Investments & Portfolio Management

Investments turn capital into a claim on future cash flows. Portfolio management is the practice of assembling those claims so the aggregate risk-and-return profile matches an investor’s objectives, constraints, and beliefs about the future. The field sits at the intersection of probability theory, microeconomics, accounting, behavioral psychology, and market microstructure — and over the last 70 years it has accumulated more Nobel Prizes than perhaps any other branch of applied finance.

This note covers the major asset classes, the canonical theories (MPT, CAPM, factor models, EMH), pricing of bonds and equities, portfolio construction, performance and attribution, the institutional landscape (asset managers, hedge funds, PE/VC), retirement and personal-finance vehicles, and the rise of crypto. Companion notes: corporate-finance-and-markets, derivatives-and-quant-finance, accounting-foundations, behavioral-economics, probability-and-statistics.

1. Asset classes

1.1 Cash and cash equivalents

The “risk-free” tier — though only nominally so; real (after-inflation) returns can be negative for long stretches (US 2021–2023 inflation 6–9%, T-bill yields 0–5%).

Treasury bills (US): zero-coupon, 4-week / 8-week / 13-week / 26-week / 52-week. Auctioned weekly; benchmark for the risk-free rate at short tenors. Issued via TreasuryDirect or primary dealers.
Money market funds: SEC Rule 2a-7 vehicles. VMFXX (Vanguard Federal Money Market) — largest US MMF, ~$300B AUM; FDRXX (Fidelity); SPAXX (Fidelity Government Cash Reserves); BIL (SPDR 1–3 Mo T-Bill ETF). Yields tracked Fed funds within 10–25 bps in 2024–2026.
Certificates of deposit (CDs): bank-issued, FDIC-insured to $250k per depositor per bank; brokered CDs trade on secondary market.
Commercial paper: short-term unsecured corporate notes (≤270 days to avoid SEC registration). A1/P1 rated paper is core MMF holding. 2008 Lehman bankruptcy broke the Reserve Primary Fund (NAV fell to $0.97) and triggered the AMLF facility.
Repos and reverse repos: collateralized overnight loans; Fed’s ON RRP facility absorbed >$2T at peak (2022–2023) when reserves were abundant.

1.2 Bonds (fixed income)

Sovereign:
- US Treasuries (T-bills, T-notes 2/3/5/7/10y, T-bonds 20/30y) — deepest market on earth, ~$27T outstanding as of 2025. Considered nominally default-free in their own currency.
- TIPS (Treasury Inflation-Protected Securities): principal indexed to CPI-U; “real yield” quoted directly. I-bonds: savings bond hybrid, fixed + inflation component, $10k/yr purchase limit per SSN.
- Foreign sovereigns: Bunds (Germany — flight-to-quality EU benchmark), JGBs (Japan — yield curve control 2016–2024), Gilts (UK), OATs (France), BTPs (Italy — peripheral spread proxy). Emerging market sovereigns trade in local currency or hard currency (USD/EUR).
Corporate bonds:
- Investment grade (Moody’s Baa3+ / S&P BBB-+) — issuers like Apple, Microsoft, JPMorgan. ICE BofA US Corp Master index proxies the asset class.
- High yield / junk (below IG) — heavy issuance by LBO sponsors. Markit CDX HY index for synthetic exposure.
- Fallen angels (downgraded from IG) vs rising stars (upgraded to IG).
Municipal bonds (US): tax-exempt at federal level (and sometimes state). General obligation vs revenue bonds. ~$4T market; Puerto Rico 2016 default + Detroit 2013 bankruptcy as case studies.
Mortgage-backed securities (MBS):
- Agency MBS — guaranteed by Fannie Mae, Freddie Mac, Ginnie Mae. Pass-through structure (TBA market enormously liquid).
- Non-agency / private-label — at heart of 2007–2008 crisis.
- CMOs (Collateralized Mortgage Obligations): tranched cash flows (PAC, support, IO, PO).
ABS (asset-backed): auto loans, credit cards, student loans, equipment leases, solar receivables.
CLOs (Collateralized Loan Obligations): leveraged-loan tranches; ~$1.2T outstanding 2025.
Convertibles: bond + embedded equity call. Tesla, Twitter (pre-2022), MicroStrategy famous issuers.

1.3 Equities

Size buckets (US):
- Mega cap (>$200B): Apple, Microsoft, Nvidia, Alphabet, Amazon, Meta, Berkshire, Saudi Aramco.
- Large cap ( $10 B -$ 200B): roughly S&P 500 universe.
- Mid cap ( $2 B -$ 10B): S&P MidCap 400, Russell Midcap.
- Small cap ( $300 M -$ 2B): Russell 2000, S&P SmallCap 600.
- Micro cap (<$300M): higher information asymmetry, lower liquidity.
Style: growth (high P/E, high P/B, high revenue growth) vs value (low multiples). Russell 1000 Growth / Value indexes split the universe.
Geography: developed markets (US, Canada, Western Europe, UK, Japan, Australia, NZ, Hong Kong, Singapore, Israel, S. Korea — MSCI EAFE excludes US/Canada) vs emerging markets (China, India, Brazil, Mexico, S. Africa, Indonesia, Saudi Arabia — MSCI EM, FTSE EM) vs frontier (Vietnam, Nigeria, Bangladesh — MSCI FM).
Sectors (GICS — 11 sectors): Energy, Materials, Industrials, Consumer Discretionary, Consumer Staples, Health Care, Financials, Information Technology, Communication Services, Utilities, Real Estate.

1.4 Real estate

Direct ownership: residential (SFR, multi-family), commercial (office, retail, industrial, hospitality). Capital-intensive, illiquid, location-specific.
REITs (Real Estate Investment Trusts, US since 1960): pass-through tax structure if ≥90% income distributed. VNQ (Vanguard Real Estate ETF) tracks MSCI US REIT index. Subsectors: data center (Equinix, Digital Realty), cell tower (American Tower, Crown Castle), industrial (Prologis), residential (Equity Residential, AvalonBay), self-storage (Public Storage, Extra Space), healthcare (Welltower, Ventas), retail (Simon Property), office (Boston Properties, SL Green).
Private REITs / non-traded: Blackstone’s BREIT (~$60B+ NAV, redemption gates triggered 2022–2023), Starwood’s SREIT — controversial NAV smoothing.
Real estate funds: open-end core (NCREIF ODCE benchmark), closed-end opportunistic / value-add.

1.5 Commodities

Precious metals: gold (GLD, IAU, GLDM; physical via Perth Mint, COMEX delivery), silver (SLV), platinum, palladium.
Energy: WTI crude (USO, OIH for services), Brent, natural gas (UNG — notorious roll-cost erosion), refined products.
Agricultural: corn (CORN), wheat (WEAT), soybeans (SOYB), coffee, sugar, cocoa, livestock.
Industrial: copper (CPER, HG=F), aluminum, nickel (LME nickel short squeeze March 2022 — trades cancelled).
Broad-basket ETFs: DBC (Invesco DB Commodity), BCI (Aberdeen Bloomberg All-Commodity), PDBC (no K-1), GSG (S&P GSCI tracking).

1.6 Alternatives

Hedge funds: ~$4T AUM industry. 2-and-20 fee model now eroded toward 1.5-and-17. See §10.
Private equity: ~$8T AUM globally (Preqin 2024). Buyout, growth, distressed, special situations, secondaries.
Venture capital: ~$3T AUM. Earliest-stage equity bets.
Infrastructure: toll roads, airports, utilities, renewables. Macquarie, Brookfield Infrastructure, IFM, Global Infrastructure Partners (BlackRock acquired 2024).
Farmland: NCREIF Farmland index; AcreTrader, FarmTogether platforms.
Art and collectibles: Sotheby’s, Christie’s. Masterworks fractional shares. Wine (Liv-ex 100), watches, classic cars.

1.7 Cryptocurrencies

BTC (Bitcoin, Nakamoto 2008/2009): 21M cap, halving every 210k blocks (~4yr). Spot ETFs approved Jan 2024 — IBIT (BlackRock — fastest ETF to $50B AUM, ~7 weeks), FBTC (Fidelity), GBTC (Grayscale converted).
ETH (Ethereum, Buterin 2014): Proof-of-Stake since the Merge Sep 15 2022. Spot ETH ETFs approved May 2024.
Stablecoins: USDC (Circle, ~ $60 B), U S D T (T e t h er,$ 140B — opaque reserves), DAI (MakerDAO, overcollateralized crypto).
DeFi: Aave (lending), Uniswap (AMM DEX), MakerDAO (DAI issuer), Compound, Curve, Lido (liquid staking).
CEX: Coinbase (NASDAQ:COIN since Apr 2021), Binance (CZ guilty plea Nov 2023, $4.3B settlement), Kraken, Bitstamp, OKX, Bybit.
NFTs and L2s: peaked 2021–2022, much smaller 2023+. L2s: Arbitrum, Optimism, Base, zkSync, StarkNet, Polygon.

1.8 Insurance products

Annuities: SPIA (single-premium immediate), deferred fixed, variable annuities (VAs), indexed annuities, QLAC (longevity insurance).
Permanent life: whole life, universal life (UL), variable universal life (VUL); cash value compounds tax-deferred; loans against policy. Common estate-planning vehicle but high fees vs term + invest difference.

2. Indices and benchmarks

A benchmark is the yardstick — both for passive replication and for active alpha measurement.

2.1 Equity indices

S&P 500 (Standard & Poor’s, 1957): 500 leading US large-caps, free-float market-cap weighted, committee-selected (must have 4 quarters consecutive GAAP profit; Tesla added Dec 2020).
Nasdaq Composite: every common-stock listing on Nasdaq (~3,000 names), cap-weighted, tech-tilted.
Nasdaq-100 (NDX): 100 largest non-financials on Nasdaq. Famous “Special Rebalance” July 2023 to dilute the Magnificent Seven.
Dow Jones Industrial Average (DJIA, 1896): 30 stocks, price-weighted (a relic — $1 p r i ce m o v e inan y nam e = s am e in d e x p o in t s; AA P L p os t - s pl i t in 2020 d ro pp e d i t sD J I A w e i g h t b y 4 x) . U ni t e d He a lt h (>$ 500/sh) currently dominates.
Russell 1000 (large+mid), Russell 2000 (small), Russell 3000 (whole investable US universe) — FTSE Russell. Annual reconstitution late June (“Russell rebal”) is the largest single-day trading volume event of the year.
MSCI World (developed, no EM), MSCI ACWI (All-Country World — incl. EM), MSCI EAFE (Europe, Australasia, Far East — ex-US/Canada), MSCI EM, MSCI Frontier.
FTSE 100 (UK), Nikkei 225 (Japan, price-weighted), TOPIX (Japan, cap-weighted), DAX 40 (Germany, total return), CAC 40 (France), Euro Stoxx 50, SMI (Switzerland), CSI 300 (China — Shanghai + Shenzhen), Hang Seng (HK), KOSPI (S. Korea), Sensex / Nifty 50 (India), Bovespa (Brazil), IPC (Mexico), ASX 200 (Australia), TSX Composite (Canada).

2.2 Bond indices

Bloomberg US Aggregate (“the Agg”): the US IG fixed-income benchmark — Treasuries + agency + IG corporates + MBS. ~$28T market value.
Bloomberg US Treasury, Bloomberg US Corp IG, Bloomberg US HY, Bloomberg Global Agg (USD-hedged or unhedged).
ICE BofA US Corp Master, ICE BofA US HY (formerly Merrill).
JPMorgan EMBI (Emerging Market Bond Index, hard currency), JPMorgan GBI-EM (local currency).
CDX IG / CDX HY / iTraxx — credit default swap indices for synthetic exposure.

2.3 Commodity & alternative indices

Bloomberg Commodity Index (BCOM) — successor to DJ-UBS, broad weighting capped by sector.
S&P GSCI — production-weighted, energy-heavy (~60% energy).
HFRX / HFRI (Hedge Fund Research), EurekaHedge — hedge fund composites (survivorship + backfill bias caveats).
Cambridge Associates / Burgiss / PitchBook — PE and VC benchmarks (vintage-year IRRs, PMEs).

3. Returns

3.1 Definitions

Holding Period Return (HPR): HPR = (P₁ − P₀ + D) / P₀.
Arithmetic mean return: simple average of HPRs across periods. Overstates compound growth.
Geometric mean return (compound, time-weighted): G = (∏(1+rᵢ))^(1/n) − 1. Equals the CAGR an investor actually experienced if no flows. Always ≤ arithmetic; difference ≈ σ²/2.
IRR (Internal Rate of Return): discount rate that zeroes NPV of cash flows. Money-weighted; sensitive to timing of contributions and distributions.
TWR (Time-Weighted Return): chain-link of sub-period HPRs between cash flows. Standard for asset manager performance reporting (GIPS) — strips out client flow timing.
MWR (Money-Weighted Return) = IRR. Standard for evaluating individual investor experience.
Real vs nominal: r_real ≈ r_nom − π. Exact: (1+r_real) = (1+r_nom)/(1+π) (Fisher equation).
After-tax: depends on ordinary-income vs LTCG vs qualified dividend treatment; municipal interest tax-exempt; deferred via 401k/IRA.

3.2 Total return decomposition

Equity total return = price return + dividend yield + buyback yield − dilution. Historically US S&P 500 ~10% nominal long-run = ~2% real earnings growth + ~2% dividend yield + ~2% inflation + ~2% multiple expansion + ~2% other (rough decade-level Jeremy Siegel / Aswath Damodaran style).

Bond total return = coupon income + price change + reinvestment. Long-run roughly = starting YTM if held to maturity.

4. Risk

4.1 Variance-based measures

Standard deviation σ: square root of variance of returns. The MPT default. Annualized: σ_annual = σ_period × √(periods/yr) — e.g. daily × √252.
Semi-deviation: σ computed only on returns below the mean. Penalizes downside.
Downside deviation: like semi-dev but vs a target (MAR, minimum acceptable return).

4.2 Tail measures

VaR (Value at Risk): worst expected loss at confidence level over horizon. VaR_95% = -5th percentile of return distribution. Computed three ways:
- Historical: empirical percentile of past returns.
- Parametric / variance-covariance: assume normality, VaR = -μ + z·σ (z = 1.645 for 95%, 2.326 for 99%).
- Monte Carlo: simulate forward distribution under chosen process.
CVaR / Expected Shortfall (ES): average loss given exceedance of VaR. Coherent risk measure (Artzner-Delbaen-Eber-Heath 1999). Basel III replaced VaR with ES at 97.5%.
Max drawdown: largest peak-to-trough loss over history. S&P 500: -86% Sep 1929 to Jun 1932; -56% Oct 2007 to Mar 2009; -34% Feb-Mar 2020 (COVID).
Calmar ratio = annualized return / |max DD|. Common for CTAs.

4.3 Beta and systematic risk

β = Cov(Rᵢ, R_m) / Var(R_m). Sensitivity of an asset to the market.
Beta = 1.0 → moves with market on average. Tech mega-caps 1.1–1.5; utilities 0.4–0.7; gold ~0; long-only hedge fund alpha strategies attempt β near 0.
Idiosyncratic risk = total variance − β²·Var(R_m). Diversifiable in theory.

4.4 Fat tails

Empirical equity returns are leptokurtic — far heavier tails than the Gaussian assumption implicit in σ. Kurtosis of daily S&P returns is 30–40 (normal = 3).

Benoit Mandelbrot (1963) — “The variation of certain speculative prices” — showed cotton-price returns followed a stable Paretian (Lévy) distribution with infinite variance. Subsequent work generalized to Lévy α-stable, Pareto, Cauchy (special case, α=1, undefined mean) for asset returns.
Implication: Sharpe ratios and VaR computed under normality systematically understate disaster risk. Taleb’s “Black Swan” rests on this.

5. Modern Portfolio Theory (MPT)

Harry Markowitz, “Portfolio Selection,” JoF 1952. Nobel 1990 (jointly with Sharpe and Miller).

5.1 The setup

Investor has N risky assets with expected return vector μ and covariance matrix Σ. Choose weights w (∑wᵢ = 1) to optimize tradeoff of:

Portfolio expected return: μ_p = wᵀμ
Portfolio variance: σ²_p = wᵀΣw

5.2 Mean-variance optimization

For a target return μ*, minimize σ²_p subject to wᵀμ = μ* and wᵀ1 = 1. Solving via Lagrangian yields a unique optimum w* for each target.

The locus of (σ_p, μ_p) pairs across all targets is the efficient frontier — the upper-left envelope. Every point on it dominates any point inside.

5.3 Capital market line and tangency portfolio

Add a risk-free asset R_f (cash, T-bills). Investor can hold any combination of R_f and any risky portfolio P:

σ on the line is linear in weight to P; expected return likewise.
The tangency portfolio T — the risky portfolio with highest Sharpe ratio — is where a line from (0, R_f) is tangent to the efficient frontier.
Two-fund separation: every mean-variance investor holds the same risky mix (T), varying only the weight to T vs cash.

Closed form (no constraints): w ∝ Σ⁻¹(μ − R_f·1). Normalize.

Garbage in, garbage out: tiny estimation errors in μ drive wild swings in w*. Michaud (1989) “the curse of optimization.”
Black-Litterman (1990): anchor priors at market-cap weights, blend in views with confidence levels.
Resampling / robust optimization: bootstrap estimates, choose weights stable across draws.
Risk parity (see §11) sidesteps μ estimation entirely.

6. CAPM — Capital Asset Pricing Model

William Sharpe (1964) “Capital Asset Prices,” JoF — Nobel 1990. Independently developed by Treynor (unpublished memo 1961), Lintner (1965), Mossin (1966).

6.1 Statement

In equilibrium, every investor holds the market portfolio combined with cash. The expected return on any asset i:

E(Rᵢ) = R_f + βᵢ · (E(R_m) − R_f)

where E(R_m) − R_f is the equity risk premium (~5–7% per annum historically in the US per Damodaran’s annual estimates; ~3.5% globally per Dimson-Marsh-Staunton).

6.2 Assumptions

Investors are mean-variance optimizers.
Homogeneous expectations (same μ, Σ).
Frictionless markets — no taxes, transaction costs, short-sale constraints; can borrow/lend at R_f.
Returns are jointly normal (or quadratic utility).
Market portfolio includes all investable wealth.

6.3 Empirical failures

Size effect: small caps earn ~3–4% premium over what CAPM predicts (Banz 1981).
Value effect: high B/M (book-to-market) stocks beat low B/M after controlling for β (Fama-French 1992).
Momentum: past 12-mo winners outperform losers (Jegadeesh-Titman 1993).
Low-volatility anomaly: low-β stocks outperform on a risk-adjusted basis (Frazzini-Pedersen 2014 “Betting Against Beta”).
Profitability and investment: high gross-profitability and conservative-investment firms outperform (Novy-Marx 2013).
Roll’s critique (1977): the true “market portfolio” is unobservable (includes human capital, real estate, private assets), so CAPM is untestable.

CAPM survives in textbooks and cost-of-capital calculations despite all this — Damodaran uses it to compute discount rates.

7. Factor models

7.1 APT (Arbitrage Pricing Theory)

Stephen Ross (1976). Multi-factor generalization of CAPM:

E(Rᵢ) = R_f + Σ_k βᵢ,k · λ_k

where λ_k are risk premia on K factors. Derivation via no-arbitrage rather than equilibrium.

7.2 Fama-French models

3-factor (1992): Market + SMB (Small Minus Big — size) + HML (High Minus Low — value by B/M).
5-factor (2015): + RMW (Robust Minus Weak — profitability) + CMA (Conservative Minus Aggressive — investment).
Carhart 4-factor (1997): 3-factor + UMD/MOM (winners minus losers, momentum).
Hou-Xue-Zhang q-factor (2015): Market + size + investment + ROE — often subsumes FF5.
FF6: 5-factor + momentum.

Factor data available from Ken French’s data library at Dartmouth Tuck.

7.3 Smart beta and ESG factors

Asset managers (AQR, BlackRock iShares, DFA, Research Affiliates, WisdomTree, Invesco) productize factor exposures — minimum volatility, quality, momentum, multi-factor ETFs.

ESG as factor: contested. MSCI, Sustainalytics, Refinitiv ratings have low pairwise correlation (~0.4–0.5). Bolton-Kacperczyk find a carbon premium; others (Pástor-Stambaugh-Taylor 2022) note ESG outperformance during 2018–2020 was driven by demand shocks, not a permanent premium.

8. Active vs passive — and the rise of indexing

John Bogle founds Vanguard (1975), launches the First Index Investment Trust (1976) — now Vanguard 500 Index (VFIAX). Ridiculed at launch (“Bogle’s folly”).
ETFs arrive: SPY (SPDR S&P 500, 1993, State Street); iShares launched by Barclays Global Investors (1996), acquired by BlackRock 2009.
2025: index funds + ETFs hold >50% of US equity AUM. Combined Vanguard + BlackRock + State Street vote ~20–25% of S&P 500 share float.
SPIVA scorecard (S&P Dow Jones Indices, semi-annual): consistently shows ~80% of active US large-cap funds underperform S&P 500 over 15-year windows after fees. Higher persistence of failure in fixed income too. EM and small-cap less clear-cut.
Active share (Cremers-Petajisto 2009): managers with high active share (>80%) outperform; “closet indexers” do not.

Implication for retail: default to broad-market index funds; reserve active for niches where information asymmetry is real (small-cap value, EM, distressed credit, private markets).

9. Efficient Market Hypothesis (EMH)

Eugene Fama (1970, 2013 Nobel — jointly with Hansen and Shiller, the last an EMH skeptic).

9.1 Three forms

Weak form: prices reflect all past trading data. Technical analysis cannot generate abnormal returns. Generally well-supported empirically.
Semi-strong form: prices reflect all public information. Fundamental analysis of public data cannot generate alpha. Supported by event studies — earnings announcements impound into prices within minutes.
Strong form: prices reflect all information, including private. Insider trading would not generate abnormal returns. Rejected (insider trades are profitable; Galleon / Rajaratnam 2011 case prosecuted on those grounds).

9.2 Event studies

Standard methodology (Fama-Fisher-Jensen-Roll 1969): estimate β over pre-event window, compute abnormal return AR = R_actual − (R_f + β·(R_m − R_f)) around event date, cumulate (CAR). Foundation of most empirical asset-pricing tests.

9.3 EMH counterevidence and behavioral finance

Shiller (1981) “Do stock prices move too much to be justified by subsequent changes in dividends?” — volatility puzzle. Cited in 2013 Nobel.
DeBondt-Thaler (1985) long-horizon reversals.
Lo (2004) “Adaptive Markets Hypothesis” — markets are adaptive not strictly efficient; arbitrage opportunities exist transiently as new strategies arise and decay.
Linked closely to behavioral-economics — equity-premium puzzle (Mehra-Prescott 1985), disposition effect (Odean 1998), home bias (French-Poterba 1991), overconfidence, loss aversion (Kahneman-Tversky).

10. Bond pricing

10.1 Present-value mechanics

Price = Σ (Cᵢ / (1+y)^tᵢ) + F/(1+y)^T, where C are coupons, F is face, y is yield to maturity (the IRR of bond cash flows).

Premium bond: coupon > yield → trades above par.
Discount bond: coupon < yield → trades below par.
Par bond: coupon = yield → trades at par.

Price-yield relationship is convex and decreasing.

10.2 Duration

Macaulay duration: D = Σ (tᵢ · PVᵢ / Price). Time-weighted average of cash-flow PVs. Units: years.
Modified duration: D_mod = D / (1+y). Use: ΔP/P ≈ −D_mod · Δy.
Effective / option-adjusted duration: numerical bumping for bonds with optionality (callables, MBS prepayment).
DV01 (dollar value of one basis point) = −D_mod · P · 0.0001. The trader’s working unit.
Key rate duration: sensitivity to a specific tenor; sum approximately = effective duration.

10.3 Convexity

Second-order: ΔP/P ≈ −D_mod·Δy + ½·C·(Δy)². Positive convexity means actual price exceeds duration-implied price for both up and down yield moves. MBS has negative convexity at low rates (prepayment risk caps upside).

10.4 Immunization and asset-liability management

Cash-flow matching: dedicate bonds whose coupons + maturities exactly fund liability stream. Used in pension de-risking (Aon, Mercer, Willis Towers Watson advisory).
Duration matching / immunization (Redington 1952): match duration of assets and liabilities to neutralize first-order interest-rate risk; convexity matching is second-order.
LDI (Liability-Driven Investing): UK pension industry standard pre-2022. The Sep 2022 LDI crisis after Truss/Kwarteng mini-budget forced Bank of England gilt-buying intervention.

10.5 Credit risk

OAS (Option-Adjusted Spread): the spread over the risk-free curve after stripping out embedded optionality value. The fixed-income trader’s primary value metric for credit.
CDS spread: market-implied default probability proxy. PD ≈ Spread / (1 − Recovery).
Structural models — Merton (1974) treats equity as a call option on firm assets. KMV / Moody’s Analytics EDF is the production version.
Reduced-form models — Jarrow-Turnbull, Duffie-Singleton — model default as a hazard-rate process.

11. Yield curve

Spot rate at tenor t: yield on zero-coupon bond maturing at t.
Par rate: coupon rate at which a bond would trade at par for that tenor.
Forward rate: implied future short rate. f(t1,t2) = ((1+y_t2)^t2 / (1+y_t1)^t1)^(1/(t2−t1)) − 1.
Bootstrapping: extract spot curve from observed par bonds tenor by tenor.
Curve fitting: Nelson-Siegel (1987) and the Svensson (1994) extension fit a parametric form to observed yields; used by central banks for curve construction.

11.1 Shape signals

Normal / upward-sloping: long > short — expansion.
Flat: late cycle.
Inverted (2y > 10y, 3m > 10y): every US recession since 1969 was preceded by 3m–10y inversion; lead time 6–24 months. NY Fed publishes a recession-probability model based on this.
Steepening / bull-steepener (short rates fall faster): early easing cycle.
Bear-flattener (short rates rise faster): tightening cycle.

11.2 Reference rate transitions

LIBOR: London Interbank Offered Rate, fixed by panel banks. Manipulation scandal 2012 (Barclays £290M, UBS $1.5 B, De u t sc h e$ 2.5B, RBS $612M settlements). Phased out 2021 (USD LIBOR fully retired June 2023).
SOFR (Secured Overnight Financing Rate): NY Fed publishes daily, based on triparty + GCF + bilateral repo. Forward-looking term SOFR via CME.
Other: €STR (Europe), SONIA (UK), TONA (Japan), SARON (Switzerland).

12. Equity valuation

12.1 Intrinsic methods

DCF (Discounted Cash Flow):
- FCFE (Free Cash Flow to Equity) discounted at cost of equity → equity value.
- FCFF (Free Cash Flow to Firm) = EBIT(1-t) + D&A − CapEx − ΔWC, discounted at WACC → enterprise value. Subtract debt to get equity.
- Terminal value: Gordon growth (FCFᵧ₊₁/(WACC−g)) or exit multiple.
Gordon Growth Model (1956): P₀ = D₁/(r−g). Single-stage perpetuity. Useful for stable mature companies (utilities, REITs).
Residual income / EVA: V = BV + Σ (RI_t / (1+r)^t), RI = NI − r·BV_{t-1}.
Dividend Discount Model (DDM): special case of FCFE for dividend-paying steady-staters.

12.2 Relative valuation (comps)

P/E: price / EPS — trailing, forward, Shiller CAPE (10-year smoothed real).
P/B: price / book value per share. Banks, REITs, insurance.
EV/EBITDA: capital-structure-neutral; industrial, telecom, media.
EV/Sales: when EBITDA is negative or distorted (SaaS, biotech).
PEG = P/E ÷ growth rate. Heuristic, not rigorous.
Sum-of-the-parts (SOTP): each segment valued separately; conglomerate discount.
LBO model: solve for IRR to PE sponsor under leverage + exit multiple assumption.

Aswath Damodaran (NYU Stern) publishes annual updates of equity risk premiums, country risk, sector multiples — the de facto reference dataset.

13. Portfolio construction

13.1 Strategic asset allocation (SAA)

Long-horizon target weights based on capital-market expectations and investor objectives. Reviewed every 1–5 years. The 60/40 portfolio (60% equity, 40% bonds) was the retail/pension default for decades. 2022’s simultaneous bond-and-equity drawdown (−18% S&P, −13% Agg) prompted “is 60/40 dead?” debates; subsequent recovery muted them.

13.2 Tactical asset allocation (TAA)

Shorter-term deviations from SAA based on valuation, macro, or momentum signals. Generally low conviction in retail; some institutional success (GMO’s 7-year forecasts).

13.3 Target-date funds (TDFs)

Default of US 401(k) plans since QDIA designation (Pension Protection Act 2006). Glide-path automatically de-risks toward retirement. Vanguard Target Retirement series, Fidelity Freedom series, T. Rowe Price, BlackRock LifePath, American Funds Target Date. ~$3T AUM. Largest single retail product category.

13.4 Risk parity

Bridgewater All Weather (Ray Dalio, mid-1990s formalized 2005). Equalize risk contribution across asset buckets (equities, nominal bonds, inflation-linked bonds, commodities) rather than capital weights. Often leveraged so total volatility matches a 60/40. Performed brilliantly 1990s–2010s; struggled in 2022 (everything sold off together — see macroeconomics on regime breaks).

13.5 100% equities debate

Cederburg-O’Doherty-Williamson (2024) argued an all-equity 50/50 domestic/international portfolio outperforms target-date funds for long horizons even at retirement, due to long-term equity premium dominating short-horizon drawdown. Controversial — assumes investor will not panic-sell during 50%+ drawdowns.

14. Performance metrics

Sharpe ratio (Sharpe 1966) = (Rᵢ − R_f) / σᵢ. Excess return per unit of total risk. Ex post or ex ante. ~1.0 is good, >2.0 exceptional, >3.0 raises suspicion.
Treynor ratio = (Rᵢ − R_f) / βᵢ. Per unit of systematic risk only.
Jensen’s alpha = Rᵢ − [R_f + βᵢ(R_m − R_f)]. Excess over CAPM expectation.
Information Ratio (IR) = (Rᵢ − R_benchmark) / TE, where TE = tracking error = σ of active return. Standard active-manager metric. Top quartile equity mutual funds: IR ~0.3–0.5.
Sortino ratio = (Rᵢ − MAR) / downside deviation. Penalizes only downside σ.
Calmar = annualized return / |max DD|.
Omega ratio = E[max(R − τ, 0)] / E[max(τ − R, 0)] — whole-distribution-aware.

15. Performance attribution

15.1 Brinson-Hood-Beebower (1986)

Decomposes active return vs benchmark into:

Allocation effect: (w_p,s − w_b,s) × (R_b,s − R_b) — overweighting outperforming sectors.
Selection effect: w_b,s × (R_p,s − R_b,s) — stock-picking within sector.
Interaction: (w_p,s − w_b,s) × (R_p,s − R_b,s).

BHB’s headline finding (“90% of variance from asset allocation”) is often misquoted — they explained variance over time, not return level.

15.2 Multi-factor attribution

Barra (now MSCI Barra) style — regress portfolio returns on factor returns (size, value, momentum, volatility, growth, leverage, industry exposures) to attribute alpha and risk.

16. Market structure and trading

NYSE: hybrid market, designated market makers (DMMs — Citadel Securities, GTS, Virtu, Hudson River). Opening + closing auctions.
Nasdaq: fully electronic since inception (1971). Multiple competing market makers.
Reg NMS (2007, US): order-protection rule, requires routing to best price across venues.
MiFID II (2018, EU): unbundling research from execution; transparency requirements.
ECNs: Electronic Communication Networks — BATS (now CBOE), Direct Edge, ARCA (NYSE-owned).
Dark pools: ATS venues, no pre-trade transparency. UBS ATS, Credit Suisse Crossfinder (closed), JPM-X, Liquidnet, ITG POSIT, Instinet, Sigma X. ~10–15% of US equity volume.
Algos that asset managers use: TWAP (Time-Weighted Average Price), VWAP (Volume-Weighted), IS (Implementation Shortfall, Perold 1988), POV (Percent of Volume), PWP (Pegged), iceberg, sniper, dark aggregators.
HFT: Virtu Financial (NASDAQ: VIRT, IPO 2015), Citadel Securities (private), Jane Street, Hudson River Trading, IMC, Optiver, DRW, Two Sigma Securities. ~50% of US equity volume.
PFOF (Payment For Order Flow): Robinhood, Schwab, E*Trade route retail flow to HFT wholesalers (Citadel Securities, Virtu, Susquehanna G1X) for rebates. SEC tightened disclosure 605/606 rules; UK + EU largely banned.
Flash Crash (May 6, 2010): Dow drops ~1000 pts in minutes; Navinder Sarao spoofing prosecution + Waddell & Reed E-mini sell algo. Led to limit-up/limit-down rules.

17. Asset management firms

17.1 Mega-passive

Firm	AUM (≈ 2025)	Notes
BlackRock	$11.5T	Larry Fink CEO; iShares ETFs; Aladdin risk platform
Vanguard	$9.5T	Mutual structure (clients own the company); Tim Buckley → Salim Ramji 2024
Fidelity Investments	$5T+	Abigail Johnson; private
State Street Global Advisors	$4T	SPDR ETFs (SPY)
Capital Group / American Funds	$2.7T	Multi-manager actively managed
Charles Schwab	$9 T c l i e n t a sse t s ($ 1T proprietary)	Retail brokerage + custody
JPMorgan Asset Management	$3.5T
BNY Mellon Investment Management	$2T
Amundi	$2.2T	Largest European AM
Invesco	$1.7T	QQQ trust

17.2 Hedge fund / quant powerhouses

Bridgewater Associates (Ray Dalio, Westport CT) — Pure Alpha, All Weather. ~$120B AUM 2024.
Renaissance Technologies (Jim Simons d. 2024, Robert Mercer) — Medallion Fund: ~66% gross / ~39% net annualized 1988–2018, employee-only; outside funds (RIEF, RIDA) much weaker.
Citadel (Ken Griffin) — Wellington multi-strat fund; +38% in 2022 (huge year). ~$65B AUM.
Millennium Management (Izzy Englander) — pod-shop multi-manager.
Two Sigma (David Siegel + John Overdeck, ex-DE Shaw).
AQR Capital Management (Cliff Asness, David Kabiller, John Liew, Robert Krail — ex-Goldman QSG). Factor investing translated to systematic mandates. Posted disappointing returns 2018–2020, strong rebound 2022–2024.
DE Shaw (David Shaw, computer scientist) — model-driven; ~$60B.
Point72 Asset Management (Steve Cohen, post-SAC Capital settlement).
TCI (The Children’s Investment Fund, Chris Hohn) — concentrated activist.
Pershing Square (Bill Ackman) — concentrated equity activist.
Elliott Management (Paul Singer) — distressed + activist.

18. Private equity

18.1 The majors

KKR (Kohlberg Kravis Roberts, founded 1976; Henry Kravis, George Roberts) — pioneered the LBO; RJR Nabisco 1989.
Blackstone (Steve Schwarzman, Hamilton “Tony” James) — diversified alts giant, $1.1T+ AUM 2024.
Apollo Global Management (Leon Black retired; Marc Rowan CEO) — credit-heavy.
The Carlyle Group — DC-based, defense/aerospace heritage.
TPG Capital — Texas Pacific Group origin; ~$240B.
Bain Capital — Mitt Romney founder.
Warburg Pincus, CVC Capital Partners (Europe), EQT (Sweden).

18.2 LBO mechanics

Sponsor uses ~30–40% equity + 60–70% debt (senior secured + mezzanine + sometimes preferred) to acquire target. Operate 3–7 years; exit via sale, IPO, or dividend recap. Returns from (1) leverage amplification, (2) operational improvement, (3) multiple expansion.

18.3 Economics

J-curve: early years show negative IRR (fees + write-downs of underperformers) before realizations create the upside.
Carry: 20% of gains above hurdle (typically 8% IRR), with catch-up provisions.
Management fee: ~2% of committed capital, transitioning to invested capital after the investment period (typically 5y).
GP commit: GP invests 1–5% of fund to align incentives.
Secondaries market: LPs sell stakes mid-fund — Ardian, Lexington, Coller, HarbourVest, StepStone. ~$130B annual volume 2024.
PME (Public Market Equivalent, Kaplan-Schoar 2005): IRR if same cash flows had been invested in a public index. PE outperformance vs S&P 500 has compressed post-2010 (Phalippou critiques).

19. Venture capital

19.1 The firms

Sequoia Capital (Don Valentine; Doug Leone, Roelof Botha leadership) — Apple, Google, Cisco, WhatsApp, Stripe, Airbnb, ByteDance.
Andreessen Horowitz (a16z) (Marc Andreessen, Ben Horowitz, 2009) — Facebook, Twitter, Coinbase, Airbnb; crypto fund.
Benchmark Capital — Uber (Bill Gurley exit), Snap, Twitter, Discord, Asana.
Accel Partners — Facebook lead Series A; Slack, Atlassian, Dropbox.
Greylock Partners — LinkedIn, Airbnb, Palo Alto Networks, Workday.
Founders Fund (Peter Thiel, Ken Howery, Luke Nosek) — SpaceX, Palantir, Stripe, Anduril.
Kleiner Perkins — historic Web 1.0 leader (Amazon, Google, Netscape, Sun); diminished relevance.
Khosla Ventures (Vinod Khosla, ex-Kleiner) — deep tech, OpenAI early.
Lightspeed Venture Partners, General Catalyst, NEA, Bessemer, Index Ventures, Insight Partners, Tiger Global, Coatue, D1 Capital.

19.2 Accelerators / seed factories

Y Combinator (Paul Graham 2005) — Airbnb, Stripe, DoorDash, Coinbase, Dropbox, Reddit, Cruise. Standardized SAFE notes in 2013 (Simple Agreement for Future Equity).
Techstars, 500 Global (formerly 500 Startups).

19.3 Funding stages and structure

Pre-seed → Seed → A → B → C → D → E → Pre-IPO.
Round sizes (2024–2025 medians, US): pre-seed ~ $1 M, see d$ 3M, A ~ $10-15 M, B$ 30M, C ~ $60 M, D +$ 100M+. Mega-rounds ($100M+) democratized post-2015.
Preferred equity: liquidation preference (1x non-participating standard; participating stacks dividends), anti-dilution (broad-based weighted-average standard; full-ratchet rare/punitive), pro rata rights, board seats, drag-along, tag-along, ROFR.
Cap tables: founder common shares + employee option pool (10–20%) + preferred series. Carta and Pulley dominant cap-table software.
J-curve: 10+ years for VC funds; venture vintage years 2010–2015 unusually strong (US enterprise SaaS + mobile).
Power-law returns: ~1 in 100 portfolio companies returns most of fund value. Diversification + access (top-tier name) dominate.

20. Hedge fund strategies

Strategy	What it does	Examples
Equity long/short	Long fundamental winners, short losers; net market exposure 0–50% typical	Lone Pine, Maverick, Viking, Coatue (“Tiger cubs” descended from Julian Robertson’s Tiger Mgmt)
Global macro	Top-down bets on rates, currencies, commodities	Brevan Howard, Bridgewater, Caxton, Element
Event-driven	Merger arb, special situations, spin-offs	Elliott, Pentwater, Magnetar
Distressed	Defaulted / near-default credit	Oaktree, Cerberus, Apollo, Centerbridge
Statistical arbitrage	Mean-reversion + factor-based equity, very-short horizon	Renaissance, DE Shaw, Two Sigma
CTA / Managed Futures	Systematic trend following across futures	Man AHL, Winton, Aspect, Millburn, Campbell
Multi-strategy	Pod shops, many sub-PMs	Citadel, Millennium, Point72, ExodusPoint, Balyasny
Long-only / 130/30	Variants of long with leveraged shorts	AQR, T. Rowe Price extensions

Composites: HFRX (investable), HFRI (broader monthly), EurekaHedge, Credit Suisse Hedge Fund Index. Bias caveats: survivorship, backfill, self-reporting.

21. Retirement and personal finance

21.1 US tax-advantaged accounts

401(k) (IRC §401(k), 1978, originated as a Ted Benna interpretation): employer-sponsored DC plan. 2025 limits: $23, 500 e m pl oyee +$ 7,500 catch-up at 50+; $11,250 enhanced catch-up at 60–63 (SECURE 2.0). Pre-tax or Roth options. Employer match commonly 50–100% up to 3–6% of salary.
403(b): nonprofits, schools, hospitals — similar to 401(k).
457(b): government and select tax-exempts.
Traditional IRA: pre-tax contribution, taxed at withdrawal. 2025 limit: $7, 000 +$ 1,000 catch-up.
Roth IRA: post-tax contribution, tax-free at withdrawal. Income phase-outs (~ $150-165 k s in g l e,$ 236–246k MFJ 2025). Backdoor Roth: nondeductible TIRA → Roth conversion sidesteps the income cap.
Mega-backdoor Roth: after-tax 401(k) contributions up to overall §415 limit ($70k 2025) then in-plan Roth conversion or in-service rollover to Roth IRA.
HSA (Health Savings Account): triple-tax-advantaged (deductible in, tax-free growth, tax-free out for qualified medical). Treated as “stealth retirement” — keep receipts and reimburse decades later.
SEP-IRA: self-employed; 25% of net SE earnings up to $70k 2025.
Solo 401(k): combines employee + employer (profit-sharing) limits for sole proprietors.
529 plan: state-sponsored, post-tax in, tax-free out for qualified education. SECURE 2.0 allows $35k lifetime 529→Roth IRA rollover.
RMDs (Required Minimum Distributions): SECURE 2.0 (Dec 2022) pushed start age to 73 (rising to 75 in 2033). Tables from IRS Pub. 590-B.

21.2 Tax management

Tax-loss harvesting: realize losses to offset gains and up to $3k ordinary income annually (US). Beware wash-sale rule (no replacement within 30 days). Wealthfront, Betterment automate; “direct indexing” (Parametric, Aperio, O’Shaughnessy, Schwab Personalized Indexing) scales it.
Asset location: hold high-tax-cost assets (taxable bonds, REITs, active funds) in tax-deferred accounts; tax-efficient (broad-market ETFs, munis) in taxable.
Roth conversion ladders: convert TIRA → Roth in low-income years to fill marginal brackets without RMD pressure later.

22. Real estate as an investment

Cap rate = Net Operating Income (NOI) / Property value. Spread over 10y Treasury is the going-in premium. Compressed 2010s, blew out 2022–2024 with rate hikes.
NOI = Gross rent − vacancy − operating expenses (excluding capex, debt service, depreciation).
FFO (Funds From Operations, NAREIT 2003 definition): NI + depreciation + amortization − gains on sales. Preferred REIT P&L metric since GAAP depreciation overstates economic cost.
AFFO: FFO − recurring capex − straight-lined rent adjustments.
1031 exchanges (IRC §1031): defer capital gains by reinvesting in like-kind real property within 180 days. Tightened post-TCJA to real estate only.
Cost segregation: accelerated depreciation by separating shorter-life components (5/7/15 year MACRS vs 27.5/39 year). Bonus depreciation phasing down: 100% (2017–2022), 80% (2023), 60% (2024), 40% (2025).
Depreciation recapture: §1250 recapture taxed at max 25% on sale.

23. Crypto investments (brief — see cryptography for tech)

BTC institutional adoption: spot ETFs Jan 2024 — IBIT, FBTC, ARKB, BITB, HODL, BTCO + Grayscale GBTC conversion. Net inflows in first year exceeded $35B.
ETH ETFs approved May 2024 — ETHA (BlackRock), FETH (Fidelity).
Stablecoin macro role: USDT + USDC + DAI > $250 B f l o a t = s i ze ab l e h o l d ero f s h or tT re a s u r i es . T e t h e r^{'} s h o l d in g s ($ 120B 13F-style portfolio) make it among top T-bill holders globally.
MicroStrategy (Michael Saylor) accumulated >$30B of BTC funded by convertible bonds + ATM equity — corporate-treasury BTC vehicle play.
Regulatory: SEC v. Coinbase, SEC v. Binance, SEC v. Ripple (2023 partial summary judgment; XRP not a security in programmatic sales). GENIUS / FIT21 / STABLE Acts in flight; CLARITY Act passed House 2025.

24. Common quantitative tools

Excel + VBA: still the lingua franca of buy-side and sell-side analysts.
Python: NumPy, pandas, SciPy, statsmodels, scikit-learn, PyPortfolioOpt, riskfolio-lib, Zipline, Backtrader, QuantLib-Python, vectorbt, mlfinlab.
R: PerformanceAnalytics, PortfolioAnalytics, quantmod, xts, zoo.
Bloomberg Terminal (~$28k/yr/seat): de facto standard. BBG Anywhere, BQuant, BQNT.
Refinitiv Eikon / LSEG Workspace, FactSet, S&P Capital IQ, Morningstar Direct, YCharts, Koyfin.
Risk systems: BlackRock Aladdin (~$22T assets on platform), MSCI BarraOne / RiskMetrics, Bloomberg PORT/MARS, Axioma, Northfield.

25. Key open problems and active debates

Equity premium puzzle: 6%+ historical equity excess return implies implausibly high risk aversion in standard CCAPM. Resolutions: rare disasters (Barro 2006), Epstein-Zin preferences, ambiguity aversion, long-run risk (Bansal-Yaron).
Bond term-premium dynamics: Adrian-Crump-Moench 5-factor model standard, but estimates noisy.
Factor decay: every published anomaly has weakened post-publication (McLean-Pontiff 2016). Are factors structural risk premia or behavioral mispricings?
Private markets transparency: PE NAV smoothing, VC mark-to-market vs mark-to-fantasy, secondaries pricing gaps.
Concentration risk: 30%+ of S&P 500 market cap in 10 names (2024–2025). Index investors involuntarily long mega-cap tech.
Climate risk pricing: physical + transition risk integration into long-bond and equity valuation. Stranded-asset risk for oil & gas.
AI in investing: signal generation, alternative data (satellite imagery, credit card panels, app downloads), Renaissance/Two Sigma applied ML for decades; LLM-based research workflows emerging 2023+.

Adjacent

corporate-finance-and-markets — capital structure, M&A, IPO mechanics, dividend policy.
derivatives-and-quant-finance — options pricing, Black-Scholes, Greeks, structured products, risk-neutral measure.
accounting-foundations — financial statement mechanics underlying any valuation.
behavioral-economics — Kahneman/Tversky/Thaler foundations; loss aversion, overconfidence, mental accounting.
macroeconomics — yield-curve drivers, monetary policy, business cycle context.
probability-and-statistics — distributions, hypothesis testing, regression, time-series mechanics underpinning σ/β/factor models.
optimization-and-numerical-methods — quadratic programming for MV optimization, convex optimization for robust portfolios.
cryptography — cryptographic primitives underlying BTC, ETH, stablecoins, custody.
securities-and-corporate-law — ‘33 Act, ‘34 Act, Reg D, Reg A+, ‘40 Act fund regulation, fiduciary duty.

Compendium

Explorer

Investments & Portfolio Management — Asset Classes, MPT, CAPM, Performance