How should inventory change your quotes?

Question

You make markets in a stock you believe is worth $100.00$ . Through random two-sided flow you've become long $20{,}000$ shares, larger than you'd like. You still think fair value is exactly $100.00$ .

How do you set your bid and ask now, versus when you were flat? Explain the principle.

Accepted Answer

Shift both quotes down, skew. Flat, you might quote 99.96 / 100.04, symmetric around fair. Long 20{,}000 shares, quote something like 99.93 / 100.01: - Your ask at 100.01 is now aggressive (only 1 cent above fair), you're offering a bargain to buyers because a sale reduces your risk. You accept less edge per trade in exchange for a better risk profile. - Your bid at 99.93 is defensive, you'll still buy, but only if paid well for adding to an oversized position. The clean way to formalize it: your reservation price, the price at which you're indifferent to trading, is no longer fair value. Wit…

How should inventory change your quotes?

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