Risk management is the discipline of deciding, before a trade is taken, how much can be lost and how that loss is contained; position sizing is its central lever — the rule that converts a risk decision into a share count. Together they govern survival and the shape of the equity curve, which is a separate question from edge (whether your entries have a statistical advantage at all). The defining truth of this whole domain, repeated from Tharp to the gambler's-ruin mathematicians, is that a positive-expectancy system can still bankrupt you if it is sized too large, while a mediocre system sized conservatively can survive indefinitely. Edge tells you whether to play; risk management tells you whether you will still be at the table to collect on it. This section maps the standard toolkit at section-overview altitude — each named technique has its own child doc with formulas, defaults, and failure modes; the job here is to show how the pieces fit and when each matters.

The core tension

Every tool in this domain trades growth against survival. Bet bigger and the equity curve compounds faster — until a normal losing streak, amplified by the larger size, produces a drawdown deep enough to force capitulation or trigger forced liquidation. The mathematics is asymmetric in two directions that recur throughout the children: (1) overbetting ruins, underbetting only slows — the penalty for sizing too large is catastrophic and permanent, the penalty for sizing too small is merely slow compounding (see Kelly and Risk of Ruin); and (2) drawdown recovery is non-linear — a 50% loss requires a 100% gain to undo (Drawdown & Recovery). Because the downside is the steep side of both curves, the entire field is biased, correctly, toward conservatism: this is why the retail 1–2% rule survives despite being "suboptimal" by growth-maximizing math.

When it matters vs. when it doesn't

Risk management is most decisive for leveraged, concentrated, or high-frequency activity — anywhere a string of losses can compound quickly against borrowed capital or a hidden common factor. It matters less for a small, fully-paid, broadly diversified long-only book held over years, where per-trade sizing is dominated by simple diversification and the main risk (systematic/market risk) cannot be sized away at all (Diversification, Index Hedges). A common error is applying gambler's-ruin urgency to a buy-and-hold index portfolio (where it is mostly irrelevant) while ignoring it in an aggressive, correlated swing book (where it is everything).

Map of the sub-topics

Position Sizing — how many shares. The base method is fixed-fractional sizing (the "1% rule": shares = risk budget ÷ stop distance), prized for robustness because it needs no estimate of edge. The edge-weighted alternative is the Kelly criterion, broken into full vs. fractional Kelly (full Kelly is growth-optimal only with known inputs and produces unbearable drawdowns, so practitioners use ½ or ¼), estimating edge & odds (the inputs are never known, only noisily estimated — the real danger), and risk of ruin (why low fractions survive). Volatility-based sizing scales share count inversely to ATR so every position carries equal dollar risk.

Stop-Loss Strategies — where to exit when wrong. Ordered roughly from crudest to most principled: fixed-percentage stops (a constant 7–8% / 10%, blind to volatility), volatility/ATR stops (a multiple of recent range), structure-based stops (just beyond the chart level that would invalidate the thesis — the most logical, sometimes the most run), time stops (an opportunity-cost exit, not a loss-control tool — a frequently muddled distinction), and trailing stops (the "let winners run" ratchet, with no free lunch between tight and loose).

R-Multiples & Expectancy and Risk/Reward & Win Rate — the profitability arithmetic. R restates every outcome in units of initial risk; expectancy is the average R per trade. The key lesson across both: win rate and reward:risk are each meaningless alone — only their fusion (expectancy) says "profitable or not," and the number is a noisy sample estimate, easily flattered by a few outliers.

Portfolio-Level Risk — risk that per-trade rules miss. Correlation & concentration risk (five 1% positions driven by one factor are a single 5% bet), Value at Risk (a loss threshold, not a worst case — silent about the tail), and drawdown & recovery (the risk a trader actually experiences and the trigger for capitulation).

Hedging Techniques — offsetting exposure rather than reducing it. Protective puts (paid insurance with a persistent long-run drag), index hedges (neutralize beta cheaply with futures or expensively with puts), pairs & market-neutral (trade market risk for convergence risk), and inverse ETFs (a precision daily tool whose reset causes multi-day drift — most harm comes from holding them long).

Leverage & Margin — the amplifier and its forced-liquidation tail risk. Diversification — the one "free lunch," which removes idiosyncratic risk but does nothing about systematic risk.

Standing & evidence

This domain is the least contested part of the broader markets corpus: there is broad agreement — academic, institutional, and retail — that controlling per-trade risk and surviving drawdowns is necessary, and the survival mathematics (gambler's ruin, Kelly's geometric-growth result) is rigorous, not folklore. The genuine disputes are about calibration, not principle: the right Kelly fraction, whether the 1–2% rule is optimal or merely safe, and whether VaR's tail-blindness makes it dangerous. One honest caveat for the corpus: the often-quoted Tharp figures that "position sizing accounts for ~60% of trading success" or "90% of professional performance variation" are widely repeated illustrative claims, not rigorously established statistics — treat them as motivational framing, not measured fact. (The "90%" is frequently traced to Brinson, Hood & Beebower's 1986/1991 studies, but those measured the variance explained by asset-allocation policy in institutional pension portfolios — a different, and itself heavily contested, finding that does not establish a number for trader position sizing.) The defensible, sourced version of the point is narrower and solid: given a fixed sequence of trade outcomes, position sizing alone produces enormous variation in final equity and risk of ruin.

System relevance

This section is the risk spine the Augustus trade-setup agent sits on. A setup is not actionable until it carries a stop (from ATR or structure-based stops) and a size (from fixed-fractional sizing): shares = (equity × risk%) / (entry − stop). Per-trade sizing must then be checked against the portfolio-level children — Augustus should refuse to treat correlated setups as independent 1% bets — and every realized outcome should be logged in R-multiples so Cairn's measured track record is expressed as expectancy across regimes. The hard caveat threaded through all the children: every guarantee ("I only risk 1%") assumes the stop actually fills, which gaps, halts, and earnings can break.

Sources

• Van K. Tharp, Trade Your Way to Financial Freedom (1999) and The Definitive Guide to Position Sizing Strategies (2008) — position sizing vs. entry, expectancy, R-multiples. (vantharpinstitute.com; TraderLion summary)
• Note on the "60% / 90%" figures: widely repeated illustrative claims attributed to Tharp (vantharpinstitute.com; Medium / theoptionpremium.com summaries) — qualified as motivational, not measured. The "90%" echoes Brinson, Hood & Beebower (Determinants of Portfolio Performance, Financial Analysts Journal 1986/1991), which measured asset-allocation-policy variance in pension funds — a contested, unrelated finding (see Ibbotson & Kaplan 2000 critique).
• Risk-of-ruin / overbetting: backtestbase.com, journalplus.co, liberatedstocktrader.com — positive-edge-still-ruins and the exponential RoR response to larger size.
• Classical gambler's-ruin and Kelly geometric-growth results — survival mathematics (cross-referenced in child docs).
• Markowitz — diversification as the "only free lunch"; systematic vs. unsystematic risk (cross-referenced in Diversification).