NISM Series V-D · Chapter 17: Strategies using Equity Futures and Equity Options

L1 · Foundation

Foundation — Futures for hedging, speculation and arbitrage

Long and short hedges with stock futures worked through both outcomes, the portfolio hedge ratio with index futures, why leverage makes futures attractive for a directional view, and cash-and-carry and reverse cash-and-carry arbitrage computed to the rupee.

15 min read · Worth 6% of the paper · Written from pages 390–424 of the official NISM workbook · Updated 18 September 2026

17.1 Futures for hedging

"Derivative instruments such as futures and options were PRIMARILY CREATED FOR MANAGING RISK."

Long hedge using stock futures

"A LONG HEDGE using stock futures is taken to hedge the price risk of a PLANNED FUTURE PURCHASE of a stock."

The setup: you want 1,500 shares of ABC Ltd, trading at Rs 455 today (10 May), but your bank deposit matures only on 20 June. "The risk is that if you do not purchase the shares today, THE SHARE PRICE MAY INCREASE RAPIDLY by 20th June." So you take a long position in the June futures at Rs 457.30, lot size 1,500 — one lot.

Scenario 1 — the price rises to Rs 520.


Cost of buying in cash market (1,500 × 520)	Rs 7,80,000
Less: gain on futures (521.20 − 457.30) × 1,500	(−) Rs 95,850
Net cost of buying the shares	Rs 6,84,150
Net cost per share	Rs 456.10

Scenario 2 — the price falls to Rs 390.


Cost of buying in cash market (1,500 × 390)	Rs 5,85,000
Add: loss on futures (457.30 − 391.10) × 1,500	(+) Rs 99,300
Net cost of buying the shares	Rs 6,84,300
Net cost per share	Rs 456.20

"The effective purchase price per share is Rs 456.10... quite close to the futures purchase price of Rs 457.30", and in the falling case Rs 456.20 — "again quite close." The conclusion: "a long position in a futures contract enables an investor to LOCK IN A PRICE for a planned purchase at a future date. Thus, WHETHER THE STOCK PRICE RISES OR FALLS over the hedge interval, THE INVESTOR CAN LARGELY ELIMINATE HIS PRICE RISK."

Note what a hedge does not do. In the falling scenario the investor would have been better off unhedged — he paid Rs 456.20 instead of Rs 390. A hedge removes the uncertainty, not the cost.

Short hedge using stock futures

"A SHORT HEDGE using stock futures is taken to hedge the price risk of a PLANNED FUTURE SALE of a stock."

The setup: you must sell 1,200 shares of PQR Ltd on 10 July to repay a personal loan. The shares trade at Rs 1,690 on 10 May, July futures at Rs 1,706, contract size 600 — so you short 2 contracts. "The risk is that between today... and the date of the planned sale..., THE STOCK PRICE MAY FALL STEEPLY."

Scenario 1 — the price falls to Rs 1,440.


Amount received in cash market (1,440 × 1,200)	Rs 17,28,000
Add: gain on short futures (1,706 − 1,441) × 600 × 2	(+) Rs 3,18,000
Total amount received	Rs 20,46,000
Selling price per share	Rs 1,705.00

Scenario 2 — the price rises to Rs 1,800. Cash proceeds are Rs 21,60,000, but the futures loss is (1,706 − 1,802) × 2 × 600 = Rs 1,15,200, giving Rs 20,44,800 and a selling price of Rs 1,704. "Again, this is quite close to the price at which you sold the July futures contracts earlier (which was at Rs 1,706)."

Hedging a portfolio with index futures

"Suppose that you have a portfolio consisting of 15 large-cap stocks from different sectors. SINCE THE PORTFOLIO IS WELL-DIVERSIFIED, THE SPECIFIC RISK IS ALMOST/NEAR ZERO. However, the portfolio is STILL SUBJECT TO THE SYSTEMATIC OR MARKET RISK."

The two alternatives: "(i) SELL THE ENTIRE PORTFOLIO TODAY AND SIT ON CASH, or (ii) REDUCE THE SYSTEMATIC RISK of your portfolio USING INDEX FUTURES."

"To hedge the systematic risk..., you need to take a SHORT position in the index futures. In this way, EVEN IF THERE IS A MARKET CRASH AND YOU MAKE A LOSS ON THE PORTFOLIO, YOU WILL MAKE A PROFIT ON THE SHORT POSITION in index futures."

With a portfolio of Rs 90,00,000, a beta of 1.3, index futures at 17,700 and a lot of 50:

"Thus, you should take a short position in 13 index futures contracts."

Futures for trading

"Investors having a BULLISH view... take a LONG position in the stock futures or index futures contract. Investors who are BEARISH... take a SHORT position."

Bullish view — long futures

A trader expects XYZ Ltd to rise from Rs 1,298 to Rs 1,350. The near-month futures trade at Rs 1,300 with a lot of 850. "A long position in a single futures contract gives the trader a position EQUIVALENT TO BUYING 850 SHARES, BUT WITHOUT PAYING THE PRICE OF 850 SHARES AT THE ONSET." Contract value Rs 11,05,000; margin at 20 per cent is Rs 2,21,000.

A week later the stock is at Rs 1,345 and the future at Rs 1,346:

	(a) Buying 850 shares	(b) Long futures (lot 850)
Cash outflow	850 × 1,298 = Rs 11,03,300	Margin = Rs 2,21,000
Profit	(1,345 − 1,298) × 850 = Rs 39,950	(1,346 − 1,300) × 850 = Rs 39,100
Return on investment	3.62%	17.69%

"This example explains why stock and index futures contracts are so popular... These contracts offer the benefit of 'LEVERAGE' so that investors can make MUCH HIGHER RETURNS ON A LOWER CAPITAL OUTLAY as compared to an outright purchase of shares."

Bearish view — short futures

A trader expects RSB Bank to fall from Rs 1,595 to Rs 1,520; the future trades at Rs 1,602 with a lot of 550. The crucial practical point: "Selling the shares today would require the trader to DELIVER these shares on the settlement date. Hence selling in cash market IS POSSIBLE ONLY IF THE TRADER HOLDS THE SHARES IN HIS DEMAT ACCOUNT. However, the trader CAN ALWAYS SHORT THE... FUTURES CONTRACT INSTEAD."

Contract value Rs 8,81,100, margin at 20 per cent Rs 1,76,220. If the future falls to 1,527, the gain is (1,602 − 1,527) × 550 = Rs 41,250, a return of 23.41 per cent. "Thus, shorting a futures contract makes it possible for market participants to EXPRESS A BEARISH VIEW on the stock or index, WITHOUT OWNING the stock or index."

Futures for arbitrage

"they compare the FAIR futures price with the ACTUAL or traded price. If the traded price is HIGHER than the fair futures price, CASH-AND-CARRY arbitrage is profitable. If the traded price is LOWER..., REVERSE CASH-AND-CARRY arbitrage becomes profitable."

Cash-and-carry arbitrage

Stock A: cash Rs 1,500, three-month futures Rs 1,550, multiplier 100, cost of carry 9 per cent per annum, i.e. "around 0.75% per month."

"Theoretical/fair price... is 1534.13 (= 1500 × e^(0.0075×3) or 1500 × e^(0.09×3/12)). Going by this theoretical price,... the 3-month futures contract on stock A is OVERVALUED." So "an arbitrageur may BUY 100 SHARES of stock A and SELL 1 FUTURES CONTRACT... This would result in the arbitrage profit of Rs 1,587 (= 100 × 15.87), which is the difference between actual and fair futures prices."

	Case I — stock rises to 1,580	Case II — stock falls to 1,480
Underlying	Profit (1,580 − 1,500) × 100 = +8,000	Loss (1,500 − 1,480) × 100 = −2,000
Futures	Loss (1,580 − 1,550) × 100 = −3,000	Profit (1,550 − 1,480) × 100 = +7,000
Gain on arbitrage	Rs 5,000	Rs 5,000
Cost of financing (34.13 × 100)	Rs 3,413	Rs 3,413
Net gain	Rs 1,587	Rs 1,587

The same answer either way — which is what a locked-in arbitrage means.

Reverse cash-and-carry arbitrage

"done when the futures contract is trading at a DISCOUNT to the cash market price." Stock B: cash Rs 100, one-month futures Rs 90, multiplier 200.

"The prices... reflect a NEGATIVE cost of carry, which offers an opportunity... as cost of carry is expected to REVERSE TO POSITIVE at some point." The assumption: "the arbitrageur HAS GOT THE STOCK to sell in the cash market... IF STOCK IS NOT AVAILABLE, ARBITRAGEUR NEEDS TO BORROW THE STOCK... In that case,... COST OF BORROWING OF STOCK SHOULD ALSO BE TAKEN INTO ACCOUNT."

He "would BUY ONE FUTURES CONTRACT at Rs 90 and SELL 200 SHARES of stock B at Rs 100 in cash market. This would result in the arbitrage profit of Rs 2,000 (= 200 × Rs 10)."

	Case I — stock rises to 110	Case II — stock falls to 85
Underlying	Loss (110 − 100) × 200 = −2,000	Profit (100 − 85) × 200 = +3,000
Futures	Profit (110 − 90) × 200 = +4,000	Loss (90 − 85) × 200 = −1,000
Net gain	Rs 2,000	Rs 2,000

Plus the interest on the sale proceeds: "the interest earned on this investment (with continuous compounding) works out to Rs 150.56 ((20000 × e^(0.09×1/12)) – 20000)", giving a total gain of Rs 2,150.56.

Think of it like this

A hedge removes uncertainty, not cost

In the ABC Ltd long hedge, the effective purchase price came to Rs 456.10 when the stock rose to 520 and Rs 456.20 when it fell to 390. Both are "quite close to the futures purchase price of Rs 457.30." That is the whole point — but notice the second case: unhedged, the investor would have paid Rs 390. A hedge is like booking a taxi fare in advance: you are protected from surge pricing, and equally you forgo the empty-road discount. "Whether the stock price rises or falls over the hedge interval, the investor can LARGELY ELIMINATE HIS PRICE RISK" — eliminate the risk, not guarantee the best outcome.

Rs 11 lakh or Rs 2.2 lakh for the same 850 shares

The bullish-view table is the clearest argument for futures in the whole workbook. Buying 850 shares costs Rs 11,03,300 and earns Rs 39,950 — a return of 3.62 per cent. A long futures position on the same 850 shares costs only the margin of Rs 2,21,000 and earns Rs 39,100 — a return of 17.69 per cent. Nearly the same rupees of profit, on a fifth of the capital. "These contracts offer the benefit of 'LEVERAGE' so that investors can make much higher returns on a lower capital outlay." And the mirror warning from Chapter 15 always applies: leverage is a double-edged sword.

You cannot sell what you do not own — unless you use futures

The bearish example contains a practical point that matters more than the arithmetic: "Selling the shares today would require the trader to DELIVER these shares on the settlement date. Hence selling in cash market IS POSSIBLE ONLY IF THE TRADER HOLDS THE SHARES IN HIS DEMAT ACCOUNT. However, the trader CAN ALWAYS SHORT THE RSB BANK FUTURES CONTRACT INSTEAD." This is why a futures market exists at all for bears — it lets a participant "express a bearish view on the stock or index, WITHOUT OWNING the stock or index." A cash market can only be sold by those who already hold; a futures market is open to both views equally.

Sell the portfolio, or sell the index

Facing a feared market crash with 15 large-cap stocks, the investor has exactly two options: "(i) SELL THE ENTIRE PORTFOLIO TODAY AND SIT ON CASH, or (ii) REDUCE THE SYSTEMATIC RISK of your portfolio USING INDEX FUTURES." The first costs brokerage, taxes and impact cost on fifteen separate stocks, and then again to rebuild. The second needs one trade in 13 contracts. Since "the portfolio is well-diversified, the specific risk is almost/near zero" and only market risk remains — precisely what an index future can transfer. Selling the house to avoid a leaky roof, against simply buying an umbrella.

The arbitrage profit is decided before the story ends

In the cash-and-carry example, the stock rising to 1,580 gives +8,000 on the shares and −3,000 on futures; falling to 1,480 gives −2,000 and +7,000. Both come to a gain of Rs 5,000, and after financing costs of Rs 3,413, both net Rs 1,587 — which is exactly "the difference between actual and fair futures prices for 100 shares", 100 × 15.87. The arbitrageur's profit was fixed at the moment he put the trade on; the price path afterwards is merely bookkeeping. That is what distinguishes him from the speculator, whose result depends entirely on what happens next.

Reverse arbitrage needs shares you may not have

Cash-and-carry needs money; reverse cash-and-carry needs shares. "The assumption in implementing this arbitrage opportunity is that the arbitrageur HAS GOT THE STOCK to sell in the cash market, which will be bought back at the time of reversing the position. IF STOCK IS NOT AVAILABLE, ARBITRAGEUR NEEDS TO BORROW THE STOCK... In that case, while analysing the profitability..., cost of borrowing of stock should ALSO be taken into account." This is the practical reason Chapter 15 noted that a dominant convenience yield can break the model entirely — when nobody will lend the asset, the reverse trade simply cannot be done.

Even the arbitrageur earns interest on the float

The reverse cash-and-carry example adds a detail easily missed. Having sold 200 shares at Rs 100, the arbitrageur holds Rs 20,000 in cash for a month: "assume that the arbitrageur can invest the proceeds from his sale... at 9% p.a. for one month. The interest earned on this investment (with continuous compounding) works out to Rs 150.56", lifting the total gain from Rs 2,000 to Rs 2,150.56. Idle money is never really idle in a professional operation — and by the same logic, the cash-and-carry arbitrageur's Rs 3,413 financing cost is the mirror of this, the price of the money he had to borrow.

Beta decides how many contracts, not the rupee value

A Rs 90 lakh portfolio is not hedged by Rs 90 lakh of index futures. The formula divides portfolio value × portfolio beta by the contract value: (1.3 × 90,00,000) ÷ (17,700 × 50) = 13.22, so 13 contracts. With a beta of 1.3, the portfolio is expected to move 13 per cent when the index moves 10 per cent, so more index exposure is needed than the rupee value alone suggests. Had the beta been 0.7, fewer contracts would do. The beta is the exchange rate between your portfolio and the index — and as Chapter 15 cautioned, it assumes the past relationship persists.

Key terms in this chapter

Bear call spread: Short a lower strike call and long a higher strike call, for a bearish view, starting with a net inflow and capping the unlimited loss of a naked short call.
Bear put spread: Long a higher strike put and short a lower strike put, for a bearish view, with the sold put reducing the cost of the bought one.
Bull call spread: Long a lower strike call and short a higher strike call, for a bullish view at reduced cost. It involves a net cash outflow, caps gains beyond the higher strike, and breaks even at the lower strike plus the net premium paid.
Bull put spread: Short a higher strike put and long a lower strike put — a net premium receipt strategy for a bullish view, where the bought put provides embedded insurance against the unlimited loss of a naked short put. Break-even is the higher strike less the net premium received.
Butterfly spread: An extension of the short straddle, adding an out-of-the-money call and put to cap its unlimited loss. Built with calls, it is long the lowest strike, short two at the middle strike and long the highest — a limited profit and limited loss strategy.
Cash-and-carry arbitrage: Buying the underlying and selling the overvalued futures contract, carrying the asset to expiry. The profit equals the gap between the actual and fair futures prices, and is the same whatever the price path — after allowing for financing cost.
Collar: A covered call plus a long out-of-the-money put, which floors the downside — at the cost of reducing the maximum profit and raising the break-even by the put premium.
Covered call: Holding a stock and writing a call against it to generate extra income and reduce the cost of acquisition. Because it caps the upside while leaving the downside open, it is a synthetic short put.
Delta hedging: Offsetting the delta of an option position with futures or stock so that the combined delta is zero. Because delta changes as the underlying moves, the hedge must be rebalanced continually.
Delta neutral position: A combined position whose delta is zero, so it is unaffected by small changes in the underlying price. The word small matters — larger moves change the delta and break the neutrality.
Future Equivalent Open Interest (FutEq OI): Open interest measured at portfolio level as net delta-adjusted open positions across futures and options for an underlying, so that futures markets mirror the underlying market and risk management is strengthened.
Long hedge with stock futures: Going long futures today to lock the price of a planned future purchase of a stock, so that a rise in the share price is offset by a gain on the futures position.
Long straddle: Long a call and a put at the same strike, profiting from a large move in either direction. The maximum loss is the total premium, suffered only if the underlying expires exactly at the strike, and there are two break-evens at strike plus and minus the total premium.
Long strangle: Long an out-of-the-money call and an out-of-the-money put at different strikes — the same outlook as a straddle but cheaper, with the maximum loss suffered anywhere between the two strikes rather than at a single point.
Portfolio hedge ratio: The number of index futures contracts needed to hedge a portfolio — portfolio beta times portfolio value, divided by the value of one index futures contract.
Put-call parity: The relationship c + X·e^(−rt) = p + S₀ between calls and puts on the same underlying with the same strike and the same maturity, applicable only to European options. A deviation between the traded and derived fair price creates a risk-free arbitrage.
Put-call ratio (PCR): The ratio of put option trading volume, or open interest, to that of calls. It is treated as a contrarian indicator — below one is bearish, above one bullish.
Reverse cash-and-carry arbitrage: Buying the undervalued futures contract and selling the underlying in the cash market, reflecting a negative cost of carry. It assumes the arbitrageur already holds the stock; otherwise he must borrow it and count the borrowing cost.
Short hedge with stock futures: Going short futures today to lock the price of a planned future sale, so that a fall in the share price is offset by a gain on the futures position.
Short straddle: Short a call and a put at the same strike, for a view that the price will remain stable. A limited profit and unlimited loss strategy that must be handled with significant care.
Short strangle: Short an out-of-the-money call and put at different strikes, for a stable market — limited profit between the strikes and unlimited loss beyond either break-even.
Vertical spread: A combination of options on the same underlying and of the same type, with the same expiry date but different strike prices. Always a limited profit and limited loss position.

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Original explanatory writing based on the official NISM workbook for Series V-D, which is published and copyrighted by NISM. Check figures against the current edition at nism.ac.in.

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