Understanding the Four Measures of Volatility
Updated from 3/8/2007 at 2:15 p.m. EST
"Volatility" is a term that is increasingly interjected into financial market commentary by the press and professionals. In fact, Bloomberg Radio has a daily "Volatility Report." While the term is being thrown around with a seemingly high degree of expertise, I find that the concept is not well understood by most commentators and the average investor. This module of TheStreet University will cover the four main types of volatility measures:
 historical volatility;
 implied volatility;
 the volatility index; and
 intraday volatility.
Type 1
:
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Historical Volatility
Volatility in its most basic form represents daily changes in stock prices. We call this historical volatility (or historic volatility) and it is the starting point for understanding volatility in the greater sense. Historic volatility is the standard deviation of the change in price of a stock or other financial instrument relative to its historic price over a period of time. That sounds quite eloquent but for the average investor who does not command an intimate knowledge of statistics, the definition is most overwhelming.
Think of a Pendulum
To help you visualize the concept of volatility, think of a pendulum like in the picture below. The pendulum is constructed from a steel ball, attached to a rope and then suspended from a ceiling.

The pendulum starts at the resting state when our ball is at point 2 (the mean). If you raise the ball to point 1 and let it go, the ball would then swing from point 1 to point 3. Over time that ball will swing back and forth always passing though point 2. If this were a stock, the difference in distance from point 1 to point 2 or from point 2 to point 3 represents the volatility in the movement of the stock price.
So as not to get into any trouble with physicists out there, the formulas for standard deviation and movement of a pendulum are different and I am not equating the two from a statistical perspective. Rather, I am only using the pendulum as a visual aide. Stocks with a swing that is greater from point 1 to point 2 vs. that of another stock will have a higher volatility than the other stock.
Now imagine a wind hitting the metal ball. The force of that wind will increase a stock's volatility. Market corrections, increases in uncertainty or other causal factors of risk will be the wind that shifts volatility higher. Say that there is no wind, but rather calm over the markets. Since there is no outside force to apply motion to the pendulum, the arc of the movement from point 1 to point 3 will decrease. This is when volatility declines. Some call this complacency, but it is generally viewed as a market with low or declining volatility.
A Look at Johnson & Johnson and Rackable Systems
For a real world example of historical volatility in action, let's look at
Johnson & Johnson
(JNJ)  Get Report
, a low volatility stock, and
Rackable Systems
(RACK)
, a high volatility stock. In the chart below, observe the relative volatilities and the deviations thereof over the course of the recent market meltdown.
Click here for a larger view of the historical volatility chart.
Volatility and Options
Volatility is one of the many important inputs  along with market price, strike price, interest rates, dividends and time  in calculating the value of an option. The most popular options pricing model is BlackScholes. If you desire to torture yourself with how the BlackScholes options pricing model works, I have provided
. When calculating an option price, one merely inputs the volatility as a given for the reference security (underlying security, in options speak) for a period of time to match the remaining days to expiration, along with the other required variables, into the BlackScholes model, and out pops the option valuation.
Note: To learn more about options, check out the Futures and Options section of TheStreet University's Getting Started index.
Type 2: Implied Volatility
The options market is a bid and offer system in which buyers and sellers come together in an auction environment to actuate price discovery and execute trades. These prices are quoted in dollars and cents. From these prices, knowing all of the other BlackScholes variables and using the BlackScholes formula, we can calculate the volatility, which is implicit from a traded price or the bid and offer. This is referred to as the option's implied volatility. Whereas historic volatility is static for a fixed given period of time, please note that implied volatility will vary for a stock based on different options strike prices. This is referred to as the volatility skew.
Johnson & Johnson and Rackable Revisited
For the same two stocks that I examined before for historical volatility, below I have presented implied volatilities. As was the case with historical volatility, the weighted implied volatilities were higher for RACK and lower for JNJ. However, the impact of the market correction was felt more by JNJ than RACK because of the already elevated implied volatility for RACK. Also, observe that the implied volatilities for both JNJ and RACK are higher than the historical volatilities. This is due to the speculative nature of options trading.
Click here for a larger view of the implied volatility chart.
Type 3: Volatility Indices
Just as we can calculate a stock's volatility or the implied volatility from its options, we can do so for an index such as the
S&P 500
(SPX)
or its exchangetraded fund equivalent, the
Spyders
(SPY)  Get Report
. This concept is taken one step further. For many indices, a volatility index has been created and is commonly quoted in the financial media. The three most common ones:
These volatility indices are a weighted average of the implied volatilities for several series of options (puts and calls). Many market participants and observers will use these indices as a gauge of market sentiment.
has some interesting information on the VIX, other volatility indices and related products.
Presented below are the volatility indices for March 6, 2007 and the week prior to that date after the market took its big oneday plunge. Note the huge surge in volatility in response to the market drop.
Also, observe the relationship between the individual stocks' implied volatilities and that of the indices. JNJ options are slightly less volatile than the S&P 500 Volatility Index and the S&P 100 Volatility Index for which it is a constituent. RACK options, on the other hand, are significantly more volatile in implied measures than options for the techheavy Nasdaq 100 Volatility Index.
Click here to view the volatility indices chart.
Type 4: Intraday Volatility
Finally, we have intraday volatility. This represents the market swings during the course of a trading day and is the most noticeable and readily available definition of volatility. Intraday volatility is the Justice Potter Stewart type of volatility because it's hard to define but you know it when you see it. A common mistake is equating intraday volatility with the implied volatility index. Both of these forms of volatility are not interchangeable, but do carry their own importance in ascertaining investor sentiment and expectations.
I have calculated two measures of market volatility using data from the S&P 500. The first is intraday volatility which reflects the difference between the high and low on the day divided by the closing price of the day for the SPX. The second, LakeView Asset Management VDEV, is a proprietary measure of volatility that I created using historical trends in the SPX to predict future volatility. The VDEV will be discussed in a future installment of this series.
Click here for a larger view the intraday volatility chart.
In summary, here is a recap of the four types of volatility:
 historical volatility  the movement of an asset or asset class relative to itself;
 implied volatility  volatility that is embedded in an option price;
 volatility index  a weighted average of implied volatilities for options on a particular index;
 intraday volatility  the price movements in a stock or index on or during a given trading day.
At the time of publication, Rothbort was long SPY, although positions can change at any time. Scott Rothbort has over 20 years of experience in the financial services industry. In 2002, Rothbort founded LakeView Asset Management, LLC, a registered investment advisor based in Millburn, N.J., which offers customized individually managed separate accounts, including proprietary long/short strategies to its high net worth clientele. Immediately prior to that, Rothbort worked at Merrill Lynch for 10 years, where he was instrumental in building the global equity derivative business and managed the global equity swap business from its inception. Rothbort previously held international assignments in Tokyo, Hong Kong and London while working for Morgan Stanley and County NatWest Securities. Rothbort holds an MBA in finance and international business from the Stern School of Business of New York University and a BS in economics and accounting from the Wharton School of Business of the University of Pennsylvania. He is a Professor of Finance and the Chief Market Strategist for the Stillman School of Business of Seton Hall University. For more information about Scott Rothbort and LakeView Asset Management, LLC, visit the company's Web site at www.lakeviewasset.com. Scott appreciates your feedback; click here to send him an email.