## Understanding Delta: a key guide for Investors and Traders - part 1

### Preface

I've written this guide on Delta for two main reasons. Firstly, Delta is a fundamental concept in options trading that I often refer to in my other articles. A thorough understanding of Delta will significantly enhance your grasp of the options market and my future other writings.

Secondly, this guide is designed to be a reference point. Whether you're a beginner or an experienced trader, it will help deepen your understanding of Delta and its role in options trading. It's my hope that this guide will be a valuable resource in your trading toolkit.

### Introduction

Whether you're a seasoned trader, a beginner just starting out, or an investor curious about options, it's important to understand the basics. One key piece of the puzzle is Delta, a term you'll often hear in the world of options trading. In this article, "Why is Delta Important for Every Investor and/or Trader?", we'll break down what Delta is and why it matters. We'll look at how Delta shows us how option prices move when the stock price changes, how it can give us a hint about an option's future, and why it's a handy tool for managing risk. This guide to Delta is designed to help everyone, no matter your experience level, make smarter decisions when trading or investing.

In this first part of the guide will cover the following chapters:

1. **Definition of Delta**: Understanding the basic concept

2. **Delta Values**: Interpreting the range and meaning

3. **Moneyness and Delta**: The relationship between Delta and the option's position relative to the market price

4. **Delta and Probability**: Using Delta to estimate potential outcomes

In a later to be published part of the guide, I will cover more advanced topics:

5. **Delta Hedging**: Strategies for risk reduction

6. **Delta and Portfolio Management**: Applying Delta to broader investment strategies

7. **Delta Neutral Strategies**: Creating a balanced portfolio

8. **Impact of Time and Volatility**: How Delta changes over time and with market fluctuations

9. **Real World Examples**: Practical applications of Delta in trading

10. **Limitations of Delta**: Understanding the constraints of Delta in market analysis

In the world of options trading, Delta is a term you'll frequently encounter. It's one of the "Greeks" - a set of five key metrics that help traders understand the risks and potential rewards of an options position. Delta, specifically, measures how much an option's price is expected to change if the price of the underlying asset (like a stock) changes by one dollar.

Let's say that again: Delta measures how much an option's price is expected to change if the price of the underlying asset (like a stock, etf, future, …) changes by one dollar (or one euro is the underlying is listed in euro).

If there is only one definition you have to learn by heart, than it's this one. Memorize it, write it on the mirror in your bathroom.

To put it simply, Delta gives you a sense of the "velocity" of an option's price. If an option has a Delta of 0.6, for example, the option's price would move $0.60 for every $1 move in the price of the underlying asset. This relationship isn't static, though - Delta can change as the price of the underlying asset shifts, and as the option gets closer to its expiration date. So, if the option price was f.e. $2, and the Delta was 0.6, and the underlying went up by $1, the new price of the option would be? $2.6 ($2 + $0.6).

In the example above we showed a positive Delta. But Delta can also be negative.

Let's consider an example of negative Delta. If you have a put option (which gives you the right to sell a stock) with a Delta of -0.5, this means the option's price is expected to decrease by $0.50 for every $1 increase in the price of the underlying stock. Conversely, if the stock's price decreases by $1, the put option's price would increase by $0.50. This negative relationship between the option's price and the stock's price is characteristic of put options, and it's what allows put option buyers to profit when stock prices fall.

But Delta can also be used for the underlying itself.

The underlying asset itself, such as a stock, is often referred to as having a Delta of 1 (or 100% when expressed as a percentage). This is because for each $1 movement in the stock's price, the value of the stock position changes by the same amount.

For instance, if you own 100 shares of a particular stock, your position would have a Delta of 100. This means if the stock price increases by $1, the total value of your stock position would increase by $100 (100 shares * $1). Conversely, if the stock price decreases by $1, the total value of your position would decrease by $100.

This concept is crucial in understanding how options can be used to mimic stock positions. For example, an option with a Delta of 0.5 is said to behave like a position in 50 shares of the underlying stock. This is why Delta is often used by options traders to understand and manage the risk of their portfolio in terms of equivalent stock positions.

Delta values for options can range from -1 to 1. The value of Delta gives us a measure of how much the price of an option is expected to change for each $1 change in the price of the underlying asset.

For call options, Delta values range from 0 to 1. A call option with a Delta of 1, or 100% when expressed as a percentage, is expected to increase by $1 for each $1 increase in the price of the underlying asset. On the other hand, a call option with a Delta of 0.5, or 50%, is expected to increase by $0.50 for each $1 increase in the price of the underlying asset.

For put options, Delta values range from -1 to 0. A put option with a Delta of -1, or -100%, is expected to increase by $1 for each $1 decrease in the price of the underlying asset. Similarly, a put option with a Delta of -0.5, or -50%, is expected to increase by $0.50 for each $1 decrease in the price of the underlying asset.

It's important to note that the Delta of an option changes as the price of the underlying asset changes. This is due to the fact that Delta is not a fixed value, but a function of the price of the underlying asset. This characteristic of Delta is known as "Delta drift."

In the next chapter, we will delve deeper into the relationship between Delta and the moneyness of an option.

The term "moneyness" in options trading refers to the relationship between the current price of the underlying asset and the strike price of the option. The Delta of an option is closely related to its moneyness.

1. **In-the-Money (ITM) Options**: An option is considered in-the-money when exercise of the option would be profitable. For call options, this is when the underlying asset's price is above the strike price. For put options, it's when the underlying asset's price is below the strike price. ITM options have Deltas close to 1 for calls and -1 for puts. This means that the price of an ITM option moves almost in sync with the price of the underlying asset.

2. **At-the-Money (ATM) Options**: An option is at-the-money when the underlying asset's price is equal to the strike price. ATM options have Deltas around 0.5 for calls and -0.5 for puts. This means that the price of an ATM option moves about half as much as the price of the underlying asset.

3. **Out-of-the-Money (OTM) Options**: An option is out-of-the-money when exercise of the option would not be profitable. For call options, this is when the underlying asset's price is below the strike price. For put options, it's when the underlying asset's price is above the strike price. OTM options have Deltas close to 0. This means that the price of an OTM option moves very little with changes in the price of the underlying asset.

Understanding the relationship between moneyness and Delta is crucial for options traders as it helps them gauge the risk and potential reward of different options strategies. In the next chapter, we will explore the interpretation of Delta as an estimate of the probability that an option will be in-the-money at expiration.

One of the most useful interpretations of Delta is as an estimate of the probability that an option will be in-the-money at expiration. This can be a powerful tool for traders when assessing the potential outcomes of an options trade.

The Delta of an option can be interpreted as the estimated probability that the option will expire in-the-money. For example, an option with a Delta of 0.7 can be interpreted as having approximately a 70% chance of being in-the-money at expiration.

This interpretation is based on the assumption that the distribution of returns of the underlying asset is lognormal, a common assumption in the Black-Scholes model of options pricing. However, it's important to note that this is a simplifying assumption and may not always hold in real-world markets.

While Delta provides a useful estimate of the probability of an option being in-the-money at expiration, it's not the only factor that traders should consider. Other factors, such as the volatility of the underlying asset and the time to expiration, can also significantly impact the outcome of an options trade.

In the next chapter, we'll delve into the concept of Delta hedging, a strategy that aims to reduce the risk associated with price movements in the underlying asset by offsetting long and short positions.

In these first four chapters of our comprehensive guide on Delta, we've laid the groundwork for understanding this crucial concept in options trading. In the upcoming chapters we'll discuss more advanced topics on Delta, namely; Delta hedging, Delta and portfolio management, Delta neutral strategies, impact of time and volatility on Delta, some real world examples and some of the limitations of Delta.