Sunday, April 12, 2015

When logs rool for graphs

It was noted this week that the monthly RBA Chart Pack had changed the scaling for property prices: The RBA is using new charts that make Sydney house prices look less bonkers
Today, the RBA released its Chart Packs updated to 2 April 2015 which revealed another insight into the lines of thinking at Martin Place.
Previously the “Housing Prices” chart in the Reserve Bank’s Chart Packs have been presented using a linear or arithmetic scale, with prices spaced equidistantly. On a linear scale, housing prices in Sydney were seen to be galloping towards the top of the chart.
In this month’s Chart Packs, however, the Reserve Bank has shifted seamlessly to a log scale, whereby equal percentage changes in housing prices are plotted as the same vertical distance on the scale.
That comes from Pete Wargent, a property buyers agent whose commentary I have some time for, which is a rarity. However I think this has been misinterpreted by some judging by comments seen elsewhere that a log scale is not 'real' or has been manipulated, and not sure this change or the timing really has much significance. The RBA chart is more illustrative than anything and a log scale is more appropriate for this purpose. The question should be why the RBA was previously using a linear scale.

A log scale, or rather semi-log scale, effectively represents changes with percentage on the Y-axis. So the distance between 100 and 200 will be the same as the distance then between 200 and 400, and then 400 to 800, etc. This is a far more 'real' way to represent changes in property prices over a period of time rather than a linear scale which will inevitably show prices heading for the stratosphere. If you look at HTW CairnsWatch you will see that Rick Carr uses a semi-log scale for his graph of Cairns property prices.

In the olden days about the only place one could procure semi-log graph paper was the bookshop at either the stock exchange or university. Early spreadsheets were pretty crude and can still be quirky. I have recently been playing with a log scale to analyse historical prices within my retro-bohemian Esplanade building following some recent sales, the first since 2008.

A linear scale with available data since 1987 looks like this:

 
The two series there represent the two different sized units within the building. The trendlines are Excel generated exponential which will curve upwards. Note that if I had excluded the most recent transactions it would have looked like valuations were heading to the stratosphere up to 2008.
 
If I graph the same data on a semi-log scale it will look like this:
 

 
A straight trendline can now be generated to make more meaningful sense for any analysis as a benchmark over time. Must do some work on those Y-axis gridlines though!

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