The bid-ask spread

This is the conceptual heart of M0. The spread (best ask − best bid) is the price of immediacy, and the market maker earns it by round-tripping: buy at the bid, sell at the ask, pocket the difference. But it is not free money — it’s compensation for three distinct things. This decomposition is the whole game.

                buy at BID 50.00        sell at ASK 50.02
   market maker ───────────────▶  +0.02 per round trip  ◀───────────────
                (to a seller)                              (to a buyer)

   the 0.02 is NOT profit — it pays for:
     1. order-processing costs   (small)
     2. inventory risk           (holding the position)
     3. adverse selection        (trading against the informed)  ← the big one

A worked example

Stock ACME, agreed to be worth about £100.00. The maker posts a two-sided quote:

   bid  99.98   ◀── MM will BUY from you here
   ask 100.02   ◀── MM will SELL to you here
   spread = 0.04 (4p)      midpoint = 100.00

Case 1 — the happy round trip. Two ordinary people trade for their own reasons; neither knows anything special:

• A seller hits the bid → MM buys 1 share at 99.98 (now long 1).
• Minutes later a buyer lifts the ask → MM sells it at 100.02 (now flat).

MM profit = 100.02 − 99.98 = 4p. The maker provided immediacy to both sides and got paid for it. Do this thousands of times a day and it adds up.

Case 2 — the painful trade (adverse selection). Someone lifts the ask at 100.02 — but they know a broker upgrade is coming and ACME is really worth 100.50:

• Informed trader buys from MM at 100.02 (MM now short 1 share).
• News breaks, price jumps to 100.50; the MM must buy a share back to get flat — at 100.50.

MM loss = 100.50 − 100.02 = 48p — wiping out 12 happy round trips (48 ÷ 4). The cruelty: at the moment of the trade the MM can’t tell the clueless buyer from the informed one — the orders look identical. They only find out afterwards, when the price moves against them.

Why the spread is exactly this wide. Suppose 1 taker in 13 is informed:

   flow                     count   P&L each     subtotal
   ─────────────────────────────────────────────────────
   uninformed round trips     12      +4p          +48p
   informed trade              1     −48p          −48p
   ─────────────────────────────────────────────────────
                                     net           ≈ 0p

At a 4p spread the maker roughly breaks even when 1-in-13 is informed. The spread isn’t arbitrary — it’s set so the steady winnings from the uninformed cover the occasional beatings from the informed. More informed flow → the maker widens the spread (say to 6p) or bleeds money. That is the adverse-selection component, made of arithmetic — and the formal version (how quotes update trade-by-trade) is M1.2.

The three components

1. Order-processing costs. The boring fixed cost of doing business — technology, exchange fees, clearing. Once dominant, now tiny for liquid names.

2. Inventory risk. The instant a maker buys at the bid, they’re holding stock, exposed to the price moving against them before they can offload it. To be coaxed into bearing that risk they demand a wider spread — and they skew their quotes to manage it (long too much inventory? quote a lower ask to sell it off). Inventory is why a maker cares about getting flat, not just about the spread.

3. Adverse selection — the big one. A maker quotes to everyone, but some takers know something the maker doesn’t (informed traders — they’ve done the work, or they have an edge). When an informed trader lifts the maker’s offer, the maker systematically loses: they sold just before the price rose. So the maker can’t win against the informed. To survive, it charges everyone the spread — and profits from the uninformed (“noise” / liquidity traders) enough to cover what it bleeds to the informed.

The spread is the maker’s levy on the uninformed to cover its losses to the informed. This is the Glosten–Milgrom insight, and the direct bridge to M1’s adverse selection and the Kyle model.

Who earns it, who pays it

Makers earn the spread; takers pay it. But makers don’t always win — they profit on average, winning on uninformed flow and losing on informed flow. That asymmetry is the entire risk of the market-making business (and the entire business of firms like Citadel Securities / Jane Street — M5).

It also explains PFOF: wholesalers fill retail orders inside the quoted spread (price improvement) precisely because retail flow is presumed uninformed — cheap and safe to trade against. They’d never offer that to a hedge fund.

What moves the spread

• Wider with volatility, illiquidity, and information asymmetry (around earnings, news — makers pull back exactly when you most want to trade).
• Tighter with competition among makers, high volume, and small tick size.

The spread you see (quoted) often isn’t what you pay (effective) — price improvement and walking the book both drive a wedge between them.

Source: Larry Harris, Trading and Exchanges, ch.13–19 (liquidity, the spread, dealers). The classic papers: Glosten–Milgrom (1985) on adverse selection, and Ho–Stoll on inventory — both foreshadow M1.