The toll booth

Every market shows two prices: the bid, where you can sell, and the ask, where you can buy. The spread is ask minus bid, and the mid is the price halfway between them. A position is only worth what you mark it at, and the usual interview convention is to mark to market at the mid. Buying at the ask and marking at the mid therefore shows an instant loss of half the spread per unit: the price of crossing the market. Profit and loss is always the quantity times the move in your favour: mark minus entry for a long, entry minus mark for a short.

Words you need

Bid and ask: The bid is the highest price a buyer is offering right now; the ask (also called the offer) is the lowest price a seller will take. To sell immediately you sell at the bid; to buy immediately you buy at the ask.e.g. A market '99 at 101': bid 99, ask 101.
Spread: Ask minus bid: the gap between the two prices.e.g. 99 at 101 has a spread of 2.
Mid: Halfway between bid and ask. Usually used as the fair mark of a position.e.g. 99 at 101 has mid 100.
Position (inventory): What you currently hold. +3 means you own 3 units; −3 means you sold 3 you did not own (short).
Long and short: Long: you own it and gain if the price rises. Short: you sold it without owning it and gain if the price falls.
P&L: Profit and loss: how much money a trade or position has made or lost.

Why it works

A long position gains when the mark rises above its entry price, and a short position gains when the mark falls below its entry price. The quantity scales the per-unit gain.

long P&L = qty × (mark - entry); short P&L = qty × (entry - mark)

Spot it: You are given a bid and ask and asked for the spread or the mid.

Technique reference and sources

Picture the market as a toll booth with two gates. You pay the ask to buy and receive the bid to sell, and the gap between them is the toll. The mid is the centerline of the road, a neutral place to mark your position. Buy 300 at the ask of 10.20 with the mid at 10.00 and you are 0.20 per unit behind the moment you pay: 300 × (10.00 - 10.20) = -60.

When this method fits

You are given a bid and ask and asked for the spread or the mid.
You must value a position after a trade or after the market moves.
An interviewer asks how much you are up or down on a fill.
You need to check the sign of a P&L before reading the number.

Read the market. Write bid and ask, then compute spread = ask - bid and mid = (bid + ask) / 2.
Fix your side. You bought if you lifted the ask, so you are long. You sold if you hit the bid, so you are short.
Pick the mark. Mark at the mid unless the problem says otherwise. Marking a long at the bid is the stricter exit view.
Apply the sign rule. Long: qty × (mark - entry). Short: qty × (entry - mark). Check the sign by asking whether the market moved toward you.

Spread and mid: Spread is the ask minus the bid; the mid is the average of the two.

10.20 - 9.80 = 0.40
(9.80 + 10.20) / 2 = 10
101.50 - 100.50 = 1

Long position: A long is worth mark minus entry per unit, times the quantity.

300 × (10 - 10.20) = -60
100 × (52 - 50) = 200

Short position: A short is worth entry minus mark per unit, times the quantity.

200 × (4.95 - 5) = -10
50 × (30 - 28) = 100

Common traps

Flipping the sign for a short position by using mark minus entry. A short gains when the price falls. Use entry minus mark: selling at 8.40 and marking at 8.10 gives 250 × (8.40 - 8.10) = 75, a gain.

Reporting the spread as the loss on a trade instead of half the spread. Crossing the market and marking at the mid costs half the spread per unit. With a 0.40 spread the loss is 0.20 per unit.

Computing the mid by averaging the wrong two numbers, such as the last trade and the ask. The mid is (bid + ask) / 2 of the current market: (9.80 + 10.20) / 2 = 10.

Another example: Long 500 bought at 20.10, market now 20.30 / 20.40

Mid: (20.30 + 20.40) / 2 = 20.35
Long P&L at the mid: 500 × (20.35 - 20.10) = 125
A stricter view marks at the bid you could sell at: 500 × (20.30 - 20.10) = 100

Source notes

These explanations and questions are written for QuantArc. Links show the underlying mathematics and learning design.

Figgie (Jane Street)
Landing page checked: Jane Street's card game that simulates elements of markets and trading, with rules, a tutorial and a learning mode. Practice companion only; its rules and strategy tips were not reviewed against these lessons. Lesson examples are original.

tradermath.org market games
Listing page checked: browser games including market making on dice, a card market-taking game, Fermi estimation and a trading game. Practice companion only; game content was not played or reviewed against these lessons. Lesson examples are original.

IES: Organizing Instruction and Study to Improve Student Learning
Supports worked examples, retrieval, explanations and spaced study. Does not establish QuantArc's exact lesson length, mastery threshold or review intervals.