By John H. Huston and Roger W. Spencer
Articles on housing valuation frequently compare housing prices to rent, often in the form of a price/rent ratio. This is a reasonable metric to employ. Rent is what one could earn on a house as an investment or, if you live in the house, it is the market value of the services generated by the house for your benefit. Thus, the price/rent ratio is essentially a P/E ratio for housing, and for any asset it would be valuable to know if the price of the asset wandered far from its historical relationship to the earnings it can generate.
However, the price/rent ratio by itself says little about the relative attractiveness of real estate as an investment. One needs to compare the price/rent ratio for housing to similar metrics for other assets. The equivalent concept for equities is obviously the stock price relative to earnings: the P/E ratio. The inverse of the bond yield is a sort of P/E ratio for bonds. We use the 10-year Treasury yield. The Treasury yield serves as a useful comparison to housing returns and is also highly correlated with the 30-year mortgage rate, which directly affects housing demand.
Since the three assets have P/E ratios that are calculated in different ways and involve different risks, it is difficult to make a comparison. However, they are related. Factors like monetary policy affect all three, and all are subject to cyclical influences. At the margin, investors compare the yields and risks of numerous assets and attempt to take advantage of perceived mispricings. During normal times, such arbitrage activities will help to move asset yields toward equilibrium, although there can be long-running distortions -- especially in a "bubble" environment. To get a rough idea of the relationships between the three assets, simple linear regressions were estimated. Figures 1, 2, and 3 below reflect the results of regressing the P/E ratio of any one asset class against the P/E ratios of the other two.
Click to enlarge images.
The figure clearly shows the tech bubble of the late 1990s. Stocks appear somewhat undervalued in late 1970s and early 1980s. The gap between actual and fitted values suggests that stocks are currently undervalued relative to bonds and housing. However, this is not a useful model for timing the market. A decline in the fitted value through a decline in housing prices or an increase in interest rates would also remove the apparent undervaluation of stocks. One could persuasively argue for either of those occurring. A decline in earnings would also be equilibrating.
The bond market equation fit is somewhat better than that of the other two markets. Actual and fitted lines move fairly well together until the Federal Reserve's recent aggressive bond-market actions. The residuals are insignificantly different from zero for most of the remainder of the period.
The figure shows periods of overvaluation followed by rapid declines in the late 1970s to early 1980s, and late 1980s to early 1990s. The recent housing "bubble" is prominent from 2003 to 2008. All three of the declines were associated with significant financial institution distress. The housing P/E ratio rises after that, but is only borderline overvalued, as bond and equity prices rise as well.
Comparing P/E Ratios for the Three Asset Classes
It is possible to make more direct comparisons of the three asset market P/E ratios, as in Figure 4 above. Note that the units for the housing P/E ratio are not comparable to the others because of the use of an index for the rent component. Robert Shiller estimates the long-run average return on housing as 3%. Rescaling the housing P/E to force that average return allows us to put the ratios on the same axes. But that adjustment is just for convenience. It is the pattern that is important and not the relative height on the graph that matters for housing. The remarkable correlation between the equity and treasury P/E ratios from 1963 to 1993 is the basis for the so-called "Fed Model." (See our previous article "Are U.S. Equities Undervalued? New Evidence From A Federal Reserve Model" for discussion of this model.)
There are flaws in the long-term housing P/E ratio displayed above and used in the regressions. Earnings, which are based on the shelter component of the CPI, do not net out maintenance and management costs and are based on the owner's estimate of the rental value. The median house price is also a problem. It is a noisy series that accounts for the appearance of Figure 3. In addition, the average size of houses and the quality of houses has increased over time. Apparent asset price inflation may simply reflect improved quality. The S&P Case-Shiller index for home price and the Owner's Equivalent Rent component of the CPI for rent are superior measures, although they also have drawbacks and limit our analysis to January 1987 to May 2013. Recomputing the housing P/E using these measures generates Figure 5, which highlights the more recent developments in the housing, stock and bond markets.
We observe a similar pattern, but the three asset "bubble" eras emerge more clearly. During this period, asset classes take turns having high P/E values. Equities take the lead in the late 1990s during the tech bubble. Housing prices soar above their "earnings" during the middle of the last decade. Treasury prices rise after the housing decline as the Federal Reserve employs quantitative easing in an attempt to stimulate the economy.
Housing price/rent ratios are a valuable tool, but are best seen in relation to alternative asset prices. In comparing housing, equity, and bond valuation, the pattern of ever-higher price waves brings to mind a recent essay by Robert Shiller titled "Bubbles Forever."
 We use Robert Shiller's cyclically adjusted price/earnings ratio (CAPE). CAPE avoids the problems in using short-term trailing earnings that may not reflect longer term returns and analysts' forecasts that may also be noisy and inaccurate. Data for Treasury yields and the CAPE, P/E ratio for the S&P 500 come from Robert Shiller's website. For this longer time horizon, the housing P/E ratio is calculated using UCLA Professor Edward Leamer's original method: median house price divided by the shelter component of the consumer price index. Data for these two variables come from the Federal Reserve Bank of St. Louis. The regression results are based on monthly observations from January 1963 to June 2013.
 Note that the units for the housing P/E are arbitrary and are again scaled to generate an average 3% return.