# Long put

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**Long put** is strategy oriented on **downturn**. Investor buys a put option with hope that price will **fall**. That would increase value of the option. Investor plans to hold the asset long. Sometimes long put is used to hedge long stock position.

The long put option can be held until it **expires**, which forces investor to buy stock at the market price, or can be sold short before **expiration**.

Long put has **limited risk**, therefore it is preferred by bears. Other method of achieving similar effect is **shorting stock**, but that strategy can be associated with **high risk level**. Moreover, options are more liquid than stocks, which allows investors to sell them **quickly**.

The stock price can fall even to almost **zero**. Therefore, the maximum profit in long put is limited to **striking price** of bought put take away option price *(P. Christoffersen, et al. 2017)*

## Long put trade[edit]

In a **long put trade** you are not purchasing the obligation, but the right, to sell the stock until it's expiration at the put strike price. This strategy should be used right after the prediction of falling in price of underlying market.

Long put ensures **unlimited profit potential** with low risk of loss. The **price** of the option is the most you can lose, regardless of how high the stock rises. When the price of stock falls below the breakeven, profit occurs. **Debit** in your trading account will be the **premium** of your long put strategy. To offset a long put, you have to sell a put at the same strike price and expiration date to close out the option *(G. A. Fontanills, T. Gentile 2001).*

## Long put payoff[edit]

The **payoff** related with a long put strategy is a function of whether the strategy exercises its right *(Gottesman A. 2016):*

- if the long put does not exercise, there is
**no transaction**so the payoff is**zero** - if the long put strategy exercises, the payoff is the difference between the
**price of the asset**that it delivers and the price that the**strategy receives**.

By exercising your long put, you are choosing to go short the underlying stock at the srike price of the put option *(G. A. Fontanills, T. Gentile 2001).*

If the underlying asset price at expiration date is **greater than or equal to** strike price - the long put option **will not exercise** and long put payoff will be **zero**. However, when aseet price at expiration date is **less than** strike price - the long put option **will be exercised** and payoff of
will be a **difference between strike price and the underlying asset price**. That difference is called *intrinsic value*.

An **equation** that describes the payoff to the long put strategy is *(Gottesman A. 2016):*

*Long put payoff = max(K - St, 0)*where*K*stands for*strike price*and*St*stands for*underlying asset price at expiration date*

## Long put profit and loss[edit]

To calculate strategy's **P&L** (profit and loss) we have to consider the **premium** that it pays at initiation.
The exercise decision at expiration is **the same as** in long put **payoff**. Furthermore, when long put option **will not be exercised**, put premium paid at initation becomes our **loss**. However, when long put strategy **will be exercised**, put premium will be **the amount reducing our profit**.

The long put's **P&L** at expiration can be expressed as *(Gottesman A. 2016):*

*Long put P&L = max(K - St, 0) - p0*where*p0*stands for*put premium paid by long put to the short put at initiation*

A **negative value** of the long put's P&L represents **loss** and a **positive value** represents **profit**.

## References[edit]

*Christoffersen P., et al. (2017). Illiquidity premia in the equity options market, The Review of Financial Studies, 31(3), 811-851.**Fontanills G. A., Gentile T. (2001). The Stock Market Course, John Wiley & Sons Inc, New York**Gottesman A. (2016). Derivates Essentials An Introduction to Forwards, Futures, Options, and Swaps, Willey & Sons Inc, New York*

**Author:** Sebastian Kopta