What is Position Delta?

The delta of an option expresses that option's expected price change relative to movements in the stock price. 

For example, a +0.50 delta call option is expected to gain $0.50 in value when the stock price increases by $1. Conversely, that same option is expected to lose $0.50 when the stock price falls by $1.

However, it's important to know how that option price change translates to profits and losses for your position, especially when trading complex positions with more than one option.

Position delta takes things a step further and estimates the profits or losses on an entire option position relative to $1 changes in the stock price.

Consider the following option position:

In this example, the call price should increase from $10 to $10.75 with a $1 increase in the stock price, and decrease from $10 to $9.25 with a $1 decrease in the stock price.

But how does this translate to profits or losses for a trader with -2 contracts (short two contracts)?

Since this trader is short the call options, they profit from price decreases. More specifically, a decrease from $10 to $9.25 represents a $0.75 profit per option contract.

Recall that an option represents 100 shares of stock, so we need to multiply the change in the option price by 100 to solve for the actual return in dollars:

($10 sale price - $9.25 current price) x 100 = +$75

Lastly, the trader in this example is short two contracts, so the $75 profit becomes a $150 profit when multiplying by two contracts.

Working through this example, we learn that the trader is expected to profit by $150 when the stock price decreases by $1. Therefore, the trader's position delta in this example is -150, as a $1 increase in the stock price should lead to $150 in losses, and a $1 decrease in the stock price should result in a profit of $150.

So, while the option's delta is +0.75, it doesn't indicate the expected profits or losses for a trader who is short two contracts. 

Analyzing the overall delta of the position solves this problem by converting an option's delta into the expected profits or losses for a specific position when the stock price changes.