Efficient Frontier
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William J. Bernstein

Why You Can’t Afford a House in San Francisco

Is there a housing bubble? Why are homes in some cities outrageously expensive, while those in other cities easily affordable? In attempting to answer these questions, I found that a simple and intuitive model of the housing market does a remarkably accurate job of predicting median prices. This model allows us to think more clearly about the state of today’s residential markets.

Imagine for a moment that we live in a world where all information about home prices is censored and both buyers and sellers—everyone, in fact—has not the faintest idea of where fair housing prices stand. In such a world, how do you estimate median prices?

Begin by assuming that most people mortgage themselves to the hilt. If the median family income in the U.S. is currently $60,000 per year and if lenders allow a mortgage/income ratio of 25%, then $1,250 per month is available for monthly payments. If the current 30-year fixed-rate mortgage is at 5.7%, then a theoretical median U.S. house price of $215,000 pops out of the spreadsheet. The actual value? $187,000. Not too shabby. (I’m ignoring the down payment, which I assume is borrowed from other sources, and thus is factored into the homeowner’s presumably prudent-borrowing decision making. In any case, the down payment seems to be going the way of disco and balanced budgets.)

Next, repeat this exercise over the past 35 years. Data sources: Mortgage rates from the Bureau of Economic Affairs, median home prices from Freddie Mac and the National Association of Realtors. Family income was simulated by multiplying the BEA per capita income figures by two, which very closely approximates the census bureau’s family figures. (The BEA approximation was used because it is a much more detailed time series.) As a dash of spice, the initial theoretical median home value in 1970, $21,141, was invested in the S&P 500 and allowed to run:

Indeed, the mortgage-to-the-hilt-at-the-30-year-fixed-rate method does a decent job of tracking median home prices.

What does this tell us about the state of the present housing market? First, with the actual median home price about 13% below that of the model prediction, there certainly is no bubble at the national level. In fact, the only time the model screamed "bubble" was in the late 1970s and early 1980s as theoretical home prices plummeted because of rapidly increasing mortgage rates. Rates peaked at over 18% in 1981, while actual home prices blithely continued climbing, albeit at a less heated pace than before.

Now that we understand what drives home prices—loan size dictated by rates and income—most everything else about the real estate market, even at the local level, falls neatly into place. For example, it might appear at first glance that falling mortgage rates are a good thing for home buyers. But for the most part, they aren’t; all that falling rates accomplish is to increase the PV (present value) number that appears in the financial calculator. The bad news is that purchase prices go up, but the good news is that mortgage payments won’t be much different than before the fall in rates. At the end of the day, new buyers will write the same monthly check to the bank, no matter what has happened to interest rates. The falling rate/rising price scenario isn’t even that good for sellers; yes, they’ll get more for their house, but this will be offset by the lower expected security returns available to the capital raised. Only the real estate agents and tax assessors are happy.

What about the "bubble zone"—California, Florida, New York City, and Boston? Simple. These areas attract an undue proportion of high wage earners, so if you move to one of these locales, you’re competing for houses against folks whose mortgage capacities are among the highest on the planet. When will home prices fall in these modern high-rent districts? When at least one of two things happens: mortgage rates rise, or the average income in these locales falls. If and when either happens is anyone’s guess. To be sure, the increasing numbers of amateur speculators in hot markets, real-estate cocktail chatter, and proliferation of books and courses about getting rich in real estate all scream "bubble." But to the extent that these prices are propelled by high-earning boomers with insufficient savings, the bust may not occur for as long as another 15 or 20 years, if at all. And let’s be clear about what we mean by "bust." As suggested by the above plot, home prices are far less volatile than either stocks or long bonds. But even a 10% to 20% fall in prices would wipe out the speculators and not a few first-time buyers who have fallen on hard times or who must relocate.

Since everyone in the housing market at a given moment pays more or less the same loan rate, what really determines the affordability of housing is where in a given area’s wage ladder you fit rather than the absolute amount of your salary. Better a teacher in Omaha than an Upper East Side internist.

The rise in the median U.S. home price between 1970 and 2004 was only 6.05%, about 1.3% more than inflation. In this period, the return of the S&P 500 was 11.41%. True, stock returns going forward aren’t going to be nearly that high, but given the retirement prospects of the boomers, neither are returns on residential real estate going to be as high as they have been in the past. I suspect that over the next few decades, the return of a prudently invested securities portfolio will outpace that of residential real estate.

About the only bit of arbitrage worth considering involves the growing gap in the high-flying markets between renting and buying. It makes no sense, as is the case in many cities, to buy a condominium for $500,000 when a similar flat can be rented for $1,800. Why the gap between rental values and mortgage payments? Thank compassionate conservatism. Rents, just like mortgage payments, are driven by salaries. Consider the widening income disparities of the past few decades, shown in this plot extracted from Pikkety and Saez’s landmark study, which displays the total national income generated by the top 1% of wage earners:


Renters tend to be poorer than homeowners. As the income disparity between high- and low-salaried individuals has grown, it’s no surprise that rental and mortgage payments have diverged.

Home prices and rents do not exist in a vacuum, and the factors that influence them are blindingly simple: the mortgage rate and the salaries of those in the market. Where these two critical values go, so go rents and home prices eventually.

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Copyright © 2005, William J. Bernstein. All rights reserved.

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