Making a Market: The Core Interview Game

At some point in almost every trading interview, someone will describe a quantity — the sum of three dice, the number of petrol stations in London, next month's rainfall — and say: "make me a market." Then they stop talking and watch you. It is the most-used exercise on the desk because it compresses the whole job into thirty seconds: estimate something, commit to a price, and then live with the consequences.

What the game actually is

You give two numbers, a bid (the price at which you will buy) and an ask or offer (the price at which you will sell). Saying "9 at 11" means: I'll buy at 9, I'll sell at 11. Crucially, you do not get to choose which side happens. The interviewer picks. They can hit your bid — sell to you at 9 — or lift your offer — buy from you at 11. You are obliged either way. That obligation is what makes it a real decision instead of a guess.

Two decisions, in order

First, the centre. Where do you think the true number sits? This is just expected value — list the outcomes, weight them, add. Say it out loud as you go, because the reasoning is most of the mark.

Second, the width. The spread is not decoration; it is the price of being wrong. Widen when you are unsure of your estimate, when the quantity is volatile, when the person opposite you plainly knows more than you do, and when you would struggle to get out of a position. Tighten when the number is nearly mechanical. A quote of "10 at 11" on a dice total is confident; "2 at 40" on the same question is a refusal to play, and interviewers say so.

Worked example: a market on three dice

You roll three fair dice and are paid, in dollars, their total. Make a market.

Fair value first. Each die averages 3.5, so by linearity the total averages $3 \times 3.5 = 10.5$. Say it: "Each die is 3.5 on average, so I'm centred at 10.5."

Now the width. The total ranges from 3 to 18 with standard deviation just under 3, so the outcome really can land far from 10.5 — but you are quoting the average, not the roll, and repeated play converges. A sensible answer is "10 at 11". You have a dollar of edge on either side, which is enough to survive an interviewer who is fishing for a mistake without being so wide that you look scared.

Then the game begins. The interviewer says: "I buy at 11." You are now short one unit at 11 against a fair value of 10.5 — you are up half a dollar in expectation. Say that out loud too.

Next: "What if I tell you one die has already landed on a 6?" Recompute rather than defend. The two unknown dice average 3.5 each, so fair value is now $6 + 3.5 + 3.5 = 13$. You are short at 11 against a fair value of 13, so you are down about 2. The correct move is to want to buy that unit back, and to quote your new market around 13 — perhaps "12 at 14" — rather than clinging to your old numbers.

Finally: "How many would you do at 11?" This is a risk-limit question. The honest answer names a size and a reason: "Five, because each unit costs me about 2 at the new fair value and I don't want more than 10 of downside on a game I've already lost information on."

What they are really grading

Nobody cares whether you said 10 at 11 or 9.5 at 11.5. They are watching whether you produce a number under pressure, whether your spread reflects your genuine uncertainty, whether you update cleanly when new information arrives, and whether you notice that being traded with is itself information — the winner's curse in miniature, and the reason real desks skew quotes against informed flow.

Practise the loop until it is automatic: estimate, quote, get filled, restate your position, requote around the new fair value. Everything else on the desk — pricing, inventory, sizing — is this loop with more zeros.