Easy math, but also easy to forget

I’ll take a break from the longer posts about the MID to do a gentle introduction to what I referred to in my introductory post as technical education.  We’ll start off with something easy so I don’t scare away any reader(s) I may have left.

Just today I was looking over the Case Shiller index numbers for October (they’re released after a 2-month lag, so this is the most recent data available).  The numbers, as released by S&P, are just index values, listed separately for 20 cities along with 10- and 20-city composite values.  I always put these raw values into a spreadsheet I’ve made that does some simple calculations on them.  For each city, I look at the month-to-month change (October’s index value compared to September’s), the year-over-year change (October’s index compared to last October’s index), and the percentage change from both the peak and the post-bubble trough.

This time, I happened to notice something about San Francisco’s values:

  • From peak to trough, SF’s index declined 46%.
  • From that trough, the index has gone up 12% as of this month.
  • From the peak to now, though, the index has declined 39%.

So, doing addition doesn’t work here.  A 46% drop followed by a 12% gain doesn’t give you a drop of 46% – 12%. The reason, of course, is that the two percentages are computed from a different baseline:  the 46% means 46% of the (much higher) peak index value, while the 12% is calculated from the (much smaller) trough value.

This isn’t rocket science, but it’s easy enough to forget when you read articles describing housing prices, along with what some might call their recent recovery (though the recovery hasn’t been particularly strong.)  There’s a natural tendency to compare numbers when they’re presented next to each other, as percentages like this often are in the press.  You might think that, since the index has increased 12%, that it’s about a quarter of the way back to its bubble-level highs after the 46% drop.  But that’s not the case:  the index will have to increase a total of 86% from its lowest point to get back to its record high.  That’s still a very long way to go!

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