The Learn series: from plain words to the math

The Learn series takes each topic from plain words to the math in four levels. Level 1 says what the idea is, Level 2 shows how it works with diagrams, Level 3 gives the formulas and worked examples, and Level 4 runs past episodes through that math. Read to the level you need; every chapter has the same four levels, so the depth stays the same from one topic to the next.

Pick a path

Unit 1 · Foundations

• Chapter 1 · How to read this series
  Where the series starts, how each chapter goes from plain words to the math and then to history, which reading path to pick, and how every number on these pages carries its source. 5 min
• Chapter 2 · Risk and return, the types
  What return and risk mean, the kinds of each, and the measures investors use: standard deviation, drawdown, Sharpe, Sortino, beta and alpha, with 2008 and 1973-74 worked through. 11 min
• Chapter 3 · Probability and statistics for investors
  Expected value, variance, the normal curve and its fat tails, correlation and diversification, sampling error and Bayes' rule, each worked with numbers and tested on 1987, 1998 and 2008. 12 min
• Chapter 4 · Time value of money and compounding
  Why money today is worth more than money later: compounding, discounting, the rule of 72, annuities, perpetuities, NPV and IRR, and real rates, tested on 1970s Treasury bills and Japan's zero-rate years. 9 min

Unit 2 · The economy

• Chapter 5 · Microeconomics: supply, demand, elasticity, market structure, moats
  How prices form, why some markets swing wildly, how market structure decides profits, and how a moat shows up as returns above the cost of capital, with three oil shocks worked through. 12 min
• Chapter 6 · Macroeconomics: GDP, inflation, unemployment, the business cycle
  What GDP, inflation and unemployment measure, how they move through the business cycle, and what fifteen US recessions since 1929 and eight yield-curve inversions since 1978 show when we run the numbers. 11 min
• Chapter 7 · Monetary and fiscal policy, the Taylor rule and the yield curve
  How the Federal Reserve and Congress move the economy, the Taylor rule worked with real data for 2019 and 2022, the yield curve's shapes, debt dynamics, and the episodes of 1979, 1994, 2008 and 2022 run through the numbers. 13 min

Unit 3 · Fixed income

• Chapter 8 · Bonds and the maths of basis points
  Why bond prices fall when interest rates rise, what a basis point does to a price, and how duration, DV01 and convexity turn a rate move into dollars, with 1981, 1994, March 2020 and 2022 worked through. 17 min
• Chapter 9 · Credit: corporate bonds, munis, ratings, spreads, default and recovery
  What a credit spread pays for, how ratings, default and recovery fit together, why munis need a tax lens, and what spreads in 2008, 2020, Detroit and Puerto Rico told investors, worked through with expected-loss maths. 13 min

Unit 4 · Equities

• Chapter 10 · Equity valuation
  What a share is worth: earnings and multiples, dividends and buybacks, the discount rate, moats measured as returns above the cost of capital, DCF and CAPE, with 1929, 2000 and 2009 worked through. 16 min
• Chapter 11 · Equity risk drivers, factors, international and emerging markets
  The four things that move stock prices, beta and the CAPM, the size, value and momentum factors, and what a currency adds abroad, with Japan 1989, Thailand 1997, emerging markets in 2008 and value's long drought worked through. 13 min

Unit 5 · Real assets and currencies

• Chapter 12 · Real estate and REITs
  How rent becomes a property value through the cap rate, how a REIT passes that income to its owners, and how rates, leverage and refinancing drive the risk, with 2008, 2022 and the post-2020 office slump worked through. 10 min
• Chapter 13 · Commodities and gold
  What moves oil, metals and crops, how futures curves and the roll shape a commodity fund's return, why gold tracks real yields, and what 1980, 2008 and April 2020 teach. 14 min
• Chapter 14 · Currencies and what moves them
  How exchange rates are quoted and what moves them: interest-rate gaps, inflation and PPP, the balance of payments, risk appetite and central banks, with interest rate parity worked through and five crises analysed. 15 min

Unit 6 · Derivatives

• Chapter 15 · Forwards, futures and swaps
  Contracts that fix a price or a rate today for a trade later: how forwards, futures and swaps pay off, how margin works, how to price and hedge with them, and what LTCM in 1998 and the 2022 gilt crisis teach. 13 min
• Chapter 16 · Options: European, American, Bermudan and exotics; binomial, Black–Scholes, the Greeks
  Calls and puts from payoffs to pricing: European, American and Bermudan styles, put-call parity, binomial trees, Black–Scholes worked through, the Greeks, the VIX, and what 1987, 2018 and March 2020 teach. 18 min
• Chapter 17 · Credit derivatives and structured products: CDS, MBS, ABS, CDOs, tranching and 2008
  Credit default swaps, mortgage-backed securities, ABS and CDOs from plain words to the math: hazard rates, prepayment and negative convexity, tranche losses and correlation, applied to the 2007–08 crisis. 17 min

Unit 7 · Portfolios and behaviour

• Chapter 18 · Portfolio construction: MPT, the efficient frontier, CAPM, factors, rebalancing
  How a mix of assets can carry less risk than its parts, the efficient frontier and the capital market line, CAPM and factors, risk-adjusted measures, and the arithmetic of drift and rebalancing, tested on 2008, 2022 and 2000 to 2009. 17 min
• Chapter 19 · Behavioural finance
  Why investors sell winners, hold losers, trade too much and buy near the top: prospect theory, the common biases, the behaviour gap and bubbles, each put in numbers and tested on 1720, 1929, 2000, 2006 and 2021. 12 min
• Chapter 20 · The 11 asset classes, deepened: risk drivers and one example per driver
  Each of the 11 asset classes from the overview article, taken apart by what moves its price: growth, rates, inflation, credit, the dollar, liquidity, policy and physical supply, with a worked number for each driver. 25 min

Unit 8 · Rules and practice

• Chapter 21 · Fiduciary duty, advisers vs brokers, the regulators
  Who may give investment advice in the US, what duty each kind of professional owes you, who regulates them, what Reg BI and the Marketing Rule changed, and how fees and too-smooth returns look in numbers. 15 min
• Chapter 22 · Accounts, taxes and the investor's plan
  The US account types and how each is taxed, capital gains and dividends, wash sales, RMDs and the step-up, then the math of asset location, Roth versus traditional and loss harvesting, and the written plan that ties them together. 15 min

All chapters

Reference pages

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