Bear Put Spread

A bear put spread is an options strategy made of two put options on the same underlying asset with the same expiry date. The trader buys a put at a higher strike and sells a put at a lower strike. The position gains when the underlying price falls, up to a fixed maximum, and its loss is limited to the amount paid to open it.

It is the debit form of the bear spread, so called because the put bought costs more than the put sold and the trader pays the difference. The strategy is also known as a long put spread or put debit spread. It suits a view that the price will decline moderately, and it costs less than buying a put outright.

The two legs are opened together as one option spread. The long put gives the right to sell the underlying at the higher strike price. The short put creates an obligation to buy at the lower strike if assigned. Between the two strikes the long put gains value as the price falls. Below the lower strike, each further gain on the long put is cancelled by a loss on the short put, so the profit stops growing.

The option premium received for the short put reduces the cost of the long put. In return the trader gives up any profit from a fall beyond the lower strike.

The key figures per share at expiry are:

• $K_H$ is the higher strike, of the put bought.
• $K_L$ is the lower strike, of the put sold.
• Net premium paid is the price of the long put minus the price of the short put.

A share trades at $100. A trader buys the $100 put for $4.00 and sells the $90 put for $1.50, both expiring in two months. The net premium is $2.50. The maximum loss is $2.50, reached if the share finishes at or above $100. The maximum profit is (100 − 90) − 2.50 = $7.50, reached at or below $90. The break-even price is 100 − 2.50 = $97.50. With a standard contract of 100 shares, the trader risks $250 to make at most $750.

If the share finishes at $94, the long put is worth $6 and the short put expires worthless. The profit is 6 − 2.50 = $3.50 per share.

Before expiry the spread's value depends on more than the share price. Its delta is negative, since it gains when the price falls, but smaller in size than the delta of a single put because the short leg offsets part of the long leg. The effect of time is mixed. When the price sits near the higher strike, the position loses value each day through theta. When the price is near or below the lower strike, time works in the trader's favor, because the spread moves toward its full width as expiry nears.

The spread is less exposed to changes in implied volatility than a single long put. A drop in volatility hurts the long leg and helps the short leg, and the two effects partly cancel.

• Long put. A single put has no cap on profit down to a price of zero but costs more and has a lower break-even.
• Bear call spread. The bear call spread expresses the same view with calls and brings in a credit at the start. It profits if the price simply fails to rise, while the bear put spread needs an actual fall.
• Short selling. Short selling the share gives a gain on any fall but has unlimited loss if the price rises and requires borrowing the shares.
• Bull call spread. The bull call spread is the mirror image for a rising view.

The whole premium is lost if the price is at or above the higher strike at expiry, and that outcome is common when the expected fall does not arrive in time. Being right about direction but late is still a loss.

Where the options are of the American option type, the short put can be assigned early once it is deep in the money, leaving the trader holding shares until the long put is exercised or sold. A price that finishes between the strikes at option expiry leads to exercise of the long put only, which creates a short share position unless the spread is closed first. Two legs also mean two bid-ask spreads and two commissions, which weigh on a position with limited profit.