Quotes and edge

Idea: A price each way

You name a bid to buy and an ask to sell. The customer picks the side.

• Value $50$, quote $49$ bid, $51$ ask
• Mid $\frac{49+51}{2}=50$, spread $51-49=2$
• Your protection: the gap and the quality of your fair value

Formula: Edge when a customer buys

$\text{edge}=n\times (A-F)$

Sold at your ask A against fair value F, on n lots.

Formula: Edge when a customer sells

$\text{edge}=n\times (F-B)$

Bought at your bid B below fair value F, on n lots.

Example: Edge on both sides

Fair value $50$, quote $49$ bid, $51$ ask. A customer buys $5$ lots, another sells $3$. Your total edge?

1. Sold $5$ at $51$: $5\times (51-50)=5$
2. Bought $3$ at $49$: $3\times (50-49)=3$
3. Total: $5+3=8$

Common mistake: Edge against your own mid

Quote $47$ bid, $48$ ask, mid $47.5$: a sale at $48$ seems to earn $0.5$.

Instead Measure against fair value. At $50$ that sale loses $48-50=-2$ per lot.

Formula: The microprice

$\text{micro}=\frac{B\times Sa+A\times Sb}{Sb+Sa}$

Each price weighted by the size on the other side. A rule of thumb, not a law.

Quick check: Lean toward the thin side

Book: $99$ bid for $3$ lots, $101$ ask for $1$ lot. What is the microprice?

Idea: Wide or tight

A wider quote earns more per trade and gets fewer trades.

• Invented numbers: $100\times 1=100$ beats $30\times 2=60$
• Widen when unsure, when the customer may know more, or when long already
• Equal flow on both sides: edge per lot $\frac{0.5+2}{2}=1.25$

Idea: Say it out loud

State your fair value first, then quote around it, then name your edge on each side.

• Say why the width is what it is
• Asked to tighten? Say what you give up per lot