# The Math Of Housing Prices

In terms of house prices, the city where I live avoided the worst of the Global Financial Crisis. There was a spurt in house prices that stopped in 2007, but after that, prices didn’t crash, they plateaued. Now, I rent a house, and I also own a house which I rent to someone else. One day, I’d like to sell the house I own, and buy one to live in. Naturally, I pay attention to newspaper headlines like “House Prices Plummet In May!”

Every time an headline like that hits the newsstands, there’s a flurry of comments from the online public. These comments fall into two groups. On the one hand, there are those who say

Ha! See? The bubble is bursting! Houses are waaay over-valued! I’m so glad I don’t have one!

On the other hand, there are those who say

The fundamentals are strong! This is a temporary dip! Houses will shoot up this year! I’m so glad I have one!

Since I both have and don’t have a house, I’m torn. Do I want house prices to go up, or down?

What does the math say?

The math says, in fact, that I should throw away the newspaper, and laugh at all the online commentary. This is because it all focuses on a completely useless number. The useless number is the “median house price”. Let me give explain what “median house price” means, and give an example to show why it’s useless.

To calculate the “median house price” for some city in some particular month, they’ll

• get a list of all the houses sold that month
• sort them from lowest price to highest
• pick the middle price

So, if the “median house price” is \$400,000, it means half of the houses sold went for more than that, and half for less. This is a completely useless number, because I don’t care about houses that are sold. I want to know

• If I decided to sell my house now, could I sell it for more than I paid for it? Would I get more if I waited?
• If I decided to buy a house now, would it be cheaper or more expensive than later?

In other words, I want some idea of the value of a particular house – or pair of houses. And I want the price it could be sold for, not the price some other house actually did sell for. The problem with the “median” house price is that it doesn’t just reflect my house value – it reflects a combination of everybody’s house value and how busy real estate agents are.

An example will point this up.

Imagine a town with two suburbs, Richland and Poorvale. Houses in Richland sell for \$1M, houses in Poorvale for only \$100k, that is, \$100,000. Suppose there are enough buyers to buy any house put on the market, but this never affects the price*.

In April, four Richland families sell out and move, as well as one Poorvale family. The Real Estate Institute computes the median house price as follows :

• They get a list of the 5 sales : \$1M, \$100k, \$1M, \$1M and \$1M
• They sort them : \$100k, \$1M, \$1M, \$1M and \$1M
• They take the middle number, \$1M, as the median house price, and tell the newspaper.

So the median house price in April is \$1M. In May, however, only one Richland family sells their property, but four Poorvale residents do. Now, the Real Estate institute does the computation as follows :

• They get a list of the 5 sales : \$100k, \$100k, \$100k, \$1M and \$100k
• They sort them : \$100k, \$100k, \$100k, \$100k and \$1M
• They take the middle number, \$100k, as the median house price, and tell the newspaper.

The median house price is now only \$100,000! Imagine the newspaper headlines!

News Flash! House Prices Plummet In May! Data from the Real Estate Institute shows that housing prices have dived by an extraordinary 90% between April and May! We asked a Really Important Sounding Expert why the value of houses was dropping. “Well, I attribute it to a softening in the economy, uncertainty in the commodoties market and the toupee of a banana-ridden aquamarine,” the expert was quoted as saying.

The “expert” can attribute it to whatever he likes of course. In reality, the value of the houses in Poorvale and Richland has not changed one bit. My investement there is safe, though static. The only thing that changed is the number of sales in each suburb.

In general, the change in median house price is caused by two things

• Changes in the value of the different types of houses that happen to go on sale
• Changes in the how often sales take place, especially if some parts of the market slow down or speed up relative to others.

Unfortunately, we tend, in our minds, to attribute it to just one thing

• Changes in the values of houses generally

or, worse,

• Changes to the value of my house.

and this is completely wrong.

This is why “median house price” is a useless number for me. I want to know about changes in the value of the house I own. I want to know about changes in the value of particular types of houses near where I’d like to live one day. Even if I knew “median house price” for particular suburbs, I still don’t know much – since even within one suburb, there are big houses, small houses, old houses, new houses, well-maintained houses, one- and two-storey houses. The median house price reflects changes in the values (potential price) of all these different types of house, as well as numbers of each type that actually got sold.

Suppose a bunch of builders cast their eye on some old, old suburb. They start buying old houses, knocking them down, rebuilding, and selling them off. Then the “median house price” for that suburb will go up, even if every individual house in the suburb is steadily losing value.

So I don’t want to know “median house price”. What I want to know is “How much will I be paid or have to pay for my house?” And that number is buried with a lot of other numbers deep deep within the “median house price”, so deep that even the math can’t pull it out.

Footnotes :

* This could easily happen, for example, if there are many similar towns dotted around the countryside.