Bull, bear and butterfly spreads
1. The idea
A spread combines options of one type, calls or puts, some bought and some sold, so that both the gain and the loss are capped. Its payoff at expiry is the sum of the payoffs of Level 1, and its profit is that payoff less the net cost: the premiums paid less the premiums received.
- A bull spread buys the option with the lower strike price, \(K_1\), and sells the one with the higher, \(K_2\). It gains when the share rises.
- A bear spread buys the option with the higher strike price and sells the one with the lower. It gains when the share falls.
- A butterfly spread uses three strike prices the same distance apart. It buys one option at the lowest, \(K_1\), and one at the highest, \(K_3\), and sells two at the middle one, \(K_2\). It gains when the share ends near \(K_2\).
An example. A share trades at $47, and four-month calls cost $4.42 with a strike price of $45 and $2.07 with $50. A bull spread buys the $45 call and sells the $50 call, for a net cost of \(4.42 - 2.07 = \$2.35\). Its payoff at expiry is zero below $45, \(S_T - 45\) between $45 and $50, and $5 above $50, where \(S_T\) is the share price at expiry. So its profit is at most \(5 - 2.35 = \$2.65\) and its loss at most $2.35, and it breaks even where \(S_T - 45 = 2.35\), at a share price of $47.35.
The profit’s line is straight between two strike prices and flat beyond the outer ones, so the largest profit and the largest loss are always at strike prices: work out the profit there and compare.
Connecting the dots. The same bull spread can be built with puts: buy the $45 put for $1.83 and sell the $50 put for $4.41, which brings in $2.58. Its payoff at expiry is exactly $5 less than the call spread’s, whatever the share does, so put-call parity makes its net cost lower by the present value of $5, \(5\,e^{-0.04 \times 4/12} = \$4.93\) at a 4% rate: \(\$2.35 - \$4.93 = -\$2.58\). Questions on spreads usually ignore the interest on the premiums, and so do the profits here.
2. Try it
If an answer is wrong, we will see what went wrong and how to fix it.
3. The spread on a chart
First, the spread’s net cost.
Now move the share price at expiry. The payoff rises from $0 to $5 between the two strike prices, and the profit is the payoff less the net cost.
4. One worked example, then your turn
The worked example is a bear spread with puts.
Now a butterfly spread with hints, one step at a time: how high can the share end before the trader loses money?
And one on your own: a bull spread built with puts.
5. Practice
Each question has new numbers. You master the skill when you get three right in a row, with at least one right answer for a bull spread, a bear spread and a butterfly spread. You can always open the solution, but then that question does not count.
6. Coming back to it
When you have mastered a skill, it comes back on the start page for a short review after 1 day. After each right answer the next review comes later: after 3, 7, 14 and then 30 days. After a wrong one, the reviews start again at 1 day.
This skill: