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035

Case 035Statistical arbitrage and event tradesWarm up

An ETF trades at Rs 101.2 while its indicative NAV is Rs 100.0. A creation unit is 50,000 units, creating costs 0.3% and trading the basket costs 0.2%. Is creation arbitrage profitable, and what closes the premium?

1The situation

Nirjhara Asset Management runs an invented index ETF on domestic large-cap shares. On a busy morning the ETF trades at Rs 101.2 while its indicative NAV, computed from live prices of the underlying basket, is Rs 100.00. An authorised participant can create new ETF units in blocks of 50,000 by delivering the basket to the fund.

The fund charges a creation fee of 0.3% of NAV, and buying the basket in the market costs about 0.2% in spread and impact.

2Your task

Work out whether creating units and selling them is profitable, how much one creation unit makes, what pushes the price back towards NAV, and what could make the premium real rather than an opportunity.

Quick check

Per ETF unit, what does the creation arbitrage make before any price move?

Worked solution

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

30-second answerThe answer to give first

Yes: the 1.2% premium beats the 0.5% cost of creating, leaving Rs 0.70 a unit, or about Rs 35,000 on one creation unit of 50,000. The participant buys the basket, delivers it for new units and sells them at Rs 101.2. That selling is what closes the premium: arbitrage keeps pushing until the price sits within about 0.5% of NAV, the band where creating no longer pays.

Step 1How does the creation trade make money?

Think of a sweet shop that sells gift boxes of assorted sweets. If the boxed version sells for more than the loose sweets inside plus the cost of the box and the packing, anyone who can pack boxes buys loose sweets, packs them and sells boxes. An authorised participant does the same: it buys the basket of shares at NAV, hands it to the fund for new ETF units, and sells those units at the higher market price. Here the market price is Rs 101.2 against a basket worth Rs 100.00, a 1.2% premium. The costs are 0.3% creation fee and 0.2% to trade the basket, Rs 0.50 a unit, so Rs 0.70 is left.

Per unit, Rs: the premium beats the cost of creatingPremium: 101.20 - 100.00+1.20Creation fee, 0.3% of NAV-0.30Trading the basket, 0.2%-0.20Profit per unit+0.70x 50,000 units in one creation unit = Rs 35,000
Of Nirjhara's Rs 1.20 premium per unit, the creation fee takes Rs 0.30 and trading the basket Rs 0.20, leaving Rs 0.70 a unit, about Rs 35,000 on one creation unit of 50,000.

Size it. One creation unit needs a basket worth about Rs 50,00,000, roughly Rs 50 lakh, and returns Rs 35,000 if prices hold still while the trade is done. That is a 0.7% return on capital tied up for hours, which is why participants act quickly and why premiums of this size rarely last. The participant also needs to sell the 50,000 new units without pushing the ETF price down too far itself; if the ETF's own order book is thin, selling the units costs part of the edge.

Step 2What closes the premium?

The arbitrage itself. Every creation adds new ETF units to the supply and they are sold into the market, so the ETF price falls towards NAV. The selling stops when the premium no longer covers the cost of creating, at about Rs 100.50; on the other side, if the ETF trades below about Rs 99.50, participants buy units and redeem them for the basket, pushing the price up. So an ETF does not trade exactly at NAV; it trades inside a band whose width is set by the cost of creating and redeeming. Cheaper, more liquid baskets mean a narrower band.

Arbitrage keeps the price inside a band around NAVno arbitragezone99.099.5100.0100.5101.0101.5102.0NAV 100.00ETF at 101.20APs create and sellAPs buy and redeemETF price, Rs, against the costs of creating or redeeming
Creation selling pushes the ETF from Rs 101.2 down towards Rs 100.50, and redemption buying would push a discounted price up towards Rs 99.50, so arbitrage holds the price inside a band of about 0.5% either side of NAV.
Step 3When is the premium not an opportunity at all?

When the indicative NAVA live estimate of the value of the basket behind each ETF unit, computed from the latest prices of its holdings. It is only as good as those prices. is stale. If some of the basket is not trading, because shares are halted or the underlying market is shut, the ETF price may be the more accurate estimate of value, and the premium is a forecast, not a free profit. For this domestic large-cap fund on a busy morning that is unlikely, but it is the first thing to check. The second is timing risk: if the basket's price rises while the participant is buying it, the edge can vanish before the units are sold, so participants hedge with index futures while they work the order.

Where candidates lose it

The usual loss is calling the full 1.2% the profit and forgetting the creation fee and the cost of buying the basket. The question gives the costs precisely so you subtract them.

The second is saying the fund manager closes the premium. The manager does nothing; participants close it by creating and selling, and the size of their costs decides how close to NAV the price is held.

What the interviewer asks next

  • The ETF trades at a 0.4% discount. What does a participant do, and does it pay?
  • Why do ETFs on foreign shares show larger premiums during the home market's trading hours?
  • How would you hedge the basket while it is being bought?
← Case 034A strategy has expected excess return of 8% and volatility of 16% a year. What is the full-Kelly leverage, what growth do full and half Kelly give, and what gross exposure would you run on Rs 200 crore?Case 036 →A stock's 36-month rolling beta has ranged from 0.7 to 1.5 and its 12-month rolling beta from 0.3 to 2.1. How much of that is estimation noise, how would you test for genuine change, and which window would you use?

Company names and figures are illustrative.

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