# Home: What is a put option?

A Put option is the right, but not the obligation, to sell the underlying asset at a given price, called strike, at or before the stated maturity of the option.

**Put Option Example**

For example, a put option on Caterpillar (CAT) with a strike of $100 and a maturity of 30 days from today will give the buyer the right to sell Caterpillar at $100 at or before the end of 30 days.

As the buyer has the right but not the obligation, if the price of Caterpillar were to be higher than $100 by the end of the 30 days, then the buyer would simply let the option expire worthless. If the price of Caterpillar were below $100 then the buyer would exercise the right to sell Caterpillar at the strike price of $100, if the buyer of the option did not already own the stock then he/she would simply buy the stock in the market at the lower price.

**Put Option Profit & Loss Chart**

The graph below shows the Profit and Loss of a long put position, where Strike price is equal to $100 and the cost of the call is equal to $10.

When the price of the stock goes down the value of the put option goes up, that is to say the price of the put option is negatively related to the price of the stock. The down side is limited to the cost of the option ($10) while the up side is limited to the strike of the stock, as the stock cannot be worth less than zero. In the case above the maximum profit for the put option buyer would be $100.

**Why Buy A Put Option?**

The driving factors behind buying a put are; to speculate on falling stock prices over the time horizon we are buying the option or hedging a long stock portfolio.

Options are usually sold in lots of 100 shares, so the total cost of 1 option on the above stock would be $1000 (10 X 100) the cost of the option per share times the amount of shares. The option however will be quoted according to its strike (100) and its expiry date, i.e. today plus 1 month. A quote list on options will look something like this:

Stock | Option | Strike | Expiry | Price |

CAT | Put | 110 | 1 week | 7 |

CAT | Put | 110 | 1 month | 18 |

CAT | Put | 105 | 1 week | 5 |

CAT | Put | 105 | 1 month | 14 |

CAT | Put | 100 | 1 week | 3 |

CAT | Put | 100 | 1 month | 10 |

Let's say we buy a Caterpillar put option strike $100 with 1 month to expiry at $10, the current price is $110. If the price of Caterpillar stays stable or increases over the following month the option will expire worthless and we will have lost $1000.

If the price of Caterpillar decreases during the month, let's say to $80, we can exercise the option, that is exercise our right to sell Caterpillar at $100 a share, if we didn't already own the Caterpillar shares then we could buy Caterpillar in the market at $80 a share, for a profit of $1000 (100-80-10, X 100) i.e. the strike price minus the market price, minus the cost of the option, times 100.

This can be contrasted to selling the Caterpillar stock short at $110 a share and when the price reaches $80, buying it back for a net profit of $3000 (110-80 X 100). This gives rise to other considerations, which are not the scope of this article, but briefly we can see that the long put option gave a return of 100% ($1000/$1000) whereas the cash position gave a return of 27.3% ($3000/$11000).

A third scenario would be that we change our minds about the performance of Caterpillar, if we no longer believe that the stock will decrease beyond its strike price we could sell the option with the same strike and expiry day and square the position. Considering the option now has 3 weeks to expiry and is worth $900, we could sell the put option at the price and receive $900, for a net loss of $100. If the price of Caterpillar were to remain stable or increase, both options would expire worthless.

If the price of Caterpillar were to move down to $80 then both options would be exercised, as we would exercise the option we bought and the put option we sold would also be exercised.

We would use the Caterpillar stock we receive when the put option we sold is exercised to sell the stock to the seller of the put option we bought.

**Selling Put Options**

The seller of a put option has the obligation to receive delivery of the asset, let's say Caterpillar stock, at the predetermined price (strike) if the option is put at or before expiry of the option.

For this obligation the seller will receive a fee, called the premium, this is calculated using a formula, most commonly the Black & Scholes formula, which uses five factors; price of the stock, strike price, time to maturity, volatility and interest rates.

Selling a put option is also known as writing a put option, the writer of a put option is exposed to receiving a stock at the strike price of the option when the market will be lower, his/her maximum risk exposure is the price of the strike, as the lowest value of a stock is zero.

In the above example of a put on Caterpillar, the writer of the put option is obligated to take delivery of the Caterpillar stock at $100 a share when the put is exercised, let's say the market price is $80, the writer may choose to hold the stock, or sell the stock into the market at $80 for a net loss of $1000 (100-80+10 X 100) i.e. strike price minus the market price, plus the option premium, times the number of shares. His/her maximum possible loss is $9000 (100-10 X 100) i.e. stock price minus the premium, times the number of shares.

**Time Value of Put Options**

The longer an option has to maturity the more expensive the option will be, this makes sense as the chances of the option being exercised before expiry are greater, this is also known as intrinsic time value. However the time value will decrease as every day goes by, as there is less time to expiry and a smaller chance of the option being exercised, therefore all things being equal the value of an option will decrease as the time to expiry becomes shorter, known as time decay. So buying long term put options gives the buyer more chances of exercising the option but it also comes at a cost.

When looking at the price of a put option we have to take into consideration, apart from the cost of the option, the strike price and time to maturity. An option that is out of the money, that is with a strike price that is far away from the cash price, will be much cheaper than an option with a strike price at the money, meaning a strike price equal to the cash price, but may offer fewer chances of actually exercising the option.

An option with a long time to expiry will offer more chances of being exercised but will come at a high price, whereas too short a time to expiry may offer a cheap call option but few chances of profitability unless the strike price is in the money.

## Additional Examples

For another type of option, please see the Call Option Tutorial.