End in sight for housing troubles?

End in sight for housing troubles? D. L. Chertok September 19, 2011 Abstract A historical relationship between home prices and family income is examined based on more than 40 s of data. A new home affordability ratio based on the average home price, family income and mortgage rates is analyzed in the historical context. This indicator is used to gauge the current state of the residential housing market in the United States. Historical data points to an imminent but slow recovery in the housing market over the next few s. Two s after the Great Recession officially ended, the state of the US housing market remains an area of significant concern and continues to attract a lot of attention from academics and practitioners. In a recent article Mizuno and Tabner (2011) discuss housing price trends in the residential markets of the US, UK and Japan using the Hosing Price Index (HPI) deflated by gross domestic product (GDP) per capita as a measure of home affordability. Beracha and Hirschey (2009) examine the trend in housing affordability in the United States based on the Hosing Price Index (HPI) and average income per capita. While the authors present compelling arguments for the use of the aforementioned indicators, it is important to note that the indices in question are not free from limitations. First, HPI data is available only from 1975 onward. Second, it covers only those sales and refinancings that have been purchased or securitized by Fannie Mae (Federal National Mortgage Association) or Freddie Mac (Federal Home Loan Mortgage Corporation). Third, even though per capita income and per capita GDP are valid proxies for housing affordability, family income (DeNavas- Walt, C., Proctor, B. and Smith, J. (2011)) reflects the purchasing power more accurately when it comes to securing a mortgage. Finally, it is easier to reduce the number of possible price outliers by using the median, rather than average values 1. D. L. Chertok, Ph. D., CFA, (daniel chertok@hotmail.com) is a quantitative analyst at XR Trading. Views expressed in this article are his own. 1

A popular alternative is the S&P/Case-Shiller Home Price Index, a widely followed benchmark of residential real estate prices in the United States based on repeat sales of existing homes. Data is available since 1987 (see, e.g., Standard and Poor s (2011)) and is not inflation-adjusted. Another publicly available index is published annually by the U.S. Census Bureau and reflects nationwide prices of new homes dating back to 1963. This index covers a longer historical period and is less volatile than its two other counterparts; in addition, it includes sales financed through sources other than Fannie Mae and Freddie Mac. Despite those differences, as can be seen from Fig. 1 2, qualitatively all three indices reflect the same developments in the U.S. housing market over the last 20 s 3. Comparison of New Home Price, S&P/Case-Shiller and HPI indices, 1987 = 1 New Home S&P/Case-Shiller HPI 2 1.75 normalized value 1.5 1.25 1 0.75 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Figure 1: Comparison of the New Home Price, Housing Price and S&P/Case- Shiller Indices, 1987-2010. Shaded areas represent recessions. For the purpose of this paper, the New Home Price (NHP) index is the most representative measure. It illustrates the evolution of the U.S. residential real estate market valuations and reflects the sector of this market that arguably has the most impact on other industries, especially construction. In Fig. 1, all three indices are normalized to their 1987 values (set to 1) and adjusted for inflation using the CPI-U-RS as the consumer price index 4, also normalized to its 1987 value. All three peaked in 2005-2006 and began their rapid decline in 2007. HPI and NHP followed each other very closely until 2000 2

and began to diverge in 2005. In a reversal of this trend, S&P/Case-Shiller converged to HPI and NHP in 2010. Per capita income and median family income for 1967-2010 are compared in Fig. 2. Both are inflation-adjusted and normalized to 1967. Evidently, CPI-adjusted income per capita and median family income, 1967-2010, 1967 = 1 "income per capita" median family income 1.95 y = 0.0233x + 1.075 R 2 = 0.9481 1.75 1.55 1.35 y = 0.0058x + 1.0342 R 2 = 0.8051 1.15 0.95 0.75 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 normalized value 1995 1997 1999 2001 2003 2005 2007 2009 Figure 2: Comparison of income per capita and median family income, 1967-2010. Shaded areas represent recessions. per capita income grew faster than family income, which may be explained by an overall reduction in family size 5. While both indices exhibit the same qualitative behavior 6, median family income (DeNavas-Walt, C., Proctor, B. and Smith, J. (2011)) is more relevant to the issue of housing affordability and is less volatile. Using the family income, NHP and mortgage rate, an affordability ratio ( Chertok (2009) ) can be constructed to gauge the state of the housing market 7. Historical data for this ratio suggests that, while housing affordability improved dramatically since 2005 indicating a possible bottom in residential real estate, recovery in this market over the next several s is likely to occur at a gradual pace. 3

Historical average affordability of a new home in the U.S. During the period from 1963 to 2010 median new home prices in the US grew at an average rate of 2.25% per while median household income grew at an average rate of 0.58% per adjusted for inflation; the corresponding statistics is presented in Table 1. Fig. 4 depicts the growth rates of median new home prices and median household income. Consistent with conventional Inflation-adjusted housing prices and median family income 1967-2010, 1967 = 1 2.5 CPI-adjusted housing prices normalized income 2 y = 0.0225x + 0.9223 R 2 = 0.8756 Mean house price 1.5 1 0.5 y = 0.0058x + 1.0342 R 2 = 0.8051 0 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 Figure 3: Evolution of the median new home price and median household income in the US, 1967-2010. Shaded areas represent recessions. wisdom, real median family income rises and falls with economic cycles. Over the last 40 s, its peaks preceded subsequent recessions, and its troughs coincided with or trailed the recessions (with the notable exception of the 2001 recession, due to the coincident easing of credit availability and proliferation of adjustable rate mortgages). The same holds true for the real new home price. It is evident from Fig. 3 that the differential between the rate of growth of new home prices and the rate of growth of the median family income reaches a trough during a recession (the trough corresponding to the 2001 recession is delayed by two s). After attaining its all-time high in 2005, this spread contracted very significantly reaching its lowest level in 38 s in 2008 before bouncing 4

Year Median new home price, non-adjusted, $ Table 1: US new home price and income statistics, 1963-2010. CPI (Dec 1977 = 100) Median income, CPI-adjusted to 2010, $ Median price, CPI-adjusted to 2010, $ Affordable monthly payment, $ 30- fixed mortgage rate, % Mortgage payment, $, 30-yr. fixed, 20% down 1963 18,000 51.4 112,132 1964 18,900 52.1 116,157 1965 20,000 52.9 121,059 1966 21,400 54.4 125,961 1967 22,700 56.1 38,771 129,564 951 1968 24,700 58.3 40,442 135,659 992 1969 25,600 60.9 41,945 134,600 1,029 1970 23,400 63.9 41,620 117,256 1,021 1971 25,200 66.7 41,215 120,975 1,011 1972 27,600 68.7 42,980 128,639 1,055 7.38 711 1.48 1973 32,500 73.0 43,848 142,555 1,076 8.04 840 1.28 1974 35,900 80.3 42,459 143,153 1,042 9.19 937 1.11 1975 39,300 86.9 41,348 144,809 1,015 9.04 935 1.08 1976 44,200 91.9 42,034 154,003 1,031 8.86 979 1.05 1977 48,800 97.7 42,300 159,936 1,038 8.84 1,015 1.02 1978 55,700 104.4 43,937 170,835 1,078 9.63 1,162 0.93 1979 62,900 114.4 43,814 176,054 1,075 11.19 1,362 0.79 1980 64,600 127.1 42,429 162,745 1,041 13.77 1,519 0.69 1981 68,900 139.2 41,724 158,490 1,024 16.63 1,770 0.58 1982 69,300 147.6 41,613 150,338 1,021 16.08 1,625 0.63 1983 75,300 153.9 41,322 156,667 1,014 13.23 1,409 0.72 1984 79,900 160.2 42,605 159,700 1,045 13.87 1,501 0.70 1985 84,300 165.7 43,402 162,902 1,065 12.42 1,383 0.77 1986 92,000 168.7 44,939 174,620 1,103 10.18 1,245 0.89 1987 104,500 174.4 45,502 191,863 1,116 10.20 1,370 0.82 1988 112,500 180.8 45,852 199,239 1,125 10.34 1,439 0.78 1989 120,000 188.6 46,670 203,733 1,145 10.32 1,469 0.78 1990 122,900 198.0 46,049 198,750 1,130 10.13 1,411 0.80 1991 120,000 205.1 44,726 187,343 1,097 9.25 1,233 0.89 1992 121,500 210.3 44,359 184,994 1,088 8.40 1,127 0.97 1993 126,500 215.5 44,143 187,960 1,083 7.33 1,034 1.05 1994 130,000 220.1 44,636 189,123 1,095 8.35 1,147 0.95 1995 133,900 225.4 46,034 190,216 1,130 7.95 1,111 1.02 1996 140,000 231.4 46,704 193,725 1,146 7.80 1,116 1.03 1997 146,000 236.4 47,665 197,755 1,170 7.60 1,117 1.05 1998 152,500 239.7 49,397 203,715 1,212 6.94 1,078 1.12 1999 161,000 244.7 50,641 210,675 1,243 7.43 1,170 1.06 2000 169,000 252.9 50,557 213,973 1,240 8.06 1,263 0.98 2001 175,200 260.0 49,455 215,766 1,213 6.97 1,145 1.06 2002 187,600 264.2 48,878 227,364 1,199 6.54 1,154 1.04 2003 195,000 270.1 48,835 231,170 1,198 5.82 1,087 1.10 2004 221,000 277.4 48,665 255,098 1,194 5.84 1,203 0.99 2005 240,900 286.7 49,202 269,048 1,207 5.86 1,271 0.95 2006 246,500 296.1 49,568 266,563 1,216 6.41 1,335 0.91 2007 247,900 304.5 50,233 260,682 1,233 6.34 1,296 0.95 2008 232,100 316.2 50,112 235,036 1,189 6.03 1,131 1.05 2009 216,700 315.0 49,777 220,277 1,181 5.04 950 1.24 2010 221,800 320.2 49,445 221,800 1,154 4.69 919 1.26 Affordability ratio 5

Difference between growth rates of housing prices and median family income 1967-2010, 1967 = 1 0.15 0.1 difference in growth rates 0.05 0-0.05-0.1-0.15 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 Figure 4: Relative difference in inflation-adjusted growth rates between the median new home price and median family income, 1968-2010. Shaded areas represent recessions. back into positive territory in 2010. A substantial correction in the residential real estate market appears to have passed through its most dramatic stage by 2010. The latest available annual data is historically consistent with continuing economic expansion during which home price growth rate should return to a historically more sustainable level relative to family income. The third important ingredient in the housing affordability mix, besides prices and income, is the availability of financing, i.e., the average mortgage rate 8. The rise (and fall) of mortgage securitization played a crucial role in improving the accessibility of credit for the average American family. Increased liquidity, thanks to wider availability of credit through securitization, has been instrumental in keeping mortgage rates low. From their heights in 1982, mortgage rates have steadily trended down in the last 28 s helping make the American Dream a reality for the majority of the population (see Fig. 5). Based on the above-mentioned three factors, an affordability ratio α can be 6

Average national mortgage rates, 1972-2010 16.5% 14.5% 12.5% rate 10.5% 8.5% 6.5% 4.5% 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 Figure 5: Average national 30- conventional mortgage rates 1972-2010. Shaded areas represent recessions. constructed as follows 9 : where: α = p a, p r (1) p a = 0.28I 12, (2) r m ( p r = 0.8H 12 1 + r m ( 1 + r m ) 360, (3) 12 1 12 ) 360 p a - affordable monthly payment based on income, p r - required monthly payment based on mortgage amount, tenor and mortgage rate (see, e.g., Fabozzi (2005)), I - annual family income, H - home purchase price, r m - mortgage rate. 7

The preceding equations assumed a conventional 30- fixed-rate mortgage with monthly advance payments of interest and no principal curtailment, a conservative underwriting ratio of principal and interest to total before-tax income of 0.28 and a down payment of 20%. The effects of property taxes and utility costs are omitted for the ease of exposition. As can be seen from Fig. 6, in 2010 historical housing affordability reached levels not seen since 1973, thanks to rapidly falling home prices and mortgage rates at their historical lows. One could reasonably conclude that, as home Affordability ratio, 1972-2010 1.60 1.40 affordable to required payment 1.20 1.00 0.80 0.60 0.40 0.20 0.00 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 Figure 6: Historical inflation-adjusted home affordability ratio, 1972-2010. Shaded areas represent recessions. affordability continues to climb, the housing market will improve. It is not obvious, however, whether this improvement will be partially offset by declining family incomes and rising mortgage rates, should inflation spawned by government spending become a reality. Factor sensitivity of home affordability is discussed in the next section. 8

What matters more: price, income or mortgage rates? As follows from (1) - (3), home affordability is linearly dependent on the family income. It is also inversely proportional to the home price since the required monthly payment is a fraction of the total home price. As a first approximation, affordability is inversely proportional to the mortgage rate. The sensitivities of home affordability are computed below: α I = α I, (4) α H = α H, (5) α = α p r r m p r r m (6) Of most interest to us are the sensitivities of the affordability ratio to relative changes in home prices, income and mortgage rates. Computing the elasticities of home affordability with respect to these parameters, we obtain: α I α I = 1, (7) α H α H α r m α = 1, (8) r m = ( ) 1 + r m 361 ( 12 1 + 361 12 r ) m ( 1 + r m ) [ ( 12 1 + r m ) ] 360. (9) 12 1 As follows from (7) - (9) the elasticity of the affordability ratio with respect to income by absolute value is exactly the same as its sensitivity to the housing price. At the end of 2010, the average conventional 30- fixed mortgage rate was 4.69%. Substituting this into (9), we obtain α r m α = 0.54. (10) r m In relative terms, home price and income currently have more influence on home affordability than mortgage rates. This gap has been widening for the last 30 s ever since the mortgage rates reached their peak as can be seen in Fig. 7. As expected, the absolute value of elasticity of the affordability ratio with respect to the mortgage rate in 2010 was at a historical low since the mortgage rate itself was at a historical low. An expected rise in mortgage rates, however, would lead to an increase in the corresponding elasticity of the affordability ratio (although this elasticity will not reach 1 unless mortgage rates exceed their levels of early 1980s). 9

1 Absolute value of elasticity of the affordability ratio with respect to mortgage rates, 1972-2010 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 elasticity Figure 7: Historical absolute value of elasticity of the affordability ratio with respect to mortgage rate, 1972-2010. Shaded areas represent recessions. Another important consideration is the relative probability of a significant relative change in the underlying variables behind the elasticity ratio. As can be seen from Fig. 8, in the past 35 s -over- relative rates of change of the mortgage rate were substantially higher than those of the median home price and family income. As evident from Table 2 10, the rate of change of the mortgage rate exhibits more than double the volatility of the rate of change of home prices and almost five times the volatility of the rate of change of family income. Table 3 indicates that a 20.8% increase in the mortgage rates (amounting to 98 b.p. at the 2010 level) would cause the affordability ratio to decrease by approximately 10.4%. At the same time, a 9.8% decrease in the real home price, which historically is almost equally as likely, would cause the affordability ratio to increase by 10.9%. A similarly historically likely 4.3% increase in the real family income would raise the affordability ratio by only 4.3%. From the probabilistic point of view, the change in mortgage rates has almost the same effect on the affordability ratio as the change in home prices. 10

Rates of change of mortgage rates, income and home price, y-o-y, 1972-2010 30% Income change, y-o-y Home price change, y-o-y mortgage rate change, y-o-y 25% 20% 15% 10% rate of change, % 5% 0% -5% -10% -15% -20% -25% 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 Figure 8: Rates of change of mortgage rates, median family income and home price, 1973-2010. Shaded areas represent recessions. Table 2: Median and standard deviation of -over- rates of change of the median home price, family income and mortgage rates, 1973-2010. Statistic Rate of change of median home price, y-o-y, % Rate of change of median family income, y-o-y, % Rate of change of mortgage rates, y-o-y, Rate of change of affordability ratio, % % Mean 1.6 0.5-0.7 0.5 Standard deviation 4.8 2.2 10.2 9.1 5th percentile -9.8-3.2-17.7-14.9 95th percentile 10.4 4.3 20.8 15.0 What lies ahead? Judging from historical data, three base scenarios can be realized with differing degrees of likelihood. The still water scenario reflects flat housing prices, low income growth and a small increase in mortgage rates. The full steam ahead scenario corresponds to a substantial uptick in housing prices, moderate income growth and lower mortgage rates. The doom-and-gloom scenario is a combina- 11

Table 3: The effects of home price, family income and mortgage rate changes on the affordability ratio. Scenario Variable change, % Rate of change of affordability ratio, % Home prices down, -9.8 10.9 5 th percentile Family income up, 95 th percentile 4.3 4.3 Mortgage rates -17.7 10.4 down, 5 th percentile tion of falling housing prices and family incomes exacerbated by rising mortgage rates. The resulting affordability ratios are presented in Table 4. The still wa- Table 4: The still water, full steam ahead and doom-and-gloom scenarios. Scenario Rate of Median Rate of Family Rate of Mortgage Afford- Rate of change of median home price, y-o-y, % home price, $ change of median family income, y-o-y, % income, $ change of mortgage rates, y-o-y, % rate, % ability ratio change of affordability ratio, % base n/a 221,800 n/a 49,445 n/a 4.69 1.26 n/a (2010) still 0.0 221,800 0.5 49,692 5.0 4.92 1.23-2.2 water full 5.0 232,890 5.0 51,917-10.0 4.22 1.33 5.7 steam ahead doomandgloom -5.0 210,710-5.0 46,973 10.0 5.16 1.19-5.2 ter scenario results in a modest decline in the affordability ratio, the full steam ahead scenario leads to a substantial increase in the affordability ratio, and the doom-and-gloom scenario leads to a substantial decrease in the affordability ratio. Historical data presented in Fig. 9 points to the first scenario as the most likely one to be realized. A local peak in the rate of growth of the affordability ratio tends to lead (or coincide with) a local peak in the rate of growth of housing prices. By historical standards, a substantial further increase in the affordability ratio appears unlikely. If this pattern were to hold, housing prices could be expected to increase within the next two s but would subsequently 12

Rates of change of home price and affordability ratio, y-o-y, 1972-2010 20% Home price change, y-o-y affordability ratio, y-o-y 15% 10% rate of change, % 5% 0% -5% -10% -15% -20% 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 Figure 9: Rates of change of home price and affordability ratio, y-o-y, 1972-2010. Shaded areas represent recessions. grow at a slower rate. An increase in mortgage rates spawned by an uptick in inflation and a decline in family income caused by an economic downturn could hamper the recovery in the housing market even further. Conclusion An unprecedented recent drop in home prices has increased the affordability of the average house for the average family in the US as measured by the affordability ratio to historically high levels. This increase can be reasonably expected to increase demand and, as a result, lead to higher home prices. Historical data implies that such an increase may be gradual with a possibility of it being hampered by rising mortgage rates and falling incomes. Since historically housing prices tend to overreact to market dislocations, it may take several s for the market to return to sustained growth. 13

Notes 1. Consider, for example, a situation where one $1,000,000 earner lives in a $1,000,000 house, one $300,000 earner lives in a $400,000 house, and two $100,000 earners live in two $200,000 houses. The average home price in this example is $450,000, and the average income is $375,000, or 5/6 of the average price. The median price is $300,000 and the median income is $200,000, or 2/3 of the average price. The median here paints a more representative picture of housing affordability, at least from an underwriter s point of view. 2. This and subsequent figures are superimposed over the time frame of recession periods as determined by the National Bureau of Economic Research (2011). 3. In fact, pairwise correlation coefficients between the three indices exceed 95%. 4. CPI-U-RS index published by the Bureau of Labor Statistics (Bureau of Labor Statistics (2011)). Its use is recommended for historical research whenever the current rental-equivalence method of measuring the cost of homeownership needs to be extrapolated to periods prior to 1983. 5. As an example, consider a family of four that went from making $50,000 a to $100,000 a. The increase in per capita income is 100%. If, during the same period, the family split into two families earning $60,000 and $40,000 with two members each, median family income would remain at $50,000. 6. They are 96% correlated. 7. For a similar quantity that does not factor in mortgage affordability see Haines and Rosen (2007) 8. Contract interest rates on commitments for 30- fixed-rate conventional first mortgages. Source: Primary Mortgage Market Survey R data provided by Freddie Mac. 9. The calculation assumes end-of-month payments for simplicity. 10. All variables are inflation-adjusted; statistics are calculated for all avaliable histories for each variable. References Beracha, E. and M. Hirschey (2009). When Will Housing Recover? Financial Analysts Journal 65 (2), 36 47. Bureau of Labor Statistics (2011). Updated CPI-U-RS, All Items and All Items Less Food and Energy, 1978-2010. http://www.bls.gov/cpi/ cpiursai1978_2010.pdf. Chertok, D. (2009). Safe house: The housing market and the end of the recession. The Investment Professional 2 (3), 18 20. DeNavas-Walt, C., Proctor, B. and Smith, J. (2011). Income, Poverty, and Health Insurance Coverage in the United States: 2010. US Census Bureau. http://www.census.gov/prod/2011pubs/p60-239.pdf. 14

Fabozzi, F. (2005). McGraw-Hill. The Handbook of Fixed Income Securities (7th ed.). Haines, C. and R. Rosen (2007). Bubble, Bubble, Toil, and Trouble. Economic Perspectives. Federal Reserve Bank of Chicago 31 (1), 16 35. http://www.chicagofed.org/webpages/publications/economic_ perspectives/2007/1qtr2007_part2_haines_rosen.cfm. Mizuno, M. and I. Tabner (2011). The margin of safety and turning points in house prices: Observations from three developed markets. Financial Analysts Journal 67 (3), 76 93. National Bureau of Economic Research (2011). Business Cycle Expansions and Contractions. http://www.nber.org/cycles.html. Standard and Poor s (2011). S&P/Case-Shiller Home Price Indices. http://www.standardandpoors.com/indices/ sp-case-shiller-home-price-indices/en/us/?indexid= spusa-cashpidff--p-us----. 15