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066

Case 066Forwards, futures and arbitrageCore

A fund holds Rs 50 crore of a stock at Rs 600. The one-month future trades at Rs 597, while carry at 7% says it should be about Rs 603.50. How does switching from the shares into cash plus futures earn extra return, and what if the discount has not closed by expiry?

1The situation

Toranmal Asset Management's large-cap equity scheme holds Rs 50 crore of Aundha Chemicals, about 8.33 lakh shares at Rs 600. The one-month single-stock future on Aundha, lot size 500, trades at Rs 597. With money-market rates at 7% a year and no dividend expected before expiry, the fund's dealer works out that the future should trade near Rs 603.50.

The dealer proposes a switch: sell the shares, park the proceeds in a one-month money-market instrument, and buy the same exposure through futures. The scheme's rules allow derivatives for this purpose within limits set by its offer document and the regulator, which the compliance team must confirm in their current form.

2Your task

Show what the switch earns, in rupees and as a share of the holding, explain why the gain does not depend on where the stock goes, and say what happens if the futures discount is still there on expiry day.

Quick check

Before working it: if Aundha falls 10% over the month, the switch compared with simply holding the shares:

Worked solution

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

30-second answerThe answer to give first

The switch adds about Rs 54 lakh, 1.1% of the holding in one month, whatever Aundha does. The cash grows to Rs 603.50 a share and the futures, bought at Rs 597, pay the expiry price less 597, so the fund ends with the share price plus Rs 6.50. At expiry the future must settle at the share price, so the discount always closes by then; the risks are having to unwind early, costs, and a dividend that would explain the discount.

Step 1Where does the extra return come from?

Imagine a dealer offers to sell you your own scooter back in a month for Rs 597, today, while you can sell it now for Rs 600 and earn a month's interest on the cash. You would sell, bank the Rs 603.50 the cash grows to, and take the scooter back for Rs 597. A future is a promise to buy the shares at a fixed price on expiry, so the fair price is the share price plus a month's interest on it, about Rs 603.50; at Rs 597 the market is selling the shares forward Rs 6.50 too cheaply. The fund can take that gift without changing its exposure to Aundha.

Sell the shares, park the cash, buy the cheap futures, and end up back in the sharesTodayHolds 8.33 lakhshares at Rs 600= Rs 50 crore1. Sell, park cashRs 50 crore at 7%for one month= Rs 603.50 a share2. Buy futures1,666 lots of 500at Rs 5971 month to expiryExpiryFutures pay S - 597Cash pays 603.50Total S + 6.50Per share, against simply holding the stock to expiryHold the sharesworth S at expiryCash plus futuresworth S + 6.50 at expiryRs 6.50 x 8.33 lakh sharesRs 54.1 lakh, 1.08%Fair value of the future: 600 x (1 + 7% / 12) = 603.50. It trades at 597, Rs 6.50 below.
Selling the shares, parking Rs 50 crore at 7% and buying 1,666 lots of futures at Rs 597 leaves the fund holding Aundha's expiry price plus Rs 6.50 a share, about Rs 54.1 lakh or 1.08% more than holding the shares.
Step 2Why does the gain not depend on where the stock goes?

Because at expiry the future settles at the share price. Each share's worth of cash has grown to Rs 603.50, and each share's worth of futures pays the expiry price less Rs 597. Add them and the fund holds the expiry price plus Rs 6.50 a share; holding the shares would have given just the expiry price, so the difference is fixed on the day the switch is done. The table works three outcomes to show the gap does not move. Lots come in 500 shares, so 1,666 lots cover 833,000 shares and the fund keeps the remaining 333 shares as stock.

Aundha at expiryHolding the shares, per shareCash plus futures, per shareExtra
Rs 540540.00546.50+6.50
Rs 600600.00606.50+6.50
Rs 660660.00666.50+6.50
Whether Aundha ends at Rs 540, Rs 600 or Rs 660, cash plus futures is worth Rs 6.50 a share more than the shares, which on 833,000 shares is about Rs 54.1 lakh.
Step 3What if the discount has not closed by expiry?

It cannot stay open at expiry: the future's final settlement price is set from the share price at the close, so the gap is forced to zero on that day. Depending on the contract's settlement terms, the fund either takes delivery or buys its shares back at that same closing price, and it ends where it started, holding Aundha, with the Rs 6.50 a share banked. The discount can widen before expiry, and if the fund has to unwind early, for example to meet heavy redemptions, it sells the futures at whatever discount then prevails and the gain can shrink or turn into a loss. Held to expiry, the gain is fixed; unwound early, it is a bet on the discount.

Four checks before doing it. First, the dividend: if Aundha is expected to pay about Rs 6.50 a share before expiry, the future should trade Rs 6.50 lower and there is no gift at all, so confirm the corporate action calendar. Second, costs: selling and later buying back Rs 50 crore of shares and trading the futures carries brokerage, taxes and market impact; at an assumed 0.10% in all, about Rs 5 lakh, the switch still adds roughly Rs 49 lakh, but the fund must use its own schedule. Third, margin: the exchange will hold part of the parked cash as margin and settle losses daily, so the cash must stay liquid. Fourth, the annualised figure, about 13% a year extra, is a reason to ask why the discount exists, usually because many holders want to do the same trade, and the trade is only as large as the futures market can take without closing the gap itself.

Where candidates lose it

Candidates say the fund is now leveraged or exposed to futures risk. It is not: the futures replace exactly the shares sold, and cash backs every rupee of them. The exposure to Aundha is the same; only its form has changed.

The second miss is forgetting the dividend. A future trading below spot is often explained by a dividend due before expiry, and the first question to ask is whether one is expected.

What the interviewer asks next

  • Aundha announces a Rs 8 dividend with a record date before expiry. Does the switch still make sense?
  • The fund faces Rs 20 crore of redemptions mid-month. What does it sell, and what can that cost?
  • Why would the futures trade at a discount to fair value in the first place, and who is on the other side of this trade?
← Case 065A bank receives fixed 6.60% on a one-week overnight index swap on Rs 500 crore. Overnight fixings are 6.50%, 6.52%, 6.55%, 6.60% and 6.58%, the last applying to Friday, Saturday and Sunday. Compound the floating leg and compute the net settlement.Case 067 →An index options book has delta of plus 800 index units, gamma of minus 1.3 units per point and vega of minus Rs 3 lakh per vol point, with the index at 22,000. Build the P&L grid for index moves of minus 2%, 0 and plus 2% and volatility moves of minus 2, 0 and plus 2 points.

Company names and figures are illustrative.

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