Fair Value and Quoting

"Make me a market" is the classic trading-floor test, and it packs a whole job into three words. Making a market means two things done in sequence. First, decide what the thing is genuinely worth — its fair value. Then quote two prices around that value: a bid, the price at which you'll buy, set a little below fair, and an ask (or offer), the price at which you'll sell, set a little above. The gap between them is your spread, and it is how you get paid.

The fair value is just your best estimate of the truth. For a game or a bet, that's the expected value — run the outcomes, weight by probability, add them up, exactly as in Expected-Value Games. For a real asset it's your model's mid-price. Either way, fair value is a single number that sits in the middle; the quote is a fence you build around it.

Why quoting both sides makes money

You don't know whether the next person wants to buy or sell, so you name a price for each. If they buy, they pay your ask (above fair) and you pocket the difference. If they sell, they hit your bid (below fair) and you've bought something for less than it's worth. As long as the flow is roughly balanced and uninformed, you win on both sides. Your average take per trade is half the spread.

Worked example: make a market on two dice

An interviewer rolls two dice out of sight and will trade the total with you. The fair value is the expected sum, $E = 3.5 + 3.5 = 7.0$. You quote 6.90 bid / 7.10 ask — a market 20 cents wide, centered on 7.

Now they trade. Suppose they buy from you at 7.10. The dice are worth 7.00 on average, so you sold for 7.10 something worth 7.00: expected profit $7.10 - 7.00 = 0.10$. Suppose instead they sell to you at 6.90. You bought for 6.90 something worth 7.00: expected profit $7.00 - 6.90 = 0.10$. Either direction, you expect to make 10 cents, the half-spread. Quote a hundred such trades against uninformed flow and you expect $10.

The catch: informed flow

That happy arithmetic assumes the person trading knows no more than you do. Often they know more. If a counterparty has already peeked at one die and it's a 6, they'll only lift your 7.10 offer when the true value is high and only hit your 6.90 bid when it's low. Now every trade goes against you — this is adverse selection, and it's the market maker's central hazard. The defense is to widen: a bigger spread both pays you more per uninformed trade and forces the informed trader to give up more edge before they bother.

How wide should you quote?

Spread width is a judgment call balancing three things: how uncertain you are about fair value (more uncertainty → wider), how much inventory risk you'll take on (see Inventory Management for Market Makers), and how much competition there is (rivals undercut you toward a tight equilibrium, the theme of Nash Equilibrium in Markets). Tight quotes win more flow but leave thin margins and less protection; wide quotes are safer but trade less. The full anatomy of what the spread has to cover is laid out in Bid-Ask Spread Decomposition.

In an interview, say your fair value out loud, quote symmetrically around it, and keep your market tight enough to sound confident but wide enough that you'd genuinely be happy trading either side. That balance is the skill.