\[ \delta_{P}=\sum_{i}w_{i}\delta_{i} \]

Here, $\delta_{p}$ is the delta of the portfolio, $w_{i}$ are the weights of the components of the portfolio, and $\delta_{i}$ are the deltas of the components of the portfolio.

For example, suppose you have a portfolio made up of a stock and call and put options on the stock, as follows:

- 25 percent in the underlying stock.
- 40 percent in call options on the underlying stock, each with a delta of 0.6.
- 35 percent in put options on the underlying stock, each with a delta of -0.3.

Because the delta of a stock is 1, the delta of your portfolio is:

0.25 * 1 + 0.4 * 0.6 + 0.35 * (-0.3)

or

0.385.

In other words, using the implications of the definition of delta, as noted here, your portfolio moves 38.5 percent of the move in the underlying stock.

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Additional material: To understand the essence of delta hedging, read this.

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