Strategies using Equity Futures and Equity Options: formula sheet

Key formulas

Long futures payoff per unit

Payoff = Price at close − Entry price

Price at close is the closing or settlement price, or the price at which you square off. Positive means profit.

Short futures payoff per unit

Payoff = Entry price − Price at close

This is the exact negative of the long payoff.

Total profit or loss

Total = Payoff per unit × Lot size × Number of lots

Always multiply by the market lot. Contract value = price × lot size.

Break-even

Break-even = Entry price (ignoring costs)

Both long and short break even at the entry price. Brokerage, taxes and charges move the true break-even slightly.

Zero-sum property

Long profit = Short loss (same price, same quantity)

Futures are a zero-sum game between the two counterparties, before costs.

Number of futures contracts to hedge a portfolio

N = β × Portfolio value ÷ (Futures price × Lot size)

Round to the nearest whole contract. Short if you hold the portfolio, long if you will buy it.

Hedge ratio (value basis)

Hedge ratio = Value of futures position ÷ Value of the exposure

With beta hedging, this equals β. A ratio of 1 is a full hedge only if β = 1.

Portfolio beta

β = Σ (weight of stock i × beta of stock i)

Weights are each stock's share of total portfolio value, adding up to 1.

Basis

Basis = Spot price − Futures price

Some texts use futures minus spot. Read the question's definition. Basis converges to zero at expiry.

Value of one futures contract

Contract value = Futures price × Lot size

Use the futures price, not the spot price, unless the question says otherwise.

Net result of a hedge

Net result = Gain or loss on cash position + Gain or loss on futures position

Short futures gain = (Entry futures price − Exit futures price) × quantity.

Fair value of futures (simple interest)

F = S × (1 + r × t)

S = spot price, r = annual interest rate, t = time to expiry in years (days ÷ 365). Use this when no dividend is given.

Fair value of futures (continuous compounding)

F = S × e^(r × t)

Use when the question says continuous compounding.

Fair value with dividend

F = S × (1 + r × t) − D

D = dividend expected before expiry. This is a single no-arbitrage price. The holder of the share in cash and carry receives D, which lowers the net cost of carry. The reverse trader forgoes D, and that is already built into the same fair value. Subtract D once, when you compute F.

Cash and carry trigger

Actual futures price > Fair value

Buy spot, sell futures. Futures are overpriced.

Reverse cash and carry trigger

Actual futures price < Fair value

Sell spot, buy futures. Futures are underpriced.

Arbitrage profit per share

Profit = |Actual futures price − Fair value|

Before transaction costs. For cash and carry it equals futures price − [S × (1 + r × t) − D], which reduces to futures price − S × (1 + r × t) only when there is no dividend.

Call value at expiry

Max(0, ST − K)

ST is spot at expiry, K is strike.

Put value at expiry

Max(0, K − ST)

Positive only when spot is below strike.

Long call profit

Max(0, ST − K) − Premium

Maximum loss = premium. Maximum profit is unlimited.

Short call profit

Premium − Max(0, ST − K)

Maximum profit = premium. Maximum loss is unlimited.

Long put profit

Max(0, K − ST) − Premium

Maximum loss = premium. Maximum profit = strike − premium (when spot falls to zero).

Short put profit

Premium − Max(0, K − ST)

Maximum profit = premium. Maximum loss = strike − premium.

Breakeven

Call: K + Premium. Put: K − Premium

Same for buyer and seller. Per-unit figures; multiply by lot size for rupees.

Covered call: net payoff at expiry

Payoff = (ST − S0) + Premium received − max(ST − K, 0)

S0 is the purchase price of the stock, ST the price at expiry, K the call strike.

Covered call: maximum profit

Max profit = (K − S0) + Premium received

Reached when ST is at or above K. Profit is capped.

Covered call: break-even

Break-even = S0 − Premium received

Below this price you make a loss. Maximum loss = S0 − Premium (if the stock falls to zero).

Protective put: net payoff at expiry

Payoff = (ST − S0) − Premium paid + max(K − ST, 0)

K is the put strike.

Protective put: maximum loss

Max loss = (S0 − K) + Premium paid

Applies when ST is at or below K. If K is below S0 the loss is still limited. Profit is unlimited.

Protective put: break-even

Break-even = S0 + Premium paid

The stock must rise by the premium before you profit.

Collar: profit and loss limits

Max profit = (Kcall − S0) + Call premium received − Put premium paid; Max loss = (S0 − Kput) − Call premium received + Put premium paid

Kput is the lower strike and Kcall the higher strike. Net premium can be a small credit or debit.

Bull call spread (debit)

Buy call at K1, sell call at K2 (K1 < K2). Net debit = premium paid − premium received

Max loss = net debit. Max profit = (K2 − K1) − net debit. Breakeven = K1 + net debit.

Bear put spread (debit)

Buy put at K2, sell put at K1 (K1 < K2). Net debit = premium paid − premium received

Max loss = net debit. Max profit = (K2 − K1) − net debit. Breakeven = K2 − net debit.

Bull put spread (credit)

Sell put at K2, buy put at K1 (K1 < K2). Net credit = premium received − premium paid

Max profit = net credit. Max loss = (K2 − K1) − net credit. Breakeven = K2 − net credit.

Bear call spread (credit)

Sell call at K1, buy call at K2 (K1 < K2). Net credit = premium received − premium paid

Max profit = net credit. Max loss = (K2 − K1) − net credit. Breakeven = K1 + net credit.

Long call butterfly

Buy 1 call at K1, sell 2 calls at K2, buy 1 call at K3, where K2 − K1 = K3 − K2

Max profit = (K2 − K1) − net debit, at K2. Max loss = net debit. Breakevens = K1 + net debit and K3 − net debit.

Calendar spread

Sell near-expiry option, buy far-expiry option, same strike and type

Net debit. Loss is limited to the debit. Best result when price is near the strike at near expiry.

Payoff per unit (multiply by lot size)

Total rupee payoff = per-unit payoff × lot size

Premiums and strikes are quoted per unit.

Long straddle: total premium

Total premium = Call premium + Put premium

This is the maximum loss of a long straddle. It happens when the price at expiry equals the strike.

Straddle breakevens

Upper breakeven = Strike + Total premium; Lower breakeven = Strike − Total premium

Same two formulas apply to long and short straddles.

Strangle breakevens

Upper breakeven = Call strike + Total premium; Lower breakeven = Put strike − Total premium

Total premium is the sum of the call and put premiums. Use the call strike for the upper point and the put strike for the lower point.

Long straddle / strangle payoff

Maximum loss = Total premium paid; Maximum profit = Unlimited on the upside, large (limited only by the price falling to zero) on the downside

For a long strangle, maximum loss occurs when expiry price lies between the two strikes (inclusive).

Short straddle / strangle payoff

Maximum profit = Total premium received; Maximum loss = Unlimited on the upside, large on the downside

For a short straddle, maximum profit occurs at expiry price equal to the strike. For a short strangle, it occurs anywhere between the two strikes.

Profit at expiry (long straddle)

Profit per unit = |Expiry price − Strike| − Total premium

Multiply by the lot size for the total rupee result.

Quick revision

• Long futures gains when price rises; short futures gains when price falls; both have unlimited potential on one side.
• Long call: loss limited to premium, gain unlimited; breakeven = strike + premium.
• Long put: loss limited to premium; breakeven = strike − premium.
• Short option seller earns only the premium as maximum profit; call seller's loss is unlimited.
• Option buyer pays premium; seller receives it. Always include it in profit calculations.
• Hedging with futures reduces price risk but leaves basis risk.
• Cash and carry: buy spot, sell futures when futures are overpriced relative to fair value.
• Reverse cash and carry: sell spot, buy futures when futures are underpriced.
• Covered call: long stock plus short call; protective put: long stock plus long put.
• Bull spread suits a rising view; bear spread suits a falling view; both limit profit and loss.
• Straddle: same strike call and put; strangle: different strikes, usually cheaper.
• Long straddle or strangle profits from a large move in either direction; short ones profit from small moves.

Common mistakes

• Using the wrong sign for a short position. Fix: For a short, always compute entry − exit. Or compute the long result and flip the sign.
• Forgetting to multiply by the lot size. Fix: Always finish with units × per-unit payoff. Check the lot size given in the question.
• Ignoring beta and dividing portfolio value by contract value only. Fix: If beta is given, multiply by it. Beta of 1 is the only case where it makes no difference.
• Using the spot index value to compute contract value. Fix: Use futures price × lot size unless the question says to use the index level.
• Reversing the trades for the two strategies Fix: Overpriced futures: sell the expensive thing (futures), buy the cheap thing (spot). Underpriced futures: do the opposite.
• Forgetting to subtract the dividend Fix: Dividends received by the holder lower the net cost of carry. Subtract D once from S × (1 + r × t) to get fair value. Do not subtract it again for each strategy.
• Ignoring the premium when computing profit. Fix: Always take the premium off for a buyer. Net profit = intrinsic value − premium.
• Using strike + premium as the breakeven for a put. Fix: Put breakeven is strike − premium, because a put gains when the price falls.
• Saying a covered call gives unlimited profit. Fix: Remember: the short call caps profit at (K − S0) + premium.
• Adding the premium for a protective put instead of subtracting it. Fix: Premium on a bought option is paid, so it reduces profit and raises break-even to S0 + premium.

Exam tips

• Read the first word of the position carefully: bought or sold. Many wrong answers come from a sign error.
• Look for the lot size in the question. Trap options often show the per-unit figure.
• Questions often ask which position has unlimited loss or limited profit. Short futures has the unlimited loss. Long futures has the limited loss.
• Know the shape of the chart: a straight line through the entry price, rising for long and falling for short.
• In papers with negative marking, skip a payoff question only if you cannot fix the direction. Most are quick to solve.
• Read whether the question asks for contracts to sell or buy. Direction is a common trap option.
• Always check whether beta is given. If it is, it must be used in the formula.
• Remember the definition: basis risk is the risk of the basis changing unpredictably. Expect conceptual MCQs on when it is lowest.