A Canadian's random thoughts on personal finance

Mar 13, 2015

Don't be fooled by a normalized line chart

Often, two hypothetical investments are compared using a chart with two lines, one per investment, "normalized" so they start at the same point.

I urge you to pay no attention to such charts.  It is far too easy to manipulate them to make whatever point you want to make.

Consider this chart showing the performance of the TSX Composite versus the NASDAQ over a two-year period:

These two lines are shown starting with the same value on the left so you can compare how they evolved from time onward.  Clearly, NASDAQ in orange was the better investment in this time period.

Below is another chart of the same two indexes.  Clearly, in this time period, TSX in blue was the better investment:

However, take a closer look.  These two charts cover almost the same period.  80% of this second chart plots the same data as the first chart.  The middle 80 weeks from July 2003 to January 2005 are included in both; only the 20 weeks on each end are different.

The trouble is that this type of chart is incredibly sensitive to the choice of starting date.  Almost unbelievably sensitive.  So sensitive that, in my mind, this kind of chart is practically useless as a tool to understand two investments.  It is a simple matter to make a chart like this say anything you want it to say.  (They can appear quite convincing; I think that may be because the mind gives too much weight to how much time one line spends above the other.)

Please don't rely on charts like this for any important decisions.


Michael James said...

Hi Patrick,

It's been a while. While reading through, I was thinking that the time one curve spent above the other influenced people, as you later mentioned. I think this is similar to how people perceive sports. If the home team leads the whole game and gives up a few points at the end to lose, the fans feel the other team stole the game, which is nonsense.

Patrick said...

Hey Michael! Great to hear from you. Last time, I think, was on one of Preet's podcasts in my car a couple of years back. :-)

Having decided passive investing was for me, I put things on autopilot and spent a few years thinking about computer science in my spare time instead of finance. Recently, I saw a graph like this used to make a point, and it reminded me of how unreliable they are, so I thought I'd make that point here.

Agreed about the sports analogy. In fact, the sensitivity to the starting point is equally valid there too: how often do you find that the losing team would actually have one if you ignore the first 15 minutes of the game?