Previously the principle of theta is explained (see article: Fundamentals 1: What is Theta). In this article the sign and magnitude of theta is explained.

## The Sign and Numerical Value of Theta

When it comes to interpretation of the theta value two key aspects are important: the sign and the magnitude of its numerical value.

### Sign of the Theta Value

Theta can have either a positive or negative value. The sign provides crucial information about the expected behavior of an option’s value over time.

- Positive Theta: A positive theta indicates that the option’s value is expected to increase as time passes. This might seem counterintuitive, as options generally experience loss in value when time passes (also called time decay). However, positive theta is often associated with option-selling strategies, where traders collect premiums upfront and aim to profit from the expected decrease in the option’s value due to time decay. In this case, a positive theta represents the potential for the option seller to generate profit as time progresses.
- Negative Theta: The more common scenario is a negative theta, which indicates that the option’s value is expected to decrease over time. Negative theta is inherent to most options, reflecting the impact of time decay. It implies that if the underlying asset doesn’t move significantly in the expected direction, the option’s value will erode gradually over time. Option buyers should be aware of negative theta’s potential effect on their positions.

### Magnitude of the Theta Value

The magnitude, or height, of theta provides insights into the intensity or speed of time decay. A higher magnitude indicates a more rapid decline in an option’s value over time, while a lower magnitude suggests a slower erosion.

## Example

Suppose you purchased a call option on XYZ Company with an expiration date of 30 days from now. The option has a theta of -0.03, indicating that its value is expected to decrease by $0.03 per day, assuming no other factors change.

Now, fast forward to the 20th day, with 10 days remaining until expiration. At this point, the option’s value will have eroded by $0.03 x 10 days = $0.30. Remember, this reduction occurs even if the price of the underlying asset remains unchanged. It’s important to note that the magnitude of theta can vary depending on various factors, including the specific option and market conditions.

Let’s take it a step further. With 10 days left until expiration, the time decay accelerates, and let’s assume the option’s theta increases to -0.05. Now, the option’s value will decrease by $0.05 per day. Over the next 10 days, the option’s value will erode by $0.05 x 10 days = $0.50. As you can see, the closer the option gets to its expiration, the faster its value declines due to time decay. This increase in speed of theta is explained the next articles.

## In Summary

understanding the numerical value of theta is crucial for interpreting time decay in options. The sign of theta, whether positive or negative, provides insights into the expected behavior of an option’s value over time. Meanwhile, the magnitude of theta indicates the speed or intensity of time decay. By grasping these two aspects, you can make more informed decisions when trading options.

**Disclaimer**

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