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072

Case 072Statistical arbitrage and event tradesWarm up

A stock will join a benchmark tracked by Rs 20,000 crore of passive money at a 0.8% weight, and it trades Rs 60 crore a day. Estimate the passive demand in days of volume and the likely price pressure around the effective date.

1The situation

The index provider has announced that Anuvratam Logistics will enter a widely tracked benchmark at the close in ten trading days, with a weight of 0.8%. About Rs 20,000 crore of index funds and exchange-traded funds track that benchmark and will buy at the effective close. A further Rs 30,000 crore of active funds use it as their benchmark.

Anuvratam has a market capitalisation of Rs 12,000 crore, of which about 35% is freely traded, and it trades about Rs 60 crore a day with daily volatility of 2.2%. A portfolio manager asks how big the forced buying is and what it does to the price.

2Your task

Compute the passive demand in rupees and in days of volume, estimate the price pressure with a simple impact model, describe the usual path around the effective date, and say what makes the estimate unreliable.

Quick check

How much stock must the passive funds buy, measured in days of Anuvratam's normal volume?

Worked solution

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

30-second answerThe answer to give first

The passive funds must buy about Rs 160 crore, 2.7 days of volume and 3.8% of the free float, and a square-root impact model puts the pressure at roughly 4% to 5%, most of it before the effective date. Demand is weight times tracking assets. Because the date and size are public, traders buy ahead and sell to the index funds at the close, so the price rises over the ten days and typically gives part of it back afterwards. How much depends on how crowded the trade is.

Step 1How large is the forced buying?

When a wedding is announced in a small town, every florist knows a fixed quantity of marigolds will be bought on one day, and prices move before the day arrives. Index inclusion is the same: the passive funds must hold 0.8% of Rs 20,000 crore, Rs 160 crore of Anuvratam, and they will buy it at the effective close so that their tracking error is zero. That is 2.7 days of the stock's normal volume and 3.8% of its Rs 4,200 crore free float. Active funds benchmarked to the index are not forced, but many will buy some to stay close to the benchmark; if half of their Rs 30,000 crore follows the weight, that adds Rs 120 crore, taking the total to Rs 280 crore or 4.7 days of volume.

Step 2What does that do to the price?

A rough answer comes from the square-root impact modelA rule of thumb that the price impact of buying a quantity Q is about the daily volatility times the square root of Q divided by daily volume.: impact of about daily volatility times the square root of the quantity in days of volume. For the passive demand alone that is 2.2% x sqrt(2.7) = 3.6%, and with the active money about 4.8%. The model was built for one trader working an order quietly, and this is the opposite: the buyer, the size and the date are all public. That changes the timing more than the size. Traders buy over the ten days and offer the stock to the index funds at the close, so the pressure shows up as a run-up before the effective date rather than a jump on it, and the closing auction itself, which may trade five times a normal day, absorbs the Rs 160 crore as about 53% of its volume.

Forced buying of 2.7 days of volume, known in advance, and what the price tends to doDaily volumeRs 60 crorePassive demandRs 160 crore = 2.7 daysPlus active fundsRs 280 crore = 4.7 daysSquare-root impact at 2.2% daily volatility:2.2% x sqrt(2.7) = 3.6% for the passive demand alone,2.2% x sqrt(4.7) = 4.8% with the active moneyStylised price path, % over the market+2%+4%announcedeffective close:passive funds buypartial reversalrun-up as traders pre-positionday 0day 10day 20day 30Shape is typical, not a forecast; the size depends on crowdingAnuvratam Logistics: 0.8% weight, Rs 20,000 crore of passive money tracking the benchmark
Anuvratam's passive buyers need Rs 160 crore, 2.7 days of its normal volume, which a square-root model prices at about 4% of pressure, and because the date is known the price tends to rise before the effective close and partly reverse afterwards.
QuantityValueHow it is found
Passive demandRs 160 crore0.8% x Rs 20,000 crore
In days of volume2.7160 / 60
Share of free float3.8%160 / 4,200
Impact, passive only3.6%2.2% x sqrt(2.7)
With half the active money4.8%2.2% x sqrt(4.7)
Share of a 5x closing auction53%160 / 300
The forced demand is a fifth of a normal week's volume and about 4% of the float, and the two impact estimates bracket the likely pressure at a few per cent, spread over the days before the effective date.
Step 3What makes the estimate unreliable?

Crowding. If many traders pre-position, the run-up is larger and the reversal after the close is larger too; if the trade is so well known that the stock has already risen on the rumour, the announcement itself moves nothing. Studies of index additions have found run-ups of a few per cent with partial reversals, but the size has shrunk as more capital chases the same event, so treat 4% to 5% as a scale, not a forecast. The second unknown is supply: a large holder who wants to sell can supply the whole Rs 160 crore at the close with no pressure at all, and a promoter-heavy register with little float does the opposite. For a trade, the usual structure is to buy after the announcement and sell into the closing auction on the effective date, sized to the chance that the reversal arrives before the close rather than after it.

Where candidates lose it

Candidates often stop at Rs 160 crore. The interviewer wants it in days of volume and as a share of float, because those are what determine whether the buying moves the price.

The second miss is predicting a jump on the effective date. The demand is public, so the price moves before the date as traders pre-position, and the question is how much reverses afterwards.

What the interviewer asks next

  • How would you measure the price pressure from past inclusions in this market, and what would you control for?
  • A stock is being deleted from the same index at a 0.8% weight. Is the effect symmetric?
  • Why might index funds choose to buy over several days and accept tracking error instead?
← Case 071A desk's stress loss hits Rs 42 crore against a Rs 40 crore limit after a volatility spike. Compare cutting positions, buying index puts at a 2.5% premium, and asking for a temporary limit increase, with numbers on each.Case 073 →You are making a market on the number of sixes in twelve dice. After you quote, six of the dice are revealed and exactly one of them is a six. Reprice, and explain what happens to your width even though the fair value does not move.

Company names and figures are illustrative.

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