How a Protective Put Combines Stock and Option Payoffs

Summary

The document clarifies how to calculate the profit of a hedged stock position that combines ownership of a share with a put option. The stock contributes its terminal value minus its initial purchase price, while the put contributes its payoff at expiration minus the option premium. Adding the stock’s price change to the put’s profit therefore accounts for the return on the entire combined position.

The answer describes the components of the hedge: the investor pays the current stock price and option premium, then receives the future stock price and any put payoff. The put payoff is determined by the strike price relative to the terminal stock price, with no payoff when the stock finishes above the strike. This is a concise payoff explanation rather than a full analysis of hedge effectiveness; it does not compare alternative hedges or discuss transaction costs, dividends, or position sizing.

Key ideas

• A protective put combines a long stock position with a long put option.
• The stock’s profit is its terminal price minus its purchase price.
• The put’s profit equals its expiration payoff minus the premium paid.
• The combined profit adds the stock price change to the option profit.

Tags

# HEDGING WITH A PUT OPTION


# HEDGING WITH A PUT OPTION












In the following example, for 3rd question and 4th question why do we have to add (Stock price in three months - Current stock price) to put option profit?

Thank you in advance.

## Answer by Kevin (score 0)

https://quant.stackexchange.com/a/48817

A hedged stock position means that you own the stock and an option to reduce the risk. For owning the stock, you pay $S_0$ but receive $S_T$ in 3 months. Similarly, your option costs $1.50$ but will give you $\max\{X-S_T,0\}$.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.