Thetatheoretically projectsDecay P&L (i.e., Cost or Compensation for absorbing movement in the stock price.)
Theta is the theoretical amount of decay (i.e., cost or compensation) an option will produce in one day. As we discussed in Decision Making, you must absorb movement in the stock price (i.e., you must realize risk) in order to generate profit or loss from decay. That's why it can be helpful to view theta as the theoretically projected cost or compensation for realized risk. Positive theta theoretically projects how much compensation you will receive each day for absorbing stock movement. Negative theta theoretically projects how much it will cost you each day to capitalize on stock movement.
Why Theta Is Important When you think of theta as theoretically projecting cost or compensation, you can ask yourself this: "For what am I being charged or compensated?" The answer is always the same: The risk posed to the position by changes in the stock price. If, for example, theta is theoretically projecting a relatively high level of compensation (i.e., a large amount of positive decay), it's because the market is expecting the underlying stock to be volatile, and potentially move quite a bit.
In addition to theoretically projecting decay, theta gives you an idea as to how your position will respond to movement in the stock price. This is because theta has an inverse relationship to Gamma. Negative gamma means movement in the stock price in one, and sometimes both, directions is undesirable. Positive theta typically means that you want very little or no movement in the stock price. The reverse is true if you have negative theta.
In our visual representation of the Greeks, theta determines the color of the top circle, as you would expect. If theta is positive, the circle is green indicating that the position will profit from decay. If the circle is red, it means theta is negative and the decay will produce losses in the position.
Interestingly, the color of the horizontal arrows in the direction row is also determined by theta. If decay has a green circle, then the horizontal direction arrows will also be green. This is a reminder that a +theta position benefits from a stable stock price. Conversely, if the decay circle is red, then the position will lose money if the stock sits still. Thus, the horizontal arrows in the Direction row will be red.
