This would be a great time to tell you exactly what option trading is really all about. Option trading is about cost and compensation for changing levels risk. When speaking about cost and compensation for risk, there are three primary variables that apply. The first is movement in the underlying asset price (e.g., XYZ's stock price). The second is time decay. The third is implied volatility.

It is useful to think of movement in the underlying asset price as the primary source of risk, and to think of time decay and implied volatility as producing the cost or compensation for changes in that risk. We can refer to the risk posed by movement in XYZ's stock price in two separate terms: realized and expected.

• Realized Risk is profit or loss to the trade that has already resulted, and that is due strictly to movement in XYZ's stock price.
• Expected Risk refers to the impact to your trade if XYZ's stock price changes by a given amount.

An option trader is continuously compensated (or charged) as the stock’s risk to his option trade changes. There is cost and compensation for both realized risk and expected risk.

• Cost and Compensation for Realized Risk (i.e., Time Decay P&L): You will either pay, or be paid, to sit there and realize risk over time. For example, you may have been paid $40 to hold an option position for a day. And during that day, XYZ stock may have moved in such a way that it produced a $35 loss. So you were paid $40 to realize a $35 loss caused by the stock’s movement, for a net of $5.
• Cost and Compensation for changes in Expected Risk (i.e., Implied Volatility P&L): In this case, you either pay, or get paid, for changes in expected (i.e., upcoming) risk. Expected risk tells us what the potential realized risk could be. We can then compare our cost or compensation for changes in expected risk to the potential impact to our trade.

In an option position, it can be helpful to view changes in the stock price as the primary source of risk to the trade. The only reason for taking this perspective is that it helps us better understand the significance of the profit or loss caused by implied volatility and time decay.

Implied volatility and time decay are, themselves, sources of risk. In addition to viewing them that way, we can also view them as producers of cost and compensation for changes in the "primary risk", which is posed by the underlying stock. When you look at it this way, you can think in terms of getting under-paid or over-paid for changes in the primary risk. This, in turn, may suggest the extent to which your options are expensive or cheap. Logical ways, such as this, for determining whether an option is relatively cheap or expensive is the name of the game. Concluding that an option is worthy of buying (it's cheap) or selling (it's expensive) is what will drive your trading decisions for the most part.

The figure above is an example of how ChartBender's Opium trade management technology breaks down the cost/compensation of an option position. The bar on the far right, showing the $35 loss, is the realized risk from movement in the stock price. Keep in mind that changes in stock price can also generate profits.

Depending on the type of option position you are in, you will either pay, or be paid, to hold that position. But why would this position be generating cost or compensation to you? The answer is because you are realizing risk just by holding the position; that is, you are absorbing the movement of the stock price.

The second bar from the right shows that $40 of compensation has been generated over the same time period in which the trader absorbed a $35 loss due to the stock's movement. Notice that the compensation exceeds the $35 loss caused by the "primary risk" of the stock's movement. The trader has been over-paid for the realized risk of the stock's movement. But from where is this $40 of compensation coming? It's coming from the decay of the option's time value.

Often times, traders look at time decay in a "stand alone" manner. They reason, "If I hold this position until expiration I'll make $1,000 from decay!" This view is problematic for a couple of key reasons, which are explained below.

Problem #1: Cost or Compensation for realized risk (i.e., decay P&L) is not being viewed in the context of the actual realized risk. After all, you must realize risk (i.e., absorb the movement of the underlying stock price) in order to make or lose money from decay. The idea that one is "making a lot" from decay is entirely relative to the amount of risk the position has actually (not theoretically) realized from the stock's movement. Bear in mind that there's nothing saying how much risk has to be realized, nor whether it will come in the form of profits or losses. $1.00 of decay profits might be great compensation if the stock's movement has generated $100 in profits. It's all relative.

Problem #2: The Greek "theta" is likely being used to theoretically project the total decay compensation at expiration (we talk about the pros and cons of theta, and all the Greeks, in the next section.) For the moment, we'll say that there is often a failure to consider that theta is inversely related to gamma. Simply put, if the position looks like it will compensate you handsomly for realizing risk, it's because the market is expecting a lot of movement in the underlying stock; that is, it is expected that the position will realize a lot of risk.

When implied volatility changes, it results in two things: 1) It produces immediate profit or loss in the option position, and 2) it determines the change in the stock's expected risk to the position.

We can therefore compare our implied volatility P&L to the changes in expected risk to see if we are being under-paid or over-paid for those changes.

If we are under-paid (or over-charged) for the change in expected risk, it suggests that our options are cheap. If we are over-paid (or under-charged), it suggests that our options are expensive.

In the figure above, our hypothetical trade has generated $95 in compensation. By isolating this portion of the total P&L, we can easily compare it to the change in expected risk (not shown here). We can then determine if the $95 represents over-payment or under-payment for the change in expected risk.

What's a good level of cost or compensation for Expected Risk?

To answer that question, we must quantify both the actual implied volatility profits and the change in the expected risk to the trade. Then all we need to do is compare the two. ChartBender's Opium application does this automatically for you. But, if you're interesting in the details of how it works, simply read on.

First, we need to forecast the impact to our trade over the next day based on a given unit of change in the underlying asset price -- Opium technology uses a degree of change equal to 1 standard deviation. We do this to determine the expected impact to our trade from a 1-standard deviation movement in the underlying asset price. The next step is to repeat this forecast at any subsequent point in time. Comparing the result from each point in time gives us the change in expected impact to our trade.

For example: at yesterday's market close (Time A), a 1-standard deviation rise in XYZ's stock price was expected to cause a profit of $100 in our position. But as of right now (Time B), a 1-standard deviation rise in XYZ is expected to produce only a $50 profit in our position. The difference between the impact at Time A and Time B is –$50. In other words, we are now expected to benefit LESS from the SAME degree of movement. For that reason, our risk has INCREASED.

Opium makes all of this easy because it quantifies and displays both the change in expected risk to your trade, and how much actual implied volatility P&L the trade has generated for that change.

This educational content is provided by ChartBender.
© 2005 ChartBender, LLC.