was planted months in advance, but the price at the time of sale was completely unknown. At the Dōjima rice market, traders developed a solution — they agreed on the price today, with delivery three months later. Both sides gained planning certainty. From this simple idea, the world's first forward contracts were born. The principle remains identical to this day.

In 1848, grain traders in Chicago founded the シカゴ商品取引所 (CBOT) — the first modern futures exchange. Farmers from the Midwest could now sell their wheat and corn harvests at a fixed price before the grain even reached the silo. Mills and traders, in turn, knew exactly what they would pay. The market created liquidity and price stability for an entire economy.

The decisive leap into the modern era came in 1972, when the Chicago Mercantile Exchange (CME) — at the urging of economist Milton Friedman — introduced financial futures on currencies for the first time. Companies could hedge exchange rate risks on an exchange rather than negotiating bilaterally with banks. Interest rate futures followed a few years later, then equity index futures. Today the global futures market encompasses more than 20 billion contracts traded per year on everything from crude oil to the S&P 500.

What Is a Future?

A future is a binding, exchange-traded contract that obligates two parties: one to buy, the other to sell — a specific underlying asset, in a fixed quantity, at a price agreed upon today, at a future date.

Three characteristics distinguish it from related instruments:

• Standardized: Contract size, delivery date, and quality specifications are set by the exchange. No room for negotiation, full interchangeability.
• Exchange-traded: Buying and selling occur through a central trading platform — transparent, rule-based, with publicly available prices.
• Obligation, not a right: Both sides must perform if the contract is held to expiration. This distinguishes futures from options, where the buyer has a right but no obligation.

Distinction from similar instruments:

• Forwards work on the same basic principle, but are OTC contracts (Over the Counter) — bilateral between two parties, individually negotiated, not standardized. No central clearing, hence counterparty risk.
• Options give the buyer the right to buy or sell an underlying asset — they may, but need not. The seller (writer) has the obligation. Futures have no such asymmetry: both sides are obligated.
• CFDs (Contracts for Difference) are also OTC, issued by a broker, often with a conflict of interest. Futures trade on regulated exchanges with a neutral counterparty.

Who Trades Futures?

Three groups make up the market participants — and each needs the others:

• Hedgers use futures to lock in the price for a real-world transaction. An oil company sells crude oil futures to secure the revenue for its next production batch. A grain mill buys wheat futures to fix input costs. For hedgers, a future is not a speculative instrument — it is insurance.
• Speculators absorb the price risk that hedgers want to shed. They bet on directional moves without ever wanting a physical underlying asset. Hedge funds, Commodity Trading Advisors (CTAs) and active retail traders belong to this group. Without speculators, hedgers would have no liquid counterparties.
• Arbitrageurs keep prices consistent — between futures and the spot market (basis trading), between different expiration months (calendar spread), or between similar contracts on different exchanges (inter-exchange). Their activity ensures that price differences do not persist.

Why Are Futures Attractive Today?

• Leverage through margin: Traders deposit only a fraction of the contract value as collateral (initial margin). With $5,000 in margin, one can control an ES contract with a notional value of more than $200,000. Leverage amplifies gains — and losses.
• Nearly continuous trading: Most futures markets trade almost 24 hours a day, 5 days a week, with a short pause of roughly 60 minutes per day. Reactions to news outside exchange hours can happen immediately.
• Central clearing with no counterparty risk: The exchange's clearinghouse (e.g., CME Clearing) steps in as counterparty to every contract. If one side defaults, the clearinghouse takes over. This eliminates the counterparty risk present in OTC forwards.
• Price transparency: Bid and ask prices are publicly available. No bid-ask spread hidden in the shadows — the market is equally visible to everyone.
• Direct market exposure: Futures replicate crude oil, indices, or interest rate expectations directly — without ETF management fees, without tracking error, without voting rights issues.

🕰️ 300 Years of Futures Exchanges — in Six Milestones

From a rice contract in Osaka to negative oil prices in 2020: the long history of futures markets can be told through six turning points. Each solved a specific problem of its time — and laid the foundation for what would follow.

1. 📅 1710 · Osaka
   Dōjima Rice Market — the world's 最初の先物取引所
   Japanese rice farmers and traders agree on standardized delivery contracts for rice in 3 and 6 months. The market develops auction mechanics, tick sizes, and a settlement procedure — centuries ahead of the West.
2. 📅 1848 · Chicago
   シカゴ商品取引所 (CBOT)
   82 traders found the first modern futures exchange. Wheat, corn, and oats are standardized — farmers can sell their harvest before planting. Formal margin rules follow in 1865.
3. 📅 1972 · Chicago
   CME · First Financial Futures
   After the end of Bretton Woods, Milton Friedman proposes to the CME that it introduce currency futures. The International Monetary Market (IMM) launches on May 16 with seven currency contracts. The futures world opens up beyond agriculture.
4. 📅 1982 · Kansas
   Value Line Index — First Equity Index Future
   On February 24, 1982, the Kansas City Board of Trade (KCBT) lists the first cash-settled equity index future. Two months later the CME follows with the S&P 500 future — the ancestor of today's ES.
5. 📅 1992 · CME Globex
   Electronic Trading
   Globex launches as an electronic after-hours trading platform. Within 15 years, screen trading displaces the legendary open-outcry pits. In 2015 CME permanently closes its last futures pits.
6. 📅 April 20, 2020
   Negative Oil · WTI May Contract closes at −$37.63
   The day before the last trading day of the May contract, demand collapses due to COVID lockdowns and storage tanks in Cushing (Oklahoma) are full. For the first time in history, one must actually pay to have oil taken away. A textbook moment for storage costs and convergence.

🗺️ The Map of This Chapter

Four parts, 22 sections. First the mechanics — contract, margin, rollover. Then commodities, from crude oil to soybeans. Then financial futures — indices, rates, forex, crypto. Finally, strategy and DACH taxation.

すべての先物契約には同じ構造的な構成要素があります。これらを理解すれば、どんな新しい契約もすぐに分類できます。

The month code in the ticker is standardized and applies to all futures markets worldwide:

Cash vs. Physical Delivery

How a contract is settled at expiration determines the risk for the retail trader:

• Cash Settlement: Index futures (ES, NQ, DAX), VIX, FX futures — the difference between entry price and settlement price is settled in cash. No physical delivery is possible.
• Physical Delivery: Commodities (Crude Oil CL, Natural Gas NG), many bond futures (ZB, ZN), some agricultural futures (wheat, corn, soybeans) — if held until the delivery month, the underlying asset is actually delivered. Retail brokers typically close positions automatically shortly before this date.

💡 Whoever needs $10,000 in capital to hold $10,000 worth of stocks controls, with the same $10,000 in futures, often $150,000–$300,000 in contract value. That is leverage — and it can ruin you faster than you have time to get out of bed.

Initial Margin

The initial margin is the minimum collateral you must post when opening a position. Typically 3–10% of the contract value — depending on the volatility of the underlying and broker policy. Example E-Mini S&P 500 (ES): contract value approx. $250,000 (5,000 × $50 multiplier), initial margin approx. $12,000 → leverage ≈ 20×. The clearinghouse (CME) sets the minimum rates; brokers may require higher amounts — never lower.

Maintenance Margin

The maintenance margin is the minimum amount that must remain in the account for the entire duration of an open position — typically 80–90% of the initial margin. If account equity falls below this threshold, for any reason, a margin call is triggered. Not eventually: immediately. The broker notifies you and expects you to top up the account to at least the initial margin level — the same trading day.

Variation Margin (Mark-to-Market)

Futures are valued daily at the settlement price — this is called mark-to-market. Profits are credited to the account, losses are deducted. Every trading day, automatically. This is the fundamental difference from stocks: if you lose $1,000, that $1,000 is immediately real and gone — not a book loss that might recover someday. The loss is cash, tonight. Those who do not internalize this will face unpleasant surprises on their account statement.

SPAN System

Standard Portfolio Analysis of Risk (SPAN) is the margin calculation system of the CME and many other exchanges. SPAN calculates risk not at the individual position level, but at the portfolio level — it accounts for spreads, inter-commodity correlations, and offsetting positions. In practice, this means: whoever holds a calendar spread or an inter-commodity spread (e.g., long crude oil / short heating oil) pays massively reduced margin — often a 70–90% discount compared to the individual positions. SPAN recognizes that the positions partially hedge each other and sets margin accordingly lower.

Portfolio Margin vs. Strategy Margin

In the US, accounts above $100,000 can apply for portfolio margin — a regulatory alternative to standard Reg-T calculation. Portfolio margin evaluates the overall risk of the portfolio under stress scenarios (like SPAN) rather than position by position. This typically leads to significantly lower margin requirements for diversified portfolios with hedges.

In Europe, ESMA sets stricter limits: retail traders are subject to strategy margin with leverage caps (e.g., 1:30 for major currency pairs, 1:20 for major equity indices, 1:10 for commodities except gold, 1:5 for individual stocks). Institutional accounts and professional traders (by application) are exempt.

Margin Call & Forced Liquidation

If account equity falls below the maintenance margin, the broker signals this — by phone, email, or automatic notification in the system. The deadline is short: typically the same trading day. If no capital is added, the broker closes positions automatically — and not necessarily the worst or largest ones. It closes those that are most liquid at the time of forced liquidation. This can mean that profitable hedges are closed while losing positions remain open — until the account is balanced.

なぜS&P 500の3月限先物は現在のS&P 500のスポット値より高いのですか？ Why does the December contract on WTI trade above today's Brent price? The answer lies in a single concept: キャリーコスト — the sum of all costs and income that arise if you were to physically buy the underlying asset and hold it until the future expires.

Fair Value Formula

F = S × (1 + r × t) − D

• F = Futures price (theoretical fair value)
• S = Spot price of the underlying (current cash price)
• r = Risk-free interest rate (annualized, e.g. 3-month T-bill rate)
• t = Time to expiration in years (e.g. 3 months = 0.25)
• D = Expected dividends or income until expiration (for index futures)

Cost-of-Carry Components

• Interest (positive carry, increases the future price): Buying and holding the underlying ties up capital. That capital must be compensated — the future must therefore be more expensive than the spot to offset this opportunity cost.
• 保管コスト (positive carry, for commodities): Tank rental, silo fees, transport, insurance — all of this costs money. For physical commodities such as crude oil, natural gas, or corn, these costs significantly increase the fair value of the future.
• 利便性利回り (negative carry, for scarce commodities): The advantage of physically owning the commodity today — because it is scarce or needed immediately. A refinery holding crude oil can react instantly to supply shortages; a future cannot. A high convenience yield pushes the futures price below the spot price (backwardation).
• 配当 (negative carry, for index futures): An index future pays no dividends, whereas the spot index (conceptually) does. Expected dividends are deducted from the fair value — they lower the futures price relative to the spot.

Example Calculation ES

Assumptions: S&P 500 spot = 5,000, risk-free rate r = 5% p.a., time to expiration t = 3 months = 0.25 years, expected dividends = 12.50 index points.

F = 5,000 × (1 + 0.05 × 0.25) − 12.50
F = 5,000 × 1.0125 − 12.50
F = 5,062.50 − 12.50
F = 5,050

The March future should therefore trade at 5,050 points. If it trades higher, it is expensive relative to its fair value (arbitrage: buy spot, short future). If it trades lower, it is cheap (arbitrage: short spot, buy future).

Basis

Basis = Spot − Future. The sign says a lot:

• Basis negative (Spot < Future): Normal — the future is more expensive because interest and storage costs dominate. Called コンタンゴ.
• Basis positive (Spot > Future): バックワーデーション — the spot is more expensive. Arises from a high convenience yield (scarcity) or when the market expects falling prices.

Basis is tied to the キャリーコスト and to supply/demand dynamics. As the remaining time to expiration decreases, it shrinks to zero: on the last trading day, F must equal S.

Convergence

As the remaining time t decreases, t → 0, so r × t → 0 and the fair value F converges toward the spot S. This is not coincidental — it is arbitrage-enforced: if on the last trading day F ≠ S, arbitrageurs could immediately buy the cheap leg and sell the expensive leg and collect the difference risk-free at settlement (which is calculated directly from the spot price). This opportunity is traded away immediately in liquid markets.

コンタンゴ (normal for commodities with storage costs):
  Futures price
    │      ╱─── Back-Month (more expensive)
    │    ╱
    │  ╱─ Front-Month
    │╱
    └───────────── Time
  → Long position loses on rolling.

バックワーデーション (scarcity, roll yield positive):
  Futures price
    │╲
    │ ╲── Front-Month (more expensive)
    │   ╲
    │     ╲── Back-Month (cheaper)
    └───────────── Time
  → Long position gains on rolling.

Every future expires. If you want to hold the position longer than the active contract runs, you must roll: close the expiring contract, open the next one. Real costs arise in this process — costs that are invisible to many retail traders.

Front-Month vs. Back-Month

Front-Month is the active, most liquid contract — typically the nearest expiration month. Back-Month refers to more distant contracts with generally lower volume and open interest. Liquidity migrates approximately 8 business days before expiration from the front-month to the next contract — recognizable by a sudden volume surge in the back-month and a drop in the front-month.

Roll シグナルs

Two key indicators show when the roll point has been reached:

• Volume shift: When the volume in the next contract exceeds the front-month volume — the market has effectively switched to the new month.
• Open interest shift: When the open interest in the next month is higher than in the front-month — large participants (institutions, CTAs) have already rolled.

Roll Yield

In contango (future more expensive than spot), a long position loses on rolling: you close the expiring contract cheaper (as it converges toward spot) and open the next one more expensively. This effect is called negative roll yield — it erodes returns without any movement in the underlying. In backwardation, the picture reverses: you close more expensively, open more cheaply → positive roll yield, a structural tailwind for the long position.

USO — the Most Expensive Lesson in Rolling

The USO (United States Oil Fund) replicates WTI crude oil through front-month futures. This sounds simple — and for millions of retail investors in the 2010s it was a very expensive lesson. WTI oil was in a stable contango: the front-month traded at around $50, the next month at $52. Every time USO rolled, it sold the cheaper contract and bought the more expensive one — a structural loss of roughly 4% per roll. With 12 rolls per year, these costs accumulated to a roll drag of ~48% p.a. While the WTI spot price largely moved sideways over 10 years, USO lost more than 80% of its value — not because oil became cheaper, but because rolling in contango systematically destroyed capital. In April 2020, when WTI futures briefly plunged to −$37 per barrel, USO was forced to roll into more distant months in a panic, losing another roughly 30% against the spot. USO is not an extreme case — it is the textbook example of what happens when roll costs are ignored.

Roll Strategies

• Calendar Roll (standard): Close the front-month 8 business days before expiry and open the back-month — follow the institutional roll window, where liquidity is highest.
• Optimal roll: Roll a few days earlier than the standard window, before the bid-ask spread widens due to concentrated roll activity from many market participants.
• Spread order (calendar spread): Submit both legs simultaneously as a single spread order — e.g., "Sell ESH26 / Buy ESM26". This significantly reduces slippage since the differential (the spread) is traded rather than two separate prices. More liquid execution, less execution risk.