The National Association of Realtors' Fuzzy Math

This is the worst website I've seen in a very long time. For one thing, it's one of those websites which starts talking at you the minute you load it: turn your speakers off before you go there, if you don't want your computer to verbally welcome you to the website. And then on top of that it's so flashed up that it doesn't have any web pages: there's only one URL, and precious little actual information.

But the worst part of all is the "facts" which greet you when you first visit the site - a site which, we're told by its parent, the National Association of Realtors, "provides resources and research about the current housing market ". "On average, the value of a home nearly doubles every 10 years," it says. "At an annual appreciation rate of 5 percent, a 10 percent down payment on a home will return 94 percent after 3 years."

d00d. w00t! FTW! If I want to double my money in three years, all I need to do is buy a house!

There's even an "equity estimator calculator" which will, for any given down payment, calculate 94% of that number for you, and tell you that you can "generally receive" that amount after 3 years. The calculator also says that "data is based off historic and current percent rate of returns," whatever that means, and cites "Harvard Universities [sic] Joint Center for Housing Studies", without citing any actual paper.

But I just don't see how the numbers can add up. OK, a 10% down payment means that you essentially have 10x leverage on your money. But even then, how on earth can a house appreciating at 5% per year return 94% after three years?

A quick visit to bankrate.com shows that a 30-year mortgage is currently 5.56%. If you're paying 5.5% on your mortgage while your house is only appreciating at 5% per year, how can you be making an annualized return of 25%?

And the NAR can't be ignoring the mortgage costs completely. If you do that, then all you need to do is look at the value of the house, which goes up by 15.8% over three years. And that sum is 158% - not 94% - of a 10% downpayment.

Let's try and work backwards here. Say the house cost $1 million, and there's a $100,000 downpayment. At the end of three years, you sell the house for $1,157,625, with no transaction costs whatsoever. You repay your $900,000 mortgage, leaving you with $257,625. Subtract your initial $100,000 downpayment, and you're left with $157,625 in gain. But your return is 94%, or $94,000. So your mortgage payments must have been $157,625 minus $94,000, which comes to $63,625. That's about $21,208 per year. And $21,208 is 2.36% of $900,000.

In other words, if your house appreciates at 5% a year, you can make 94% in three years - if you can buy and sell with zero transaction costs, and if you can find a mortgage at 2.36%.

Somehow I doubt that Harvard's Joint Center for Housing Studies is going around writing papers assuming mortgage rates of 2.36%.

Or is there some other way of getting to that 94% figure?

(HT: Jackson)

Update: Eddie, in the comments, gets to the 94% figure another way, which might be the method the NAR is using. Sell the house for $1.158 million after three years, and then spend the $63,625 in transaction costs by paying 5.5% of the sale price to your Realtor. Presto - a 94% return, assuming that your mortgage cost you nothing. Or, as Eddie puts it, "interest, property taxes and maintenance are a cost of living if not life itself". Got that? A mortgage isn't the cost of a house, it's a cost of life itself, and therefore shouldn't be included in your return calculation. Clever.