# Volatility

Simply put, volatility is a measure of the movement of the price of a stock or other security. A stock that sees wide swings in its price is said to have a large amount of volatility as compared to a stock whose price stays in a narrow band.

Stock volatility, sometimes referred to as "historical volatility" or "realized volatility" is a measure of how much the stock price has moved around in the past. Stock volatility is an estimate. Methods for calculating stock volatility vary so the information presented by two sources might not match exactly.

## Historical Close-to-Close Volatility

In some places throughout the site, we will refer to close-to-close historical volatility (C-C Vol). This volatility is measured from historical prices, and the log returns of one day's closing stock price from the previous day's close. Volatility is the standard deviation in those returns.

C-C Volatility is perhaps the simplest form of historical volatility used in options evaluation, but in many cases, it can produce less than desired results.

## Historical Open-High-Low-Close Volatility

Open-High-Low-Close Volatility (OHLC Vol) is a much more complex calculation of historical volatility, and it uses a stock's full open-high-low-close price history to calculate. There are many formulas to calculate volatility using OHLC, but the version that we use at MarketChameleon.com is based on the Yang-Zhang estimator.

The benefit of OHLC volatility calculation is that it incorporates more elements to get a better sense of what happened throughout the day. If a stock closes at 65.00 one night and 65.00 the next, it appears to have little volatility over that day. But if you see that on the second day, it actually opened at 62.00 and went as high as 68.00 and as low as 61.00, you can see that there was much more activity in the stock over the course of that day.

## One-Day Vol vs. Historical

On a stock's overview page, we list the one-day volatility for the current day. It's calculated using the OHLC formula, using the current day's OHLC and the closing price from the previous day. The number is annualized, meaning the volatility for the day is extrapolated out to a full year, so that it can be compared against the one-year volatility for the stock.

We do the same thing for the last 20 days. When we list the 20-Day Volatility as 25.0, this doesn't mean that the stock moved 25% in the last 20 days, but rather that it can be compared with a 25% volatility for a full year.

## Implied Volatility

Implied volatility (IV) is a measure of how much the stock is expected to move around in the future, and it is determined by the prices in the market and how much volatility those prices are implying. IV is calculated from option premium and other inputs/assumptions, like dividends, interest rates, and time until expiration. Generally option premiums are forward-looking because they take into account information about future events that is generally available to investors. If investors anticipate that volatility will increase in the future, they will express that sentiment by paying higher premiums.

The standardized nature of the volatility allows us to use it is a yardstick to compare historical volatility, implied volatility and volatility across different attributes such as expiration and strike. We can even compare the volatility of two different securities.

If we compare historical volatility with the IV for a given security and the IV is the higher of the two, then the market is pricing in an increase in volatility.

Volatility is expressed as a positive number. It is a standard deviation move of a stock in 1 year. If we say a stock has a volatility of 20 then we believe there is a 67% (+/- 1 standard deviation) probability the stock will move within +/- 20% in 1 year. To get the expected move for less than 1 year we divide the volatility by the square root of time (or fraction of the year) to get the expected move for that time period. Since IV is an estimate and the IV calculation requires many inputs and a number of assumptions, the IV data generated from different sources can be expected to differ somewhat.

MarketChameleon.com presents historical stock volatility and implied volatility for a stock on the stock’s "Implied Volatility" page.

## IV Percent Rank

MarketChameleon.com builds on and simplifies the concept of Implied Volatility with an indicator called "IV Percent Rank". The IV % Rank is a coarse indicator of the IV of a stock relative to its historical volatility trend. The IV % Rank can be "Elevated", "Moderate" or "Subdued". If the IV % Rank of a stock is anything other than "Moderate" then the investor should be aware that the implied volatility for a stock is outside the normal range. All stocks whose IV % Rank is "Elevated" or "Subdued" are listed in the Implied Volatility Rankings Report.