FRM Exam Part I · Trading Strategies

Bull and Bear Spreads: Payoffs, Profit and Breakeven

Updated 11 October 2026 · Fact-checked

A bull spread buys an option at a lower strike and sells one at a higher strike, same expiry, to profit from a moderate rise. A bear spread does the opposite for a moderate fall. Profit and loss are both capped. Solve by finding the net premium, the strike gap and the breakeven.

Understand Bull and Bear Spreads

A vertical spread combines two options of the same type (both calls or both puts), on the same underlying and with the same expiry, but with different strike prices. You buy one and sell the other. The sold option's premium offsets part of the cost of the bought option, so the position is cheaper than a single option. The price you pay for that saving is a capped profit.

A bull spread profits when the asset price rises. With calls, you buy the call at the lower strike K1 and sell the call at the higher strike K2. Because a lower-strike call costs more, you pay a net premium (a net debit). Above K2 the gain stops growing, because the short call's loss cancels the long call's further gain. Below K1 both calls expire worthless and you lose only the net premium.

A bear spread profits when the price falls. With puts, you buy the put at the higher strike K2 and sell the put at the lower strike K1. A higher-strike put costs more, so this is also a net debit. The maximum gain occurs when the price is at or below K1. The maximum loss is the net premium, if the price is at or above K2.

You can build each spread with either option type. A bull spread with puts means buying the low-strike put and selling the high-strike put. That gives you a net credit, and the maximum profit is the credit received. A bear spread with calls means selling the low-strike call and buying the high-strike call, which also gives a net credit. The shape of the payoff is the same for both constructions. Only the cash flow at the start differs.

In both cases the payoff is bounded between 0 and K2 − K1 before the premiums are counted. Neither spread has unlimited loss, which is why they suit a moderate view rather than a strong one.

Key formulas to remember

Bull call spread payoff at expiry: Payoff = max(S − K1, 0) − max(S − K2, 0), with K1 < K2; Ranges from 0 (S ≤ K1) to K2 − K1 (S ≥ K2). Profit = payoff − net premium.
Bull call spread: net cost, max profit, max loss: Net debit = C(K1) − C(K2); Max profit = (K2 − K1) − net debit; Max loss = net debit; C(K1) > C(K2) because the lower strike call is worth more.
Bull call spread breakeven: Breakeven = K1 + net debit; Profit is zero when S equals this level.
Bear put spread payoff at expiry: Payoff = max(K2 − S, 0) − max(K1 − S, 0), with K1 < K2; Long the high-strike put, short the low-strike put. Ranges from 0 (S ≥ K2) to K2 − K1 (S ≤ K1).
Bear put spread: net cost, max profit, max loss: Net debit = P(K2) − P(K1); Max profit = (K2 − K1) − net debit; Max loss = net debit; P(K2) > P(K1) because the higher strike put is worth more.
Bear put spread breakeven: Breakeven = K2 − net debit; Profit is zero when S equals this level.
Credit spread versions: Max profit = net credit; Max loss = (K2 − K1) − net credit; Applies to a bull put spread and a bear call spread. Breakeven for the bull put spread = K2 − credit. Breakeven for the bear call spread = K1 + credit.

How to solve Bull and Bear Spreads questions

Use the same routine for any bull or bear spread question. It works for calls or puts, and for debit or credit spreads.

1Identify the view: moderate rise means bull spread, moderate fall means bear spread.
2Write down which option you buy and which you sell at K1 (lower) and K2 (higher). Bull call: buy K1, sell K2. Bear put: buy K2, sell K1.
3Compute the net premium. Premium paid minus premium received. Positive means debit, negative means credit.
4Compute the strike gap K2 − K1. This is the maximum payoff before premiums.
5Max profit and max loss: for a debit spread, max profit = gap − debit and max loss = debit. For a credit spread, max profit = credit and max loss = gap − credit.
6Find the breakeven using the formula for that spread. Check it lies between K1 and K2.
7If asked for profit at a given price S, compute the payoff of each leg, add them, then subtract the net debit (or add the net credit).

Quickest way: Gap, cost, then two bounds

When to use it: Use this for multiple-choice questions asking for maximum profit, maximum loss or breakeven of a vertical spread.

Gap = K2 − K1. Net debit = price of the option you buy − price of the option you sell.
For a debit spread: max loss = debit, max profit = gap − debit. The two always add up to the gap.
Breakeven: a bull call spread is K1 + debit. A bear put spread is K2 − debit.
Sanity check: the breakeven must sit inside the K1 to K2 range, and max profit must be positive. If the debit is larger than the gap, you have the legs reversed.

Common mistakes in Bull and Bear Spreads

Reversing the legs, for example buying the high-strike call in a bull call spread.
Students remember 'buy one, sell one' but not which strike goes with which.
Fix: For a debit spread you always buy the more expensive option. Calls: the lower strike costs more. Puts: the higher strike costs more.
Forgetting the net premium and quoting the payoff as the profit.
The payoff formula looks complete, so the premium is overlooked.
Fix: Always write profit = payoff − net debit (or + net credit). Maximum profit is the gap minus the debit.
Stating that a bull spread has unlimited upside.
Confusing it with a single long call.
Fix: The short call at K2 caps the gain. Maximum payoff is K2 − K1.
Using the wrong breakeven formula for the bear put spread, such as K1 + debit.
Students copy the bull spread breakeven.
Fix: The bear put spread profits when the price falls, so breakeven is K2 − debit, below the higher strike.
Assuming a spread always costs money (a debit).
Only the bull call and bear put examples are practised.
Fix: A bull put spread and a bear call spread give a net credit. Then max profit is the credit and max loss is the gap minus the credit.
Mixing up the view and the option type, for example thinking a put spread must be bearish.
Puts are linked in memory with falling prices.
Fix: The view depends on which strike you buy. Buying the lower strike and selling the higher strike is bullish, whether you use calls or puts.

Worked examples

Example 1

A stock trades at $50. An investor buys a 3-month call with strike $45 for $7.00 and sells a 3-month call with strike $55 for $2.50. Find the net cost, maximum profit, maximum loss and breakeven.

Show the solution

This is a bull call spread: buy the lower strike K1 = 45, sell the higher strike K2 = 55.
Net debit = 7.00 − 2.50 = $4.50.
Strike gap = 55 − 45 = $10.
Maximum profit = 10 − 4.50 = $5.50, reached when S ≥ 55.
Maximum loss = net debit = $4.50, reached when S ≤ 45.
Breakeven = K1 + debit = 45 + 4.50 = $49.50.

Answer: Net cost $4.50; maximum profit $5.50; maximum loss $4.50; breakeven $49.50.

Example 2

An investor expects a moderate fall in an index. She buys a put with strike 1,000 for 48 and sells a put with strike 900 for 14. What is her profit per unit if the index finishes at 880 at expiry, and what is the breakeven?

Show the solution

This is a bear put spread: buy the higher strike K2 = 1,000, sell the lower strike K1 = 900.
Net debit = 48 − 14 = 34.
Payoff of long put at S = 880: max(1,000 − 880, 0) = 120.
Payoff of short put: −max(900 − 880, 0) = −20.
Total payoff = 120 − 20 = 100, which equals the strike gap (1,000 − 900), as expected for S ≤ K1.
Profit = 100 − 34 = 66.
Breakeven = K2 − debit = 1,000 − 34 = 966.

Answer: Profit is 66 per unit at S = 880; breakeven is 966.

Exam tips

Questions usually give two option prices and two strikes. Find the net debit first, then everything else follows.
Check that max profit plus max loss equals the strike gap for a debit spread. It catches arithmetic slips quickly.
Read the question for the option type. A bull put spread is a credit spread, so the profit and loss formulas change.
Expect conceptual questions comparing a spread with a single option: lower cost, capped profit, limited loss.
Draw the payoff in your head: flat, a slope between K1 and K2, then flat. This helps with 'what happens if the price is above K2' questions.

Practice questions from Trading Strategies

Bull and Bear Spreads in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Bull and Bear Spreads: frequently asked questions

What is the difference between a bull spread and a bear spread?

A bull spread profits when the underlying price rises moderately. You buy the lower strike and sell the higher strike. A bear spread profits when the price falls moderately. You buy the higher strike and sell the lower strike. Both have capped profit and capped loss.

How do I calculate profit on a bull call spread?

Compute the payoff of the long call minus the payoff of the short call at the final price. Then subtract the net premium paid. Profit is capped at the strike gap minus the net debit.

Why use a spread instead of a single option?

Selling the second option cuts the upfront cost. The trade-off is that you give up gains beyond the second strike. It suits a view that the price will move, but only by a moderate amount.

Can a vertical spread be built with puts for a bullish view?

Yes. Buying a low-strike put and selling a high-strike put is a bull put spread. You receive a net credit. Maximum profit is that credit, and maximum loss is the strike gap minus the credit.