 "Option traders must have an even greater focus on volatility, as it plays a much bigger role in their profitability--or lack thereof" Dan Passarelli.

Here is the story we hear from most new traders, "I bought a call on XYZ, and then XYZ moved up in price, but my call lost money. I don't understand, what went wrong?" Most beginning options traders will find themselves in this situation at some point, and the answer is always the same, "volatility dropped." The role volatility plays in an options' price is usually underestimated by options traders.

Volatility is the heart (and soul) of options trading. In our option pricing model volatility is our only unknown factor which makes it the most critical factor to understand. There are three different types of volatility that we will discuss and the role they play in options: historical, implied and expected volatility.

### What Is Standard Deviation

Standard deviation is a statistical term that measures that amount of variability around a mean (don't worry we will explain). The notation for standard deviation is sigma, and it will be our measure of volatility. Standard deviation is usually an annualized number and is expressed as a percentage.

Enough with the technical jargon, let's look at an example.

The Option Prophet (sym: TOP) is trading at \$35 and has a standard deviation of 10%. A 1-standard deviation move in the stock will put the end price at \$31.50 or \$38.50 (35 +/- (35 x 10%) or 35 +/- 3.5).

Now if TOP is trading at \$100 and has a standard deviation of 20% we can expect a 1-standard deviation move to end the stock price at \$80 or \$120.

One thing we can note is that standard deviation is non-directional and different stocks will have different standard deviations no matter what their price is. The size of the movement a stock undergoes will determine the standard deviation. If a stock regularly makes more substantial moves than it will have a larger standard deviation.

We can use standard deviation to assign probabilities of where a stock will close every day. When these occurrences, or stock closing prices, are plotted on a graph it creates a normal distribution or bell-shaped curve.

What this curve tells us is that 68% of the time a stock will close within a 1-standard deviation of its average price. This makes sense since most stocks don't make large an unpredictable moves. Most of the time a stock will move about the same each day, little by little.

When we use the bell curve to look at 2-standard deviations out we can see that a stock's closing price will fall within that range 95% of the time. Looking out to 3-standard deviations we can see that a stock's closing price will fall within that range 99.7% of the time.

### Why Does Standard Deviation Matter In The Real World?

To better explain why standard deviation matters let's look at it in practical real-world terms.

Example 1:

TOP is trading at \$50 and has a 15% standard deviation. I think it is poised to go higher, so I want to buy a call to profit from this move. I can buy an out-of-the-money, in-the-money, or at-the-money call to take advantage of an increase in price. Being cheap I want to go with an out-of-the-money call since the premium will be less than my other choices. After a quick peek at the option chain, I decided to take a long call on the 60 strike.

Was this a good selection for strikes? This trade might make money but are the odds in my favor? Looking at a 1-standard deviation move in TOP we can see the range will be between \$42.50 to \$57.50. If a 1-standard deviation move accounts for 68% of all the closing prices, we have missed the high probability strikes because we are sitting outside this move.

How could we have made this a better trade? Next time when we are looking at strikes, instead of picking a random out-of-the-money strike we can pick on that has a high probability of going in-the-money.

Example 2:

TOP is trading at \$30 and has a 20% standard deviation. It seems like it has been range bound so I want to add on an iron condor to take advantage. I have a lot of choices for strikes to sell on TOP but I want to short the 17 put, and long the 15 put and short the 43 call and long the 45 call.

Was this a good selection for strikes? The idea of an iron condor is to get the stock to end up in between your short strikes, in this case, the 17 and 43. If we look at a 1-standard deviation move, we see our range is \$24 to \$36. If 68% of the moves will end between those two prices, our condor is looking good so far. Now let's extend this out to 2-standard deviations, \$18 to \$42. We know that a stock will have a closing price between \$18 and \$42 95% of the time. Our iron condor's strike is sitting just outside of 2-standard deviations so there is only a 5% chance that our closing price will end up in our iron condor's strikes.

### What Is Historical Volatility?

Historical volatility, also known as realized volatility, is the annualized standard deviation of daily returns. Realized volatility tells us how volatile a stock has already been based on past closing prices. When determining your historical volatility, you need to pick a time period to measure. Typical time periods would be 10, 20, 30, 60 and 360 days back. Make a note here that when discussing the days in the past we are only talking about trading days. So a look back over the last 20 days for historical volatility is looking back through a full month. Typically we use a 20 and 30-day look back period.

Based on the time period you select you could see a very different historical volatility for that underlying. If a company released earnings 17 days ago your historical volatility for a 20 day time period will be a lot higher than it would if you only measured the volatility for the last 10 days.

The story that historical volatility does not tell is how much a stock has moved during the day. Since we only use the closing prices to calculate our volatility, we could be missing a bigger picture if there is a lot of intraday movement just to have the underlying finish with little change. This could skew the numbers to make it volatility smaller even though the movement throughout the day is quite significant.

### What Is Implied Volatility?

Implied volatility is where all the magic happens in the options market. Implied volatility is forward-looking and shows the "implied" movement in a stock's future volatility. It tells you how traders think the stock will move. Implied volatility is always expressed as a percentage, non-directional and on an annual basis.

The higher the implied volatility, the more people think the stock's price will move. Stocks listed on the Dow Jones are value stocks, so a lot of movement is not expected. Thus, they have lower implied volatility. Growth stocks or small caps found on the Russell 2000, conversely, are expected to move around a lot, so they carry higher implied volatility.

When we look at implied volatility, we should see that the percentage we are given is a 1-standard deviation move from the stock price. Knowing this and now about standard deviation, we should be able to generate probabilities and odds for where our underlying will move.

There is a correlation between historical volatility and implied volatility. Typically the two will move in tandem with historical volatility lagging behind a bit. If we have earnings coming up in 20 days, our realized volatility can begin to flatten out or even decline as traders wait to buy and sell the stock until earnings. At the same time, there is also a big unknown when it comes to earnings which will cause implied volatility to climb. Traders will be unsure how much a company will move once they release earnings. They could beat all expectations and send the stock higher, or they could fall right in line and cause the stock not to move.

If the stock makes a significant move after earnings, in either direction, our realized volatility will begin to climb. At the same time, our implied volatility will start to fall because now there is not an unknown earnings announcement.

When trading options, your implied volatility is going to be your largest component. Some strategies will be focused purely on volatility such as a long straddle or long strangle. Other strategies could be focused on a lack or declining implied volatility such as iron condor, short straddle and short strangle.

When we look back at our Black-Scholes option pricing model, we see our one unknown is implied volatility. The way we find this number is by filling out all of the other factors and the actual market price for the option and then solving for implied volatility. In fact, if a stock does not have any options traded on it, you cannot find implied volatility for that stock.

### Expected Volatility

When talking about implied volatility, we noted that it is an annualized figure. Most people don't trade options one year out, so we need to break it down into more manageable terms. There is a simple formula we can use to get implied volatility to the time period we require.

The formula is:

IV / SQRT(256) = 1 day expected move

Where does the 256 come from? There are 365 days in a year but only 252 days are trade days. The other days are market holidays and weekends. The reason we use 256 instead of 252 is that the square root of 256 is 16 versus the square root of 252 which is 15.8745078664. Using 256 will not skew your numbers but any great deal.

Our formula will simplify to:

IV / 16 = 1 day expected move

If TOP is trading at \$40 with an implied volatility of 30% we can calculate a 1 day expected move as:

0.30 / 16 = 0.01875 or 1.875%

We can then expect TOP to end up at \$39.25 or \$40.75 (40 +/- (40 x 1.875%) or (40 +/- 0.75).

One day usually doesn't tell us what we want to know, however, so we must use a more manageable time period such as 20 days.

If we want to use more than one day our formula becomes:

(IV / 16) x (SQRT(Number of days we want to use))

Using the numbers above and to look out for 20 days we have:

(0.30 / 16 ) x (SQRT(20))
(0.01875) x (4.4721)
0.08385 or 8.385%

In 20 days there is a 68% chance that TOP will finish between \$36.65 and \$43.35.

### Conclusion

As we begin to scratch the surface of volatility, we can already start to see how integral our understanding of volatility will play into how we profit with options. By using standard deviation, implied volatility and expected volatility you can know where the underlying is expected to move for the options you wish to trade. You will also use this knowledge to help select different types of options strategies and the various strikes you will trade.

Remember the three types of volatility and their jobs:

• Historical volatility shows how the stock has moved in the past, usually 20 or 30 trading days back.
• Implied volatility: shows the expected move one year out.
• Expected volatility: turns implied volatility into more manageable and realistic time frame.  