The mechanic
A market maker quotes a bid and an ask. Buy at the bid, sell at the ask, and the difference is captured - if you can do both without the price moving against you.
What the spread is compensation for
Three distinct things, and interviewers like you to separate them.
Adverse selection. Some counterparties know something you do not. When they trade with you, you lose. The spread must be wide enough that profits from uninformed flow cover losses to informed flow. See adverse selection.
Inventory risk. After buying, you hold a position with price risk until you can offload it. That risk has a cost, which scales with volatility and with how long you expect to hold. See inventory risk.
Operating costs. Exchange fees, clearing, technology, capital. Real but usually the smallest component in a competitive market.
What determines its width
Working from those three components, the drivers follow directly:
- Volatility up raises inventory risk, so the spread widens.
- Liquidity up reduces expected holding time, so the spread narrows.
- More informed traders raises adverse selection, so the spread widens - which is why spreads gap out before earnings announcements.
- More competition compresses the spread toward the cost floor.
That last point is why liquid index futures trade at a tick and a small-cap option does not.
The market maker's profit
Not "half the spread times volume" - that ignores the losses. The correct framing:
Profit = (spread captured from uninformed flow) - (losses to informed flow) - (inventory losses) - (costs)
A market maker with a high fill rate and a widening loss per fill is being picked off, and the fix is a wider or skewed quote, not more volume.
In the interview
If asked "why do market makers make money", the weak answer is "they buy low and sell high". The strong one names adverse selection as the thing the spread is priced against, and observes that a market maker with no adverse selection would quote almost zero width.
Practise in market making.