the expected move and the normal distribution

Selling Premium with Statistics

By:Dr. Jim Schultz

Today's Lesson: Understanding the versatility of Implied Volatility

  • Implied volatility is used to not only price options, but also to build the anticipated ranges of a stock.
  • In statistics, the observations in a normal distribution will fall between +/-1 standard deviation 68% of the time.
  • Knowing the connection between the expected move and normal distribution is quite useful in selling premium.

Implied volatility (IV) in the market might be the most versatile metric of all. Not only is it used to approximate the fear in the market and determine option prices themselves, but it is also used to forecast the anticipated range of stock price movement for any stock in the market—a calculation more commonly referred to as the expected move.

Generally speaking, if Apple (AAPL) has an IV of 40% over the course of a given expiration cycle, and International Business Machines (IBM) has an IV of 20% over the course of that same expiration cycle, then the market is anticipating AAPL stock to be twice as volatile as IBM. In other words, the expected move for AAPL will be much wider than the expected move for IBM, as the higher IV is making room for potentially wilder swings on either side of the market. 

Connection to statistics

The expected move derives its name from statistics, and more specifically the normal distribution. Given enough occurrences and over a long enough time window, stock price movements always fall into a normal distribution, or bell curve, and approximately 68% of the time, the observations in a normally distributed data set will fall within the range of -1 to +1 standard deviation.

Expected moves and short options

This is no coincidence, as it maps perfectly into the expected move. The lower end of the expected move always maps to the -1 standard deviation marker, and the upper end of the expected move always maps to the +1 standard deviation marker. As premium sellers, this is incredibly valuable information, as we look to build our trades, analyze our strategies, and ultimately select our strikes. For example, by selling premium around the expected move in something like a short strangle, we know that our probability of profit on that strategy will be around 68%—given that the probability of that +/-1 standard deviation is the same 68%.

Jim Schultz, a quantitative expert and finance Ph.D., has been trading the markets for nearly two decades. He hosts From Theory to Practice, Monday-Friday on tastylive, where he explains theoretical trading concepts and provides a practical application of those concepts to a trading portfolio. @jschultzf3

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