Break-even point

An option that finishes in the money has not necessarily made money. The buyer paid a premium before anything happened, and that premium has to be earned back before the first rupee of profit appears.

The break-even point is where the payoff exactly cancels the premium. Above it a long call profits; below it a long put profits; and in between the option can be in the money and still a loss.

The same idea applies to a futures position, where the break-even is the price at which the cost of carrying the underlying has been recovered.

Every strategy in the options chapter is built from the same two rules, applied to the net premium.

• Long call: BEP = Strike + Premium. You need the underlying above the strike by at least what you paid.
• Long put: BEP = Strike − Premium.
• Short call / short put: the same numbers, read from the other side — they are where the writer's premium is exhausted.
• Vertical spread: use the net premium. For a bull call spread, BEP = lower strike + net premium paid. For a bullish put spread, BEP = higher strike − net premium received.
• Straddle: two break-evens, at Strike − Total Premium and Strike + Total Premium. The position loses inside that band and profits outside it in either direction.

For a futures position, the break-even futures price is spot plus net cost of carry — interest paid to fund the asset, less income earned on it.

Long call BEP        = Strike + Premium              (X + P)
Long put  BEP        = Strike − Premium              (X − P)

Bull call spread BEP = Lower strike  + Net premium paid
Bullish put spread   = Higher strike − Net premium received

Straddle             = Strike − Total premium  AND  Strike + Total premium

Futures BEP          = Spot + Cost of carry

A long call. Index at 17,562; buy the 17,500 call at Rs 95.

BEP = 17,500 + 95 = 17,595

At 17,595 the payoff is Rs 95 and the premium was Rs 95 — net zero. At 18,000 the payoff is Rs 500, so the profit is Rs 500 − Rs 95 = Rs 405. At 17,550 the option is in the money and you still lose Rs 45.

A short put. Write the 17,500 put at Rs 150, lot size 50.

BEP           = 17,500 − 150 = 17,350
Premium banked = 150 × 50    = Rs 7,500
Contract value = 17,500 × 50 = Rs 8,75,000

Above 17,350 the writer keeps some or all of Rs 7,500. Below it, the losses begin and do not stop.

A bull call spread. Long the 17,500 call at Rs 185, short the 17,800 call at Rs 61.

Net premium paid = 185 − 61 = 124
BEP              = 17,500 + 124 = 17,624
Maximum profit   = (17,800 − 17,500) − 124 = Rs 176
Maximum loss     = Rs 124

A bullish put spread. Short the 17,500 put at Rs 125, long the 17,000 put at Rs 34.

Net premium received = 125 − 34 = 91
BEP                  = 17,500 − 91 = 17,409
Maximum profit       = Rs 91       Maximum loss = Rs 409

An interest rate option. On 1 October 2021, 6.10% GOI 2031 trades at Rs 98.40. Buy the 98.50 call at a premium of Rs 0.20.

BEP = 98.50 + 0.20 = Rs 98.70

At Rs 98.70 you exercise, buy at 98.50, sell at 98.70, make Rs 0.20 — and you already paid Rs 0.20. At Rs 98.90 the gross gain is Rs 0.40 and the net profit is Rs 0.20. At Rs 98.25 you abandon the option and lose the Rs 0.20 premium, and nothing more.

A long straddle. Buy the 6,000 call at Rs 257 and the 6,000 put at Rs 136.

Total premium = 257 + 136 = 393
Lower BEP = 6,000 − 393 = 5,607      Upper BEP = 6,000 + 393 = 6,393

At 5,300 the net flow is +Rs 307; at 6,700 it is also +Rs 307. Between 5,607 and 6,393 the position loses — the straddle needs a big move, not a correct one.

Chapter 16 (Introduction to Options) derives the call BEP as strike plus premium and the put BEP as strike minus premium from the payoff tables. Chapter 17 (Strategies using Equity Futures and Equity Options) computes the BEP for every spread, straddle and strangle, and Chapter 21 does the same for options on government securities — all the figures above are from those chapters. This is the single most computationally reliable topic in the derivatives modules: expect at least one direct BEP calculation and one strategy question giving strikes and premiums.

• In the money is not profitable. An option can be exercised and still lose money if the payoff is smaller than the premium. The BEP is where the two meet.
• Use the net premium for a spread, not the premium of one leg. The commonest arithmetic slip in Chapter 17.
• The writer's break-even is the same number as the buyer's. It is a zero-sum contract; only the sign of the profit flips.
• A straddle has two break-evens, not one. Missing the lower one means missing half the payoff diagram.
• BEP ignores brokerage, statutory levies and the cost of margin. It is the theoretical break-even, not the point at which a real account turns positive.
• For a futures position the break-even is spot plus cost of carry, and cost of carry differs between participants — the workbook says so explicitly.