Mind the gap

When comparing two time series, one typically wants to discuss the size of the gap as it changes over time.  This Business Week chart, for example, depicted for readers the expanding gap between intra-day high and low prices of the S&P 500 for 2008.


This chart construct is effective at pointing out large changes but lacks precision in conveying smaller differences, or trends.  It is always a good idea to plot the gap directly, as we will show below.

More importantly, a better choice of scale can help a lot.  By focusing exclusively on variability (extreme values), this chart hides the relevant information of the closing prices of the S&P.  A point spread of a 100 points means more when the index is at 800 than at 1200.  In order to capture this, we can divide the point spread by the opening price of that day so we say the gap is one-eighth or one-twelfth of the opening price. 

The junkart version makes both changes.  The top chart fixes the scale, plotting the point spread as a percentage of daily opening prices.  Relative to the original chart, the variability in the front part of 2008 was muted because the index was at higher levels back then. 

The bottom chart plots the gap sizes (lengths of the high-low lines).  It is without doubt that directly plotting the gaps showcases the key message.  The current level of volatility is more than double what occurred at the beginning of the year.

If one wants to illuminate the trend as opposed to daily fluctuations, a further improvement will be using moving averages.

For those interested, shown below is a scatter plot that compares the original point spread and the derived point spread, which shows that the change is not trivial.

 

Reference: "The Market: A Daily Roller Coaster", Business Week, Oct 27 2008.

Comments

[Bernard Lebelle]

Very similar to the NYTimes "The Pulse of Uncertainty" charts back in January.
I like the retreatment performed to show the gaps size and the "twice as much" effect.
One of the things that I would consider to put things in perspective is the volume of trade done during that days. We have seen before that on certain occasions, where less actors are at work (ie. bank holidays in Europe, summer periods...) less volume can bring higher volatility..
Seems to me this should be embeded somehow to fine-tune the analysis.

[Simi]

Do you know where, I can find the data for this original chart. So I can try to produce some different graphs