On Regression to the Mean

Recent statistics have confirmed what many have long feared - the end of the housing boom in many parts of the country. There is now increasing talk of "a return to normal" in the nation's real estate markets - a return to "normal levels of appreciation" some say.

Does it really work that way?

If the boom is indeed over, after a huge run-up in prices in recent years, why would price appreciation return to normal?

Isn't it more likely that prices would return to normal, as in a regression to the mean?

In probability and statistics, regression to the mean describes the tendency for things to return to normal, whatever it is that normal might be. In the case of housing, a regression to the mean would imply a return to long established price trends based on historical levels of appreciation.

Regression to the mean is something that many homeowners and homebuyers are likely to learn about in the years ahead since most things behave this way. Despite the best efforts of homebuilders and originators of mortgage credit, housing is not likely to be an exception.

Back to the long-term trend, not to the normal rate of change

Regression to the mean does not imply a return to a normal rate of change, but rather, a return to the long-term trend - what would be expected as an end result years from now given historical averages.

So, for example, if the average annual appreciation for real estate in a particular area is seven percent, and a few years of twenty or thirty percent appreciation occur, a regression to the mean implies a return to the long-term trend that was in place before the rapid price increases.

Looking at the last few decades of home price data in Phoenix and in the U.S. in the chart below, the situation become a bit more clear. While home prices on a national level have risen briskly in the last few years, this part of Arizona seems to have set a few records in recent years.
A long-term average of six or seven percent appreciation seems reasonable from looking at the chart above, but after the increases of the last few years, it's natural to wonder what might lie ahead. If the late-70s to mid-90s experience is any example, there are sure to be some below average years of appreciation coming to Phoenix.

But, how far below average?

It depends on how quickly prices move back to the mean.

If the average increase is seven percent, what would it look like to revert to the mean after consecutive years of ten percent, 32 percent, and 26 percent appreciation as was the case in Phoenix?

That same question arose in a recent Money Magazine article where a reader asked for advice regarding an upcoming rent vs. buy decision, one of many considerations in their relocation to Phoenix. Here's the advice that was offered:

The first thing you need to ask yourself is how long you plan to live in Phoenix. If you'll stay less than two years (five in a city that's growing more slowly than this one), go ahead and rent because by the time you pay closing costs and broker's fees on a purchase and sale, you'll lose 5% to 10% of the home's value.

If you plan to stay longer, the math gets fuzzier. Unlike some cities, Phoenix has an abundant supply of single-family rental housing. And home prices have risen faster than rents lately, which has made renting unusually attractive. Consider our simplified calculations: You can rent a three-bedroom, two-bath house in a nice neighborhood for about $14,600 a year, including renters insurance. The same home might sell for $450,000. With your $70,000 down payment, if you took out a 30-year fixed-rate mortgage, you'd be spending some $31,100 annually after tax deductions, including insurance, property taxes and maintenance.

Measured by cash flow, renting is cheaper, hands down. But home ownership is also an investment decision. To make up the $16,500 annual difference in cash outlay, your property would have to appreciate by about 3.7% a year. If you think you'll see growth of that much or more, buying might be the way to go. But the market is tough to call. Phoenix's prices are up 11.8% from a year ago, according to the National Association of Realtors, but that rate obviously can't be sustained. And if Phoenix's long-term growth rate were to drop back to the U.S. historical average of 6.7% appreciation a year, the adjustment could be painful.

Now, the advisor does a pretty good job of explaining the situation up until the point where long-term appreciation is involved. It seems that, as a nation, we have difficulty in this regard, perhaps accustomed to having our gratification instantly whenever possible.

According to OFHEO data, since 1978, there has been little difference in the "long-term growth rate" between the nation's housing stock and the housing stock in Phoenix - six percent and seven percent, respectively. And even if there were a big difference, that last sentence in the advice above, no matter how many times you read it - it just doesn't make any sense.

Given what is going on in Phoenix right now, 'ghost towns' appearing here and there, many homeowners would surely be pleased with the prospect of resuming the long-term growth rate of near seven percent, but that is not likely to happen.

What the writer was probably trying to describe was the painful adjustment process in reverting to long-term trends, or in regressing to the mean. Those painful possibilities, both for the renter seeking advice and for the many thousands of others pondering an Arizona real estate purchase, are shown below.

The chart shows two curves - actual home price data through the second quarter of 2006 and the long-term trend projected from 2003, when many homebuyers stopped caring about prices paid, using the historical average of 7 percent appreciation.
A couple of quick calculations help to demonstrate the possibilities. If it takes six years for Phoenix home prices to make it back to the long-term trend, that would leave a homebuyer down $10,000 on a $450,000 home purchased today, in addition to repairs and other expenses. That doesn't sound too bad, but six years is a long time.

If the process took eight or ten years, this would leave the homeowner in the black by $72,000 and $130,000, respectively. Interestingly, taking the $16,500 per year saved by renting, as noted above, and banking it at just four percent yields $111,000 and $133,000 for the same periods.

Naturally, the worst case would be the two-year and four-year price moves where today's $450,000 home would be worth $297,000 and $383,000, respectively. Ouch!

But the prospects for homeowners could potentially be worse than that shown above - in addition to there being a tendency to revert to the mean, there is also a tendency to overshoot during the process. This is what happens when an entire nation sours on the idea of owning something - think common stocks in 2002, and maybe real estate sometime in the years ahead.

On the bright side, it's always possible that things will be different this time.