Monday, March 26, 2007

Some boring statistics

Prices or compounding interest follow a geometric progression, such that the slopes at later times look steeper than at earlier times. This leads to a misleading impression that the latest runup is much bigger than previous ones, as in the plot below.



In the upper plot, the blue line is average single-family-housing prices in Victoria. It looks quite alarming towards the end. However, if you look at the lower line, the percentage change is not much different than the previous cycle that started in 1985. (the black line is the CPI-adjusted real hosuing price).



Here I have plotted the curve at a constant percentage increase for each of the price indexes. Now the current rise does not look so precipitous.



This made even more clear if we use a log plot so that a constant percent increase looks like a straight line. The current runup is above the trend, but not disastorously must-drop-30% so.



Finally, the most intuitive (for me) way to see this is to line up the prices at t=0 and apply the percentage increases to the starting points. If we do this, we see that the current runup (blue) is slightly steeper than the previous one, but not dramatically so (and I could have started in 2000 to make this even less dramatic). It has exceded the total change from 1979, but not by much, but is nowhere near the peak if we think the 1985 runup is any guide.

The point is not that the market in Victoria will keep rising. No market is like the next, and I think most signs indicate a cooling. The point is that the rise from 2000- now is not unprecendented nor is it particularly sharp.