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# Swim Lessons: How Volatility and The Rule of 16 Can Offer Perspective

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March 2, 2017

We'll cover this topic on Swim Lessons next Wednesday, March 8th in the thinkorswim Platform. Learn more.

Quick! What’s the square root of 252!?

a)      Can I phone a friend?

b)      What does the number 252 have to do with trading?

c)       Are we allowed to use our smartphones?

d)      Approximately 16

Now that I have your attention (or at least gave you an anxiety-inducing flashback of Math class), the answer is… D! Although, you might be still strongly considering Option B: What does the number 252 have to do with trading?  The answer? The Rule of 16.

The number 252 is significant to traders because there are 252 trading days in a year. The square root of 252 is (approximately) 16, hence 'The Rule of 16'. More on the significance of this number later.

As my colleague Kevin Hincks explains in Understanding the Rule of 16, Options Volatility Skew, and VIX, the ‘Rule of 16’ can be used as a measuring stick to test if market movement and measured volatility are in line. This same logic can be extended to the practice of comparing implied and historical volatility on an individual stock.

How could this sort of analysis help us out? One word – perspective. And the 'Rule of 16' can help us get there.

## The Rule Of 16: Why Should You Care?

For option traders, volatility can sometimes make or break a trade. The 'Rule of 16' offers another perspective on volatility measurements. Volatility refers to the amount of variance or changes in a security’s value, and is measured by standard deviation. Since volatility is standard deviation, we need to multiply it by the square root of time. Not by time itself. This allows traders to quickly annualize volatility for perspective. Since there are 252 trading days in a year, and the square root of 252 is 16, we will multiply volatility by 16 to get our annualized volatility amount.

Let’s illustrate this formula with an example. Suppose a stock has an implied volatility (IV) of 16. According to the 'Rule of 16', the market is implying that, about 68.2% (or two-thirds) of the time, the stock might trade up or down by 1%. If the IV is 32, the market is expecting a 2% move about 68.2% (or two-thirds) of the time.

It works the other way, too—you can "annualize" a daily reading by multiplying it by 16. For example, suppose a stock has had a couple moves of 1.8%, and you think a 1.8% daily move might be typical in the near future. If so, you would be expecting an annualized volatility level of (1.8 X 16 =  28.8%). Comparing your expectation to the current IV might indicate whether you believe an option is overpriced, underpriced, or fairly priced.

Using the 'Rule of 16' offers perspective. It allows us to see the bigger picture when it comes to volatility. Now that we have a basic understanding of the 'Rule of 16', let's dive into how else volatility can offer perspective when considering an option trade.

### Volatility Perspective—Implied and Historical

Suppose we're looking to buy or sell an option. We may try to apply the old adage, “Buy low; Sell high”. But how can we be sure if the option price is high or low, relative to it's historical performance? Enter...implied and historical volatility.

Implied volatility (IV) is the expected movement of the stock’s price throughout the duration of the option contract. Generally, a higher IV means the market is more uncertain about the stability of the underlying stock. This uncertainty and higher IV results in a more expensive options price (or premium).

“Great… but how does this offer us perspective, Scott?” Glad you asked.

We can compare the current implied volatility to a measure of the stock's historical volatility (HV)—an annualized standard deviation of past stock price movements, to gauge if the market is more, or less, certain about a stock’s stability.

Of course, we don't need to calculate all of these implied and historical volatilities—options trading software, such as the thinkorswim® platform from TD Ameritrade, can do it for us. Figure 1 shows a typical options grid. For each expiration date, the implied volatility for an at-the-money option is shown in the far right column (15.28% for the 3 MAR 17 series, 15.86% for the 10 MAR series, and so on). Also, in the lower left, "Today's Options Statistics," offers a host of information including the range of implied and historical volatility over the last 52 weeks, and a percentile rank of both IV and HV.

FIGURE 1: OPTIONS STATISTICS.

The 52-week IV range in this example stock is 0.13 to 0.346, or 13% to 34.6%. Today's volatility in in the 18th percentile of IV readings over the past 52 weeks, but its HV is in the 54th percentile. Source: The thinkorswim® platform from TD Ameritrade. For illustrative purposes only. Past performance does not guarantee future results.

## Scratching The Surface

Of course, these general measurements—implied and historical volatility and the Rule of 16— in and of themselves don't tell you whether an option is overpriced or underpriced. How volatile has the broader market been lately? When is the company expected to release its next earnings report? Any merger or acquisition discussions in the pipeline?

Plus, the  examples above only looked at volatility of at-the-money options. And a typical bell curve assumes no skew between the upside and downside. But stock option prices, in general, the IV of an out-of-the-money (OTM) put is at a higher level than OTM call volatility. This comes from the theory that stocks fall faster than they rise.

In other words, there are a ton of reasons an option may be priced as it is, and there are no guarantees; only probabilities, and even the probabilities vary. But looking at an options price in the context of historical versus implied volatility, and by using the Rule of 16, you may gain some perspective.

## Want To Dig Deeper?

Join Swim Lessons on Wednesday March 8th at 10:30 AM CT as Kevin Hincks and and I dive deeper into Volatility and the Rule of 16!

TD Ameritrade clients can join Swim Lessons by launching thinkorswim®, and navigating to Support/Chat > Chat Rooms > Swim Lessons > Watch.

Not a TD Ameritrade client? You can still watch Swim Lessons by registering for a free, 60-day trial of thinkorswim paperMoney®