With recent market activity reminding traders that prices can go down as well as up, we’re suddenly starting to hear more about volatility again. Today we’ll discuss the different types of volatility related to stocks and ETFs.

The first type of volatility is *Historical Volatility*, or HV, which may also be referred to as *Realized Volatility*. Historical volatility is something that we can observe and measure based on the past price movements of a security. It is typically calculated as the standard deviation of the security’s daily returns over some lookback period. For example, the 30-day historical volatility, or HV(30), calculates the standard deviation of the daily gain or loss from each of the past 30 trading days.

Volatility is almost always expressed in annual terms, regardless of the lookback period. Therefore, if a stock has an HV(30) value of 45, it means that if the stock continued to move as it has for the past 30 days, it would likely experience a total price change of 45% (up or down) over the next year. If we assume that daily returns are normally distributed, then we can infer that there is approximately a 68% probability of the price landing somewhere in this range.

Although HV is an expression of how much a stock’s price may change in a year, it’s more typically used as a way of comparing the recent price behavior of two securities. If XYZ has an HV(100) value of 25 and PQR has an HV(100) value of 75, then we know that PQR has experienced more extreme price changes over the past five trading months.

Sometimes you’ll hear *Beta* used as a measure of *Relative Volatility*. From a mathematical standpoint, Beta is the correlation coefficient between two price series. The Beta value of a stock or ETF is most often computed relative to the market as a whole, which in most cases means the S&P 500 for the US market. A Beta value greater than 1 means that the stock generally moves more than the market, while a value of less than 1 means that the stock typically moves less than the overall market. Negative values, i.e. negative correlations, mean that the stock price has a tendency to fall when the market rises, and vice versa.

The final type of volatility that we’ll address today is *Implied Volatility*, or IV. Implied volatility cannot be calculated from historical prices of the stock, but rather is the byproduct of an options pricing model. In simplest terms, IV is an expression of the market’s expectation of the future volatility of the stock price between now and the option’s expiration. Market participants “express” themselves via the prices they are willing to pay for option contracts. Like HV, implied volatility is always annualized to make comparison of values more straightforward.

Each unique option contract, i.e. combination of put or call, strike price, and expiration date, will generate a different implied volatility value. These values are often combined to provide some sort of “consensus opinion” of the IV of the stock. For example, your trading platform may display an IV value for each expiration date, which was likely calculated with some type of weighted average of all the different strike prices for that expiration. The different IV values for each expiration date will indicate whether the market is expecting more volatility in a specific time-frame, like when quarterly earnings are announced.

You might also see IV expressed over a constant lookahead period such as 30 days. The CBOE Volatility Index, or VIX, is the most popular metric of this type. While a full discussion is beyond the scope of this article, the basic idea behind the VIX and similar measures of this type is to use front month and second month option prices to create a synthetic ATM option contract that expires in exactly 30 days. This synthetic contract can then be used to generate an implied volatility value. Note that in the case of VIX and related indices, 30 days means 30 calendar days (approximately one month), not 30 trading days.