Risk management

Analysis decides what to buy; risk management decides how much, and how much is the decision that determines survival. The uncomfortable truth of professional investing is that the second decision matters more: a mediocre picker with great sizing outlasts a great picker with mediocre sizing, because the great picker is eventually wrong big, once, and once is enough.

The arithmetic of ruin

Why the downside is not symmetric

lose 10% -> need +11% back     lose 33% -> need +50%
lose 50% -> need +100%         lose 90% -> need +900%

and the compounding version: a strategy that returns +30%/-20% in
alternating years averages +5% and COMPOUNDS at +2%: the drawdowns
eat the average. Survival is not a constraint on returns; over long
horizons it is the source of them.

Position sizing: the unit of risk, not the unit of money

The professional habit is sizing in risk units: decide what fraction of capital a position may plausibly cost you, then let that budget and the position's risk set the dollars.

Two standard sizing rules

risk-budget sizing:
  size = (capital x risk per position) / expected drawdown of the position
  e.g. 1% budget, position could plausibly fall 25% -> size = 4% of book

volatility-parity sizing:
  size ∝ 1 / asset volatility
  the 60% vol asset gets a quarter the dollars of the 15% vol asset,
  so each contributes similar risk (crypto sizes itself this way)

Conviction scales within a band, not to infinity. Funds run tiers (1-2% starters, 5% high conviction, hard caps at 8-10%) because certainty is exactly what the worst losses felt like from the inside.
Correlated positions are one position. Five AI stocks are one bet with five tickers; the book's real concentration is by DRIVER (rates, one customer, one theme), not by line count.
Liquidity bounds size. A position you cannot exit inside days without moving the price is bigger than its percentage suggests.

Kelly: the ceiling, not the target

The Kelly criterion

f* = edge / odds     (for a simple bet: p - (1-p)/b)

f* maximizes long-run compound growth IF your edge estimate is exact.
overbetting f* does not just add risk, it REDUCES growth, and 2x Kelly
compounds to ruin. Since edges are estimated (and overestimated),
practitioners run quarter-to-half Kelly, and read f* mostly as a CAP:
"never above this even when certain", because certainty is the tell.

The efficient frontier, as a risk tool

The frontier and the full construction menu (mean-variance and its error-maximizing failure, minimum variance, Black-Litterman, risk parity, volatility targeting, equal weight) are treated in full in Portfolio optimization. From the risk side, three of its lessons do the daily work:

The marginal question. Never "is this asset good?" but "does the book's return-per-risk improve when I add it at this size?" An excellent asset correlated with everything you own can move the portfolio BELOW its frontier.
Diversification is the cheapest risk reduction, and the amount you hold is set by correlation, not by position count: ten positions on one driver are one position.
Choose the construction method by what you can estimate. Confident views deserve Black-Litterman discipline; no views deserve risk parity or equal weight; and pretending to precision you lack is how optimizers maximize your errors.

Drawdown control: rules that bind the future self

Rule	Mechanism	Cost
Drawdown ladder	At -5% book: no adds. At -10%: gross halved. At -15%: flat, full review	Sometimes de-risks right before recovery
Volatility targeting	Scale gross down as realized vol rises	Sells after losses by construction
Tail hedges	Small standing budget for far OTM puts	A drag most years; pays in the year that matters
Cash as a position	Unspent risk budget is dry powder, not failure	Underperforms in melt-ups

Every rule above costs expected return; that is not a flaw. Each is an insurance premium against the state of the world in which decisions get made by a person mid-drawdown, who is measurably not the person who set the rules. Funds enforce these through a risk officer with authority precisely because self-enforcement fails when it is needed; individuals must be their own, which is why the rules are written down, dated, and boring.

Risk management is what remains when you are wrong

Every technique on this page assumes the thesis has failed: sizing assumes some positions lose, the falsifier assumes this one might, the ladder assumes several fail together, the tail hedge assumes the correlations betray you too. None of it is pessimism. It is the machinery that lets you take real risk with the part of the portfolio that should, because the whole can survive the outcome. Confidence in the thesis is never a reason to skip it; confidence is a property of every disaster's owner, the morning before.

Glossary for this guide

Risk budget: The loss a position or book is permitted to plausibly cost, decided before entry. Sizing in risk units instead of dollars is the professional habit that keeps one mistake survivable.
Position sizing: How much. The decision that determines survival, made by rule (risk budgets, volatility parity, caps) precisely because the moments it matters most are the moments judgment is worst.
Kelly criterion: The bet fraction that maximizes long-run compound growth IF the edge estimate is exact. Overbetting it reduces growth and doubles toward ruin; practitioners run fractions of it and read it as a ceiling.
Correlation: How much two assets move together, from -1 to +1. The input diversification lives on, and the one that betrays you: correlations measured in calm lurch toward one in a crash.
Efficient frontier: The upper-left edge of all possible portfolios: no more return without more risk, no less risk without surrendering return. The durable use is the marginal question: does adding this asset move the frontier up?
Risk parity: Weighting so each asset contributes equal RISK rather than equal dollars: a 60/40 is ~90% equity risk in disguise. Honest about diversification; dependent on leverage and on bonds staying diversifiers, which 2022 tested.
Black-Litterman: Start from the market portfolio's implied returns as the neutral prior; tilt only where you hold explicit views, in proportion to stated confidence. The institutional standard for blending judgment with structure without letting the optimizer run wild.
Volatility targeting: Holding the portfolio's risk level constant by scaling exposure down in storms and up in calm. Changes when you take risk rather than where; sells after losses by construction.
Maximum drawdown: The deepest peak-to-trough loss in a period. The risk number investors quit over, and the one with cruel arithmetic: -50% needs +100% to repair.
Tail hedge: A standing position whose job is to pay in crashes: far out-of-the-money puts, long volatility. A drag most years by design; the premium buys the year that matters.
Dry powder: Unspent capacity, held on purpose: cash or unused risk budget available when prices are best. Not a failure to be invested; an option on everyone else's forced selling.
Gross and net exposure: Gross is longs plus shorts (total capital at work, leverage included); net is longs minus shorts (directional bet). The two dials a book's risk is actually steered with.