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064

Case 064Execution and market microstructureCore

A market maker quotes a stock with a 5 paise spread, earning 2.5 paise per filled share plus a 0.2 paise exchange rebate, but 40% of fills are followed by a 5 paise adverse move. What does it net per share, and at what share of toxic fills does it break even?

1The situation

Chakrika Markets quotes a liquid stock on both sides with a 5 paise spread and fills about 1,500,000 shares a day. Each fill earns half the spread, 2.5 paise a share, against the mid, and the exchange pays a rebate of 0.2 paise a share to the side that provided liquidity.

Chakrika's post-trade analysis finds that 40% of its fills are followed, within a few seconds, by a 5 paise move in the mid price against its new position: it buys just before the price falls, or sells just before it rises. The other fills see no systematic move. The head of the desk asks what the business really earns and how much worse the flow can get.

2Your task

Compute net earnings per share and per day, find the break-even share of toxic fills, and say what widening the spread would and would not fix.

Quick check

What does Chakrika net per share filled?

Worked solution

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

30-second answerThe answer to give first

Chakrika nets 0.7 paise a share, about Rs 10,500 a day, and breaks even when 54% of fills are toxic. Half the spread plus the rebate earns 2.7 paise; adverse selection costs 40% x 5 = 2.0 paise. Each extra 10 points of toxic flow costs 0.5 paise, so a modest shift in who trades with Chakrika wipes out the business. Widening the spread helps only if the toxic share does not rise with it.

Step 1Where does a market maker's money come from, and where does it go?

A money changer at an airport buys dollars at one price and sells at a slightly higher one, and earns the gap on every customer. Most customers are travellers who simply need currency. A few know the rate is about to move. The market maker earns half the spread on every fill but loses to the informed minority, and its profit is the gap between the two, not the spread itself. The loss to informed traders is called adverse selectionThe cost a market maker bears because the counterparties most eager to trade with it are often those who know the price is about to move against it.: the fills Chakrika gets most readily are disproportionately the ones it should not want.

Step 2What does the flow net per share?

Income per share is 2.5 paise of half-spread plus 0.2 paise of rebate, 2.7 paise. Adverse selection costs 40% of fills times 5 paise, 2.0 paise averaged across all fills, so net is 0.7 paise a share. On 1,500,000 shares a day that is about Rs 10,500, before technology, exchange fees and the capital the inventory ties up. The rebate is 0.2 paise of a 0.7 paise margin: without it, the business would keep only about 0.5 paise.

Per share filled, paise: what the spread pays and what toxic flow takes+2.5Half-spread+0.2Rebate2.7Gross-2.0Adverse selection0.7NetAdverse selection = 40% of fills x 5 paise = 2.0 paise per share, averaged over all fills
Chakrika earns 2.5 paise of half-spread and 0.2 paise of rebate on every share it fills, but four fills in ten are followed by a 5 paise move against it, which takes 2.0 paise of that and leaves 0.7 paise.
Step 3How much worse can the flow get before the business loses money?

Net per share is 2.7 minus 5 times the toxic share. It reaches zero when the toxic share is 2.7 / 5 = 54%, only 14 points above today's 40%. Each 10 points of toxic share costs 0.5 paise a share, Rs 7,500 a day at this volume. A new fast trader in the stock, or a large fund starting to work an order through it, can move the toxic share by that much in a week, which is why market makers watch their post-fill price moves more closely than their fill volume.

Net per share against the share of toxic fills-1+1+2+30today: 40% toxic, +0.7 paisebreak-even 54%losing money0%20%40%60%80%Share of fills followed by a 5 paise adverse move. Vertical: net paise per share
Chakrika's net earnings fall by 0.5 paise a share for every 10 points of toxic flow, from 2.7 paise with no informed traders to 0.7 paise at today's 40%, and turn negative beyond 54%.
Step 4Would widening the spread fix it?

Partly, and less than it looks. A 6 paise spread raises the half-spread to 3.0 paise. But a wider quote mainly drives away the uninformed traders, who have a choice, while informed traders still trade because their 5 paise edge covers the extra cost, so the toxic share rises. If it rose from 40% to 50%, net would be 3.0 + 0.2 - 2.5 = 0.7 paise, no better than before, on fewer shares. The levers that work attack adverse selection directly: faster quote updates so stale prices are picked off less often, skewing quotes away from signals of informed flow, and separating flow by source where the venue allows it.

Where candidates lose it

The common answer stops at 2.7 paise, half-spread plus rebate, as if every fill were profitable. A market maker's business is the residual after adverse selection, and here that residual is about a quarter of the gross.

The second miss is assuming a wider spread raises profit in proportion. Spread width changes who trades with you, and the traders who leave are the profitable ones.

What the interviewer asks next

  • How would you measure the toxic share from Chakrika's own fill data?
  • If the rebate were removed, what spread would Chakrika need to keep the same net at 40% toxic flow?
  • Why might the toxic share be higher just before the market closes?
← Case 063A small-cap backtest built on today's index members returns 22% a year over ten years. Over that period 30% of the original universe was delisted, with an average return of -60% in the year before delisting. Estimate the survivorship bias.Case 065 →You are asked to build a model of monthly rents for 5,000 Mumbai flats from carpet area, floor, distance to the nearest station and building age. Choose the target, the features and the validation scheme, and interpret a coefficient of 0.9 on log area.

Company names and figures are illustrative.

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