Inventory and P&L

Idea: What a trade leaves behind

Edge comes at the trade. What stays is a position, and the price moves it.

• Long: net lots you own. Short: net lots you owe
• Marking to the close values the open lots at the closing price
• A real sale would go through a bid, below that mark

Example: Realised and unrealised

Buy $10$ lots at $50$, sell $4$ at $52$, close at $49$. Total profit and loss?

1. Position: $10-4=6$ long
2. Closed lots: $4\times (52-50)=8$
3. Open lots: $6\times (49-50)=-6$, total $8-6=2$

Formula: One line per fill

$\text{buy}:n\times (M-p),\text{sell}:n\times (p-M)$

Compare each fill of n lots at price p with the mark M. No matching of buys to sells.

Common mistake: Reporting only closed trades

The realised $8$ looks healthy, yet the book is up only $2$: the open lots lost money.

Instead Total profit always includes the position, valued at the mark.

Idea: Lean your quotes

A position turns spread trading into a price bet. Skew both quotes the same way so customers help you out.

• Long $6$: each move of $1$ against you costs $6\times 1=6$
• Long: shift both quotes down. Short: shift both up
• Same width, new centre, fair value unchanged

Example: A skewed quote

Long $6$, fair value $49$, half-spread $1$, shift $0.1$ per lot. Where is the bid?

1. Ask: $49+1-0.1\times 6=49.4$
2. Bid: $49-1-0.1\times 6=47.4$

Quick check: Edge on the reducing trade

With that quote, $47.4$ bid, $49.4$ ask and fair value $49$, what is your edge per lot on a sale?

Idea: Say it out loud

Say your position first, then how you value it: "I am long $6$, marked at $49$."

• Heavy book: say you are leaning, not changing your view
• Recompute both quotes after every fill