Back out the imbalance from a microprice

Question

A stock is bid 100.50 and offered at 101.00. A colleague tells you the book's microprice is 100.80 but does not give you the resting sizes. What fraction of the top-of-book size is sitting on the bid? What does that say about the likely next tick?

Accepted Answer

The microprice can be written as the bid plus a fraction of the spread, where the fraction is the bid's share of total resting size: P{	ext{micro}} = P{	ext{bid}} + (P{	ext{ask}} - P{	ext{bid}})\,I, \qquad I = \frac{Q{	ext{bid}}}{Q{	ext{bid}} + Q{	ext{ask}}}. Solve for I: I = \frac{P{	ext{micro}} - P{	ext{bid}}}{P{	ext{ask}} - P{	ext{bid}}} = \frac{100.80 - 100.50}{101.00 - 100.50} = \frac{0.30}{0.50} = 0.6. So 60\% of the top-of-book size rests on the bid. For instance, if there are 1000 shares total, that is 600 bid and 400 ask; any split with the bid holding 60\% produces the sa…

Back out the imbalance from a microprice

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