Corporate Finance & Financial Markets

1. At a glance

Finance is the engineering of capital allocation across time and risk. Every financial decision — buying a bond, building a factory, issuing equity, hedging a currency — reduces to: what is the present value of an uncertain stream of future cash flows, and to whom should the claims be distributed? The discipline rests on two pillars:

Corporate finance — the firm-side problem. Three core decisions: the investment decision (which real assets and projects to fund), the financing decision (what mix of debt and equity to issue), and the payout decision (dividends, buybacks, retained earnings). The objective function is shareholder value maximization, qualified by stakeholder considerations.
Financial markets — the investor-side problem. Pricing claims, allocating savings across investors, transferring risk, providing liquidity, and aggregating information into prices. Spans equity, fixed income, FX, commodities, and derivatives.

The two are inseparable. Markets price the firm’s securities, and that pricing feeds back into the firm’s cost of capital, which governs which projects are NPV-positive. Modigliani-Miller (1958) formalized this duality: in a frictionless world, firm value is determined by the assets, not the capital structure.

Modern landscape (2024-26). Deep technology and AI are now structural in finance, not adjuncts. Algorithmic and high-frequency trading dominate US equity volume (>70% of executed shares). Private capital — buyout, growth, private credit, infrastructure, secondaries — exceeds $13 T A U M g l o ba ll y (P re q in 2024), w i t h p r i v a t ecre d i t a l o n e ab o v e$ 1.5T and the largest managers (Apollo, Blackstone, KKR, Ares, Carlyle, Brookfield) increasingly resembling diversified financial conglomerates. The 2022 rate-shock regime has not unwound: Fed funds in the 4.25-4.50% range entering 2026, ECB deposit rate 2.25%, BoJ 0.50% (post-YCC exit), with the US 10-year Treasury anchored above 4%. Dominant themes 2024-26: (a) hyperscaler AI infrastructure capex (Microsoft, Google, Meta, Amazon collectively >$200B run-rate), (b) GLP-1 / obesity-drug valuations (Eli Lilly, Novo Nordisk), (c) energy-transition project finance and IRA tax-credit transferability, (d) partial IPO drought recovery (Arm, Reddit, Astera Labs, CoreWeave), (e) M&A revival 2024 after a dormant 2022-23, (f) institutionalization of digital assets via spot Bitcoin (Jan 2024) and Ether (Jul 2024) ETFs.

2. Time Value of Money (TVM)

Every other valuation construct compounds out of TVM. A dollar today is worth more than a dollar tomorrow because today’s dollar can be invested risk-free, and because a future dollar is uncertain.

Discrete present value. For a single cash flow $C$ received at time $t$ with discount rate $r$ per period:

$P V = \frac{C}{( 1 + r ) ^{t}}, F V = C \cdot (1 + r)^{t}$

Annuity. A stream of $C$ per period for $n$ periods:

$P V_{annuity} = C \cdot \frac{1 - ( 1 + r ) ^{- n}}{r}, F V_{annuity} = C \cdot \frac{( 1 + r ) ^{n} - 1}{r}$

Perpetuity (constant cash flow forever): $P V = C / r$ .

Growing perpetuity (Gordon, 1962):

$P V = \frac{C _{1}}{r - g}, valid for g < r$

This is the Gordon Dividend Discount Model (DDM) when $C_{1}$ is next-period dividend.

Compounding frequency. With $m$ compounding periods per year and stated rate $r$ :

$F V = C \cdot (1 + \frac{r}{m})^{m t}$

As $m \to \infty$ , continuous compounding: $F V = C \cdot e^{r t}$ , and $P V = C \cdot e^{- r t}$ . Continuous compounding is the standard convention in derivatives pricing.

Effective vs stated rate. APR (nominal) versus EAR (effective annual rate):

$E A R = (1 + \frac{A PR}{m})^{m} - 1$

Fisher equation (real vs nominal): $(1 + r_{n}) = (1 + r_{r}) (1 + π)$ . To first order, $r_{n} \approx r_{r} + π$ . Crucial for inflation-linked instruments (TIPS, linkers, real-yield curves) and for cross-border comparison when inflation differentials are large.

3. Discount rate and cost of capital

The discount rate is the most important input in valuation — and the hardest to estimate. It must reflect the opportunity cost of capital for an investment of equivalent risk.

Capital Asset Pricing Model (CAPM)

Independently derived by Sharpe (1964), Lintner (1965), and Mossin (1966); Sharpe shared the 1990 Nobel Prize with Markowitz and Miller. Under the assumptions of mean-variance investors, homogeneous expectations, frictionless markets, and a single risk-free rate:

$E [r_{i}] = r_{f} + β_{i} \cdot (E [r_{m}] - r_{f}), β_{i} = \frac{Cov ( r _{i} , r _{m} )}{Var ( r _{m} )}$

Only systematic (market-correlated) risk earns a premium; idiosyncratic risk is diversifiable.

Multifactor extensions

CAPM’s empirical performance is mixed. Subsequent factor models add risk premia for traits not captured by market beta:

Fama-French 3-factor (Fama & French, 1993, JFE): market, size (SMB — Small Minus Big), value (HML — High Minus Low book-to-market).
Carhart 4-factor (Carhart, 1997, J. Finance): adds momentum (WML / UMD).
Fama-French 5-factor (Fama & French, 2015, JFE): adds profitability (RMW — Robust Minus Weak) and investment (CMA — Conservative Minus Aggressive).
Q-factor model (Hou, Xue, Zhang, 2015): market, size, investment, profitability.
Arbitrage Pricing Theory (APT) (Ross, 1976, JET): expected return is linear in any number of priced factors; identifies factors empirically rather than from preferences.

Risk-free rate

Practitioners use the on-the-run Treasury yield matching the asset’s horizon: the 10-year Treasury for long-dated equity valuations, the 3-month T-bill for short horizons. After the 2023 LIBOR cessation, derivative discounting moved to SOFR (Secured Overnight Financing Rate) for USD, ESTR for EUR, SONIA for GBP, TONA for JPY, SARON for CHF.

Equity risk premium

The forward-looking ERP — $E [r_{m}] - r_{f}$ — is unobservable. Approaches:

Historical — long-run US arithmetic mean is roughly 5-6% over Treasuries (Ibbotson/Morningstar/Damodaran annual updates).
Implied — back out from index dividend models; Damodaran publishes a monthly implied ERP; running near 4.0-4.5% on the S&P 500 in early 2026.
Survey — Graham-Harvey CFO survey; Welch academic survey.

A typical valuation uses an ERP of 4.5-6.0%, sensitivity-tested.

WACC

The Weighted Average Cost of Capital is the firm-level discount rate for free cash flow to the firm (FCFF):

$W A CC = \frac{E}{V} \cdot r_{e} + \frac{D}{V} \cdot r_{d} \cdot (1 - t)$

where $E$ is the market value of equity, $D$ the market value of debt, $V = E + D$ , $r_{e}$ the cost of equity (from CAPM or multifactor), $r_{d}$ the pretax cost of debt (yield to maturity on outstanding debt), and $t$ the marginal tax rate. The $(1 - t)$ factor captures the tax deductibility of interest.

Beta estimation

Regression beta — OLS regress weekly or monthly firm return on market return over 2-5 years; standard error often high.
Levered vs unlevered beta — Hamada (1972): $β_{L} = β_{U} \cdot [1 + (1 - t) (D / E)]$ . Strip out a firm’s leverage to compare across capital structures.
Bottom-up beta — average unlevered betas of pure-play peers, then relever at the target firm’s capital structure. Standard practice for divisions, private companies, and IPO candidates.
Adjusted beta — Bloomberg’s two-thirds-raw-plus-one-third-1.0 adjustment (Blume, 1971), reflecting mean reversion.

4. Capital budgeting

The toolkit for accepting or rejecting investment projects.

Net Present Value (NPV). The undisputed first-best rule.

$NP V = - C_{0} + \sum_{t = 1}^{T} \frac{FC F _{t}}{( 1 + W A CC ) ^{t}}$

Accept all positive-NPV projects; rank by NPV when capital-constrained.

Internal Rate of Return (IRR). The discount rate at which NPV equals zero. Accept if $I RR > W A CC$ . Pitfalls: (1) multiple IRRs when cash-flow signs alternate, (2) reinvestment assumption — IRR implicitly assumes intermediate cash flows are reinvested at IRR, often unrealistic, (3) scale problems when comparing mutually exclusive projects.

Modified IRR (MIRR). Compounds positive cash flows at the reinvestment rate (cost of capital) and discounts negative cash flows at the finance rate, then solves for the rate. Eliminates the reinvestment ambiguity and the multiple-IRR pathology.

Payback period. Time to recover the initial outlay. Ignores time value and post-payback cash flows. Discounted payback corrects the first defect but not the second. Useful as a liquidity heuristic, never as a sole decision rule.

Profitability Index (PI). $P I = P V (inflows) / C_{0}$ . Accept if $P I > 1$ ; rank by PI under capital rationing.

Real options (Trigeorgis, 1996; Dixit & Pindyck, 1994 “Investment Under Uncertainty”). Treat managerial flexibility — to delay, expand, contract, abandon, switch inputs — as embedded options on the underlying project. Value via Black-Scholes-style closed forms (for European-style flexibility), binomial trees (Cox-Ross-Rubinstein, 1979), or Monte Carlo (Longstaff-Schwartz, 2001, for American-style). Especially relevant for R&D, natural-resource projects, staged tech investments, and lease-vs-buy decisions.

Risk-adjusted methods.

Decision trees for sequential decisions under discrete uncertainty.
Monte Carlo simulation for continuous distributions on multiple inputs; outputs are full NPV distributions, not point estimates.
Sensitivity analysis — one variable at a time; produces a tornado diagram identifying the inputs the answer is most fragile to.
Scenario analysis — coherent bundles (recession, base, upside).
Certainty-equivalent approach — adjust cash flows for risk and discount at $r_{f}$ , rather than discounting risky cash flows at a higher rate.

5. Capital structure

How the firm finances itself — debt versus equity, and the gradations in between (preferred, convertibles, mezzanine, hybrids).

Modigliani-Miller (MM)

Proposition I (1958, AER) — in perfect markets (no taxes, no bankruptcy costs, no information asymmetry, no transaction costs), firm value is independent of capital structure: $V_{L} = V_{U}$ . Investors can replicate any capital structure via personal leverage (“homemade leverage”).

Proposition II — the cost of equity rises linearly with leverage: $r_{e} = r_{0} + (D / E) (r_{0} - r_{d})$ , where $r_{0}$ is the unlevered cost of capital. Higher leverage means higher equity risk and exactly offsetting cheaper debt, so WACC is invariant.

Modigliani won the 1985 Nobel; Miller shared the 1990 Nobel.

MM with taxes (1963). Interest is tax-deductible. The interest tax shield raises firm value: $V_{L} = V_{U} + t D$ for permanent debt at constant tax rate. Taken literally, optimal capital structure is 100% debt — patently counterfactual, motivating the next two theories.

Trade-off theory

Optimal leverage balances the tax shield against financial-distress costs: direct (legal/administrative bankruptcy costs, fire-sale asset liquidation) and indirect (lost customers, supplier squeeze, employee flight, underinvestment, asset substitution). The optimum is interior. Empirically, firms appear to revert slowly toward target leverage ratios (partial-adjustment models), and target ratios correlate with tangibility, profitability, size, and industry.

Pecking order theory

Myers & Majluf (1984). Under information asymmetry, managers prefer financing sources in order: (1) internal funds (retained earnings), (2) safe debt, (3) risky debt, (4) equity as a last resort. Equity issuance signals overvaluation, so share prices typically fall on announcement (Asquith-Mullins, 1986). Pecking order explains why profitable firms often have low leverage — they fund from earnings.

Agency costs

Jensen & Meckling (1976, JFE). Debt and equity each impose agency costs.

Equity agency cost — managers consume perks, empire-build, hold excessive cash. Debt service disciplines free cash flow (Jensen, 1986, “free cash flow” hypothesis).
Debt agency cost — asset substitution (shifting to risky projects post-financing), underinvestment / debt overhang (Myers, 1977 — equity-holders skip positive-NPV projects whose surplus accrues to bondholders), risk-shifting near distress.

Capital structure choice trades these costs against each other; covenants, security, maturity structure, and convertibles are mechanisms to mitigate them.

Empirical drivers

Cross-sectional regressions (Rajan-Zingales, 1995; Frank-Goyal, 2009) find leverage rising with tangibility and size, falling with profitability and market-to-book. Industry effects dominate firm effects. Lemmon-Roberts-Zender (2008) show leverage ratios are remarkably persistent — most variation is firm-specific and stable.

6. Payout policy

How firms return capital to shareholders: dividends, share repurchases, and special distributions.

Dividend signaling. Lintner (1956) — managers smooth dividends and are reluctant to cut. Bhattacharya (1979), Miller-Rock (1985), John-Williams (1985) — dividends as costly signals of permanent earnings.

Clientele effects. Tax-disadvantaged investors (high-bracket individuals) prefer capital-gains-paying buybacks; tax-exempt investors (pension funds, endowments) are indifferent or prefer dividends for cash-flow needs.

Buybacks vs dividends. Buybacks dominate dividends in aggregate US corporate payout since the late 1990s and have continued accelerating post the 2017 TCJA. Mechanically: open-market repurchase, accelerated share repurchase (ASR), tender offer, Dutch auction, or privately negotiated. The 1% excise tax on buybacks under the Inflation Reduction Act took effect 1 Jan 2023; proposals to raise it to 4% have circulated but not passed as of 2026.

Dividend irrelevance (Miller-Miller, 1961). In perfect markets, payout policy is irrelevant — investors can manufacture any desired payout via homemade dividends (selling shares).

Empirical payout patterns 2024-26. S&P 500 aggregate buybacks ran $800 B -$ 950B annually 2023-25, with Apple consistently the largest single repurchaser ($90B+ authorizations). Dividend growth has lagged. Initiating-dividend firms (Meta in 2024, Alphabet in 2024, Salesforce in 2024) reflects maturation of large-cap tech.

7. Working capital and cash management

Operating cycle = DIO (Days Inventory Outstanding) + DSO (Days Sales Outstanding). Cash conversion cycle (CCC) = DIO + DSO − DPO (Days Payables Outstanding).

A negative CCC — collecting from customers before paying suppliers — is a hallmark of strong working-capital businesses (Costco, Apple historically, Amazon retail). Inventory management is dominated by just-in-time (JIT) Toyota-style systems, though COVID-era supply-chain shocks (2020-22) and US-China decoupling (2018-26) have shifted some firms toward just-in-case redundancy.

Cash management instruments: T-bills, money-market funds (government, prime, tax-exempt; Rule 2a-7), commercial paper, repos, Eurodollar deposits, sweep accounts. Treasury function software: Kyriba, GTreasury, Coupa Treasury, FIS Quantum.

Supply-chain finance (SCF) — buyer-led programs that let suppliers receive early payment from a bank against the buyer’s credit. Roughly $2T annual volume globally; the Greensill collapse (2021) exposed accounting opacity (reverse-factoring as off-balance-sheet debt), prompting an IFRS/FASB disclosure push.

8. Mergers and acquisitions

Buyer types

Strategic buyers — operating companies acquiring for synergies (revenue cross-sell, cost consolidation, capability acquisition, tax). Typically pay more, hold longer.
Financial buyers — private equity firms acquiring with the intent to improve operations, lever the balance sheet, and exit in 3-7 years.

Synergies

Revenue synergies — cross-selling, geographic expansion, pricing power. Empirically the hardest to realize and the most overestimated in pitch books.
Cost synergies — duplicated overhead elimination (CFO, IR, HR, real estate), procurement scale, manufacturing consolidation, IT rationalization. More reliably realized.
Financial synergies — tax shields, debt capacity increase, diversification (largely value-neutral for diversified shareholders).
Synergy realization is typically modeled with a phasing curve (e.g. 30%/70%/100% over years 1-3) and one-time integration costs ( $1 o f in t e g r a t i o n cos tp er$ 1-$1.50 of run-rate cost synergy is a heuristic).

Premiums

Control premiums on US public-target M&A typically run 20-40% over the unaffected price (one-day premium); the median 2024 announced strategic-deal premium was around 30%. Hostile-bid premiums skew higher to overcome target-board resistance.

Method of payment

All-cash — bidder is confident in valuation; signals strength; target shareholders crystallize gains immediately (and pay tax).
All-stock — fixed-exchange-ratio or fixed-value structure; tax-deferred reorganization (Type A/B/C reorgs under IRC §368); signals bidder may believe its shares are overvalued (Travlos, 1987; Loughran-Vijh, 1997).
Mixed / collar deals — partial cash, partial stock; collars cap exchange-ratio risk between announcement and close.

Accounting

Purchase price allocation (PPA) under ASC 805 / IFRS 3. Allocate to identifiable tangible and intangible assets at fair value; the residual is goodwill.
Goodwill is not amortized; tested annually for impairment (ASC 350). Large write-downs are common after misfired deals (e.g. AOL-Time Warner, Kraft-Heinz).
Identifiable intangibles — customer relationships, technology, trade names, IPR&D — are amortized over their useful lives.

Antitrust

United States — HSR Act (1976) premerger notification; Sherman §7 substantive review; reviewed by DOJ Antitrust and FTC (allocation by industry). 2023-26 has seen aggressive enforcement under the Khan FTC and Kanter DOJ regimes against Big Tech and consolidation generally (Microsoft-Activision approved with concessions; JetBlue-Spirit blocked 2024; Kroger-Albertsons blocked 2024).
European Union — EU Merger Regulation (Regulation 139/2004) review by DG COMP; Phase I and Phase II review; remedy negotiations.
United Kingdom — Competition and Markets Authority (CMA); post-Brexit, the CMA is a globally important reviewer (Microsoft-Activision initially blocked, then approved with cloud-streaming divestiture 2023).
China — State Administration for Market Regulation (SAMR), successor to MOFCOM. Aggressive use of conditional clearances to extract concessions.
Other — Bundeskartellamt (Germany), JFTC (Japan), KFTC (Korea), CADE (Brazil), CCI (India), ACCC (Australia).

LBOs

The leveraged buyout: PE firm acquires a target with 50-70% debt, holds for 3-7 years, exits via sale or IPO. Returns from (i) EBITDA growth, (ii) multiple expansion, (iii) debt paydown.

Fund structure — limited partnership; GP (general partner, the PE firm) commits 1-5%; LPs (limited partners — pension funds, sovereign wealth, endowments, insurance, family offices, fund-of-funds) commit the rest.
Fees — classic “2 and 20”: 2% annual management fee on committed (or invested) capital, 20% carried interest above an 8% preferred return hurdle, often with GP catch-up. Megafund management fees have compressed below 2% post-2010.
Performance metrics — IRR, MOIC (multiple of invested capital, = TVPI), DPI (distributions to paid-in — realized cash returned), RVPI (residual value to paid-in — unrealized), TVPI = DPI + RVPI.
Leverage — senior secured (term loan B), second lien, mezzanine, HoldCo PIK; covenant-lite is now the norm in broadly syndicated and direct-lending markets.
Operational improvement — 100-day plan, EBITDA bridge, working-capital release, pricing actions, sourcing.

SPACs and IPOs

Traditional IPO — book-built offering with bookrunners (Goldman, Morgan Stanley, JPM, BofA, Citi, Jefferies, Barclays); 6-7% gross spread for small caps, 3-4% for megacaps; SEC S-1 filing; 25-day quiet period and 180-day lockup.
Direct listing — existing shares list on exchange; no underwriters, no new capital (until 2020 NYSE primary direct listings rule). Used by Spotify (2018), Slack (2019), Coinbase (2021).
SPACs (Special Purpose Acquisition Companies) — blank-check company IPOs first, then merges with a target (“de-SPAC”). Boom 2020-21 (610 SPAC IPOs in 2021), bust 2022-24 amid redemption waves, weak post-merger performance, and SEC 2024 SPAC rules tightening sponsor disclosures and removing the PSLRA forward-looking-statements safe harbor for projections.
2024-25 IPO recovery — Arm Holdings (Sep 2023, $54B), Birkenstock (Oct 2023), Reddit (Mar 2024), Astera Labs (Mar 2024), Rubrik (Apr 2024), CoreWeave (Mar 2025). Still well below the 2021 peak.

9. Equity markets

Stock exchanges

Exchange	Country	Notes
NYSE	US	Specialist/DMM model; largest by listed market cap (~$30T).
NASDAQ	US	All-electronic; tech-heavy.
Cboe US Equities (BZX, BYX, EDGX, EDGA)	US	Three exchanges + dark pool.
LSE	UK	London Stock Exchange; main + AIM.
Tokyo Stock Exchange (TSE)	Japan	Prime, Standard, Growth (post-2022 segmentation).
Shanghai (SSE) + Shenzhen (SZSE)	China	A-shares (mainland), B-shares (USD/HKD), STAR Market (SSE), ChiNext (SZSE).
Hong Kong Exchanges (HKEX)	HK	China connectivity (Stock Connect).
Euronext	Pan-EU	Amsterdam, Paris, Brussels, Lisbon, Dublin, Oslo, Milan.
Deutsche Börse Xetra	Germany	DAX 40.
NSE + BSE	India	NSE dominates volume; Nifty 50, Sensex.
B3	Brazil	Bovespa (Ibovespa).
TSX + TSXV	Canada	Toronto.
SIX	Switzerland	SMI.
KRX	Korea	KOSPI 200, KOSDAQ.
ASX	Australia	ASX 200.
SGX	Singapore	Regional hub.
JSE	South Africa	All-Share index.

Order types

Market — execute immediately at best available price.
Limit — execute only at or better than the specified price.
Stop / stop-limit — triggers a market or limit order when a trigger price prints.
IOC (Immediate Or Cancel), FOK (Fill Or Kill), GTC (Good Till Canceled), GTD (Good Till Date).
Midpoint peg — pegged to the NBBO midpoint; common in dark pools and odd-lot routing.
Hidden — not displayed on the order book; reduces price impact but yields execution priority.
Iceberg — visible portion + larger hidden quantity.
Algorithmic parent orders — VWAP, TWAP, POV (Percentage of Volume), IS (Implementation Shortfall), Liquidity Seeking, Close. Implemented as child-order schedules across venues.

Microstructure

Reg NMS (US, 2007) — Order Protection Rule (Rule 611), Sub-Penny Rule (Rule 612), Access Rule, Market Data revenue allocation. SEC’s 2024-25 equity market structure rulemaking is amending tick sizes, access fees, round-lot definitions, and round-lot best-bid-and-offer disclosure (NBBO 2.0).
MiFID II (EU, 2018) — pre- and post-trade transparency across lit, dark (with caps), SI (systematic internaliser), and periodic-auction venues; research unbundling (the controversial inducement rules partially relaxed in 2024).
Tick size — minimum price increment; one cent for most US stocks since decimalization (2001); fractional sub-penny pricing in midpoint dark venues.
NBBO — National Best Bid and Offer; computed by the SIPs (UTP, CTA).
Maker-taker / inverted fees — exchanges pay rebates to liquidity providers and charge takers; some venues (BYX, EDGA) invert this.
PFOF (Payment for Order Flow) — retail wholesalers (Citadel Securities, Virtu, Susquehanna G1X, Wolverine, Two Sigma Securities, Jane Street) pay brokers (Robinhood, Schwab/TDA, E*Trade) to internalize retail flow. Banned in the UK; under heightened SEC scrutiny (Rule 605/606 amendments).

High-frequency trading and electronic market making

Dominated by a small set of proprietary firms: Citadel Securities, Jane Street, Virtu Financial, Optiver, IMC, Hudson River Trading (HRT), Jump Trading, Tower Research Capital, Susquehanna, Flow Traders, DRW, XTX, Maven Securities. Strategies: market making, statistical arbitrage, latency arbitrage, ETF NAV arbitrage, index rebalancing. Infrastructure: co-location at Mahwah (NYSE), Carteret (NASDAQ), Secaucus (NY4), Slough (LD4), Aurora (CME), Tokyo (TY3). Microwave + millimeter-wave + shortwave links between Chicago and New Jersey have collapsed latency to within a few percent of physical light-in-vacuum.

Indices

US — S&P 500 (large cap), S&P 400 (mid), S&P 600 (small), S&P 1500 (composite), Russell 1000/2000/3000, Russell Microcap, Dow Jones Industrial Average (price-weighted, 30 stocks), Nasdaq 100 (NDX), Nasdaq Composite, Wilshire 5000.
Global / international — MSCI ACWI (All-Country World Index), MSCI World (developed), MSCI Emerging Markets, MSCI Frontier; FTSE 100, FTSE 250, FTSE All-Share, FTSE All-World; STOXX 600, STOXX 50; Euro STOXX 50.
Country — DAX 40 (Germany), CAC 40 (France), AEX (Netherlands), IBEX 35 (Spain), FTSE MIB (Italy), SMI (Switzerland), Nikkei 225 + TOPIX (Japan), CSI 300 + SSE Composite + STAR 50 (China), Hang Seng + HSCEI (Hong Kong), KOSPI 200 (Korea), Nifty 50 + Sensex 30 (India), Bovespa Ibovespa (Brazil), S&P/TSX Composite (Canada), ASX 200 (Australia).

ETFs and passive investing

The exchange-traded fund — a 1993 innovation (SPDR S&P 500, ticker SPY, listed 22 Jan 1993) — is the single most important asset-management product of the past three decades. Global ETF AUM crossed $14 T in 2024 (ETFG I), w i t h U SETF A U M ab o v e$ 10T. Issuers: BlackRock iShares, Vanguard, State Street SPDR, Invesco, Charles Schwab, JPM, First Trust, ProShares. Largest single ETFs (assets, end-2024): VOO (Vanguard S&P 500, $560 B + — o v er t oo k SP Y), SP Y ($ 580B), IVV (iShares S&P 500), QQQ (Nasdaq-100), VTI (Vanguard Total Market), VEA, IEFA, AGG, BND.

Categories: broad-market index, sector, factor / smart beta, thematic, fixed-income, commodity, currency, leveraged/inverse (Direxion, ProShares), active (ARK, Dimensional, JEPI/JEPQ income), defined-outcome / buffered (Innovator, First Trust), and the explosive 2024 growth of spot Bitcoin ETFs (IBIT, FBTC, ARKB, BITB) and spot Ether ETFs (ETHA, FETH, ETHE-converted).

Mutual funds remain the larger pool by AUM ($25T+ US) but have been net outflows for a decade as money flows to passive ETFs and target-date funds. Index-fund pricing was pioneered by Jack Bogle (Vanguard 500 Index Fund, 1976); average expense ratio of US equity index funds has fallen below 0.10%, with zero-fee products (Fidelity ZERO series, BlackRock TXFZ) at the extreme.

10. Fixed income

The largest financial market — global bond markets exceed $130T (SIFMA, BIS).

Bond basics. A bond is a contractual claim to coupon payments plus principal at maturity. Price equals the present value of the cash-flow stream:

$P = \sum_{t = 1}^{N} \frac{C}{( 1 + y ) ^{t}} + \frac{F}{( 1 + y ) ^{N}}$

where $y$ is the yield to maturity (YTM), $C$ the periodic coupon, $F$ face value.

Macaulay duration — weighted-average time to cash flows.
Modified duration $= D_{Mac} / (1 + y)$ — first-order price sensitivity to yields: $Δ P / P \approx - D_{mod} \cdot Δ y$ .
Convexity — second-order correction: $Δ P / P \approx - D_{mod} Δ y + \frac{1}{2} C Δ y^{2}$ . Positive convexity is desirable; callable bonds and MBS exhibit negative convexity in certain regions.
DV01 / PV01 — dollar value of a 1bp yield change. Standard risk metric on bond desks.

Treasuries

The US Treasury market is the world’s largest single bond market (~$28T outstanding 2026). Instruments:

T-bills — discount instruments with maturities ≤ 1 year (4, 8, 13, 17, 26, 52 weeks).
T-notes — 2, 3, 5, 7, 10 year, semi-annual coupon.
T-bonds — 20 and 30 year, semi-annual coupon.
TIPS — Treasury Inflation-Protected Securities; principal indexed to CPI-U. 5, 10, 30 year.
FRNs — 2-year floating-rate notes indexed to the 13-week T-bill rate.

Auction calendar is published quarterly (Treasury Refunding); primary dealers (24 firms as of 2026, including the major US, EU, Japanese, and Canadian banks) underwrite the auctions. Secondary market is dealer-intermediated OTC, with electronic platforms (Bloomberg, MarketAxess, Tradeweb, BrokerTec, Dealerweb).

Other sovereigns and supras

Bunds (Germany), OATs (France), BTPs (Italy), Bonos (Spain), Gilts (UK), JGBs (Japan), GoCs (Canada), ACGBs (Australia), KTBs (Korea). EM sovereigns trade in USD (“hard currency”) and local currency; benchmarks JPM EMBI Global, GBI-EM. Supranationals: World Bank IBRD, EIB, KfW, EBRD, ADB, IADB.

Munis

US state and local government bonds. ~$4T outstanding. Interest is generally exempt from US federal income tax (and, for in-state holders, from state tax) — the tax-equivalent yield is the headline pricing concept. General obligation (GO) vs revenue bonds. Insurance from monolines (now diminished post-2008): Assured Guaranty, BAM, Build America Mutual. Major events: Detroit (2013), Puerto Rico (2017, PROMESA restructuring), Jefferson County AL (2011).

Corporates

Investment grade (IG) — rated BBB-/Baa3 or higher by S&P/Fitch/Moody’s. Benchmarks: Bloomberg US Aggregate, Bloomberg US Corporate.
High yield (HY) / junk — rated below BBB-. Benchmarks: Bloomberg HY, ICE BofA HY (H0A0).
Crossover — at the IG/HY boundary; rating-trigger sensitivity (e.g. fallen angels — IG-to-HY downgrades that force forced selling by mandate-constrained IG holders).
144A / Reg S — private-placement formats with eased disclosure; standard for the HY new-issue market.
Hybrid capital — preferred stock, contingent convertible (CoCo) AT1 bonds, deeply subordinated debt; CoCo write-down/conversion of $17B of Credit Suisse AT1s in March 2023 (UBS acquisition) repriced the European AT1 market.

Yield curve

The set of yields-to-maturity by maturity. Shapes:

Normal (upward sloping) — long rates above short; reflects term premium and expectations of higher future short rates.
Inverted — short rates above long; historically a recession predictor (US 10s-2s, 10s-3m).
Flat / humped — transition states.

Three curve formats: spot/zero curve (yields on zero-coupon bonds for each maturity), par curve (coupon yields at which bonds price to par), forward curve (implied future short rates).

Spreads

The yield premium over Treasuries:

Nominal spread — straight yield differential.
Z-spread — parallel shift to the spot curve that prices the bond.
OAS (Option-Adjusted Spread) — Z-spread net of embedded-option value, the standard for callables and MBS.
Asset swap spread — over the swap curve.
Credit default swap (CDS) spread / basis — bond spread vs CDS spread for the same name and tenor.

Credit ratings

Big three: Moody’s, S&P Global Ratings, Fitch. Scales (S&P/Fitch / Moody’s): AAA/Aaa, AA+/Aa1, AA/Aa2, AA-/Aa3, A+/A1 … down through C/Ca and D (default). Big-three NRSRO designation by SEC; additional NRSROs include DBRS Morningstar, Kroll Bond Rating Agency (KBRA), AM Best (insurance), Egan-Jones.

Credit default swaps

A CDS is a bilateral contract under which the protection buyer pays a periodic spread to the protection seller; the seller pays par minus the auction-determined recovery if a credit event (bankruptcy, failure to pay, restructuring) occurs. Single-name CDS trade OTC; CDS indices trade as standardized products — CDX IG / HY (Markit/IHS Markit, now S&P Global) for North America, iTraxx Main / Crossover / Senior Financials / Sub Financials for Europe, iTraxx Asia ex-Japan and iTraxx Australia. Standardized coupons (100bp IG, 500bp HY) and upfront-fee mechanics post-2009 (“Big Bang” + “Small Bang” protocols).

Securitization

MBS — Mortgage-Backed Securities. Agency (Fannie Mae, Freddie Mac, Ginnie Mae) — credit-risk-free, prepayment-risky. Non-agency / private-label — credit-risky.
CMO — Collateralized Mortgage Obligation; tranches by prepayment exposure (PAC, sequential, IO, PO, Z).
ABS — Asset-Backed Securities collateralized by auto loans, credit-card receivables, student loans, equipment, aircraft, royalties.
CMBS — Commercial Mortgage-Backed Securities; conduit and SASB (single-asset-single-borrower).
CLO — Collateralized Loan Obligation; mostly broadly-syndicated-loan collateral; equity, mezzanine, senior tranches; managed by CLO managers (Carlyle, Blackstone, Ares, KKR, GSO, Onex Credit, BlackRock, PGIM, Bain Capital Credit, Voya).

The 2007-09 crisis was, at its core, a securitization crisis — overcollateralized subprime RMBS and ABS CDOs, model failure on correlation, monoline-insurer collapse. Post-crisis reforms: risk retention (Dodd-Frank §941 “skin in the game”, 5%), enhanced disclosure (Reg AB II), credit-rating reforms.

Rates derivatives

Interest rate swap (IRS) — exchange fixed-for-floating coupons. The single largest derivative market by notional ($400T+, BIS). Cleared at LCH SwapClear, CME, Eurex.
Forward rate agreement (FRA) — single-period forward swap.
Swaption — option to enter a swap (payer or receiver).
Cap / floor / collar — series of options on a floating rate.
Overnight Index Swap (OIS) — swap on the compounded overnight risk-free rate. Post-2008 OIS replaced LIBOR-based swaps as the discount curve for collateralized derivatives.
LIBOR cessation — USD LIBOR settings ceased 30 June 2023 (with synthetic 1m/3m/6m through Sep 2024); replaced by SOFR (Secured Overnight Financing Rate), administered by the NY Fed. Other RFRs: ESTR (€), SONIA (£), TONA (¥), SARON (CHF). The transition required repapering of trillions of legacy contracts (ISDA 2020 IBOR Fallbacks Protocol).

11. Derivatives

A derivative is a contract whose payoff depends on the value of an underlying.

Forwards and futures

Forward — bilateral OTC contract to exchange an asset at a future date at a specified price.
Future — exchange-traded, standardized forward; daily mark-to-market, initial + variation margin posted to a CCP (Central Counterparty). Major exchanges: CME Group (E-mini S&P, Eurodollar/SOFR futures, Treasury futures, FX, metals, ag), ICE (Brent, gasoil, sugar, cotton), Eurex (Bund, Bobl, Schatz, DAX, Euro Stoxx 50), CBOE (VIX), HKEX, OSE (Osaka — Nikkei), SGX, B3.
Pricing (cost-of-carry): $F = S \cdot e^{(r - q + u - y) T}$ , with storage cost $u$ and convenience yield $y$ .

Options

Call — right (not obligation) to buy at strike $K$ . Payoff at expiry: $max (S_{T} - K, 0)$ .
Put — right to sell. Payoff: $max (K - S_{T}, 0)$ .
Intrinsic value + time value = option premium.
American — exercisable any time before expiry; European — only at expiry; Bermudan — at a discrete set of dates.

Black-Scholes-Merton (1973). Black & Scholes (J. Polit. Econ., 1973) and Merton (Bell J., 1973). Closed-form European-option pricing under geometric Brownian motion. Scholes and Merton shared the 1997 Nobel; Black had died in 1995. For a non-dividend stock:

$C = S Φ (d_{1}) - K e^{- r T} Φ (d_{2}), P = K e^{- r T} Φ (- d_{2}) - S Φ (- d_{1})$

$d_{1} = \frac{l n ( S / K ) + ( r + \frac{1}{2} σ ^{2} ) T}{σ T}, d_{2} = d_{1} - σ T$

Extensions: continuous dividend yield (Merton 1973), foreign-currency (Garman-Kohlhagen 1983), commodity futures (Black 1976).

Greeks. First- and higher-order sensitivities to inputs:

Delta ( $Δ = \partial C / \partial S$ ) — directional exposure.
Gamma ( $Γ = \partial^{2} C / \partial S^{2}$ ) — convexity of delta.
Vega ( $ν = \partial C / \partial σ$ ) — volatility exposure.
Theta ( $Θ = \partial C / \partial t$ ) — time decay.
Rho ( $ρ = \partial C / \partial r$ ) — rate exposure.
Higher order: vanna ( $\partial Δ/ \partial σ$ ), volga ( $\partial^{2} C / \partial σ^{2}$ ), charm ( $\partial Δ/ \partial t$ ).

Volatility surface. Empirically, implied volatility varies with strike (smile/skew) and expiry (term structure). Equity index options exhibit a pronounced negative skew — out-of-the-money puts trade rich relative to OTM calls — reflecting crash-risk hedging demand. Single-stock options often exhibit a smile. Modeling: local-vol (Dupire 1994), stochastic-vol (Heston 1993, SABR Hagan et al. 2002), Bates jump-diffusion, Variance Gamma (Madan-Carr-Chang 1998), rough-vol (Gatheral-Jaisson-Rosenbaum 2018).

Binomial tree (Cox-Ross-Rubinstein, 1979, JFE). Discrete-time lattice model with up/down moves; recovers Black-Scholes in the continuous limit; standard for American-option early-exercise.

Monte Carlo simulation for path-dependent and high-dimensional payoffs. Longstaff-Schwartz (2001) least-squares method handles American options under MC.

Exotic options. Barrier (knock-in, knock-out), Asian (average-strike or average-rate), lookback, digital / binary, cliquet, autocallables, accumulators, range accruals, quanto, basket, rainbow.

Swaps

Periodic exchange of cash flows on a notional principal.

Interest rate swap (IRS) — fixed for floating.
Currency swap — exchange of principal and interest in two currencies; includes the cross-currency basis swap (cross-currency basis = USD funding premium for foreign banks).
Equity swap / total return swap (TRS) — pay floating financing, receive total return on an equity, basket, or index. Used for synthetic prime brokerage; the Archegos blow-up (March 2021) was concentrated TRS exposure.
Commodity swap — fixed for floating on an oil or gas index.
Variance / volatility swap — payoff tied to realized variance or vol of an underlying.

VIX

The Cboe Volatility Index (introduced 1993, methodology revised 2003). The 30-day implied volatility of S&P 500 options, computed from a strike-weighted basket. Tradable via VIX futures (since 2004), VIX options (since 2006), and ETPs (VXX, UVXY, SVXY). The 5 Feb 2018 “Volmageddon” wiped out XIV (a short-vol ETN). Related: VVIX (vol of vol), MOVE (Treasury vol), CVIX/JPM G7 (FX vol), OVX (oil vol).

12. Foreign exchange

The world’s largest financial market by turnover: $7.5 trillion per day (BIS Triennial Central Bank Survey, April 2022; updated 2025 survey forthcoming).

Spot — settlement T+2 typically (T+1 for USD/CAD).
Forward outright — settlement at a future date at a contracted rate.
FX swap — simultaneous spot + opposite forward; the dominant instrument type by volume (49% of FX turnover, BIS 2022).
Currency option — vanilla, barrier, exotic.
NDF (non-deliverable forward) — cash-settled forward for restricted currencies (CNY, INR, KRW, BRL, TWD).

Carry trade. Borrow low-yielding currency (JPY, CHF historically), invest in high-yielding (BRL, ZAR, MXN, AUD/NZD). Profitable on average over time but exposes to severe drawdowns in risk-off episodes (the 2008 unwind, August 2024 yen-carry unwind triggered by BoJ hike + soft US payroll).

Parity conditions.

Covered interest parity (CIP) — $F / S = (1 + r_{dom}) / (1 + r_{for})$ . Holds tightly in normal markets via arbitrage in FX-forward markets; broke down after 2008 (the “cross-currency basis” puzzle).
Uncovered interest parity (UIP) — $E [S_{t + 1}] / S_{t} = (1 + r_{dom}) / (1 + r_{for})$ . Fails empirically (the forward premium puzzle / Fama 1984); high-yielders tend to appreciate, not depreciate.
Purchasing power parity (PPP) — relative price levels converge in real exchange rates; absolute PPP fails, relative PPP only over very long horizons.

Major pairs. EUR/USD, USD/JPY, GBP/USD, USD/CHF, USD/CAD, AUD/USD, NZD/USD. Crosses derived from majors. Emerging pairs: USD/CNH (offshore yuan), USD/INR, USD/BRL, USD/MXN, USD/TRY, USD/ZAR. USD remains overwhelmingly dominant — over 88% of trades have USD on one side (BIS 2022).

Reserve currency status. USD share of allocated reserves around 58-59% (IMF COFER), down from 71% in 2000; EUR ~20%, JPY ~6%, GBP ~5%, CNY ~2.5%, with the latter growing slowly. Dollar dominance persists despite recurrent talk of de-dollarization (BRICS payment-rail discussions, increased CNY trade invoicing, Saudi-China yuan oil pilots).

FX trading venues. EBS (now part of CME Group), Reuters Matching (Refinitiv/LSEG), FXSpotStream, Hotspot (Cboe FX), EuroLN (Euronext), Currenex, FXall (Refinitiv/LSEG), 360T (Deutsche Börse), bilateral electronic SDPs (single-dealer platforms — JPM eXecute, Citi Velocity, Barclays BARX, UBS Neo). The FX Global Code (2017, updated 2021) is the principles-based conduct framework.

13. Portfolio theory and asset allocation

Markowitz mean-variance optimization

Markowitz (1952, J. Finance; “Portfolio Selection”) — choose asset weights $w$ to minimize portfolio variance $w^{⊤} Σ w$ subject to a target expected return $w^{⊤} μ = μ_{p}$ and $w^{⊤} 1 = 1$ . The set of efficient $(μ_{p}, σ_{p})$ portfolios is the efficient frontier. With a risk-free asset, the frontier becomes the Capital Market Line tangent to the tangency / market portfolio. Markowitz shared the 1990 Nobel.

Performance metrics

Sharpe ratio (Sharpe, 1966) — $(r - r_{f}) / σ$ . Excess return per unit of total volatility.
Treynor ratio — $(r - r_{f}) / β$ . Per unit of systematic risk.
Sortino ratio — replaces volatility with downside deviation; better for skewed return distributions.
Information ratio — active return / tracking error vs benchmark. Standard for active manager evaluation.
Jensen’s alpha — intercept in CAPM regression of fund excess return on market excess return.
Calmar ratio — annualized return / maximum drawdown.
Omega ratio — probability-weighted gains over losses above a threshold.
Multifactor alpha — intercept in 3- to 7-factor regression; standard for academic and consultant evaluation.

MPT critiques

Fat-tailed returns — Gaussian assumption underestimates extreme risk. Mandelbrot (1963), Taleb (2007).
Correlation breakdown — correlations rise toward 1 in crises (the “diversification fails when you need it most” problem). 2008, 2020 March, 2022 simultaneous bond + equity drawdown.
Parameter sensitivity — mean-variance optimization is notoriously unstable in estimated inputs; small input changes produce extreme weight shifts. Mitigated by Black-Litterman (Black & Litterman, 1992; Goldman Sachs), which blends market-implied returns with subjective views via Bayesian shrinkage.
Single-period assumption — multi-period (Merton 1969, 1971) introduces hedging demand against changes in the investment opportunity set.

Factor investing

Empirically observed return premia (“anomalies” or “risk factors”) that have persisted across markets and decades:

Value — high book-to-market, earnings-yield, FCF-yield stocks outperform low. Graham & Dodd 1934; Fama-French 1992.
Momentum — winners over 3-12 months continue to outperform; losers continue to underperform. Jegadeesh & Titman (1993).
Quality — high profitability, stable earnings, low leverage, conservative accounting. Novy-Marx (2013), Asness-Frazzini-Pedersen (2019).
Low volatility / Betting Against Beta — low-vol / low-beta stocks earn risk-adjusted premia. Black (1972), Frazzini-Pedersen (2014).
Size — small-cap premium (SMB). Banz (1981); contested in recent decades.
Carry — across asset classes (FX, rates, commodities, equities), high-yielding instruments outperform on average.
Defensive / quality minus junk — Asness-Frazzini-Pedersen (2019).

Risk parity and All Weather

Risk parity allocates capital so each asset contributes equally to portfolio risk, then levers the portfolio to a target volatility. Bridgewater’s All Weather strategy (Ray Dalio, late 1990s) generalized this across four macroeconomic environments (rising/falling growth × rising/falling inflation). 2022 was a brutal year for risk parity (simultaneous stock + bond drawdown); recovery 2023-25.

Smart beta and factor ETFs

Rules-based exposure to factor premia via low-cost ETFs. Issuers: iShares MSCI factor ETFs (QUAL, MTUM, USMV, VLUE, SIZE), Invesco S&P 500 Pure Value/Growth, JPM, Goldman ActiveBeta, AQR mutual funds, Dimensional ETFs (DFA converted many mutuals to ETFs 2021-22). Industry AUM exceeds $1.5T.

Asset allocation in practice

Strategic asset allocation (SAA) — long-run policy weights; reviewed every 3-5 years; informed by capital-market assumptions (CMAs) published annually by BlackRock, JPM, Vanguard, Goldman, Schroders, Robeco, AQR, BNY Mellon, Northern Trust.
Tactical asset allocation (TAA) — short-to-medium-horizon deviations.
Target-date funds (TDFs) — glide paths shifting from equities to bonds with age; the dominant default option in US 401(k) plans (~$3.5T AUM 2024).
The 60/40 portfolio — 60% equities / 40% bonds — was foundational for decades but suffered the worst calendar-year drawdown on record in 2022 (-17% for a US 60/40). Reconsidered in many institutional reviews 2023-25; supplements (private credit, infrastructure, trend, gold, TIPS) are increasingly standard.

14. Behavioral finance

The application of psychology to financial decision-making, challenging the strict rationality of CAPM and EMH.

Prospect theory (Kahneman & Tversky, 1979, Econometrica). Investors evaluate outcomes relative to a reference point, are risk-averse over gains and risk-seeking over losses, weight probabilities nonlinearly, and exhibit loss aversion — losses hurt about 2-2.5x more than equivalent gains. Kahneman won the 2002 Nobel.
Disposition effect — investors sell winners too early and hold losers too long (Shefrin-Statman 1985, Odean 1998).
Herding and bubbles — Shiller (1981, 2000 “Irrational Exuberance”; 2013 Nobel). Excess volatility relative to dividend fundamentals; rational + irrational components of bubbles.
Limits to arbitrage (Shleifer & Vishny, 1997, J. Finance). Smart-money arbitrage is bounded by capital constraints, agency frictions, and noise-trader risk; mispricings can persist.
Overconfidence — Barber & Odean (2000) — retail traders underperform by trading too much, with men more affected than women.
Anchoring — initial price points anchor subsequent estimates (target prices, IPO pricing, M&A premium negotiations).
Home bias — investors over-allocate to domestic equities relative to ICAPM predictions.
Familiarity bias — over-weighting employer stock; Enron-employee 401(k) holdings is the canonical cautionary case.
Mental accounting (Thaler 1985, 2017 Nobel) — irrational segmentation of fungible money.
Narrative economics (Shiller 2017, 2019 book) — stories drive aggregate behavior; relevant to meme-stock and crypto episodes.

15. Banking and intermediation

Bank types

Commercial banks — deposit-taking, lending, payments. Largest US: JPMorgan Chase, Bank of America, Citigroup, Wells Fargo, US Bancorp, PNC, Truist, Goldman Sachs (Marcus), Capital One. Globally G-SIBs include HSBC, BNP Paribas, Crédit Agricole, Deutsche Bank, Barclays, UBS (post-Credit Suisse), Santander, ING, Mitsubishi UFJ, Sumitomo Mitsui, Mizuho, ICBC, China Construction Bank, Agricultural Bank of China, Bank of China.
Investment banks — capital raising (DCM/ECM), M&A advisory, sales & trading, prime brokerage, research. Bulge bracket: Goldman, Morgan Stanley, JPM IB, BofA IB, Citi, Barclays, UBS (Investment Bank), Deutsche, BNP Paribas CIB. Middle market and boutiques: Lazard, Evercore, Houlihan Lokey, Moelis, PJT Partners, Centerview, Perella Weinberg, Raine, Allen & Co, Greenhill, Guggenheim, Jefferies.
Universal banks — combine all activities (US since Gramm-Leach-Bliley 1999; European model long-standing).

Legal structure history

Glass-Steagall Act (1933) — separated commercial and investment banking after the Great Depression.
Gramm-Leach-Bliley Act (1999) — repealed Glass-Steagall’s Section 20 affiliation restrictions; enabled universal banks.
Dodd-Frank Act (2010) — post-2008 crisis omnibus reform: Title I (resolution authority), Title II (orderly liquidation), Title VII (OTC derivatives, central clearing), Volcker Rule (Title VI §619, proprietary trading restrictions, effective 2014, simplified 2020). 2018 EGRRCPA raised the SIFI threshold from $50 Bt o$ 250B.
CHOICE Act / partial repeal proposals — periodically circulated; partial Volcker simplification 2020.

Basel framework

International capital and liquidity standards from the Basel Committee on Banking Supervision (BCBS) at the BIS.

Basel I (1988) — credit risk-weighted assets, 8% minimum capital.
Basel II (2004) — three-pillar approach; market risk, credit risk (Standardized / IRB), operational risk; criticized for procyclicality and excessive reliance on internal models.
Basel III (2010, post-crisis) — Common Equity Tier 1 (CET1) ≥ 4.5% RWAs, total capital ≥ 8%, capital conservation buffer (2.5%), countercyclical buffer (0-2.5%), G-SIB buffer (1.0-3.5%, top bucket reserved), Tier 1 leverage ratio (3%, with G-SIB add-on), Liquidity Coverage Ratio (LCR ≥ 100%), Net Stable Funding Ratio (NSFR ≥ 100%).
Basel III “Endgame” / Basel IV (finalized 2017) — output floor (72.5% of standardized RWAs), revised standardized credit + market + operational risk approaches. US implementation proposal July 2023 was significantly softened in 2024-25 revisions amid industry pushback.

Stress tests

Annual supervisory exercises projecting bank capital under severely adverse macro scenarios.

United States — Fed CCAR / DFAST. Public disclosure of bank-by-bank projected losses and capital ratios.
EU — EBA stress test, biennial since 2014.
UK — Bank of England Annual Cyclical Scenario (ACS).
Japan — BoJ FSR macro stress test.

Shadow banking and non-bank finance

Non-bank financial intermediation (NBFI). FSB estimates around $63T (narrow measure, 2023). Includes money market funds, fixed-income mutual funds, hedge funds, securitization vehicles, private credit funds, finance companies, BDCs. Vulnerabilities exposed in March 2020 (Treasury basis blow-up, money-market-fund redemptions, mutual-fund liquidity mismatch), spring 2023 (Silicon Valley Bank uninsured-deposit run, Signature, First Republic, Credit Suisse Tier 1 wipeout). MMF reforms (2010, 2014, 2023) — floating NAV for institutional prime, gates and fees, swing pricing.

Repo and money markets

The repurchase market ($5T+ daily volume) is where Treasuries are financed overnight. Triparty (BNY Mellon agent), bilateral, GCF, sponsored cleared repo (FICC). The Fed conducts open-market operations through the SRF (Standing Repo Facility) and ON RRP (Overnight Reverse Repo Facility). The September 2019 repo spike (rates hit 10%) and the March 2020 dash-for-cash drove the Fed’s standing facility decisions. The SEC’s December 2023 final rule mandates central clearing of Treasury repos (June 2026) and Treasury cash secondary (December 2026).

16. Fintech, crypto, and DeFi (2024-26)

Payments

Stripe — developer-first payments API; 2024 valuation around $70B. Stripe Treasury, Issuing, Capital expand into embedded banking.
Adyen — Dutch unified-payments platform; public since 2018.
Block (formerly Square) — Square seller, Cash App, Afterpay (acquired 2022), TIDAL, TBD (Bitcoin), Spiral.
PayPal — Venmo, Braintree, Xoom; volumes ~$1.5T annually.
Wise (formerly TransferWise) — cross-border consumer FX.
Mercado Pago — LatAm payments / wallet from MercadoLibre.
Indian rails — UPI (Unified Payments Interface), >10B transactions per month, the world’s largest real-time payment system; NPCI-operated.
Brazilian rails — Pix, BCB-operated, >50% of payment transactions.
EU rails — SEPA Instant; Wero (EPI consumer wallet).
Real-time gross settlement — Fedwire, CHIPS, TARGET2 (now T2/T2S), CHATS, BOJ-NET. FedNow (US instant-payment system) launched July 2023.

Buy Now Pay Later (BNPL)

Affirm, Klarna, Afterpay (Block), Zip, Sezzle, PayPal Pay-in-4. Pay-in-4 (interest-free) and longer installment products. Profitability remains challenged; CFPB classified BNPL providers as credit-card issuers for many regulatory purposes (May 2024).

Wealth management and robo-advisors

Betterment, Wealthfront, Schwab Intelligent Portfolios, Vanguard Personal Advisor / Digital Advisor, Fidelity Go, SoFi Invest. Combined AUM ~$1T+ but growth has moderated as incumbents compete on price and adviser-augmented hybrid models. Direct indexing (Wealthfront, Schwab Personalized Indexing, Vanguard Personalized Indexing, Aperio—BlackRock, Parametric—Morgan Stanley) is the fastest-growing affluent product.

Embedded finance and BaaS

Banking primitives consumed via API by non-bank platforms.

Stripe Treasury (with Goldman, Evolve, Bond), Plaid (account aggregation), Unit, Treasury Prime, Synctera, Solid (defunct 2024 after enforcement), Synapse (collapsed 2024, exposing the regulatory perimeter problem in BaaS).
Aggregation rails — Plaid, MX, Finicity (Mastercard), Yodlee (Envestnet), Akoya.
The OCC, FDIC, and Fed have issued joint third-party-risk guidance (2023) and BaaS-focused consent orders against several sponsor banks (Cross River, Blue Ridge, Choice, Lineage). CFPB Section 1033 final rule (Oct 2024) establishes a consumer right to data portability.

Crypto

Bitcoin (Nakamoto, 2008 whitepaper; genesis block 3 Jan 2009). Market cap ~ $1.5 - 2 T 2024 - 25 d e p e n d in g o n p r i ce . Sp o tB i t co in ETF s a pp ro v e d b y SEC 10 J an 2024 (I B I TBl a c k R oc k, FBTCF i d e l i t y, A R K B A R K /21 S ha res, B I TBB i tw i se, BTCO I n v esco / G a l a x y, EZBCF r ank l in T e m pl e t o n, GBTCG r a ysc a l eco n v ers i o n, e t c .) . C o mbin e d ETF a sse t s ab o v e$ 100B by year-end 2024.
Ethereum (Buterin 2014 whitepaper; mainnet July 2015). PoS since The Merge (Sep 2022). Spot Ether ETFs approved July 2024.
Solana — Anatoly Yakovenko, Anza/Solana Labs; high-throughput L1; mainnet 2020. Solana ETFs filed 2024-25; firm-deadline 2026.
Layer 2s on Ethereum — Arbitrum One (Offchain Labs), OP Mainnet (Optimism Foundation), Base (Coinbase), Polygon zkEVM, zkSync Era (Matter Labs), Starknet (StarkWare), Linea (Consensys), Scroll, Mantle.
Other L1s — Avalanche, Sui (Mysten), Aptos, Cosmos / IBC, Polkadot, Near, TON (Telegram-backed), Cardano.

DeFi

Decentralized finance — open, permissionless, on-chain finance protocols.

DEX / AMM — Uniswap (V2 constant-product 2020, V3 concentrated-liquidity 2021, V4 hooks 2024), Curve (stablecoin-optimized), Balancer, SushiSwap, PancakeSwap (BNB), Trader Joe (Avalanche).
Lending — Aave (formerly ETHLend), Compound, MakerDAO / Sky (USDS / DAI), Spark Protocol, Morpho, Euler v2, Silo, Fluid (formerly Instadapp Lite).
Liquid staking (LSTs) — Lido (stETH), Rocket Pool (rETH), Frax, Coinbase cbETH, Binance bETH.
Restaking — EigenLayer (mainnet 2024) introduced restaking of ETH/LSTs to secure additional services (AVSs); spawned the “actively-validated-service” ecosystem (EigenDA, Lagrange, etc.) and a wave of liquid restaking tokens (Ether.fi, Renzo, Kelp, Puffer).
Stablecoin protocols — Sky USDS (MakerDAO rebrand 2024), Frax FRAX/sFRAX, crvUSD (Curve), GHO (Aave).
Perpetual DEXs — dYdX (v4 own chain on Cosmos), GMX (Arbitrum/Avalanche), Hyperliquid (own L1, 2024 breakout), Vertex, Jupiter (Solana perps).

Stablecoins

USDT (Tether) — $150B+ market cap 2024-25, the dominant offshore dollar.
USDC (Circle) — $40-60B range; tighter US reserve disclosures; reduced post-SVB (March 2023 depeg episode).
PYUSD (PayPal/Paxos) — launched 2023, gradually expanded.
FDUSD (First Digital), TUSD (TrueUSD), BUSD (Binance, wound down 2023 after NYDFS action).
Algorithmic / decentralized — Sky USDS, crvUSD, GHO, FRAX. UST/Luna catastrophic depeg May 2022 ended pure-algo stablecoin experimentation.

CBDCs

China — e-CNY in extended pilot since 2020 across major cities; cross-border experiments with mBridge.
Nigeria — eNaira (2021); limited adoption.
Bahamas — Sand Dollar (2020); first general-purpose CBDC.
Jamaica — JAM-DEX (2022).
EU — Digital Euro investigation phase complete; preparation phase 2023-25; rulemaking advanced 2024-26 but no live retail issuance.
US — Project Hamilton (Boston Fed / MIT DCI) technical research; no political consensus for issuance, executive order Jan 2025 prohibited federal digital-dollar work.
Brazil — Drex (rebrand of Real Digital), tokenized-deposit / wholesale focus.
UK — Digital Pound design phase ongoing.

Real-World Asset (RWA) tokenization

Bringing off-chain assets on-chain.

BlackRock BUIDL (BlackRock USD Institutional Digital Liquidity Fund) — tokenized money-market fund on Ethereum, launched March 2024 via Securitize; >$600M AUM by year-end 2024.
Ondo Finance — OUSG (tokenized short-term Treasuries), USDY.
Maple Finance — institutional private credit on-chain.
Franklin Templeton FOBXX / Benji platform — tokenized money market.
Hashnote USYC.
Tokenized private credit (Centrifuge), commercial real estate (RealT), carbon credits (Toucan, KlimaDAO).

Total tokenized RWA TVL surpassed $10B by end-2024 (RWA.xyz) and continues to grow as the buyer base extends from crypto-native treasuries to traditional asset managers.

17. Risk management

Value at Risk (VaR)

Maximum loss not exceeded with confidence level $α$ over horizon $h$ . Common: 1-day 99% VaR. Methods:

Historical simulation — empirical quantile of historical P&L over rolling window.
Parametric / variance-covariance — assumes normality; closed-form via portfolio volatility.
Monte Carlo — simulate factor distribution, revalue portfolio, take quantile.

VaR critiques: non-coherent (fails subadditivity), insensitive to tail beyond the cutoff. Expected Shortfall (ES, CVaR) — conditional expectation of loss given exceedance of VaR threshold — is coherent and is the Basel FRTB market-risk capital metric replacing VaR.

Stress testing

Scenarios beyond statistical tails:

Regulatory — Fed CCAR/DFAST, EBA stress test, BoE ACS.
Internal / management — bespoke macro and idiosyncratic scenarios.
Reverse stress test — find the scenario that would cause failure.

Risk taxonomy

Market risk — equity, rates, FX, commodities, credit-spread.
Credit risk — default and migration.
Counterparty credit risk (CCR) — derivatives counterparties; CVA/DVA/FVA pricing adjustments (XVA suite).
Liquidity risk — funding (rolling debt) and market (asset-liquidation).
Operational risk — fraud, fails, cyber, legal, conduct.
Model risk — wrong model, wrong inputs, misuse. SR 11-7 (Fed/OCC, 2011) is the canonical US guidance.
Strategic and reputational risk.

Tail risk and black swans

Taleb (2007, “The Black Swan”) on rare high-impact events. Practitioners hedge via long-vol overlays, OTM put protection, gold, trend-following CTAs, and tail-risk funds (Universa, 36 South, Capstone). 2008, 2010 flash crash, 2020 March, August 2024 yen-carry unwind all illustrate fat-tail behavior.

Risk-neutral vs physical measure

In derivative pricing, expectations under the risk-neutral measure $Q$ (or equivalent martingale measure) are used for pricing, while real-world / physical measure $P$ is used for risk management, capital, and historical backtesting. Practitioners must consistently translate (Girsanov theorem). Confusing the two is a common source of model-risk losses.

18. Accounting basics

Standards

US GAAP — established by FASB. Codified in the Accounting Standards Codification (ASC). Topic-based numbering (e.g. ASC 606 revenue, ASC 805 business combinations, ASC 842 leases, ASC 326 CECL credit losses).
IFRS — IASB. Used in 140+ jurisdictions including the EU, UK, Australia, Canada, much of Asia and LatAm. Counterparts: IFRS 15 revenue, IFRS 3 business combinations, IFRS 16 leases, IFRS 9 financial instruments.
Cross-border filers — US-listed foreign private issuers may file under IFRS with the SEC without GAAP reconciliation; US issuers must report under GAAP.

Three statements

Balance Sheet — Assets = Liabilities + Equity at a point in time.
Income Statement — Revenue, expenses, net income over a period.
Cash Flow Statement — Operating, investing, financing cash flows; reconciles net income to cash. Direct vs indirect method.

Accrual vs cash

Accrual recognizes revenue when earned and expenses when incurred, regardless of cash movement. Cash basis recognizes when cash moves. Public companies and audited financials are accrual.

Common metrics and ratios

Profitability.

EBITDA = Earnings before interest, taxes, depreciation, amortization. A pre-capital-structure, pre-tax, pre-non-cash measure of operating profitability. Widely used but not GAAP; reconciliation to net income required (Reg G).
EBIT = Operating income.
Net income.
Gross margin, operating margin, net margin.

Returns.

ROIC = NOPAT / Invested Capital. The single most important compounding metric for long-term value creation.
ROE = Net income / Book equity.
ROA = Net income / Total assets.
ROCE = EBIT / Capital Employed.

Working-capital efficiency.

DSO = AR / Revenue × 365 (days sales outstanding).
DPO = AP / COGS × 365 (days payables outstanding).
DIO = Inventory / COGS × 365 (days inventory outstanding).
Cash conversion cycle = DIO + DSO − DPO.

Leverage.

Debt / EBITDA — common credit metric.
Net debt / EBITDA — netting cash.
Debt / Equity, Debt / Total Capital.

Coverage.

EBITDA / Interest expense.
(EBITDA − Capex) / Interest — for capital-intensive businesses.
DSCR = NOI / Debt service — for real estate.
Fixed charge coverage.

Cash flow.

FCFF (Free Cash Flow to Firm) = EBIT(1−t) + D&A − Capex − ΔNWC.
FCFE (Free Cash Flow to Equity) = FCFF − Net interest after tax + Net borrowing.

Revenue recognition

ASC 606 / IFRS 15 (effective 2018) — five-step model: (1) identify the contract, (2) identify performance obligations, (3) determine transaction price, (4) allocate price to obligations, (5) recognize revenue when obligations are satisfied. Major change for SaaS (multi-element arrangements), media, telecom, construction.

Stock-based compensation

SBC is a real expense (ASC 718 / IFRS 2), measured at grant-date fair value (Black-Scholes or Monte Carlo for performance awards). Dilutes existing shareholders. Tech companies often present “adjusted” EBITDA and operating income excluding SBC — practitioners should treat SBC as a real cost when comparing tech valuations (Damodaran, Buffett, multiple Big 4 white papers).

Non-GAAP measures

Common adjustments: SBC, restructuring, M&A integration, amortization of acquired intangibles, impairments, gain/loss on debt extinguishment, litigation. Reg G and Item 10(e) of Reg S-K require quantitative reconciliation to the most directly comparable GAAP measure and equal-or-greater prominence to GAAP. SEC continues to police aggressive non-GAAP through comment letters and enforcement.

Recent updates

ASC 326 (CECL) — Current Expected Credit Loss model; replaced incurred-loss for loans and HTM securities; effective 2020 for large public banks, 2023 for smaller filers.
ASC 842 / IFRS 16 (Leases) — operating leases on-balance-sheet as right-of-use assets + lease liabilities; effective 2019 (GAAP for public, 2022 for non-public; IFRS 2019).
ASU 2023-09 (Income Taxes) — enhanced rate-reconciliation and cash-taxes-paid disclosure; effective FY2025.
ASU 2023-07 (Segment Reporting) — enhanced disclosure of segment expenses; effective FY2024.

19. Valuation methods

The valuation toolkit, used for IPO pricing, M&A, fairness opinions, ESOP appraisals, impairment testing, transfer pricing, and active investing.

DCF (Discounted Cash Flow)

The first-principles method. Project free cash flows over an explicit horizon (typically 5-10 years), apply a terminal value (Gordon-growth perpetuity or exit multiple), discount to present at WACC. Sensitivity-test on revenue CAGR, margin trajectory, terminal growth, terminal multiple, discount rate. Critique: garbage-in-garbage-out; terminal value often >70% of enterprise value, making the most uncertain input dominant.

Comparable trading multiples

Apply observed multiples from a peer-set of public companies to the target’s metrics.

EV / Revenue — used for unprofitable or capex-light businesses (early-stage SaaS).
EV / EBITDA — most common cross-industry multiple.
EV / EBIT — adjusts for D&A differences.
EV / (EBITDA − Capex) — for capex-heavy businesses (cable, telecom, energy).
P / E — equity-side; sensitive to leverage and tax.
PEG = P/E ÷ growth — Lynch heuristic.
P / B — book-value-driven; banks, insurers, asset-heavy industrials.
EV / Reserves, EV / Production — oil and gas.
Price / AUM — asset managers.
EV / Subscriber, EV / DAU — consumer subscription, social platforms.

Precedent transactions

Multiples paid in completed M&A deals; capture control premium. Adjust for vintage, sector cycle, deal structure, regulatory burden.

LBO modeling

Solve for the maximum entry multiple consistent with a target equity IRR (typically 20-25% for mid-market, 15-20% for megacap). Inputs: entry EV, debt capacity, EBITDA trajectory, exit multiple, holding period.

Sum-of-the-parts (SOTP)

Value each segment with the most appropriate method, sum, then subtract net debt and corporate-cost capitalized value. Standard for conglomerates (Berkshire, GE pre-breakup, 3M, Honeywell, Danaher, Roper).

Real options

Black-Scholes-style valuation of managerial flexibility. Especially relevant for biotech (option to develop), commodities (option to develop reserves), R&D-heavy tech, and lease-vs-buy or rent-vs-buy decisions.

Industry-specific

Asset managers — Price / AUM, EV / FY+1 EBITDA, FCF yield; consider performance-fee variability.
REITs — NAV (Net Asset Value) based on property cap rates; P/FFO and P/AFFO (Funds From Operations and Adjusted FFO, NAREIT standards).
Oil & gas E&P — NAV with reserve-engineering-attested reserves (PV-10, PV-15); EV / EBITDAX; PUDs (Proved Undeveloped) vs PDPs (Proved Developed Producing).
Banks — P/TBV (Tangible Book Value); ROTCE (Return on Tangible Common Equity); CET1 ratio; dividend discount with regulatory capital constraints.
Insurance — P/EV (Embedded Value) for life insurers; combined ratio for P&C.
Consumer subscription / streaming — LTV / CAC, churn, gross-to-net retention.
SaaS — Rule of 40 (revenue growth % + FCF margin % ≥ 40), net revenue retention (NRR) ≥ 120% is best-in-class, gross dollar retention ≥ 95%, CAC payback ≤ 18 months, magic number = ΔARR / S&M.

20. Quantitative finance

Stochastic calculus

The continuous-time mathematics underlying derivatives. See [[Math/stochastic-calculus]] for the core machinery — Brownian motion, Itô’s lemma, the Itô isometry, stochastic differential equations (SDEs), Girsanov’s theorem (measure change), Feynman-Kac theorem (linking PDE expectations to SDE solutions).

Canonical SDEs:

Geometric Brownian motion (Black-Scholes underlying): $d S = μ S d t + σ S d W$ .
Ornstein-Uhlenbeck (mean-reverting): $d r = κ (θ - r) d t + σ d W$ — Vasicek interest-rate model (1977).
Cox-Ingersoll-Ross (1985, mean-reverting with $r$ diffusion): $d r = κ (θ - r) d t + σ r d W$ — keeps rates non-negative.
Hull-White (1990) — extended Vasicek with time-dependent drift to fit the initial term structure.
Heston (1993) — stochastic volatility: $d S = μ S d t + v S d W_{1}$ , $d v = κ (θ - v) d t + σ_{v} v d W_{2}$ with $ρ$ correlation.
SABR (Hagan-Kumar-Lesniewski-Woodward, 2002) — industry-standard for swaption volatility-cube interpolation.

Numerical methods

PDE / finite-difference methods — explicit, implicit, Crank-Nicolson schemes for the Black-Scholes PDE and extensions. ADI for multi-dimensional.
Monte Carlo — first-best for high-dimensional and path-dependent. Variance reduction: antithetic variates, control variates, importance sampling, stratified sampling, quasi-random (Sobol, Halton). Multi-level Monte Carlo (Giles 2008) for SDE discretization-error control.
Tree methods — binomial (CRR), trinomial (Boyle 1986); naturally accommodate American exercise.
Fourier methods — Carr-Madan (1999), COS method (Fang-Oosterlee 2008) for characteristic-function-based pricing.

Market microstructure modeling

Limit order book (LOB) dynamics — empirical regularities (Bouchaud-Mézard-Potters); queue-based models (Cont-Stoikov-Talreja 2010); reduced-form (Avellaneda-Stoikov 2008 — the “AS model” canonical for market-making bid/ask quotes under inventory + adverse-selection risk).
Optimal execution — Almgren-Chriss (2000) — optimal liquidation balancing market impact (temporary + permanent) and execution-risk variance. Modern extensions: Cartea-Jaimungal-Penalva (2015 textbook), Guéant (2016).
Reinforcement learning for execution and market making — DDPG, PPO, deep recurrent Q-networks; production at JP Morgan LOXM, Tower Research, Hudson River, Jane Street.

Statistical arbitrage and pairs trading

Mean-reversion strategies on cointegrated baskets. PCA-based factor neutralization. Industry pioneers: Morgan Stanley Process Driven Trading (Tartaglia 1980s), DE Shaw, Renaissance Technologies, Two Sigma, PDT Partners, Citadel Tactical Trading, Millennium, ExodusPoint, Balyasny, Point72.

Major quant shops

Renaissance Technologies — Jim Simons (d. 2024); Medallion Fund (closed to outsiders, ~66% gross / ~39% net annualized over 30+ years), RIEF/RIDA open-to-LP funds.
Two Sigma — David Siegel and John Overdeck.
Citadel — Ken Griffin; multiple business lines (Wellington, Tactical Trading, Global Equities, Global Fixed Income, Surveyor, Ashler, Citadel Securities for market making).
DE Shaw — David Shaw; quant + fundamental hybrid.
Jane Street — ETF market-making giant; trades >$20T in ETFs annually.
Hudson River Trading, Jump Trading, Tower Research Capital, XTX Markets, Optiver, IMC, Susquehanna, Flow Traders, DRW, PDT Partners, AQR Capital, Man Group / AHL / Numeric, Acadian Asset Management.

21. 2024-26 trends

AI in finance. Every bulge-bracket bank has deployed internal LLM copilots: Goldman Sachs GSAI (internal generative AI platform), Morgan Stanley AI @ Morgan Stanley (built on OpenAI), JPM IndexGPT / LLM Suite, BofA Erica + employee LLM tools, Citi Stylus. Equity research, M&A pitch generation, due-diligence summarization, regulatory-filing parsing, contract review, and KYC document processing have moved into LLM-assisted workflows.
Private credit. Direct lending to middle-market and upper-middle-market borrowers, often LBOs, by private credit funds — Apollo, Blackstone Credit, KKR, Ares, Blue Owl, Sixth Street, Golub, HPS, GoldenTree, Antares, Oaktree. ~ $1.5 T + A U M 2024 (P re q in), w i t h t h e l a r g es t u ni t r an c h eco mmi t m e n t se x cee d in g$ 5B for single deals (e.g. Finastra refinancing 2023, Cotiviti 2024). Direct lending now rivals BSL for sub-investment-grade financing.
Private equity recovery. 2024 buyout volume rebounded after a slow 2022-23. Take-privates remain an important deal source (Smartsheet, Squarespace, Stamps.com prior years). Secondaries volume hit record $150B+ as LPs sought liquidity.
GLP-1 / obesity drugs. Eli Lilly market cap above $700B at peak, Novo Nordisk became the most valuable European company in 2024. Re-rated valuations across the GLP-1 ecosystem and adjacent sectors (food, fitness, medical devices).
AI infrastructure capex. Microsoft, Google, Meta, Amazon collectively running $200 B + ann u a l c a p e x 2024 - 25, p r ima r i l yo n d a t a ce n t ers an d A I a cce l er a t ors . N v i d iama r k e t c a p s u r p a sse d$ 3T in 2024. Power and grid constraints have become the binding capacity bottleneck; new gas turbine, nuclear PPA, and SMR contracts are dominating utility news (Constellation-Microsoft Three Mile Island restart, Amazon-Talen nuclear PPA, Oracle 1.2GW nuclear announcement).
RWA tokenization. $10B+ on-chain (RWA.xyz), led by BUIDL, OUSG, Hashnote, Maple. BlackRock and Franklin Templeton are bringing institutional rails (Securitize, Onyx).
60/40 reconsidered. Post-2022 simultaneous stock-bond drawdown spawned widespread strategic-asset-allocation reviews; trend-following CTAs, gold, private credit, infrastructure increasingly added.
IPO drought partial recovery. 2024 saw the return of larger IPOs (Reddit, Astera Labs, Rubrik, CoreWeave 2025), though backlog remains heavy and SPAC issuance dormant.
2022-26 rate regime. Fed funds plateaued in the 4.25-4.50% range entering 2026 after the 2022-23 tightening cycle and modest 2024-25 cuts. The “higher for longer” narrative has become the working assumption; yield curve persistent inversion through 2024 with intermittent steepening 2025-26.

22. Software and tools

Market data terminals — Bloomberg Professional (Terminal), LSEG Workspace (formerly Refinitiv Eikon, merged with Datastream), FactSet, S&P Capital IQ Pro, Koyfin (consumer-friendly), TradingView (charting + retail).
Private markets — PitchBook (Morningstar), Preqin (BlackRock-acquired 2024), Crunchbase, CB Insights, Dealroom.
Macroeconomic / fundamental — Haver Analytics, Macrobond, CEIC.
Modeling — Excel (still dominant), Python (pandas, NumPy, SciPy, statsmodels, scikit-learn, QuantLib, zipline, backtrader, vectorbt, lean/QuantConnect), R (tidyverse, quantmod, PerformanceAnalytics), Julia (QuantEcon.jl, DifferentialEquations.jl), C++ (HFT/derivatives engines), Rust (low-latency systems).
Derivatives libraries — QuantLib (open-source, C++ with Python/Java bindings), Numerix, FINCAD, MathWorks Financial Toolbox.
Risk — KMV / Moody’s Analytics RiskCalc / EDF, MSCI RiskMetrics / Barra, Bloomberg PORT/MARS, Numerix, Murex, Calypso (Adenza/Nasdaq), SAS Risk Management, Quantifi.
Order management / execution — Bloomberg AIM, Aladdin (BlackRock), Charles River (State Street), SS&C Eze, FlexTrade, Trading Technologies (TT) for futures, Fidessa (ION).
Modeling resources — Mergers & Inquisitions, Wall Street Prep, Breaking Into Wall Street, Damodaran’s website + courses (NYU Stern), CFA Institute curriculum.

23. Cross-references

[[Finance/_index]] — library overview and planned subdomains.
[[Economics/microeconomics-foundations]] — supply/demand, market structure, externalities, asymmetric information underpinning corporate finance.
[[Math/stochastic-calculus]] — Brownian motion, Itô calculus, SDEs for derivatives pricing.
[[Math/probability-fundamentals]] — distributions, copulas, dependence structures, tail behavior.
[[Math/hypothesis-testing-mle]] — statistical inference for asset pricing tests and event studies.
[[Math/causal-inference]] — counterfactual reasoning for trading-strategy and policy evaluation; A/B testing on strategies.
[[Compute/_index]] — algorithmic trading infrastructure, ML pipelines, low-latency systems for HFT and risk.
[[Law/_index]] (TBD) — securities regulation, contract, bankruptcy.
[[EnergyMarkets/_index]] (TBD) — commodity finance and trading.

24. Citations

Textbooks (current editions).

Brealey, Myers, Allen, Edmans — Principles of Corporate Finance, 14th ed., McGraw-Hill, 2023.
Damodaran — Investment Valuation, 4th ed., Wiley, 2024. Damodaran’s NYU Stern website remains the standard public reference for inputs (ERP, betas, growth rates).
Hull — Options, Futures, and Other Derivatives, 11th ed., Pearson, 2021.
Berk, DeMarzo — Corporate Finance, 6th ed., Pearson, 2023.
Bodie, Kane, Marcus — Investments, 13th ed., McGraw-Hill, 2024.
Cochrane — Asset Pricing, rev. ed., Princeton University Press, 2005.
Fabozzi — Bond Markets, Analysis, and Strategies, 10th ed., MIT Press, 2021.
Tuckman, Serrat — Fixed Income Securities, 4th ed., Wiley, 2022.
Stulz — Risk Management & Derivatives, South-Western, 2003.
Cartea, Jaimungal, Penalva — Algorithmic and High-Frequency Trading, Cambridge, 2015.

Foundational papers.

Markowitz, H. (1952). “Portfolio Selection.” Journal of Finance 7(1): 77-91.
Modigliani, F., and Miller, M. H. (1958). “The Cost of Capital, Corporation Finance and the Theory of Investment.” American Economic Review 48(3): 261-297.
Sharpe, W. F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance 19(3): 425-442.
Lintner, J. (1965). “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” RES 47: 13-37.
Black, F., and Scholes, M. (1973). “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81(3): 637-654.
Merton, R. C. (1973). “Theory of Rational Option Pricing.” Bell J. of Economics 4: 141-183.
Ross, S. A. (1976). “The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory 13(3): 341-360.
Jensen, M., and Meckling, W. (1976). “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure.” JFE 3: 305-360.
Myers, S. C., and Majluf, N. S. (1984). “Corporate Financing and Investment Decisions When Firms Have Information That Investors Do Not Have.” JFE 13: 187-221.
Cox, J. C., Ross, S. A., and Rubinstein, M. (1979). “Option Pricing: A Simplified Approach.” JFE 7: 229-263.
Fama, E. F., and French, K. R. (1993). “Common Risk Factors in the Returns on Stocks and Bonds.” JFE 33: 3-56.
Kahneman, D., and Tversky, A. (1979). “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica 47: 263-291.

Nobel Prize in Economic Sciences (finance-relevant laureates). Modigliani 1985; Markowitz, Sharpe, Miller 1990; Scholes, Merton 1997; Akerlof, Spence, Stiglitz 2001 (asymmetric information); Kahneman 2002 (behavioral); Engle, Granger 2003 (volatility / cointegration); Fama, Hansen, Shiller 2013 (asset prices); Tirole 2014 (market power & regulation); Thaler 2017 (behavioral); Banerjee, Duflo, Kremer 2019 (development); Bernanke, Diamond, Dybvig 2022 (banks and financial crises); Card, Angrist, Imbens 2021 (causal inference).

Regulatory and institutional sources. SEC (www.sec.gov), Federal Reserve (www.federalreserve.gov), CFTC, OCC, FDIC, FINRA, MSRB, OFAC; FSB; BIS, BCBS, IOSCO; FCA + PRA (UK); ESMA + ECB + EBA (EU); MAS (Singapore); JFSA + BoJ (Japan); HKMA + SFC (HK); SAMR + CSRC + PBoC (China); SEBI + RBI (India); ASIC + APRA (Australia); OSFI (Canada); FINMA (Switzerland); CVM + BCB (Brazil); CNV (Argentina); SBIF / CMF (Chile).

Industry references. SIFMA US capital markets factbook; ISDA derivatives statistics; BIS Triennial Central Bank Survey (FX & OTC derivatives); ICI fact book (mutual fund + ETF); ETFGI monthly ETF reports; Preqin private capital data; PitchBook PE/VC; Bain Global Private Equity Report (annual); McKinsey Global Banking Annual Review; Federal Reserve Financial Stability Report; IMF Global Financial Stability Report (semiannual).

Compendium

Explorer

Corporate Finance & Financial Markets — Finance Reference