Wednesday, February 11, 2009

Thinking About Volatility (First in a Series)

Lately I have been fielding a large number of questions about historical volatility, implied volatility and a variety of related subjects. For this reason, it seems like a good time to kick off what I envision as a series of educational posts on the subject.

First I would like to start out with my own definition of volatility and then throw out some thought starters.

Definition: Volatility is a measure of the degree of change in the price of a security

There are a number of ways to think about changes in the price of a security. For instance, changes in price may be described in terms of:

  • magnitude (amplitude) – how far?
  • frequency – how often?
  • duration – how long?
  • trend – unidirectional or choppy?
  • direction – up or down?

In terms of measurement, common ways to measure price changes include:

  • close to close
  • open to close (intra-bar; excludes gaps)
  • bar to bar maximum (e.g. Average True Range)

Of course each investor has their preferred unit of time, with each bar representing a minute, five minutes, one day or whatever.

By convention, most investors think of volatility in terms of changes in price, but I submit that volatility be measured in the following units:

  • points
  • percentage (of price)
  • standard deviations

Looking back at the definition, I sometimes like to think of volatility more broadly than I have formally defined it. Consider that volatility can be defined in terms of:

  • price
  • volume
  • trend (degree of trending vs. choppiness)

Finally, consider that once measured, volatility can be compared to a number of possible benchmarks. These include:

  • external aggregate (broad index)
  • relative to peers (sector index, sector ETF, other representative ETF)
  • relative to self (including historical volatility and prior implied volatility levels)

I will touch upon all these subjects and more in the coming days and weeks.


Fitz said...

I liked the post, and it did make me think. Respectfully suggest you tag this budding set of posts, against a future archiving, I think it could be a memorable set

Bill Luby said...

Excellent suggestion, Fitz.

For the record I have added an "educational" tag to this posts and to the five posts that appear in the "VIX - Educational Posts" section of the blog in the right hand column. I have also decided to unveil a new "volatility" tage that I will try to use sparingly, but should incorporate this series in full.

As an aside, I always like to get input from those who have an interest in epistemology.



Kurt Osis said...


What you're getting at is that therm structure of volatility for american options does not work properly. There are lots of different combinations of price movements that could cause implied volatility to match realized volatility but different patterns of realized price movements have different effects on implied volatility even when they represent the same realized volatility. For example when the market when up 10% in one day in October the VIX went.... down.

Anonymous said...

This series is necessary. Too many beginners (and others) never grasp the concept of volatility. Good idea!

One quibble: Can volatility be measured in terms of standard deviations? You must know the volatility to calculate the standard deviation.


Kurt Osis said...

uh Mark..... "volatility" is defined as standard deviation. if you know the sample's standard deviation (standard error) then you know the volatility and vise versa.

leo00o83 said...


Great post!

Do you or did you ever study NYSE/NASDAQ advancing volume - declining volume's volatility?

I know TRIN makes the correlation between breadth and volume but I haven't seen any studies about their volatility, neither A/D issues nor volume.

Bill Luby said...

Some excellent comments here.


Well said regarding the value of the term structure, or lack thereof.


Tough crowd! I hear what you are saying. What I intended to convey is that with the same daily price move you can get different results when calculating the volatility of that move if the move is measured in points, percentage terms or standard deviations.

Yes measuring the volatility of standard deviations is volatility of volatility, but they can be calculated sequentially. Frankly, it was Jeff Augen's book that got me thinking more about daily standard deviations.


That is a very interesting question. I had not thought about using an indicator as the underlying in terms of analyzing volatility, but since the TRIN is one of my favorites, maybe I should take a look at it.

[Unfortunately my one man R&D department is swamped with projects and should be writing a book right now...]



Anonymous said...

Looking forward to the series, posting on our site, best wishes.

Anonymous said...


This is not exactly to do with this post but I thought it was closer to this education subject rather than your latest post as I write (which is about Regional Banks).

Yesterday (February 12th) the US markets shot up quite dramatically just before the close. I noticed that the VIX dropped steeply at the same time.

However, when I came to look at the daily moves (close vs close) the S&P500 was only up 0.2% on the day while the VIX was down over 7% I think. Although not totally unprecedented that was quite a striking ratio.

Do you think that 'last minute' action and excitement in the market can give a 'biased' or exaggerated or overly emotion affected result to the closing Implied Volatility number?

Not sure if this is vitally important as I'm sure that things even out over time but I did wonder.


Bill Luby said...

To answer your question first, I do believe that the action in the VIX going into the close has a tendency to be exaggerated during sharp market moves, particularly when the broad market indices are falling rapidly.

While various types of portfolio protection can be purchased around the clock, those looking to buy put protection via SPX puts have until the close of index options trading (4:15 p.m. ET) to do so -- at least in the most liquid market environment.

In my opinion, anyone who postpones buying put protection until the end of the day "to see how bad things get" is likely to be less price sensitive just before the close and be more concerned about filling an order than getting it at the best possible price -- or not at all.

Regarding yesterday's VIX, it was strangely unfearful, particularly during 12:30 - 1:15 p.m. ET, when the SPX sold off fairly substantially, while the VIX hardly moved.



Anonymous said...

Thanks Bill, that was interesting.

It may be the your last paragraph was however the key...and the most telling point.

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