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?

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.

Comments

[Expat:]

Sounds like modern, accepted accounting principles to me! What works for corporate America can work for YOU!

Even more cynically, is it possible the NAR (isn't it eery how close that is to NRA?) is calculating its commission as being a 94% return on your downpayment?

2008 Jan 09 11:13 PM

[brechtp:]

I can't argue that the site is any good but your computation skills might be worse, or maybe it's your understanding of how a mortgage works. Let's ignore the fact that there is no such thing as 10% down on $1M and assume that you did that to give yourself a break with the numbers. At the end of 3 years your mortgage balance would be $860,786.04 unless you also think you're going to get an interest only 10% down jumbo. And the fact is you do have to pay to live somewhere - don't you? I suppose unless you live with your mom. The NAR may be eternally optimistic and slightly misguided in their press marketing efforts but it isn't some evil organization out to trick you into buying a home - gimme a break.

2008 Jan 10 09:39 AM

[User 138189:]

It might not be Evil but their primary goal is getting you to buy or sell a house and they are going to do whatever they can to convince you that it is a great investment. Right now housing is NOT a great investment unless you buy the house of your dreams and never plan on selling it.

2008 Jan 10 10:03 AM

[Charlie9:]

There's an industry standard way of calculating a rate of return on an investment with cash flows, it's called internal rate of return (IRR). Essentially, you would have the same ending amount as if you put the money in a saving account that yielded the IRR.

In the example, your inital deposit would be the amount paid at purchase closing (down payment, escows, comissions, etc...). Monthly mortgage payments would be the same as monthly deposits in the savings account. The ending amount would be whatever check was received after the selling closing. I guess you could justify amounts saved in rent as the equivalent of a withdrawal from the account.

I used to write software that calculated returns on these kind of investments that was used by many major banks and investment houses and this was the generally accepted compliant way to determine the rate of return. I used to get in arguments with the accountants about the numbers being wrong and I had to convince them that this was how it was done and that the numbers were in fact correct.

2008 Jan 10 01:02 PM

[Johnny Bitc...:]

The NAR is deceptive and the deception is systematic in that they would purport to be an information provider to home consumers. Obviously they selectively choose statistics and other doubtful informaton in order to provide their true constituents, the real estate salesman, with ammunition to bamboozle the credit driven American citizen.

There are all sort of legal arguments about freedom of speech and they won't really claim to be unbiased, but I don't think it's unfair to call them evil if you believe they are systematically deceptive.

So the NAR is evil, but their evil is perfectly legal within the bounds of a sad and corrupt system of credit and home finance.

It is sad that numerically incompetent Americans are not better protected from the salesman at the NAR. It is sad that professional economists would accept a job as statistician to the salesforce - very sad.

But the sadness, corruption, and evil is reality.

jbd.

2008 Jan 10 01:44 PM

[watteau:]

NAR should update their calculator to "how much money can you lose if you buy now", put in a 6,1% depreciation on a house, plus mortgage costs, plus purchase and sales costs (after all, realtor costs strangely don't show up here. Does that mean, that realtors got so shameful of their work that they now work for free)?

2008 Jan 12 10:42 PM

[watteau:]

Another idea for a NAR "Bankruptcy Estimate Calculator".

It works with check boxes.

1. Listen to your realtor. Check.

2. Read NAR info. Check.

3. Let your realtor advise you on a loan. Check.

4. Pay a hefty fee for these services. Check.

5. Receive the approximate date of your bankruptcy.

If NAR was an a person, and an investment counselor, he would be in jail.

2008 Jan 12 10:48 PM