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054

Case 054Hedging with futuresWarm up

A fund receives Rs 200 crore at 3 pm that it cannot invest in stocks before the close. How does it equitise with index futures at 22,000, lot 50, and what does it save if the index rises 1.5% overnight?

1The situation

Visapur Mutual Fund runs a Satpura 50 index fund. At 3 pm a large institutional investor's Rs 200 crore subscription lands, too late for the dealing desk to buy fifty stocks in the right weights before the 3.30 pm close. The fund's mandate is to track the index, so cash that sits idle overnight is tracking errorThe gap between a fund's return and its benchmark's return. For an index fund, idle cash is one of the main sources..

Satpura 50 futures trade at 22,000 with a contract size of 50 index units. The fund can buy futures in the last half hour, then buy the stocks over the next day and sell the futures as it goes. Overnight, the index rises 1.5%.

2Your task

How many contracts does the fund buy, what shortfall against the benchmark does it avoid, and what does it need to run the position?

Quick check

Before working it: roughly how many contracts cover Rs 200 crore?

Worked solution

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

30-second answerThe answer to give first

Buy 1,818 contracts; they avoid a shortfall of about Rs 3 crore on a 1.5% rise. One contract covers 50 units at 22,000, Rs 11 lakh, and Rs 200 crore divided by that is 1818.2, rounded down to 1,818. A 1.5% rise is 330 points, and 1,818 contracts times 50 times 330 is Rs 3.00 crore, almost exactly what Rs 200 crore of idle cash would have missed. The fund needs margin, a broker line and a plan to unwind as it buys stock.

Step 1What is the fund trying to buy with the futures?

Time. A family that has agreed to buy a house but cannot complete for a month sometimes asks the seller to fix the price today; a futures contract does the same for an index. EquitisationUsing index futures to give cash the return of the equity market until the cash can be invested in the underlying shares. replaces the fifty stock purchases with one trade whose value moves with the index, so the Rs 200 crore behaves like invested money from 3.15 pm onward. The fund is not speculating; its mandate already says the money should be in the index, and the futures put it there faster than the cash desk can.

Step 2How many contracts, and why round down?

One contract is 50 index units, so at 22,000 it carries Rs 1,100,000 of exposure. Rs 200 crore divided by Rs 11 lakh is 1818.18. Buy 1,818 contracts, covering Rs 199.98 crore, and leave the odd Rs 2 lakh in cash; rounding up would put the fund slightly long the index with money it does not have, and a fraction of a contract cannot be traded anyway.

The relationship
n=⌊200×10722,000×50⌋=1,818gain=1,818×50×330≈Rs 3.0 croren = \left\lfloor \frac{200 \times 10^{7}}{22{,}000 \times 50} \right\rfloor = 1{,}818 \qquad \text{gain} = 1{,}818 \times 50 \times 330 \approx \text{Rs } 3.0 \text{ crore}
200 x 10^7the Rs 200 crore inflow in rupees
22,000 x 50rupee value of one contract, Rs 11 lakh
330a 1.5% rise on 22,000, in index points
What it says in wordsContracts are the cash divided by the rupee value of one contract, rounded down; the gain is contracts times units per contract times the index move in points.
Futures hold the new money in the market until the stocks can be boughtDay 1, 3 pmRs 200 crore arrivescash, not investedDay 1, 3.15 pmBuy 1,818 futuresat 22,000, Rs 11 lakh eachOvernightIndex +1.5%22,000 to 22,330Day 2Buy stocks, sell futuresfutures gain Rs 3.0 croreWithout futures: Rs 200 crore sits in cash while the index gains 1.5%,a shortfall of Rs 3 crore against the benchmark on day one alone.With futures: 1,818 contracts x 50 x 330 points = Rs 3.00 crore, the gap closed.
Buying 1,818 contracts at 3.15 pm keeps the Rs 200 crore in the market, so when the index rises 1.5% overnight the futures earn Rs 3.00 crore and the fund avoids a Rs 3 crore shortfall against its benchmark.
Step 3What does the position need in order to run?

Three practical things, and interviewers at asset managers ask about all of them. Initial margin: the clearing corporation sets it, and the fund must confirm the current level, but illustratively at 10% of notional that is about Rs 20 crore of the Rs 200 crore parked with the broker rather than earning overnight interest. Variation margin: if the index had fallen 1.5% instead, the fund would pay out Rs 3.00 crore the next morning, which is the same loss the stocks would have shown, just settled in cash a day earlier. And the unwind: as the dealing desk buys each basket of stock on day two, it sells the matching number of contracts, so exposure never doubles. The futures gain is not extra return; it is the index return the cash would otherwise have missed, and the regulation on how much of a fund's assets can sit in derivatives is a figure to confirm with the current rules, not to recall from memory.

Say the limitation. Futures track the index through the basis, and if the futures are expensive to spot at 3.15 pm the fund pays a little of the gain away when it unwinds. Over one night that is small; over a week of slow stock buying it can matter.

Where candidates lose it

Candidates divide Rs 200 crore by 22,000 and get 90,909, forgetting the contract carries 50 units. Always write the rupee value of one contract before dividing.

The second miss is describing the Rs 3 crore as profit. It is the benchmark return the fund was obliged to deliver; the futures prevented a shortfall rather than creating a gain, and that is how an index fund's committee will read it.

What the interviewer asks next

  • The fund buys the stocks over three days instead of one. How does the unwind schedule change?
  • Futures trade at 22,060 while the index is at 22,000. Does that change the number of contracts or only the cost?
  • Redemptions of Rs 100 crore arrive at 3 pm instead. What is the mirror-image trade?
← Case 053A five-year convertible with Rs 1,000 face converts into 8 shares. The stock is Rs 110, the straight bond is worth Rs 880 and a five-year call struck at Rs 125 is worth Rs 25. Value the convertible and its conversion premium.Case 055 →A client with Rs 10 lakh is bullish on a Rs 2,000 stock, lot 250. Two lots of futures, or ten lots of the one-month 2,100 call at Rs 40? Show the outcomes at 1,900, 2,050 and 2,300.

Company names and figures are illustrative.

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