Pôle Thématique · 20 Notes Publiées
Kelly Margin Leverage Sizing research topics and source records from QuantCalc Tools. Position sizing and margin mechanics dictate whether a positive-expectancy edge compounds exponentially or hits forced liquidation; this quantitative hub unifies Kelly math, CCP margin, and close-out thresholds.
Position sizing and margin mechanics dictate whether a positive-expectancy edge compounds exponentially or hits forced liquidation; this quantitative hub unifies Kelly math, CCP margin, and close-out thresholds.
Textbook f* = p - q/b assumes losing 100% of staked capital on every losing trade; derive the exact generalized asymmetric stop-loss Kelly formula f* = p/a - q/b for real financial markets.
Under geometric Brownian motion, continuous log-optimal leverage equals excess arithmetic drift divided by variance; prove the exact c*(2-c) fractional Kelly parabola and Sharpe^2 growth ceiling.
Multi-asset Kelly weights f* = Sigma^(-1)*(mu - r_f) point in the exact direction of the Markowitz Maximum-Sharpe Tangency Portfolio; master eigenvalue condition numbers and Ledoit-Wolf shrinkage.
Trading at Full Kelly carries an exact 50% probability of losing half your capital and a 20% probability of an -80% crash; derive exact fractional Kelly drawdown probability laws to cap tail pain.
Under UK FCA COBS 22.5 and ESMA product intervention rules, retail CFD and FX accounts face tiered 3.33%–50% initial margin floors plus mandatory automated liquidation at 50% of total Initial Margin.
Liquidation fires at the Maintenance Margin threshold BEFORE your equity hits the zero-equity Bankruptcy Price; master exact isolated vs cross-margin liquidation formulas and fee buffers.
Cleared futures margin migrated from 1988 16-scenario SPAN grids to CME SPAN 2 Historical VaR; master exact Pod aggregation, concentration add-ons, and full-Initial-Margin top-up calls.
Why did the entire global banking system converge on one single open-source sensitivity formula for uncleared swaps and FX options? Master exact ISDA SIMM v2.6 variance-covariance aggregation.
Assuming 1 standard FX lot always equals $10.00 per pip over-sizes EUR/GBP trades by +27% and mis-sizes USD/JPY by +52%; master exact three-case quote-to-account currency lot sizing math.
Under static Reg T rules, a fully delta-hedged stock-plus-put collar still locks 50% initial margin, whereas FINRA Rule 4210 Portfolio Margin prices worst-case -15%/+15% TIMS stress.
Betting a constant $2,000 per trade carries an exponential Markov absorption Risk of Ruin (q/p)^N, whereas scaling risk dynamically as a fixed percentage of live equity transforms ruin geometry.
Opening a 1.0x Short Inverse Coin-Margined perpetual CANNOT be liquidated even if price rises to infinity, while a 2.0x Long Inverse perpetual gets wiped out on a -33.3% drop—not -50%!
Equal-dollar portfolios let volatile equities and commodities dictate 88% of P&L variance; master exact Wilder ATR stop sizing, Inverse-Volatility weights, and Equal Risk Contribution (ERC) math.
Solvency does not guarantee survival when intraday CCP Variation Margin must settle in T+0 cash; derive Brunnermeier-Pedersen margin spirals and stress-tested liquidity buffer math.
Real trading logs contain partial exits, scratch trades, and fat-tailed outliers rather than two neat binary outcomes; derive Ralph Vince Optimal f and largest-loss contract scaling.
Selling far out-of-the-money naked puts locks deceptive 10% minimum margin in calm markets—until a -12% crash triggers a 450% margin explosion from simultaneous spot, OTM, and Vega shocks!
A 2.0% Treasury repo haircut unlocks 50x theoretical balance-sheet leverage—until a haircut hike to 6.0% forces an instant two-thirds fire sale; master exact repo carry and haircut-run math.
Feeding raw historical sample means into multi-asset Kelly creates wild corner portfolios; anchor expected returns in Black-Litterman market equilibrium and scale views by Bayesian posterior precision.
Standard stop-loss orders turn into market orders on a Monday morning gap and fill 400 pips worse; prove how Guaranteed Stop-Loss Orders (GSLOs) replicate barrier put options and cap margin!
CAGR calculator →
Compound annual growth rate between two values, with a year-by-year projection.
FX forward rate calculator →
Forward exchange rate and forward points from spot and two interest rates (covered interest parity).
Value at Risk (VaR) calculator →
Parametric VaR and Expected Shortfall for a position, at 95% or 99% confidence.
Two mathematical reasons: first, Full Kelly assumes you know true expected return mu and volatility sigma with zero estimation error—whereas overestimating mu by 2x accidentally pushes you onto the 2.0*f* zero-growth cliff! Second, even with known parameters, Full Kelly endures a 1/k probability of shrinking equity to 1/k (a 50% chance of a -50% drawdown).
Initial Margin (IM) is the collateral required to open a position; Maintenance Margin (MM) is the minimum equity floor required to keep it open. If a futures account dips $1 below MM, you must wire cash all the way back up to full IM; if a Reg T equity margin account dips below 25%/30% MM, you only top back up to MM.
Cross-margining lowers the probability that a single noisy wick liquidates one small position (by sharing free equity across the whole account), BUT if an un-stopped runaway trade breaches cross-margin maintenance, it liquidates your ENTIRE account balance rather than capping loss at one isolated margin bucket!
Under post-2008 BCBS-IOSCO uncleared margin rules, both Dealer A and Institutional Client B must post 99% 10-day SIMM Initial Margin into segregated third-party custodians so that if either party defaults, surviving close-out replacement risk is funded without creating systemic contagion.
Kelly examined a gambler receiving a noisy binary communication channel with crossover error probability q = 1 - p! On even-money odds (b = a = 1), optimal bet f* = p - q = 2p - 1 yields maximum asymptotic exponential growth rate ln(2) + p*ln(p) + q*ln(q)—which is literally Shannon’s channel capacity in nats per transmission!
A negative Kelly fraction (for example, p = 60%, q = 40%, R = 0.50 -> r* = 0.60 - 0.80 = -0.20) proves your strategy has NEGATIVE mathematical expectancy (0.60*0.50 - 0.40*1 = -$0.10 per $1 risked)! Unless you can take the opposite side of the trade (excluding transaction costs), optimal allocation is strictly f* = 0.