Why Buying a Stock and Buying a Put Option is Equivalent to Buying a Call Option
When it comes to options trading, understanding the payoff structures of different strategies is crucial for making informed investment decisions. Specifically, the concept that buying a stock and buying a put option can be considered equivalent to buying a call option is an intriguing one. This article will delve into the details of these strategies, their payoff structures, and how they relate to each other.
1. Definitions
Buying a Stock: When you buy a stock, you own a share of the company and benefit from any price appreciation and dividends. Buying a Put Option: A put option gives you the right but not the obligation to sell a stock at a predetermined strike price before the option expires. Buying a Call Option: A call option gives you the right but not the obligation to buy a stock at a predetermined strike price before the option expires.2. Payoff Structures
The core difference in payoff structures between these strategies is what happens to your investment based on the stock price.
2.1 Buying a Stock
The payoff from buying a stock is linear. If the stock price rises, your profit increases directly with the price increase. Conversely, if the stock price falls, your losses occur proportionally.
2.2 Buying a Put Option
The payoff from buying a put option is inversely related to the stock price. This means that if the stock price falls below the strike price, the put option increases in value, potentially offsetting losses from the stock you own.
2.3 Buying a Call Option
The payoff from buying a call option is also linear but only applies when the stock price exceeds the strike price. In this case, you benefit from the difference between the stock price and the strike price minus the premium paid for the option.
3. Combining a Stock and a Put Option
A key insight is understanding how combining a stock with a put option can create a position that resembles a call option.
3.1 Creating a Position Similar to a Call Option
If the stock price rises, you benefit from the stock's appreciation. If the stock price falls, the put option provides protection, allowing you to sell the stock at the strike price, thereby limiting your losses.4. Equivalence of Strategies
From a payoff perspective, the combination of buying a stock and a put option offers a similar outcome under certain conditions.
4.1 When the Stock Price Rises
Buying a stock, buying a put, and buying a call all result in profits.4.2 When the Stock Price Falls
Buying a stock with a put limits your losses, whereas a call option loses its premium if the stock price falls below the strike price.5. An Example
Consider the following scenario:
Variable Value Initial Stock Price 100 Strike Price of Put/Call 100 Premium of the Put 5 Premium of the Call 55.1 Buying Stock
If the stock goes to 120, you gain 20. If it goes to 80, you lose 20.
5.2 Buying a Put
If the stock goes to 80, you can sell it at 100, making a profit of 20 and effectively limiting your losses on the stock.
5.3 Buying a Call
If the stock goes to 120, you gain (120 - 100) - 5 15.
Conclusion
In summary, the combination of buying a stock and a put option creates a payoff structure similar to that of a call option, allowing for upside potential while limiting downside risk.
This understanding can be a valuable tool for investors looking to diversify their strategies and hedge against potential market downturns.