Correlation of mortgage rates with real housing prices: how increasing inflation could affect housing prices

I was talking with a friend who was telling me that it was the absolute perfect time to buy a house because housing prices have tumbled and interest rates are low.

I asked him, "What happens to housing prices if there is inflation and rates go up?"

"Housing prices should go up with inflation as they do for all goods. Housing is a natural hedge for inflation"

Did my friend have a point? Yes and no.

Yes, he was right that in a high inflationary environment, housing prices should rise with all other assets. Rents will go up, as will the price of all the inputs into housing such as lumber and labor costs.

Obviously, housing prices will go up to reflect this reality.

But no, when inflation and thus nominal interest rates increase, housing prices tumble. When rates fall, housing prices tend to increase.

Relationship between mortgage rates and housing prices

You can see an obvious correlation by looking at the following graph of interest rates and the log of real housing. The two black circles are areas where the correlation is obvious. The third red circle is an area where the correlation seems less relevant.

30 year fixed Mortgage rate and change in real home appreciation from 1970 to 2006

The simplest explanation for this correlation comes down to payment. Most people have to finance their homes. As such, they make housing decision based upon monthly payment, i.e. what they can afford. If a borrower with 2,000.00 available per month for a mortgage, they could afford to finance about $372,500 over 30 years with a 5% rate. If that rate were to increase to 10%, the amount they could afford to finance would drop by almost 40% to $273,000.

From 1982 to 2003, there was a long term trend of dropping mortgage rates. During this same term, we had a general improvement in the change in housing prices. The exception was 1990 to 1991 where there is a period of negative changes to housing prices that aren't explained by the mortgage rates. Also, from 2003 to 2006, mortgage rates stabilized, but housing increased dramatically. New products such became popular such as subprime mortgages and payment option arms that allowed lower payments so people could afford more housing and thus drive up the price even while mortgage rates were stable.

But just how quickly do prices react to changes in interest rates?

We did a regression analysis of interest rates and real housing prices over the last thirty years. When we do a year over year analysis while looking at the change of real housing prices over the same timeframe, we get no correlation (see table). When we took a look at the data with a lag, we get more interesting results.

For the mortgage rate information I am using Freddie Mac 30 year fixed mortgage rates. I am taking the average rate over the course of one calendar year. I use the change (or log) of the mortgage rate in the regression. Because it is averaged, the functional rate is close to the middle of the year. For housing data, I am use beginning-of-year real housing pricing data from Shiller. Then I take the change (or log) of this figure. Keep in mind that we are looking at real housing prices less inflation. If you looked at nominal rates in a high inflationary environment, prices might be nominally stagnant, but the real prices might actually have dropped.

As we are using middle of the year mortgage rate data and beginning of year housing data, a 1 year lag in the data is actually closer to a 6 month lag. And a comparison of year to year data would be middle of year mortgage data with beginning of year housing data. Thus, a comparison of year to year data should be statistically insignificant and that is exactly what the results show.

There are other reasons to believe that the changes to the interest rates would not immediately transfer to home prices. Indeed, we found that the lag could be up to three years (2 ½ years). This could be partially explained by the following:
  • Real Estate market is illiquid as selling a home can take several weeks if not months.
  • Appraisal values are based upon sales price comparisons which can be several months old.
  • Financing a purchase of a home could be difficult if sale value is significantly above appraisal value
  • Individuals may be inclined to wait rather than sell if the neighbouring homes sold for more.
With a one, two and three year time lag, all give us significant results at the 90% level. Only year two gives us significant results at the 95% level. Year 1 and Year 3 are very close to the threshold of being significant at the 95% level.

Regression results of Changes of Real Housing prices against changes in 30-year Fixed Mortgage Rate

YearsHousing LagCoefficientInterceptR^2 (% Explained)Significant at 95%Significant at 90%
1972–2006No Lag-0.0220.0180.002 (0.2%)NoNo
1972–20051 year-0.1490.0180.109 (10.9%)NoYes
1972–20042 years-0.1820.0180.174 (17.4%)YesYes
1972–20033 year-0.1420.0210.103 (10.3%)NoYes

Regression Analysis

The coefficient is the calculation that would be used to forecast housing price changes based solely upon interest rates. For example, using a housing lag of 2 years (1 ½ years ), if today there were a 100% increase in mortgage rates (5% to 10%), we would expect a housing drop of 16.6% (-.182+.018) in year 2. The R-squared is the percentage of the change that is explained by the mortgage rate change. If R-squared were 1.00, then 100% of the changes to the housing prices are explained by changes in the mortgage rate. A figure of .174 means that less than 20% of the changes of the housing prices are explained by the changes in the mortgage rate. In other words, there is a lot of other factors which combined are even more relevant than just the mortgage rate.

Why is R-squared so low?

The previous graph shows that when there are large changes to the mortgage rate, the relevance is much greater than the R-squared we calculated. Mortgage rates being stable allows other issues dominate. If there were a large scale increase in inflation (say from 1% today to 6% three years from now), that would increase the nominal mortgage rate from about 5% today to 10% credit spreads being equal. The R-squared, or significance would likely shoot way up.

How do we use these numbers?

With an R-squared of .174, less than 20% of the change is explained by the mortgage rate. Consequently, I would not use the coefficients and intercept to forecast when there are small changes in the mortgage rates as other factors would dominate. What I am most concerned about is a large scale increases in inflation and how this would affect real housing prices. In the case of large scale increases, forecasting using the coefficients would be acceptable as the mortgage rate would dominate.

Adding the effect from multiple years

While using the data with a 2 year lag is the only dataset that is relevant at the 95%, years 1, 2 and 3 are relevant at the 90% level. The coefficients and r-squared values suggest that changes to housing prices come slowly over time as a bell curve with the majority of the changes coming in year 2, but significant changes also occur in years 1 and 3.

One way to capture the effect of multiple years would be to simply add the coefficients from years 1, 2 and 3, in which case we would get a coefficient of -0.473. However, given that there are different R-squared and different levels of significance, it would be a challenge to know the level of confidence we would have in our forecasting. Also, I would not be comfortable using data that did not have a higher significance level.

The more proper way to capture multiple years would be to take the product of the changes over three years. If we regress that dataset against the changes in the mortgage rate we get a dataset which captures the effect of a change in the interest rate on multiple years.

Regression results of Changes of Multiyear Real Housing prices against Mortgage Rate

YearsCombined YearsCoefficientInterceptR^2 (% Explained)Significant at 95%Significant at 90%
1972–20032 years -0.2680.0230.155 (15.5%)YesYes
1972–20033 year-0.3390.0380.133 (13.3%)YesYes

Scatterplot of 3-year combined real housing increase against change in the mortgage rate

Current Interest Rate Volatility

But how do we know where the interest rate will be in the future? We can estimate the volatility of the mortgage rate by looking at the history of the 30-year treasury yields. I also looked at different terms 5-year and 10-year and my volatility figures were very similar. When we extrapolate this data into the mortgage rate, we are assuming that credit spreads do not change. We also assume that the change in interest rate is normally distributed, and we realize that the nominal interest rate cannot go below 0%. The annual volatility is 4.22%. This means that there is roughly a 16% probability that the annual mortgage rate will be above 9.22% (5% + 4.22%) one year from now.

ProductDaily volatilityMonthly VolatilityAnnual Volatility
30 year treasury Yield

The big picture

Using these results, we can ask ourselves what is the most that the interest rate could change in a given year. Given the current rates at about 5%, we would be wise to understand the risk to housing given current scenarios (See below). We must remember when discussing these numbers that they are the real housing less inflation. If there was a significant increase in inflation, prices may just stagnate while in real terms they lose 10% a year.

Secondly when dealing with statistics you always have upper and lower bounds which bracket your expected mean. In this case the brackets are quite large. The coefficient has an upper and lower bound 0.30 above and below the expected mean. That means while on the lower end, with 95% accuracy the mortgage rates could have negligible effect, on the higher end, we could have a much higher coefficient than is currently predicted. -0.63.

The intercept value is .038 which means that on average we should expect a 3.8% increase in housing over a 3 year period of time, even if there is no change to the mortgage rate. So when we conduct our scenario analysis, we see that a simple increase in the mortgage rate from 5 to 7.5, we would expect to see a 13% decrease in housing prices over three years. The worst case scenario at 95% would be a 45.8% drop. If inflation really showed its ugly head and rates go to 11.75%, we would expect a 30% drop in real housing prices with a worst case scenario of a 45% drop.

Scenario Analysis

ScenarioProbability of event Expected ChangeWorst Case at 95%Timeframe
Increase 2.5% in one year
Over 2 ½ years
Increase 6.75% over 3 years
Over 5 ½ years


Given the risk of future inflation, housing is a poor bet at best and a catastrophe at worst. While not wanting to sound alarm bells, the potential on the downside is apparent. On the upside, the real housing prices stay flat but the lower bounds are quite concerning.

Correlation of Interest Rates and Housing Prices


  1. There are quite a few statistical errors here.

    From 1977 to present, the annualized volatility of the 30 yr yield is around 15% (to 1 standard deviation). So if we start at 4% yield today, a 3 standard deviation move will take us either 2.2% or 5.8%. (.3% chance of that happening on an annual basis...). 68% chance we get to 4.6% or 3.4% by the end of the year. That's assuming a normal distribution is even the right distribution to choose ... My statistics has quickly gotten rusty, but there is a test to determine this as well. My point that still holds: is that your #s concerning probability of where rates are within 1 yr are way off, regardless of chosen distribution.

    That said, with an inflation-induced change in price level, lets say rents follow price level changes. The higher interest rate (to account for the change in expected return given higher inflation expectations) will result in a lower multiple. Better to use finance tools rather than statistical regression to resolve this problem mathematically. Too many errors come from misusing statistical data, as far as valuation...

    So let's test this. Scenario: Price level quickly doubles from 1 to 2. Everything moves up linearly in CPI (fat chance). Interest rate goes from 5% to 10%. (lets assume the market believes the change in price level is a one time event, which is why 10% is so low.)

    Lets assume this means my house commands a rent of $4000/month (after price change) instead of $2000/month (before price change). Lets say no expenses (prop tax, etc) just to keep the model extremely simple. The expected return on the asset is 10% instead of 5%. Lets price it like a perpetuity to keep it simpler. Fundamental value starts at $480K with $2k/month price (24K/.05). It ends at $480k (48K/.10). The real money to be made is when inflation moderates and expected return on assets falls back to 5%. Then suddenly (48K/.05) = $960K. That's what 1983-1999 was about. So yes, in real terms durable tangible assets are often hurt immediately by inflation. But inflation rates are usually a volatile series, often tending to stabilize in the long run. This helps them catch up (in real terms). Worst case, your new high wage has devalued the debt associated with home loan you took before the inflation occurred.

  2. Michael, thanks for your comments. I see where you are coming in on the IR volatility. Where are you getting your annualized Vol numbers?

    I get my numbers by looking at the current daily vol over the last 45 days and annualizing it.

    That to me is the most obvious reason why your numbers and mine might differ is because you are using a historical rate, I am using the last 45 days and using that as my daily vol and then annualizing it, you take the historical. The two numbers could differ dramatically. Volatility as you know has been a bit crazy lately.

    As an aside, I am not a statician, nor do I play one on TV. I have been a mortgage trader for some time and developed some similar models used to forecast prices based upon IR changes.

    Now that I am without my bloomberg terminal (it hurts you know), I am having to calculate things like vol manually and rely on people like you to tell me when I am off base.

    I like your analysis. That is a quick and dirty way to see how the interest rate effects prices. In my analysis, the effect was not immediate, but took about 2 1/2 years to take effect.

  3. The last 45 trading days (of the 30 yr) has an annualized daily vol of 29%, about double over the historical. That takes us to 7.48% yield on an upside move over the next year (3 standard deviations up).

    Standard deviation daily is about 1.9%. (then multiple that times sqrt(252) to get annualized volatility).

  4. This was fantastic info ive been commrnting on blogs for weeks trying to increase my page rank this will really help me thanks


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