Using Delta to Select Covered Calls

09/25/2012 6:00 am EST

Focus: OPTIONS

Alan Ellman

President, The Blue Collar Investor Corp.

Alan Ellman explains this crucially important Greek and how option traders can use it to their advantage.

When studying option trading basics and the Greeks, we learn about our exposure to risk. Those of us who study options are constantly reading and hearing that delta, one of the Greeks, is one of the most powerful influences over option value. Because of this, I thought it prudent we discuss this subject in greater detail.

Definition
Delta measures the amount an option price will change as a result of a $1 price change of the underlying security (stock, ETF). Other major factors that impact option value include the price of the stock, implied volatility, and time to expiration. Since call options rise and fall directly with the price of the stock, they are assigned deltas between 0 and 1.

Look at delta as a bet: What is the percentage chance that the option will end up in-the-money (lower than the market value of the stock) or be exercised by expiration Friday? The higher the delta value, the greater the chance of this happening. A delta of .9 or 90%, for example, means that the strike price will almost definitely end up in-the-money

In the scenario where we sold a $50 call and the stock was trading at $70 with one week remaining, the delta would be at or near 1 and for every $1 change in the price of the stock; the option will also change by approximately $1. This is typical of deep I-T-M strikes.

For at-the-money strikes, deltas will be closer to .5 or 50%. In this scenario, for every $1 change in the price of the underlying, the option value will change by 50 cents, reflecting about a 50-50 chance that the strike will end up I-T-M.

For deep out-of-the-money strikes, deltas would be quite low, between .1 to .2 or 10% to 20%, for example. If we sold the $50 call and the stock was trading @ $30, the chances of that $50 strike ending up I-T-M are quite low. If the stock price moves up or down by $1, the option value will change by perhaps 10 cents because of the low delta.

The chart below summarizes the approximate deltas for the one-month options we sell when writing covered calls:

chart
Click to Enlarge

Delta increases as the strike moves further I-T-M and decreases as the strike moves deeper O-T-M. This can be visualized in the graph below:

chart
Click to Enlarge

Factors influencing delta: 

  • Stock price: As we can see from the above figures, an increase in stock price (red arrow) moves the strike towards I-T-M status and the delta will increase.

  • Time: Delta will change as we approach expiration Friday. I-T-M strikes will show increasing deltas because of the higher likelihood of ending with intrinsic value (less time to move O-T-M). O-T-M strikes will show decreasing deltas because of the lower likelihood of turning things around and ending up I-T-M. 

What Delta Teaches Us About Risk 
We learn why O-T-M calls present more risk. These calls have low deltas. If the stock drops in value, the option price will decline at a much slower pace (because of the low delta). This will make it more expensive to buy back the option if we are looking to institute an exit strategy and/or close our position. 

Summary 
Deltas measure the probability of an option ending I-T-M, or stated differently, with intrinsic value:

  • I-T-M strikes: highest deltas

  • A-T-M strikes: deltas near 50% or .5

  • O-T-M strikes: low deltas 

Strike selection based on delta:

  • I-T-M strikes: if bearish or conservative as option premiums will decline faster with decreasing share price making it easier to close our positions.

  • A-T-M strikes: for maximum premium return.

  • O-T-M strikes: if bullish so option premium AND share appreciation can be realized.

Conclusion
Understanding the relationship of delta to our option premiums will make us sharper investors, as it will allow us to select the best strike price for a given situation. 

Alan Ellman can be found at TheBlueCollarInvestor.com.

Related Articles on OPTIONS