How does inventory risk affect market-maker quotes?

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AcadiFi · Accepted Answer

Market makers hold inventory from trading and face price risk until they can offset. Risk-averse MMs demand compensation: the larger their current inventory (positive or negative), the more they shade quotes to encourage offsetting trades. Stoll (1978) model: optimal spread proportional to price volatility, inventory size, and risk aversion. Simplified: inventory_premium = gamma * sigma^2 * |I|, where gamma is risk aversion, sigma price volatility, and I current inventory. Example: Bayshore Equipment MM has current long inventory of 50,000 shares of a stock with daily vol $0.80, gamma=0.05. Inventory premium = 0.05 * 0.80^2 * 50,000 = $1,600 implicit cost, translating to quote shading of ~$0.032 on typical lot size. Behaviorally, when inventory is long, MM lowers both bid and ask (asymmetric shading) to encourage sells to them and discourage buys from them. When short, MM raises both. The 'reservation price' moves with inventory. The resulting spread is widened at the reference midpoint but the quotes are skewed. ```mermaid flowchart LR A[Long inventory] --> B[Lower both quotes
encourage sales] C[Short inventory] --> D[Raise both quotes
encourage buys] E[Balanced] --> F[Tight symmetric spread] ``` Risk management: inventory risk creates endogenous liquidity cycles. After a large one-sided trade, MM inventory deviates from zero, spreads widen, and follow-on trades cost more — explaining momentum in execution costs after news. Algorithmic traders model MM inventory to predict short-term spread dynamics and time submissions.

How does inventory risk affect market-maker quotes?

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