So as expected last Friday’s daily blog post about XIV / VXX performance during the financial crisis prompted numerous follow up questions which of course are always welcome so thank you for that. For those that missed the post, it’s here.
Today’s daily blog post is an extension of one of those follow up questions, and it has to do with:
Linear price scale vs Logarithmic price scale
First I’ll quickly talk about the difference, and then because they were such a big hit I’d like to use last weeks historical XIV price charts as examples to show the difference.
– Linear price scale charts are plotted in such a way that on the Y axis (left vertical side of the chart) there is an equal distance between prices, and price change is represented by the same vertical distance on the scale.
Example: So a price change of 5$ would be represented the same as any other price change of 5$, regardless of the starting price. A move from 5-10 would cover the same vertical distance on the chart as a price change from 20-25.
Linear price scale charts are the majority of the ones you see out there, and the reason I also use them is mostly due to people’s familiarity with them. It’s what people are used to seeing and doesn’t usually require any further explanation.
– Logarithmic price scale charts show percentage changes plotted on the Y axis (left side) so that two equal percentage changes will cover the same vertical distance on the chart.
Example: Using the previous example, a price change from 5-10 is a 100% gain, where as a move from 20-25 is only a 25% gain.
If a logarithmic price scale chart is used, the move from 5-10 would visually look like 4 times the magnitude, which in terms of percentage change it is.
* Before we look at examples, let me remind you about last Friday’s blog post which contained plenty of disclaimers and caveats with respect to simulated XIV price data before the products official launch on November 30th, 2010. Please review that article if you’re not clear on why these simulated prices may not be accurate.
XIV prices simulated back to 2004: (Linear price scale)
If we look at those three distinct drawdowns (2008, 2011, 2015) because the price changes happened at three different starting points it’s hard to actually get a feel for the relative scale of them.
XIV prices simulated back to 2004: (showing 3 drawdowns)
One potential way to solve this problem is to plot it on a logarithmic price scale chart that evenly displays percentage moves.
XIV prices simulated back to 2004: (logarithmic price scale)
As far as percentage price changes it’s more clear now. The drawdown during the 2008 financial crisis was in fact the biggest, and the 2015 drawdown now visually is the smallest of the three, which it was.
Recall from the previous blog post I also mentioned that the performance of our VTS Tactical Volatility strategy was quite consistent over time as well, except for a pretty glaring difference during the financial crisis. On a linear price scale it’s not as clear, but on a logarithmic chart you’ll see what I mean.
* Again massive disclaimer here when using simulated XIV price data that is quite likely not accurate. There’s a reason I very rarely show these charts. Data before Nov 30th, 2010 is not reliable enough to draw any meaningful conclusions.
Tactical Volatility performance since 2004: (linear scale)
Tactical Volatility performance since 2004: (logarithmic scale)
Like I said, pretty consistent for 13 years besides a very fortuitous period in 2008 (green circle). And obviously we know looking back with 20/20 hindsight that was due to the biggest market crash since the great depression. Whether we get that lucky in the future or not is yet to be seen. There’s no doubt that if markets do decline, the more violent the better with respect to long volatility products like VXX and VXZ.
Linear price scale vs logarithmic price scale
They are both useful in different situations for displaying data but like I said the linear scale is very likely the more common one you’ve encountered.
As a general rule, if we’re looking at a shorter time frame and we’re looking at reasonably consistent percentage changes over time, then the linear scale is visually more familiar and it’s what I use for nearly all of my charts on the website.
But as the years go by, linear charts will look more distorted and there will come a time when it will be more visually accurate and appealing to be using logarithmic charts.
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