How much inventory before you must hedge?

Question

Your desk is comfortable risking about \50{,}000 of one-day P&L swing on any single position. The stock you make markets in has a daily volatility of \2.00 per share (one standard deviation). Right now, after a wave of one-sided selling, you find yourself long 30{,}000 shares. What's your inventory limit in shares? Are you over it, and if so, what do you do?

Accepted Answer

Turn the dollar limit into shares. Your one-day risk from holding q shares is roughly 	ext{risk} = q 	imes \sigma = q 	imes \2.00. Setting that equal to your \50{,}000 tolerance: q{\max} = \frac{50{,}000}{2.00} = 25{,}000 	ext{ shares.} So your comfortable inventory limit is 25{,}000 shares (long or short). Are you over? You're long 30{,}000, which is 5{,}000 over the limit. Your current one-day risk is 30{,}000 	imes 2 = \60{,}000, above tolerance. What to do. Two levers, usually used together: 1. Skew hard to attract sellers-to-you off and buyers-of-yours on, bias your quotes down so t…

How much inventory before you must hedge?

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