How to play "make me a market"

A market is two prices: a bid, where you will buy, and an ask (or offer), where you will sell. "45 at 55" means you buy at 45 and sell at 55. The midpoint is your fair value; the gap between the prices is your width. Quoted that way, you are happy to trade either side – which is what the interviewer will test.

Build an estimate from parts you can defend, and say each one. For a known distribution – the sum of two dice, the highest card from three draws – compute the expectation exactly. For an unknown quantity, decompose it: floors times windows per floor, people times trips per day. The estimation lesson gives the method.

Your width should reflect how sure you are. On the sum of two dice you know the distribution exactly, so a tight market around 7 is right. On windows in a building, a width of ten percent of your estimate would be reckless. A useful rule: quote roughly the interval you would bet holds the true value – the same judgement as Interval estimation and the confidence intervals lesson.

Too wide and nobody trades with you; interviewers will often say "tighter". Too tight and anyone with better information takes you apart. Neither extreme is the answer – the answer is a width you can justify.

When the interviewer buys from you at your ask, two things have happened: you are now short, and someone thought your price was too low. Both should move your next quote up. If they keep buying, your fair value was probably wrong – this is adverse selection, the subject of reading the fill.

• Skew, do not just widen. Widening after a trade says you are less sure; moving both prices up says you have learned something and want to buy back. Usually the second is right.
• Keep your width roughly constant unless the trade genuinely made you less certain.
• Track your position and average price. You will be asked for them.

As your position grows, skew your quotes to reduce it: if you are long, lower both prices so you are more likely to sell. The inventory lesson shows why a market maker prices from a reservation price, not the raw fair value.

At the end, expect: "What is your position? Your average price? Your P&L if the true value is X? What would you do differently?" Answer each precisely. A good answer to the last one names a specific decision, not a general lesson.

• Quoting a single number instead of two prices.
• Refusing to commit until you have "more information" – the game is about acting under uncertainty.
• Widening every time you are traded, until your market is useless.
• Losing track of your position halfway through.
• Treating the interviewer as noise when they trade the same side repeatedly.

Read theoretical value, width and skew and the trading game, then run the market simulator. It trades against your quotes round by round, mixes informed and uninformed counterparties, and grades your width, your skew and your P&L against a reference market maker on the same seed.