Risk & Position Sizing

Learning objectives

By the end you can:

1. State the two definitions of risk and judge when each applies. Give the practitioner's definition (risk = the probability and magnitude of a permanent loss of capital) and the academic one (risk = volatility / beta), explain why the difference is not semantic, and argue fairly for the case where volatility genuinely is risk (when you might be a forced seller).
2. Formalize risk as probability × magnitude of impairment and explain Howard Marks's central point: that risk is an ex ante property of a decision that is largely invisible, cannot be read off a track record, and is not the same as the volatility you can measure after the fact.
3. Use the margin of safety as your primary risk-control tool and connect it directly to sizing: a wider margin of safety shrinks the downside d, which mathematically justifies (but never mandates) a larger position.
4. Name and detect the four ways capital is permanently impaired (business deterioration, overpaying for a good business, leverage/forced selling, and fraud) and map each to the diagnostics you already own from Phases 1–5.
5. Size a position with Kelly and fractional Kelly. Re-derive f* from the growth-of-wealth objective, compute it for capped-downside investments (f* = p/d − q/u), read the geometric-growth curve, and justify half- or quarter-Kelly from estimation error, drawdown tolerance, and correlation, showing numerically that double Kelly earns zero growth.
6. Apply the conviction × downside heuristic, bigger where conviction is high and downside small, smaller or pass where either fails, using a sizing matrix that embeds an implicit "no single mistake costs more than ~2.5% of the portfolio" rule.
7. Decompose apparent diversification into factor exposure. Show why 30 names loaded on one factor (Indian NBFCs, US regional banks, oil) is one bet, compute the correlation floor σ√ρ and the effective number of independent bets n/[1+(n−1)ρ], and resize to a factor cap.
8. Apply the anti-ruin overlay. Set single-name and factor caps, refuse leverage that can force selling, size smaller under Knightian uncertainty than under quantifiable risk, and explain why survival is a mathematical (ergodic), not a merely prudent, first-order goal.

Prerequisites & connections

Builds on. M6.03 (Mental Models & Decision Science) is the direct parent: it derived the intuition of Kelly (f* = (b·p − q)/b, read as edge/odds), the investing generalization (f* = p/d − q/u), the risk-vs-uncertainty distinction (Knight), and ergodicity/ruin-avoidance, all as theory. This module is the practice: the same tools re-derived a little deeper and turned into a live sizing policy you can run on a real position tomorrow. M6.01 (Graham to Buffett) gave you the margin of safety as a valuation idea; here it becomes a sizing idea. M6.02 §4.9 staged the concentration-vs-diversification debate and Pabrai's Dhandho asymmetry ("heads I win, tails I don't lose much"); this module supplies the mathematics that adjudicates both. M3.02 (Risk, Return & the ERP) is where you met the academic definition of risk (variance, beta, CAPM, the efficient frontier), which we now put in honest dialogue with the practitioner's definition. M2.03 (Returns on Capital) and M2.07 (fraud screens) supply the impairment diagnostics; M5.01–M5.02 (banks, NBFCs) supply the canonical hidden-correlation factor (Indian credit); M3.05 (reverse DCF) is how you quantify "what's priced in," which is the raw material for estimating the downside d.

Feeds forward. M9.02 (Portfolio Construction) takes single-position sizing and assembles the book (opportunity-cost hurdles, cash as a position, the factor menu, active vs passive) using the factor-exposure lens built here. M9.03 (Selling & Mistakes) adds "position grown beyond tolerance" as one of the five legitimate sell triggers, which is this module's caps enforced through time. M9.04 (The Process) wires sizing into the checklist → journal → calibration loop. Phase 10's capstones require a sized recommendation, not just a valuation: a thesis with no position size attached is graded incomplete. And the app's portfolio simulator scores you, from here on, on whether your sizes were survivable and process-consistent, never on whether they happened to pay.