The problem with graphs

Tuesday, September 2nd, 2008

Take a look at this graph. It accompanies a story on the BBC News website about the property market and today’s announcement of Government measures to boost flagging sales.

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The graph plots the change in house prices as measured by two banks, The Nationwide and The Halifax. On the face of it things look pretty dreadful.

Except that the graph is wrong*. The values it is plotting are ‘rates of change’, so it’s a bit like plotting a car’s speed by plotting its acceleration and deceleration. You wouldn’t really do that as you can’t use such a graph to say what the car’s actual speed is at any one time, without making some tortuous calculations.

Let’s give an example. The graph plots changing values from April 2007 to August 2008. But the individual points relate to the relative change in house prices during the year to that date. So if you look at the point for the Halifax figures in April 2007 you see approximately 11%. What that means is that a house bought in April 2006 for £100,000 (good luck finding one that cheap) was typically worth £110,000 in April 2007.
Now look at April 2008. The graph shows that house prices fell by 1% in the previous 12 months. So that house which was worth £110,000 is now worth £108,900 – so it’s still 8.9% higher than it was two years previously.

What you can’t do with this graph is look at the August 2008 part of the graph and say what the value of that house is now, because it wasn’t bought in August 2007 – the figure is meaningless, therefore the graph is meaningless. (This is the same problem you get with monthly inflation figures – a figure of, say, 5% might be seen as high but it means prices went up 5% over the last 12 months, not in the last month. If prices stay at the same level, inflation will be 0% but that doesn’t mean things are getting cheaper. It means they’re staying just as expensive as before)

If I had bought that house in April 2006 I couldn’t use these figures, or this graph, to predict what the house is ‘worth’ now. But that would still be irrelevant unless I was thinking of selling now. But house purchasers don’t tend to buy and sell in a year, but after several years (often decades). A graph on that principle would show a steady and sustained increase in the value of houses. There’s a lot of people worrying over nothing – if you’re not thinking of selling your house then you have nothing to worry about, yet this graph is intended to make you worry.

(Let’s say that house price inflation stood at -10% in April 2009, then I could calculate the value of my home. It would be £98,010 – a drop in value for sure but of £1,990. In other words my house would be worth 1.99% less than it was when I bought it, not 10% less. See how it works?)

The only conclusion I can draw from this graph is that whoever inserted it is attempting to make things look more dramatic than they really are.
Which leads to a suggestion: the best way to increase confidence in the property market would be to ban stupid measures of the market that plot relative values over 12 months. The housing market doesn’t work on such small cycles.

(*Actually, ‘wrong’ is not the word, rather it’s ‘misleading’, but it’s so misleading it might as well be wrong)

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