@vince.quant: How do you sell 1 million shares without crashing the price? Trade too fast and you move the market against yourself through market impact. Trade too slowly and you remain exposed to price risk while you still hold the position. In their 2000 paper, Almgren and Chriss formalized this problem by minimizing expected execution cost plus a risk penalty. The result is a closed-form optimal liquidation schedule. A risk-neutral trader (λ = 0) gets a simple TWAP: equal slices over time. As risk aversion increases, the schedule becomes increasingly front-loaded, selling more shares early to reduce exposure. The key parameter is κ (kappa): higher volatility, higher risk aversion, or higher liquidity all push the trader to exit faster. Why this matters: the intuition behind Almgren-Chriss still sits underneath many arrival-price and optimal execution algorithms used by institutional trading desks today. Limitations: Assumes linear temporary and permanent market impact, while real market impact is often nonlinear and concave. Uses a static execution schedule fixed in advance, without reacting to realized price moves. Assumes an arithmetic Brownian motion with constant volatility and no drift. Measures risk using variance only, ignoring tail risk and extreme events. Source: Almgren & Chriss (2000), Optimal Execution of Portfolio Transactions. #finance #quant #trading #algotrading #stocks

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Tuesday 16 June 2026 23:20:31 GMT