Case 017Execution and market microstructureHard

A strategy earns 25 bps gross per trade in stocks with Rs 40 crore daily volume and 2% daily volatility, with impact equal to volatility times the square root of participation. Compare running it with Rs 10 crore and with Rs 1,000 crore.

ScotiabankToronto · 2025

The situation

Paramjyoti Capital has a short-horizon equity strategy that earns 25 bps per trade before costs. It trades a universe of mid-caps that each turn over about Rs 40 crore a day and move about 2% a day. Each trade puts 2% of the book's capital into one stock, and the book rotates fully about 100 times a year.

The desk's impact model says that a trade costs the stock's daily volatility times the square root of its participation, the trade's size over daily volume. The firm asks what happens if the strategy is run with Rs 10 crore, and what happens with Rs 1,000 crore.

Your task

Compute the impact and net edge per trade at both sizes, find the capital at which the edge disappears and at which total P&L peaks, and say how you would deploy the larger sum.

Quick check

At Rs 1,000 crore, roughly what does each trade cost in impact?

Worked solution

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

30-second answerThe answer to give first

At Rs 10 crore each trade nets about 11 bps; at Rs 1,000 crore it loses about 116 bps. A Rs 20 lakh trade is 0.5% of daily volume and costs 14 bps; a Rs 20 crore trade is half the day's volume and costs 141 bps. The edge vanishes at about Rs 31 crore, and total P&L peaks near Rs 14 crore. The larger sum needs deeper stocks or slower signals, not this strategy.

Step 1What does one trade cost at each size?

Work out the participation first. At Rs 10 crore, a trade is 2% of capital, Rs 20 lakh, which is 0.5% of a Rs 40 crore day. Impact is 2% times the square root of 0.005, about 14.1 bps, leaving 10.9 bps of the 25 bps edge. At Rs 1,000 crore the same trade is Rs 20 crore, half the day's volume, and costs about 141 bps. A hundred times the size costs ten times as much per rupee, because market impactThe adverse move in price caused by your own buying or selling, as your order uses up the liquidity available at the current price. grows with the square root of participation. A vegetable seller who buys one crate at the morning market pays the posted price; one who buys half the market's stock moves the price against himself on every crate.

The relationship

\text{impact} = \sigma\sqrt{\frac{Q}{V}} \qquad 2\%\sqrt{\frac{0.2}{40}} \approx 14.1\text{ bps} \qquad 2\%\sqrt{\frac{20}{40}} \approx 141\text{ bps}

\sigma	the stock's daily volatility, 2%
Q	size of one trade, Rs crore
V	the stock's daily traded value, Rs 40 crore

What it says in wordsThe cost of a trade rises with the square root of the share of the day's volume it takes.

Net edge per trade falls from 10.9 bps at Rs 10 crore to zero at about Rs 31 crore and to about -116 bps at Rs 1,000 crore, because impact grows with the square root of trade size while the 25 bps gross edge stays fixed.

Step 2At what size does the strategy stop paying?

Set impact equal to the edge. Impact reaches 25 bps when participation is 1.5625%, a trade of Rs 62.5 lakh, which is a book of about Rs 31 crore. Total P&L peaks well before that, because each extra rupee lowers the edge on every rupee already in. Capital times net edge is largest when impact is two thirds of the gross edge, at about Rs 14 crore, where each trade nets 8.3 bps and the book makes about Rs 1.16 crore a year, against Rs 1.09 crore at Rs 10 crore.

At 100 rotations a year, annual P&L rises to a peak of about Rs 1.16 crore at Rs 14 crore of capital and falls back to zero at Rs 31 crore, so beyond the peak every extra rupee of capital lowers the money made.

Step 3So how would you deploy Rs 1,000 crore?

Not in this strategy as it stands. The fix is to lower participation: trade stocks with far more volume, spread each trade over several days, or hold positions longer so the book turns over less. In stocks trading Rs 2,000 crore a day, the same Rs 20 crore trade is 1% of volume and costs about 20 bps, so a 25 bps edge would survive, if the signal works in large caps at all. Spreading trades over days lowers impact but lets the short-horizon signal decay before the position is built. Each option trades edge for capacity, and the honest answer for a billion is usually a slower, lower-edge strategy run alongside this one at its own capacity.

Say the limits of the model. The square-root law is an empirical rule with a coefficient that varies by market; real costs also include the spread, fees and the impact of other funds trading the same signal. The shape of the answer is robust even where the numbers are not: small books can run fast signals in small stocks, large ones cannot.

Where candidates lose it

The common loss is scaling P&L linearly: if Rs 10 crore makes Rs 1 crore a year, Rs 1,000 crore makes Rs 100 crore. That assumes costs per rupee do not change with size, which is false the moment you are a large share of the day's volume.

The second is assuming impact scales in proportion to size, so a hundred times the capital costs a hundred times as much. It scales with the square root, which is why the strategy survives up to about Rs 31 crore rather than dying at about Rs 18 crore.

What the interviewer asks next

How would you measure this strategy's real impact coefficient from your own fills?
If ten other funds trade the same signal, what happens to your capacity?
How should the firm charge a strategy for the capacity it uses?
Would you rather run Rs 14 crore here or Rs 100 crore in a strategy with 8 bps of edge in large caps?

Asked at Scotiabank, Sales and Trading, Toronto, 2025 (Wall Street Oasis): How would you allocate 1 million vs 1 billion

Company names and figures are illustrative.