The Equation Series
Menu
The Edge Equation cover

Trading & Options · Volume 6 of the Equation Series

The Edge Equation

How Traders and Trading Systems Create, Capture and Destroy Value

By Thomas Kofi Annan · First edition, 2026

In 2025 Americans and the firms that served them traded more listed options than in any year before. 3% on 2024, and logged the 32 busiest days in its history. 2% in July 2026 (Cboe). On the other side of much of that trading sat a small number of firms. Read more

25
chapters
24
industry studies
100
companies
751
moves

Complete EditionBest value

Everything above, at the best price

PDF + EPUB + M4B

$99

Buy Complete Edition

The Book

25 chapters · ~109,000 words

PDF + EPUB, plus the narrative edition

$29

Buy The Book

Research Companion

24 studies · 100 profiles · 751 moves · ~1.6 million words

PDF + EPUB, plus the narrative edition

$59

Buy Research Companion

Audiobook

17 hr 28 min across 1 volume

M4B (chaptered)

$39

Buy Audiobook

From the preface

The edge equation

In 2025 Americans and the firms that served them traded more listed options than in any year before. The Options Clearing Corporation cleared about 15.26 billion contracts, up 24.3% on 2024, and logged the 32 busiest days in its history. Options on the S&P 500 index that expired on the day they were traded made up a record 59% of the index's options volume for the year, and 66.2% in July 2026 (Cboe). On the other side of much of that trading sat a small number of firms. Reuters reported in April 2026, from documents and anonymous sources that the firms did not confirm, that Jane Street's net trading revenue in 2025 was about $39.6 billion, a figure that reportedly included gains from revaluing private stakes, and that Hudson River Trading and Citadel Securities had about $12 billion each. In India, whose National Stock Exchange had become the world's largest derivatives exchange by contracts traded, the securities regulator had found that 93% of 1.13 crore individual futures and options traders lost money over the three years to March 2024, about ₹1.81 lakh crore in all (SEBI, September 2024). The same contracts, at the same prices, made a few firms some of the most profitable businesses in finance and made most of the individuals who traded them poorer.

The difference is rarely the cleverness of the idea. This book argues that durable trading profit exists only when four things are true at once, and that the factors multiply rather than add: if any is zero, the result is zero. There must be an edge: a positive expected value after costs, with a source that can be named, a risk premium someone pays to shed, a behavioural or structural mispricing, information, or speed and liquidity provision, and evidence that survives out of sample. There must be survival: sizing and leverage such that the worst plausible sequence of results does not end the game, whether it arrives as a margin call, an overnight gap or the crash that a seller of insurance is paid to bear. There must be execution: costs, liquidity, capacity, technology and operations that let the edge be captured at the size the trader needs. And there must be discipline and adaptation: following the rules through drawdowns, watching for decay, and capital that stays. Around those four factors sit two forces that no trader controls, the market regime and the rules. They do not decide whether a trader is sound, but they decide how long an unsound one survives. Most of the failures in this book come from treating one factor as proven because another was: a high win rate mistaken for an edge, a backtest mistaken for evidence, an edge mistaken for survival, a zero commission mistaken for zero cost, and a good five years mistaken for a strategy.

The twenty-five chapters develop that view in seven parts. Part I explains why most traders lose and a few firms win, how trading became a business, who is on the other side of a trade, and how to tell evidence of an edge from a story about one. Part II takes the markets and their players in turn: options and the business of selling insurance, volatility as an asset, market makers and the speed business, hedge funds, quants and pod shops, trend followers and macro traders, exchanges, brokers and the retail boom, and futures, foreign exchange and crypto. Part III examines what it takes to build a system that works: an edge that can be named, options income done right and wrong, trend, momentum and factors, arbitrage and relative value, sizing and survival, and costs, taxes and execution. Part IV covers capacity, crowding and decay, the rules and regulators that license trading, blow-ups and how they happen, and technology, data and artificial intelligence. Part V turns to people: the psychology of trading, and how a trading business or career is built. Part VI reads five cases side by side and sets out the scorecard of the companion's 118 trading systems, and the Practical Reference supplies worked examples, checklists, a glossary and a guide to the evidence. Each chapter opens with a documented case, explains the mechanics it illustrates, works one stylized example and closes by naming the factor of the equation on which its case turned.

The book · ~109,000 words

Contents

Each chapter has a free preview of its opening and section list.

Trading and Options Research Companion · Part I

24 industry studies

The companion opens with an in-depth study of each part of the industry, backed by 12 technical exhibits: worked examples, diligence checklists and case studies.

01Where Trading Profits Come From: Risk Premia, Skill and StructureEvery trade has two sides, and before costs the gains of one side are the losses of the other. William Sharpe set out the arithmetic in "The Arithmetic of Active Management" (*Financial Analysts Journal* 47(1), Jan/Feb 1991, 7–9): the average actively managed dollar must earn the market return before costs, so after costs it must earn less. For a derivatives market, where every contract is a promise between two parties, the arithmetic is even stricter. Ignoring the risk premium on the underlying, the gross profit and loss on all open SPX options, E-mini futures and VIX futures sums to zero, and fees, spreads and taxes make the total negative. Yet a small number of trading firms earn very large, steady profits. Reuters reported in April 2026, from documents and anonymous sources, that Jane Street made ~$39.6bn of net trading revenue in 2025, a record. Part of that reportedly came from revaluing private stakes, including Anthropic. Hudson River Trading reported ~$12.3bn and Citadel Securities ~$12.2bn (up ~25% on 2024). None of the firms confirmed the figures (Shared facts). On the other side of many of the same kinds of contracts, India's regulator SEBI found that ~89% of individual equity futures-and-options traders lost money in FY22, and 93% of 1.13 crore individuals over FY22–FY24 cumulatively (SEBI press release 37/2024, 23 Sep 2024; the FY22 figure is from an earlier SEBI study — verify). Both facts hold together because trading profit is not luck spread evenly. It is a transfer, and it flows in predictable directions. This section names the five sources of edge: (1) risk premia paid for bearing risk others want to shed; (2) behavioural mispricing; (3) structural and flow edges; (4) information and analysis; (5) speed and liquidity provision. For each it asks who is on the other side and why they keep paying. It then grades the evidence that most active traders lose, and the narrower evidence that some win. The companion worked example builds a stylized market of four trader types and follows where the money goes in a year.+ 1 exhibit02Options Fundamentals: Payoffs, Pricing and the GreeksAn option is a right without an obligation. A call gives its buyer the right to buy an asset at a fixed strike price until or on an expiry date; a put gives the right to sell. The buyer pays a premium up front. The seller, or writer, keeps the premium and takes on the obligation. That asymmetry makes options the instrument through which most of this knowledge base's systems are expressed: insurance, lottery tickets, income strategies, volatility trades and market making. The modern listed market began when the Chicago Board Options Exchange opened on 26 Apr 1973 with calls on 16 stocks; 911 contracts traded on the first day (OCC 50th-anniversary history; Cboe 40th-anniversary release). A month later the *Journal of Political Economy* published Fischer Black and Myron Scholes' pricing formula, and Robert Merton's companion paper appeared in the *Bell Journal of Economics and Management Science* the same year (vol. 4, no. 1, Spring 1973, 141–183); Scholes and Merton received the 1997 Nobel prize "for a new method to determine the value of derivatives"; Black had died in 1995 and was not eligible (FRBSF Economic Letter, Feb 1998; NBER). Half a century later US listed options trade on an unprecedented scale: ~15.2bn contracts in 2025 (OCC, Jan 2026), and same-day-expiry contracts reached a record 66.2% of SPX volume in Jul 2026 (Cboe; both Shared facts). Every US equity or index option contract covers 100 units of the underlying, so a quoted premium of $2.45 costs $245 per contract. This section explains payoffs and moneyness, American and European exercise and assignment (including early exercise around dividends), put–call parity, the three pricing approaches that matter (Bachelier 1900, Black–Scholes–Merton 1973, and the Cox–Ross–Rubinstein binomial tree of 1979), the Greeks and how they trade off, implied volatility and the skew that appeared after the 1987 crash, and the contract details (SPX versus SPY versus XSP, cash versus physical settlement, AM versus PM settlement) that decide what a trade actually does. The companion worked example delta-hedges a stylized option for ten days to show where an options trader's profit really comes from: the race between gamma and theta.+ 1 exhibit03Volatility: Implied vs Realised and the Variance Risk PremiumAn option's price is mostly a bet on how much the underlying will move. The market states that bet as implied volatility, the volatility that makes a pricing model return the option's price. What later happens is realised volatility, the annualised standard deviation of the underlying's returns over the option's life. For US equity indices, implied has been higher than realised most of the time. Option sellers collect the gap, the variance risk premium (VRP), and give it back in bursts when markets fall. The academic evidence for the premium is strong. Peter Carr and Liuren Wu ("Variance Risk Premiums", *Review of Financial Studies* 22(3), 2009) built synthetic variance-swap rates from option prices and found strongly negative variance risk premiums on five stock indices and 35 individual stocks. That means buyers of variance paid more, on average, than variance later delivered. Bollerslev, Tauchen and Zhou ("Expected Stock Returns and Variance Risk Premia", *RFS* 22(11), 2009) showed that the gap between implied and realised variance predicted quarterly US stock returns over 1990–2007. The crash risk is just as well documented. The Cboe Volatility Index, the VIX, closed at a record 82.69 on 16 Mar 2020, and its intraday record is 89.53 on 24 Oct 2008 (Cboe data as reported by CNBC and others). On 5 Feb 2018 the VIX rose ~116% in a day (37.32 vs 17.31, +115.6% close to close), still its largest one-day percentage rise in Cboe's series to Nov 2026. Credit Suisse's inverse-VIX note XIV lost ~94.5% ($5.99 redemption vs $108.3681) after hours and was terminated (Shared facts). On 5 Aug 2024 the VIX reached ~65–66 before the US open, which the BIS called its biggest one-day spike, and closed near 38 (BIS Bulletin 95; SEC DERA working paper; reported). Volatility has also become a traded asset class. VIX options averaged a record ~862,000 contracts a day in 2025, up from ~830,000 in 2024 (Cboe full-year volume release, Jan 2026). Exchange-traded products let retail accounts go long or short VIX futures in a brokerage account, and the long products have lost most of their value over every multi-year period they have existed (section 7). This section defines the volatilities, explains the VIX and its futures curve, sets out the evidence for the VRP and how big it is, shows why long-volatility products decay and short-volatility products blow up, and covers skew, dispersion and correlation premia. The companion worked example computes the roll yield of VIX futures and the decay of a stylized long-VIX product over a calm year.+ 1 exhibit04Market Microstructure: Order Types, Spreads and ExecutionEvery trading system in this knowledge base is tested on prices. Every one of them is paid in fills. The difference between the two is execution cost: the bid–ask spread, the market impact of the trader's own orders, fees and rebates, and what the price did while the order was waiting. For a long-term investor it is a rounding error. For a high-turnover system it is often the whole edge (08; Appendix A of the main book computes cost drag by turnover). The rules that decide where an order goes are set in the United States by the SEC's Regulation NMS, adopted in June 2005 and fully phased in by October 2007 (SEC releases). The minimum price increment is set by decimal pricing, completed for exchange-listed stocks and options on 29 Jan 2001 and for Nasdaq on 9 Apr 2001 (SEC). The venues are now numerous. The SEC's staff counted 18 US options exchanges operating as of April 2026, with IEX Options and a second MEMX options venue expected (SEC staff paper, Apr 2026; Cboe). They cleared a record ~15.2bn options contracts in 2025 (OCC; Shared facts). Retail orders mostly do not reach an exchange first. In 2022 brokers sent more than 90% of marketable retail orders in US-listed stocks to six wholesalers, with Citadel Securities taking the largest share, ~41% (Congressional Research Service, Feb 2024, citing SEC data). The wholesalers pay brokers for that flow, and retail options orders earn brokers the most: Robinhood reported $314m of options transaction revenue in Q4 2025 against $94m from equities (company release, 10 Feb 2026). The SEC's 2022 proposals to force retail orders into auctions (the Order Competition Rule) and to create a federal best-execution rule (Regulation Best Execution) were formally withdrawn in June 2025 (SEC withdrawal notice; law-firm summaries). Above all of this sits the physics of liquidity. Across markets and decades, the price impact of a large order grows roughly with the square root of its size relative to volume, not in proportion to it (Almgren, Thum, Hauptmann and Li, *Risk*, 2005; Tóth et al., *Physical Review X*, 2011). This section explains order books, spreads and the NBBO, order types, maker–taker fees and payment for order flow, options auctions and the US options exchanges, market impact and the square-root law, implementation shortfall, dark pools and tick sizes. The companion worked example prices a stylized order of 2% of a stock's daily volume executed four different ways.+ 1 exhibit05Backtesting, Overfitting and the Evidence ProblemA backtest is a simulation of what a set of trading rules would have earned on past data. It is the cheapest experiment in finance, and the most often abused. A researcher with a laptop can test thousands of rule variations in an afternoon, and some will look excellent by chance. Campbell Harvey, Yan Liu and Heqing Zhu counted several hundred factors proposed in the academic literature to explain stock returns and argued that, given how many had been tried, a new factor should clear a t-statistic of about 3.0, not the conventional 2.0 ("…and the Cross-Section of Expected Returns", *Review of Financial Studies* 29(1), 2016, 5–68; 316 factors examined; t-ratio cut-off of about 3.0 — NBER WP 20592 abstract and journal record). David McLean and Jeffrey Pontiff studied 97 published anomalies and found their returns were about 26% lower out of sample and about 58% lower after publication ("Does Academic Research Destroy Stock Return Predictability?", *Journal of Finance*, 2016; figures checked against the paper in S04). Those are the results for peer-reviewed research. Vendor backtests, course sellers' screenshots and "AI bot" marketing face no such review (blueprint rule 4, categories (d) and (e)). This section explains how backtests mislead: look-ahead bias, survivorship, data snooping and selection, unrealistic fills, ignored costs and borrow, regime dependence. It covers the statistical tools that correct for them: the multiple-testing haircut, the deflated Sharpe ratio and the probability of backtest overfitting of David Bailey and Marcos López de Prado, walk-forward and out-of-sample tests, and paper versus live records. It also sets out how this knowledge base grades evidence. The companion worked example simulates 1,000 strategies with no edge at all and finds the best one shows a Sharpe ratio of 1.82 over five years and a t-statistic above 4, then loses money out of sample. A second file gives 20 questions to ask of any backtest.+ 2 exhibits06Position Sizing, Risk of Ruin, Drawdowns and Portfolio ConstructionA trading system with a genuine edge can still go broke, and one with a modest edge can compound for decades. The difference is how much is bet each time and how the bets are combined. That is the second factor of the book's edge equation, survival: sizing and leverage such that the worst plausible sequence of outcomes does not end the game. The mathematics is old. John L. Kelly Jr. of Bell Labs showed in 1956 that a gambler with an edge maximises the long-run growth of capital by betting a fixed fraction of wealth proportional to that edge ("A New Interpretation of Information Rate", *Bell System Technical Journal*, July 1956), and Edward Thorp carried the idea from blackjack to warrants and options ("Optimal Gambling Systems for Favorable Games", *Review of the International Statistical Institute*, 1969; Princeton Newport Partners). The arithmetic of loss is older still: a 50% drawdown needs a 100% gain to recover, a 90% drawdown a 900% gain. What sizing cannot do is make an estimate of edge more accurate. Full Kelly on an overestimated edge is over-betting, and over-betting at twice the true Kelly fraction has an expected growth rate of zero. The blow-ups this KB documents — Long-Term Capital Management in 1998, LJM Partners in February 2018 (~80% lost in days, Shared facts), Optionsellers.com in November 2018, Archegos in March 2021 — were sizing failures before they were anything else: each held positions whose plausible worst case was larger than the capital behind them. Meanwhile the businesses that survive longest, from the Turtle rules of 1983 (risk a fixed fraction of equity per unit of volatility) to the multi-manager platforms that cut a manager's capital after a drawdown of a few percent (Millennium, Citadel — reported, verify), are built around explicit, dull rules for how much to risk. This section covers fixed-fractional and volatility-targeted sizing, Kelly and fractional Kelly, risk of ruin, drawdown arithmetic, what stop-losses do and do not do, correlation and diversification across systems, and risk parity. The companion worked example combines three stylized systems — trend, short-volatility carry and mean reversion — and shows how much of a portfolio's apparent safety depends on what happens in the few weeks when they all lose together.+ 1 exhibit07Leverage, Margin, Funding and LiquidationLeverage is how a small edge becomes a large return, and how a correct trade becomes a forced loss. Every leveraged position in this KB rests on a promise to post collateral, and every margin system has the same three parts: an initial requirement to open the position, a maintenance level below which the lender calls for more, and a liquidation process when the call is not met. In US securities accounts the rules are layered. The Federal Reserve's Regulation T sets the initial requirement for buying stock on margin at 50% of the purchase price; FINRA Rule 4210 sets maintenance (25% of current market value for long margin securities — FINRA Regulatory Notice 12-44) and a $2,000 minimum equity for a margin account (Shared facts); brokers' "house" requirements sit on top. On 14 Apr 2026 the SEC approved FINRA's replacement of the pattern-day-trader rule and its $25,000 minimum with new intraday margin standards, effective 4 Jun 2026, with an optional phase-in to 20 Oct 2027 (FINRA Regulatory Notice 26-10; Shared facts). Options sellers face separate formulas (for an uncovered equity option, 20% of the underlying's value less any out-of-the-money amount, minimum 10%, plus the premium — Cboe Margin Manual); larger accounts can use portfolio margin, which sets the requirement by stress-testing the whole account (minimum $100,000 of equity at firms with full real-time intraday monitoring — FINRA guidance, verify current text). Futures margin is set by the clearing house as a performance bond — CME's SPAN, now being replaced by SPAN 2 (equity futures moved in Oct–Nov 2024, CME clearing notices) — and is settled in cash every day. Off-exchange, prime brokers lend through margin loans, repo and total return swaps; Archegos used swaps at several banks to build concentrated positions that no single bank saw in full, and its default on 26 Mar 2021 cost banks more than $10bn (Credit Suisse ~$5.5bn, Nomura ~$2.9bn — Shared facts). Crypto venues run the most aggressive version: automated liquidation engines and auto-deleveraging (ADL) of winning traders; on 10–11 Oct 2025 more than $19bn of leveraged crypto positions were liquidated in about a day, the largest such event recorded (CoinGlass data, as reported). This section explains how each margin system works, how funding and repo carry leverage through the financial system, how margin calls turn into liquidation cascades, and how to read leverage claims. Section 06 covers how much risk to take; this section covers how leverage is supplied, and taken away.08Costs, Taxes, Accounts and Trader Tax StatusA trading edge is measured after costs and after tax, and both are larger and more complicated than the "zero commission" headline suggests. US online brokers cut commissions on stock trades to zero in October 2019 (Schwab announced on 1 Oct 2019, effective 7 Oct; TD Ameritrade the same evening, effective 3 Oct; E*Trade on 2 Oct, effective 7 Oct — AP, InvestmentNews and BNN Bloomberg reports; Schwab kept $0.65 per options contract), and Robinhood had offered them since its launch. But a trader still pays the bid–ask spread, per-contract options commissions at most brokers, exchange, clearing and regulatory fees (the SEC's Section 31 fee rose from $0.00 to $20.60 per million dollars of sales on 4 Apr 2026 — SEC fee rate advisory), borrow fees on short sales, margin interest, and the indirect cost of order routing and payment for order flow (04). Then the tax system takes its share, and for US traders the rules depend on the instrument as much as on the trade. Gains on Section 1256 contracts — regulated futures and broad-based index options such as SPX — are marked to market at year end and taxed 60% long-term, 40% short-term regardless of holding period (Form 6781); the same economic trade in SPY options is an ordinary equity option, taxed short-term if held a year or less. The wash-sale rule (§1091) disallows a loss if substantially identical securities, including options to buy them, are bought within 30 days before or after the sale — and a replacement bought in an IRA makes the disallowance permanent (Rev. Rul. 2008-5, as summarised in secondary sources). Straddle rules (§1092, 1981) defer losses on positions offset by unrealised gains; constructive-sale rules (§1259, 1997) tax "locking in" an appreciated position. A full-time trader may qualify for trader tax status and elect §475(f) mark-to-market accounting, which converts gains and losses to ordinary and removes the wash-sale problem — but only by an election made by the unextended due date of the prior year's return (IRS guidance and private letter rulings, as web-checked). Europe adds transaction taxes: France's financial transaction tax on purchases of large French companies' shares rose from 0.3% to 0.4% in April 2025; Italy's, introduced in March 2013, was doubled from 1 Jan 2026 (reported); the UK charges 0.5% stamp duty or SDRT on most share purchases. This section sets out the cost stack, US tax rules for traders (rule 10 — every rule here should be checked against current IRS text before use), the main account types and the European taxes. It has no worked example of its own: the main book's Appendix A computes cost and tax drag by turnover (A.3), and this section refers to it. Nothing here is tax advice.09US Options Markets: Exchanges, Clearing and 0DTEThe US listed options market is the largest in the world by premium and by the variety of what it lists. It is also the fastest-changing part of American trading. It began on 26 Apr 1973, when the Chicago Board Options Exchange opened in a smokers' lounge of the Chicago Board of Trade with standardised calls on a handful of stocks (16 classes on the first day, 911 contracts — OCC 50th-anniversary history), a month before Black and Scholes published their pricing formula. Fifty-two years later the Options Clearing Corporation (OCC), which stands behind every listed US equity and index option, cleared 15,207,163,554 options contracts in 2025, up 24.4% from 12,224,227,606 in 2024, inside a total of 15,263,912,452 cleared contracts (OCC release, 5 Jan 2026). OCC logged its 32 highest-volume days ever in 2025, two of them above 100m contracts, and a single-day record of ~110m on 10 Oct 2025, beating the >100m of 4 Apr 2025 (Cboe, "The State of the Options Industry: 2025"). The growth has a shape. Zero-days-to-expiry (0DTE) options, contracts bought and sold on the day they expire, were ~47% of S&P 500 index option (SPX) volume in 2024, a record 59% for full-year 2025 and a record 66.2% in July 2026 (Cboe monthly volume release, Aug 2026; always "share of SPX volume", not of all options). The market is spread across 16 to 18 exchanges owned by five groups (Cboe, Nasdaq, NYSE/ICE, MIAX, and BOX and MEMX; count verify), all of them trading the same multiply-listed equity options, while the most valuable index products (SPX, VIX) are proprietary to Cboe. Around them sit wholesalers that buy retail orders, market makers that hedge every trade, a single clearing house, and a tax code that treats an SPX option very differently from an option on the SPY exchange-traded fund that tracks the same index. This section explains how the market came to look like this, how its pieces fit, why 0DTE took over index options, what is known (and not) about who wins and loses, and how to choose between SPX, SPY and XSP. The companion worked example runs the same stylized trade through all three and shows what settlement style, assignment and Section 1256 tax do to the result.+ 1 exhibit10Futures, Commodities and the CMEA futures contract is a standardised promise to buy or sell a fixed quantity of something on a future date at a price agreed today, traded on an exchange and guaranteed by a clearing house that stands between buyer and seller. Futures began as a farmers' and merchants' hedge in grain and became the most leveraged, most liquid and most regulated way to trade almost anything: stock indices, Treasury yields, interest rates, currencies, oil, gas, metals, grains, livestock and, since 2017, bitcoin. The United States dominates the business through one company. CME Group, which grew from the Chicago Mercantile Exchange and absorbed the Chicago Board of Trade (founded 1848, from memory, verify; merger closed 12 Jul 2007) and NYMEX (closed 22 Aug 2008; both dates as settled in the Finance KB), reported a record average daily volume (ADV) of 28.1m contracts in 2025 and record annual revenue of ~$6.5bn (+6%) (CME results release, 4 Feb 2026), then a third-quarter record ADV of 29.4m contracts in Q3 2026, with open interest of 128m contracts at the end of September (CME release, 21 Oct 2026). Worldwide, futures are the growing half of listed derivatives: the Futures Industry Association (FIA) counted 30.64bn futures contracts traded in 2025 (+8.6%), while total listed futures and options fell 42.2% to 119.3bn because Indian index-options volume collapsed after SEBI's 2024 measures (FIA, Jan 2026). Futures also produced the most famous price in recent trading history: the May 2020 WTI crude contract settled at −$37.63 a barrel on 20 Apr 2020 (Shared facts), because holders who could not take delivery had to pay someone to take their oil. This section explains how futures work (margin, marking to market, delivery, cash settlement), the history from the Chicago pits to Globex, the equity-index contracts that retail traders use (the E-mini S&P 500 of 1997 and the Micro E-mini of 2019), the term structure of commodity prices (contango, backwardation and roll yield), what negative oil taught, who regulates futures (the CFTC, speculative position limits and the weekly Commitments of Traders report), who trades them (hedgers, speculators, CTAs, market makers and retail), and the futures markets of Europe and Asia. It has no worked example (not a ★ section); two small stylized tables, computed in Python, illustrate roll yield and contract size.11FX, Rates and Global Macro MarketsCurrencies and interest rates are the largest markets in the world and the ones in which individual traders have the least natural edge. The Bank for International Settlements' Triennial Survey put global foreign-exchange turnover at $9.6 trillion a day in April 2025, up 28% from $7.5 trillion in April 2022 (BIS press release, 30 Sep 2025; the BIS's December 2025 Quarterly Review gives ~$9.5 trillion, +27% — use either with its date), of which spot was ~$3 trillion and FX swaps ~$4 trillion; daily turnover in OTC interest-rate derivatives rose ~59% to ~$7.9 trillion (BIS, 30 Sep 2025). Most of that is dealers, banks, asset managers and corporations moving and hedging money, not speculation. But these markets also produced some of trading's most famous single bets and worst blow-ups. On 16 Sep 1992 ("Black Wednesday") sterling left the European Exchange Rate Mechanism after George Soros's Quantum Fund and others sold it short (Shared facts, C04: Quantum's short >$10bn; profit usually given as ~$1bn, with $1.8bn and "over £1bn" also reported — none audited). On 15 Jan 2015 the Swiss National Bank removed its EUR/CHF 1.20 floor without warning, and the franc's jump left retail FX customers of FXCM owing the broker $275.1m (FY2015 10-K; the company's Jan 2015 release said over $225m — Settled by C15), which was rescued by a $300m Leucadia loan (Shared facts; credit agreement of 16 Jan 2015). On 5 Aug 2024 the unwinding of yen-funded carry trades sent the Nikkei 225 down 12.4% in a day (AP/Nikkei reports) and the VIX to 65.73 intraday (Cboe data; close 38.57). And in March 2020 the "dash for cash" disrupted the US Treasury market, the world's benchmark safe asset, partly as hedge funds unwound leveraged cash-futures basis trades (Federal Reserve FEDS Note, Aug 2023). This section explains how FX and rates markets are organised (dealers, ECNs, non-bank liquidity providers, the fix), retail FX and CFDs and the rules that cap them (ESMA 2018; the CFTC's retail forex rules), the carry trade and its crashes, Treasury futures and the basis trade, central banks as the market's main event risk, and global macro as a trading style from Soros to the pod shops. It has no worked example (not a ★ section); a small stylized carry table is computed in Python.12Crypto Trading: Perpetuals, Options and Market StructureCrypto is the market where trading's oldest lessons were relearned fastest. It trades 24 hours a day, seven days a week, on hundreds of venues that combine the roles of exchange, broker, custodian, clearing house and sometimes market maker; it offers leverage of 100 times or more on offshore platforms; and its dominant instrument is one that did not exist before 2016, the perpetual swap, a future that never expires and is kept close to the spot price by periodic funding payments between longs and shorts. BitMEX launched the first, its XBTUSD perpetual, on 13 May 2016 (BitMEX announcement). Since then crypto has produced the largest single-day forced liquidation in its history — about $19bn of leveraged positions liquidated in 24 hours on 10–11 Oct 2025, after a US tariff announcement on Chinese imports (CoinGlass data as reported; CoinGlass itself said the true figure was likely higher because Binance reports only one liquidation order per second) — and one of the largest frauds in financial history, the collapse of FTX and its trading affiliate Alameda Research in November 2022. It has also moved onshore in the United States. The SEC approved eleven spot bitcoin exchange-traded products on 10 Jan 2024, and ten began trading the next day with ~$4.6bn of first-day volume (reported); options on BlackRock's iShares Bitcoin Trust (IBIT) began trading on Nasdaq on 19 Nov 2024, with ~354,000 contracts and ~$1.9bn of notional on day one (reported). Coinbase closed its purchase of Deribit, the dominant crypto options exchange, on 14 Aug 2025 (~$2.9bn headline; Finance Shared facts) and listed CFTC-regulated "perpetual-style" futures on 21 Jul 2025; the CFTC announced on 4 Dec 2025 that listed spot crypto would trade on CFTC-registered exchanges (reported). This section explains spot and perpetual markets and funding, crypto options, basis and cash-and-carry trades, exchange and counterparty risk (FTX), liquidation engines and auto-deleveraging, the US ETF and options market, the market makers, wash trading and fake volume, and the 2025–26 rules. It has no worked example (not a ★ section); two small stylized tables on funding and leverage are computed in Python.13Market Makers, HFT and Proprietary Trading FirmsThe most consistently profitable traders in the world are not hedge funds or famous individuals but a small group of private firms that buy and sell all day without wanting to own anything at the end of it. They make markets — posting bids and offers in stocks, options, ETFs, futures, bonds and currencies — and they trade on their own capital, so their profits are net trading revenue rather than fees. Almost none of them publishes accounts. The best figures available for 2025 come from documents and anonymous sources reported by Reuters in April 2026, which the firms did not confirm: Jane Street ~$39.6bn (a record; part reportedly from revaluing private stakes, including Anthropic), Hudson River Trading ~$12.3bn and Citadel Securities ~$12.2bn (+25% vs 2024). Citadel Securities then reported a record ~$7.3bn of trading revenue in Q2 2026 (Bloomberg via Hedgeweek, reported). Those numbers, larger than the trading revenue of most global banks, rest on a business that earns fractions of a cent per share and loses on many individual trades. The public evidence for how it works comes from the few listed firms: Virtu Financial's 2014 IPO filing disclosed a single losing day in 1,238 (S-1, 10 Mar 2014, 2009–13), updated to one in 1,485 in the IPO prospectus (16 Apr 2015). The public evidence for how it fails comes from Knight Capital, which lost more than $460m in ~45 minutes on 1 Aug 2012 (SEC order; Knight's early estimate ~$440m) from a faulty software deployment (Shared facts), and from the Flash Crash of 6 May 2010. This section explains what market makers and high-frequency traders do and earn, who the firms are, the latency race and what it costs everyone else, options and ETF market making, payment for order flow, regulation and the big cases. The companion worked example computes the "sniping tax" that a latency race imposes on investors, following Budish, Cramton and Shim (2015).+ 1 exhibit14Hedge Funds, Quant Funds and Multi-Manager PlatformsA hedge fund is a legal wrapper, not a strategy: a private pool, open only to wealthy and institutional investors, that may go short, use leverage and derivatives, and charges a performance fee. Inside the wrapper sits almost every trading system in this knowledge base, from Ed Thorp's warrant hedging in the late 1960s to the statistical arbitrage of Renaissance Technologies and the hundreds of risk-limited "pods" of Millennium and Citadel. The industry is larger than it has ever been. Hedge Fund Research (HFR) put global hedge-fund capital at a record ~$5.22 trillion at the end of Q1 2026, then ~$5.6 trillion after a record ~$409bn gain in Q2 2026, and ~$5.64 trillion at the end of Q3 2026, the sixteenth straight quarterly rise (HFR releases and Opalesque/Hedgeweek coverage; the Q2 and Q3 figures from secondary coverage, verify against HFR). Returns were the best in years: the HFRI Fund Weighted Composite gained ~+12.5% in 2025 (HFR, Jan 2026 report; the 8 Jan release said +12.6%), its strongest calendar year since 2009, net of fees and equal-weighted across reporting funds. The big multi-manager platforms reported 2025 returns of ~17.5% at Point72, ~16.7% at Balyasny, ~10.5% at Millennium and ~10.2% at Citadel's flagship Wellington fund (Reuters, from people familiar; reported, net of fees, unaudited). Under those headlines sit the facts this section is about. Investors in multi-manager funds keep a shrinking share of gross profit because the funds pass most of their costs to clients: Citadel's three flagship multi-strategy funds were charged nearly $4.5bn of operating costs in 2025 (Bloomberg, from bond offering documents; reported). Quant funds' edge decays as it is published and copied (McLean–Pontiff 2016). Industry indices flatter the average fund because the dead stop reporting. And the most famous record of all, Renaissance's Medallion fund, reported at ~66% a year gross and ~39% net of fees (arithmetic averages, 1988–2018; later reports extend to 1988–2021), belongs to a fund closed to outsiders, while Renaissance's outside funds reportedly fell ~14–16% in October 2025 alone (Shared facts; reported). This section explains the wrapper and its fees, the quant pioneers, the pod-shop model and its war for talent, capacity and decay, what the industry has returned against a plain 60/40 portfolio, prime brokerage, and what 13F filings can and cannot tell you.15Managed Futures, CTAs and Trend FollowingTrend following is the trading system with the best evidence in this knowledge base and one of the hardest to live with. The rule is simple: buy futures markets that have been rising, sell those that have been falling, size each position by its volatility, and hold until the trend reverses. Peer-reviewed research finds it profitable across ~58 futures and forwards for more than 25 years (Moskowitz, Ooi and Pedersen, *Journal of Financial Economics*, 2012) and, in a longer backtest, across 67 markets back to 1880 (Hurst, Ooi and Pedersen, *Journal of Portfolio Management*, Fall 2017). A live industry of commodity trading advisors (CTAs) has run it for fifty years — Campbell & Company has traded the Campbell Fund since 1 Jan 1972, Dunn Capital since 1974, Man AHL since 1987 — and their records are published in indices. Those indices show why trend following earns its reputation as "crisis alpha": the SG Trend Index gained ~+27.3% in 2022, its best year, and the SG CTA Index ~+20.1%, while US stocks and bonds fell together (Société Générale indices via Hedgeweek and AlphaWeek, reported). They also show why investors give up on it: the SG Trend Index lost ~3.3% in 2023 (StoneX, reported), fell ~10.5% in the first half of 2025 before ending the year up only ~2.4% (Alternatives Watch; Top Traders Unplugged, reported), and spent most of 2011–2019 earning little. Industry assets are large and growing again: BarclayHedge put managed-futures assets at ~$364.8bn at the end of 2025 and ~$425.5bn at the end of Q1 2026 (BarclayHedge/ION Analytics table, units inferred as $bn). This section explains the CTA as a business and a registration category, the rules of trend following, the founders (Dunn, Campbell, the Turtles and Chesapeake, Man AHL, Winton and Aspect), the indices and what they show by year, crisis alpha in 2008 and 2022, the lean decade, the research and its replication by cheap ETFs, fees and capacity, and how to judge a trend follower's record.16Retail Trading: Brokers, Apps, Gamification and OutcomesRetail trading is the part of this knowledge base where the gap between what is sold and what the evidence shows is widest. The product has never been cheaper to use. US online stock commissions went to zero when Schwab, TD Ameritrade and E*Trade cut them in October 2019, following Robinhood (founded 2013), whose zero-commission app launched in March 2015 (Robinhood profile); options can be traded from a phone in minutes; and the pattern day trader rule's $25,000 minimum was eliminated by FINRA amendments the SEC approved on 14 Apr 2026, effective 4 Jun 2026 (Shared facts). The business is large: Robinhood reported ~$4.47bn of revenue and ~$1.88bn of net income for 2025 and more than 27m funded customers in Q1 2026 (company release, 10 Feb 2026: ~$4.5bn revenue, ~$1.9bn net income, 27.0m funded customers at end-2025; the Q1 2026 figure is from a secondary summary). Retail orders became a large share of US options volume in 2020–21, and the 0DTE boom took S&P 500 index options to a record 66.2% same-day share of SPX volume in July 2026 (Shared facts). The outcomes evidence points the other way. The most careful studies, from US brokerage records (Barber and Odean, 2000), from Taiwan's complete day-trading records, from Brazil's futures market (Chague, De-Losso and Giovannetti, 2019: 97% of those who persisted for more than 300 days lost money — working-paper abstract), from SEBI's studies of Indian equity derivatives (93% of 1.13 crore individual F&O traders lost money over FY22–FY24, SEBI PR 37/2024 of 23 Sep 2024; ~91% in FY25 and 87.7% in FY26 — Settled by C16; the FY22-only ~89% figure is from SEBI's earlier study, verify), and from the loss percentages that European CFD brokers must publish under ESMA's 2018 rules, all find that most active retail traders lose money after costs, and that a very small minority win persistently. Regulators have acted on the design of the products as well as their disclosure: the SEC's $65m settlement with Robinhood over payment for order flow (17 Dec 2020), FINRA's $57m fine plus ~$12.6m restitution (30 Jun 2021), and Massachusetts's gamification case, settled by consent order for $7.5m on 18 Jan 2024. This section explains how US retail brokerage became free at the point of use and who pays instead, how apps design for engagement, options approval and the 2020–21 boom, GameStop, the PDT repeal, prop-firm "challenges" and copy trading, and what the outcomes evidence says. The companion worked example computes what a habit of buying weekly out-of-the-money calls costs a year when options are priced with a skew and a variance risk premium.+ 1 exhibit17Regulation: SEC, CFTC, FINRA and Global RulesEvery trading edge in this knowledge base is exercised under a licence. Rules decide who may trade what, with how much leverage, through which intermediary, with what disclosure, and who is liable when it goes wrong. They change, and when they change they move money between traders, brokers, market makers and exchanges. Some recent examples:18Manipulation, Fraud, Rogue Traders and Trading ScamsSome trading profits are not edge at all. They are taken from other traders by deceit, or they are losses hidden until they are too big to hide. The edge equation still applies: a manipulator's "edge" depends on the licence to trade, so its true expected value includes the fine, the ban and the prison term. A rogue trader's "edge" is a control failure, so the survival factor is zero for the bank. A scam's "edge" is a transfer from its customers, so the system grade is F by definition. Some cases in brief:19Blow-Ups, Crashes and Liquidity SpiralsTrading blow-ups are rarely caused by a bad idea. More often a good idea is held too large, with borrowed money, in the same positions as everyone else, in an instrument that cannot be sold when it matters. Some cases in brief:+ 1 exhibit20Trading Psychology, Behaviour and DisciplineThe fourth factor of the edge equation, discipline and adaptation, is where good systems most often fail in practice. A rule with a positive expected value after costs earns nothing if the trader stops following it in a drawdown, doubles up after a loss, or sells the winners and keeps the losers. Behavioural finance has measured these habits in brokerage, exchange and tax records for forty years, and the findings are unusually consistent. Some anchors:21Technology, Data, Algorithms and AI in TradingTechnology sits in the execution factor of the edge equation, and for some firms it is the edge itself. It can also zero the survival factor in minutes. Some anchors:22Building a Trading Business: Prop Firms, Funds and CareersA trading edge becomes a business only when someone supplies capital, someone carries the risk, and someone can be paid without the edge being given away. The paths differ in who owns each of those, and in which of the book's four factors (edge, survival, execution, discipline) the business model rewards or hides. In brief:23Options Strategy Selection and Trade ManagementAn options position is a set of bets on direction, volatility and time, made through contracts with fixed strikes and expiries, and settled by a clearing house that can assign the other side at its own convenience. Strategy selection means choosing the structure that matches a view. Trade management means deciding what to do when the view meets the market. Both are where retail options education spends most of its time, and where the evidence is thinnest. In brief:+ 1 exhibit24History of Trading from Dojima Rice to 0DTETrading is older than the stock market, and options are older than the theory that prices them. The instruments in this knowledge base were mostly invented before anyone could value them; the theory arrived later, and the technology arrived last. The milestones in brief:

Trading and Options Research Companion · Part II

100 companies, 751 strategic moves

A profile of each company, followed by its defining moves year by year from 1892 to 2026: what was decided, why, how it was financed, and what happened next.

Browse all 100 →

Companion · Trading Systems Catalogue

118 documented trading systems, graded A–F on the evidence

Each system covers what it does, where its edge comes from, its mechanics, costs, capacity and risks, how it fails, who is documented using it, and whether its track record is live or only backtested.

Options Income and Premium Selling (10)
  • Calendar and Diagonal Spreads
  • Cash Secured Put Write
  • Collar and Protective Put
  • Covered Call Buy Write
  • Iron Butterfly and Butterflies
  • Iron Condor and Credit Spreads
  • Ratio Spreads and Jade Lizard
  • Short Strangle and Straddle
  • The Wheel
  • ZeroDTE Premium Selling
Volatility Risk Premium and Volatility Trading (10)
  • Delta Hedged Short Options Variance Risk Premium
  • Dispersion and Correlation Trading
  • Earnings Implied Move Selling
  • Gamma Scalping Long Options
  • Long VIX and Tail Hedging Overlays
  • Short VIX Futures Roll Carry
  • Skew and Risk Reversal Trading
  • Term Structure Trading
  • Variance and Volatility Swaps
  • Volatility Arbitrage Forecast vs Implied
Trend Following and Time Series Momentum (10)
  • Channel and ATR Breakout Systems
  • Crisis Alpha Trend Plus Equity
  • Darvas Box
  • Dual Momentum
  • Long Term Trend Commodities
  • Moving Average Crossover and 200 Day Filter
  • Time Series Momentum Diversified Futures
  • Trend Following on Single Stocks
  • Turtle Donchian Breakout
  • Volatility Targeted Trend
Cross Sectional Factors and Anomalies (11)
  • CAN SLIM
  • Cross Sectional Momentum
  • Greenblatt Magic Formula
  • Low Volatility and Betting Against Beta
  • Multi Factor Smart Beta
  • Piotroski F Score
  • Post Earnings Announcement Drift
  • Quality and Profitability
  • Short Term Reversal
  • Size Small Cap Premium
  • Value HML
Mean Reversion and Statistical Arbitrage (9)
  • Bollinger Band Reversion
  • ETF and Closed End Fund Discount Arbitrage
  • Index Reconstitution and Rebalancing
  • Leveraged ETF Rebalancing Flow
  • Opening Gap Fade
  • Overnight vs Intraday Returns
  • Pairs Trading
  • RSI2 and Short Term Oversold Index
  • Residual Statistical Arbitrage
Carry and Relative Value (10)
  • Bond Carry and Roll Down
  • Capital Structure Arbitrage
  • Commodity Roll Yield and Curve Carry
  • Convertible Arbitrage
  • Crypto Perpetual Funding Basis
  • Dividend and Tax Arbitrage
  • FX Carry Trade
  • Merger Arbitrage
  • On the Run Off the Run
  • Treasury Cash Futures Basis Trade
Event Driven and Calendar Effects (10)
  • Analyst Revision and Short Interest Signals
  • Earnings Announcement Premium
  • FOMC Pre Announcement Drift
  • Insider Buying and Clone Strategies
  • January and Holiday Effects
  • Options Expiration Week Effects
  • SPAC Trust Floor Arbitrage
  • Sell in May Halloween
  • Spin Offs
  • Turn of the Month
Market Making and Liquidity Provision (8)
  • Block and Risk Trading
  • Crypto Market Making
  • ETF Market Making
  • Equity Market Making and HFT
  • Latency Arbitrage
  • Options Market Making Delta Hedged
  • Rebate Capture
  • Retail Order Flow Internalisation PFOF
Arbitrage (8)
  • ADR and Dual Listed Share Arbitrage
  • Box Spreads as Financing
  • Closed End Fund Activist Arbitrage
  • Cross Exchange Crypto Arbitrage
  • Index Arbitrage Futures vs Basket
  • Prediction Market and Sports Arbitrage
  • Put Call Parity Conversions and Reversals
  • Triangular and Cross Venue FX Arbitrage
Macro Allocation and Spread Trading (8)
  • Commodity Spread Trading Crack and Crush
  • Currency Peg and Central Bank Trades
  • Global Macro Discretionary
  • Risk Parity
  • Seasonal Futures Spreads
  • Sixty Forty Rebalancing Premium
  • Tactical Asset Allocation Momentum Rotation
  • Yield Curve Steepener Flattener
Tail Hedging and Convexity (7)
  • Barbell Taleb Style
  • CDS and Credit Shorts
  • Long Volatility Funds Allocation
  • Put Spread Collars
  • Systematic OTM Put Buying
  • Trend Plus Tail Combination
  • VIX Call Overlays
Retail and Day Trading Systems (12)
  • Buying Short Dated OTM Options Lottery
  • Candlestick Patterns
  • Chart Patterns Head and Shoulders and Friends
  • Copy Trading and Signal Services
  • Elliott Wave and Fibonacci
  • Leveraged ETF Buy and Hold
  • Martingale and Grid Bots
  • Momentum Growth Swing Trading SEPA VCP
  • Opening Range Breakout
  • Prop Firm Challenges
  • Smart Money Concepts ICT
  • VWAP Reversion and Scalping
Machine Learning Alternative Data and AI (5)
  • Alternative Data Satellite Card Web
  • LLM and AI Trading Bots
  • Machine Learning Return Prediction
  • News and Social Sentiment
  • Order Book and Microstructure ML

Audiobook & narrative editions

17 hr 28 min of narration

Both volumes are rewritten as narrative editions that read straight through, in long-form prose instead of tables. The audiobook is narrated from those editions as chaptered M4B files that play in Apple Books, VLC, BookPlayer and most audiobook apps.

  • The Book17 hr 28 min

Appendix C

Glossary: 161 terms

Read the full glossary →
0DTE
An option traded on the day it expires ("zero days to expiry"); same-day options made up a record 66.2% of SPX volume in July 2026 (Cboe).
60/40 treatment
The tax treatment of Section 1256 contracts, under which gains and losses count as 60% long-term and 40% short-term whatever the holding period.
Adverse selection
The loss a liquidity provider suffers from trading with counterparties who know more than it does about the next price move.
Alpha
Return not explained by exposure to the market or to known factors; what remains after a factor regression.
Alternative data
Non-traditional data, such as card transactions, satellite images or web traffic, used to forecast prices or company results.
American option
An option that can be exercised at any time before expiry; most US single-stock and ETF options are American.
Anchoring
Fixing on a reference number, such as the purchase price or a round number, when judging value.
Arbitrage
Buying and selling the same or equivalent claims at different prices to lock in the difference; in practice most arbitrage carries some risk of the gap widening before it closes.

From the blog

Read before you buy

All 7 articles →

The Edge Equation

Learn the framework from the book. Test it against the companion.

Choose an edition

More in the series