Case 002Market making and trading scenariosCore

A market maker faces order flow of which 20% comes from traders who know the price will move Rs 4 in their favour. What half-spread breaks even, and what happens when the informed share doubles?

The situation

Kenjal Capital makes a two-way market in a mid-cap stock. Of the orders that hit its quotes, 80% come from traders with no information, who are as likely to buy as to sell and whose trades carry no signal. The other 20% come from traders who know the stock is about to move Rs 4, and who trade only in the direction of that move: they buy at Kenjal's ask just before the price rises Rs 4, or sell at its bid just before it falls Rs 4.

Kenjal quotes a bid and an ask the same distance either side of its estimate of fair value. Every order is for one share. Inventory and the cost of carrying it are ignored for this question.

Your task

What is the smallest half-spread at which Kenjal expects to break even, and what does the quote become if the informed share rises to 40%?

Quick check

At a 20% informed share, roughly what half-spread does Kenjal need?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The break-even half-spread is Rs 0.80, and it doubles to Rs 1.60 when the informed share doubles to 40%. On every uninformed trade Kenjal earns the half-spread; on every informed trade it loses the Rs 4 jump less the half-spread. Setting the expected gain equal to the expected loss gives a half-spread of the informed share times the jump. The spread is the price of adverse selection, and it is linear in how much of the flow is informed.

Step 1Where does the spread come from if there is no inventory cost?

Picture a second-hand phone dealer who pays the same price to everyone. Most sellers are honest, but one in five knows the phone has a fault that will show up next week. The dealer cannot tell them apart, so the only defence is to pay everyone a little less, enough that the honest trades cover the losses on the faulty ones. Kenjal is that dealer: the half-spread is what the uninformed pay so that the market maker can afford to be picked off by the informed. This is adverse selectionThe cost a market maker bears because the traders most eager to deal with it are the ones who know something it does not., and it exists even when carrying inventory costs nothing.

The relationship

0.8\,s - 0.2\,(4 - s) = 0 \quad\Rightarrow\quad s = 0.2 \times 4 = 0.80

s	the half-spread, the distance from fair value to the bid or to the ask
0.8, 0.2	the shares of uninformed and informed orders
4	the move the informed traders know is coming, in rupees

What it says in wordsThe expected gain from uninformed trades, 0.8 times the half-spread, must cover the expected loss on informed trades, 0.2 times the jump less the half-spread. Both sides equal when the half-spread is the informed share times the jump.

Check the two cases. An uninformed buyer pays the ask, fair value plus Rs 0.80, and the price does not move, so Kenjal keeps Rs 0.80. An informed buyer pays the same ask and the price then rises Rs 4, so Kenjal, now short at fair value plus 0.80, is down Rs 3.20. Expected profit per trade is 0.8 times 0.80 minus 0.2 times 3.20, which is 0.64 minus 0.64, zero. The quoted spread, ask less bid, is Rs 1.60, and any narrower quote loses money on average.

With a Rs 4 information jump, the break-even half-spread is a straight line in the informed share of flow: Rs 0.80 when 20% of orders are informed, Rs 1.60 when 40% are, and the whole Rs 4 jump if every order were informed, at which point nobody uninformed would trade.

Step 2What happens at 40% informed, and why does it matter beyond the arithmetic?

The same equation with 0.6 and 0.4 gives s equal to 0.4 times 4, Rs 1.60, a quoted spread of Rs 3.20. The relationship is linear, so doubling the informed share doubles the spread, and a market where the informed share approaches 100% has a spread equal to the jump and no reason for anyone uninformed to trade. That is the mechanism behind spreads widening before results announcements: the market maker does not know the number, but it knows that a larger share of the orders arriving now come from people who think they do. Say the direction of causation out loud, because it is what the interviewer is testing: the spread widens because the mix of flow changed, not because volatility was higher in the past.

Step 3What is left out, and what would you add on a real desk?

Three things. The jump is treated as known and fixed at Rs 4; in practice the market maker estimates it from how much prices move after trades. Inventory is ignored, and a desk that has accumulated a long position would skew both quotes down to attract sellers. And orders are one share each; informed traders trade size, so a desk widens the spread for larger orders, which is why the quote depends on quantity. The one-line model is still the right first answer because it isolates the piece that candidates most often cannot explain: why a market maker with no costs and no inventory still needs a spread.

Where candidates lose it

Candidates often answer Rs 4, reasoning that the market maker must cover the whole jump. That ignores the 80% of trades that pay the spread and earn it back. The spread is the probability-weighted jump, not the jump.

The second loss is forgetting that the informed trader also pays the half-spread, so the loss on an informed trade is 4 minus s, not 4. Writing 0.8 s equals 0.2 times 4 gives Rs 1.00 instead of Rs 0.80, and the interviewer will ask you to reconcile the two.

What the interviewer asks next

Kenjal is long 5,000 shares it wants to shed. How does it move the bid and the ask?
Informed traders can trade 10 shares at a time while uninformed trade one. What is the break-even half-spread now?
How would you estimate the informed share and the jump from a day of trade data?
Why do spreads widen in the minutes before a results announcement even when nothing has been published?

Company names and figures are illustrative.