Tails of Price Changes

July 22, 2011

by Ben Gimpert

3 comments

Bell curves and real estate price changes.

Histograms are a visual way to summarize a huge set of numbers. The horizontal axis covers the range of numbers, while the height of the vertical columns shows how many occurrences of that number turn up in the data. Even when the histogram looks mostly like the classic bell curve, the slight differences tell a story.

Here is a histogram of quarterly changes in Altos Research residential real estate prices:

Ask Price Changes
(three month changes in the median ask price of single-family homes, across about 300 random zipcodes with significant inventory, across our entire history)

This chart gives good perspective into the recent behavior of the housing markets. The histogram has a long positive tail, so we know there were many quarters when property prices rallied. However the center of the distribution is slightly negative, where we find most of the histogram’s “weight.” This center is around negative one percent, and shows the credit crisis hitting a broad set of markets. There is also plenty of weight outside of the positive or negative ten percent range, which suggests how volatile real estate prices can be even over a whole quarter. The situation is even more extreme if we chart sold prices the same way:

Sold Price Changes
(three month changes in the median sold price of single-family homes, across about 300 random zipcodes with significant inventory, across our entire history)

There is much less volatility in list prices, as we can see by comparing the width of these two histograms. This is because active asking prices are sampled across a much larger population. Sold prices vary drastically, since one or two quirky transactions have an over-sized impact on a median or average of a small sample. I talked about this sample size problem in my earlier Fungal Houses post.

These histograms visualize the consistency of home price movement. Common automated valuation models are subject to wild swings in valuation opinions, because they are built on lagging sold price data. This is why some AVMs can see a six-figure change in a property’s valuation in one day.

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