This is the capstone. Seven lessons turned the deceptively simple act of “quoting a bid and an ask” into a quantitative discipline. You learned to decompose a market maker’s P&L into spread capture minus adverse selection minus inventory cost plus net rebates — and why “the spread” is never guaranteed profit, only a gross number that markouts ruthlessly net down. You derived the Avellaneda–Stoikov reservation price and optimal spread, watched how risk aversion, volatility, and the horizon clock bend your quotes, and saw the inventory term melt to zero at the close. You turned that math into inventory skewing — a linear lean that steers your book back to flat without ever widening the spread. You met adverse selection head-on through Glosten–Milgrom, where the spread is a pure Bayesian premium against informed flow, not a fee. You played the queue as price–time priority, fill-probability bets, and an option that is most toxic at the front. You ran the latency arms race — stale-quote sniping, microwave beating fiber, Budish–Cramton–Shim’s batch-auction fix, and IEX’s speed bump. And you closed the loop with maker-taker economics: rebates, the Reg NMS access-fee cap, inverted venues, PFOF, and why rebates are never free money. No formula sheet, no hints, no take-backs.
Big picture
High-Frequency Market Making — the whole ladder
- High-Frequency Market Making
- P&L decomposition
- P&L ≈ spread capture − adverse selection − inventory cost + (rebates − fees)
- Markouts = empirical adverse-selection measure (price drift after fill)
- Realized vs mark-to-mid; effective ≠ quoted spread
- Avellaneda–Stoikov
- Reservation price r = s − q·γ·σ²·(T−t)
- Optimal spread δ = γσ²(T−t) + (2/γ)ln(1+γ/k)
- Quotes = r ± δ/2; inventory term → 0 at the close
- Inventory & skewing
- Skew = −q·γσ²(T−t), linear in inventory
- Both quotes shift together — steer without re-sizing the spread
- Skewing → inventory mean-reversion; limits force costly unwinds
- Adverse selection / Glosten–Milgrom
- Market orders are informative: ask = E[V|buy], bid = E[V|sell]
- Spread = pure adverse-selection premium, even with zero inventory cost
- PIN/VPIN/toxicity; the spread is not just a fee
- Queue & book dynamics
- Price–time priority; at a 1-tick spread you compete on time
- Fill prob falls with size-ahead, rises with trade-rate; cancels help
- Order-book imbalance = (bid−ask)/(bid+ask) predicts the next move
- Latency arms race
- Stale-quote sniping = adverse selection by speed
- Microwave ≈ c beats fiber ≈ 2/3 c (NJ–Chicago ~4.5 vs ~6.5 ms)
- Budish–Cramton–Shim: batch auctions; IEX 350µs speed bump
- Maker-taker & rebates
- Maker rebate / taker fee; Reg NMS cap $0.0030/share
- Inverted (taker-maker) venues; tiered pricing entrenches scale
- PFOF buys uninformed retail flow; rebates aren’t free money
- P&L decomposition
One run, one shot
This exam is graded and irreversible. Each question locks the moment you submit it — there is no Back button, no retry, and no Restart. A wrong answer simply fails that question and the exam moves on. The pass mark is 70%, and your pass/fail score appears only at the very end. Read every option before you commit.
A desk reports it 'captured the half-spread on 2 million shares' and assumes that is its profit. What is the core flaw in that reasoning?
Select an answer to continue.
Where this sits on the ladder
You’ve reached the top of the high-frequency market-making track — from the P&L identity all the way to rebate economics and best-execution conflicts. The next course on the ladder is onchain-arbitrage-and-cross-dex-mev, where these same ideas — adverse selection, latency races, and being paid for order flow — reappear in a world of mempools, blockspace auctions, and cross-DEX price gaps.