Calculating Position Delta

To calculate the position delta for a standard equity option position, the following formula can be used:

The following table demonstrates this formula applied to various simple option positions:

It's important to note that when selling options or shares of stock short, the number of contracts traded is a negative number. Using negative numbers to indicate short positions is conventional in the trading industry.

Here are the main points to take away from this table:

➜  When short contracts (negative number of contracts), the position delta will have the opposite sign of the option's delta.

➜  A share of stock has a delta of +1.00, which results in positive position delta when buying shares and negative delta when shorting shares.

➜  A positive position delta represents a position that profits from stock price increases and loses money from stock price decreases. For example, the +630 delta position is expected to profit by $630 with a $1 increase in the share price and lose $630 after a $1 decrease in the share price.

➜  A negative position delta represents a position that profits from stock price decreases and loses money from stock price increases. For example, the -83,700 delta position is expected to lose $83,700 with a $1 increase in the share price and profit by $83,700 with a $1 drop in the share price.

At this point, we've discussed position delta and how to calculate it for simple positions. In the next, we'll calculate the delta of more complex positions.

Position Delta of Complex Positions

Calculating the delta of a more complex option position is simple. All you have to do is sum up the position delta for each option in the strategy. As an example, let's calculate the overall delta for a hypothetical long call spread:

In this example, the five long calls generate a delta of +375 while the five short calls generate a delta of -125. Adding these two deltas together leaves us with a net position delta of +250.

Next, we'll calculate the overall delta for a hypothetical short iron condor, which is a strategy that includes four different options:

In this example, the long puts and calls generate -30 and +30 deltas respectively, resulting in zero delta exposure. However, a 0.35 call and a -0.25 put are sold, resulting in a slightly bearish bias. The net position delta of this iron condor is -30, which indicates an expected $30 profit when the stock price falls by $1 and a $30 loss when the stock rises by $1.