Introduction

In the world of options trading and risk management, understanding how a portfolio’s value changes concerning the underlying asset’s price movement is crucial. This understanding is captured by a concept known as “Delta.” In this chapter, we will explore how to define and calculate the delta of a portfolio. Delta measures the sensitivity of a portfolio’s value to changes in the price of the underlying asset. It’s a fundamental Greek that provides valuable insights into risk exposure and hedging strategies.

Delta for a Portfolio

Delta represents the change in the value of an option or portfolio for a one-unit change in the price of the underlying asset. For individual options, delta ranges between -1 and 1 . A call option typically has a positive delta, while a put option has a negative delta. Delta for a portfolio is calculated as the weighted average of the individual options’ deltas within the portfolio. The formula for delta of a portfolio is as follows:

$$\text{Portfolio Delta}=\sum(\text{Option Delta} \times \text {Option Quantity})$$

Where:

• Portfolio Delta is the delta of the entire portfolio
• Option Delta is the delta of an individual option within the portfolio
• Option Quantity is the quantity of the specific option in the portfolio

Example: Let’s consider a portfolio consisting of three options:

• Call Option A with a delta of 0.6 and a quantity of 5 contracts
• Put Option B with a delta of -0.4 and a quantity of 3 contracts
• Call Option C with a delta of 0.7 and a quantity of 2 contracts

To calculate the portfolio delta:

$\text{Portfolio Delta}$= $(0.6 \times 5) + (−0.4 \times 3) + (0.7 \times 2)$ = $43+(−1.2) + 1.4 = 3.2$

The portfolio’s delta is 3.2. This means that for every one-unit increase in the underlying asset’s price, the portfolio’s value is expected to increase by USD 3.2.