Dan Cimiluca

The Right Time to Buy?

Interest Rates and Housing Markets

GitHub Repository

Introduction

The Federal Reserve cut interest rates in early 2020 to historic lows in order to combat a potential economic crisis in the wake of the COVID-19 pandemic. As unemployment rates began to skyrocket experts within the banking and finance industries believed another housing crisis could be on the horizon, thinking mortgage defaults would soon follow.

Cutting rates is one of the most powerful tools in the Feds arsenal to combat an economic downturn and promote the movement of cash throughout an economy. Borrowers can save thousands each year over the life of their mortgage by waiting to buy until a rate cut. Because of this, conventional wisdom says to buy while rates are low. But is it always the most cost effective to purchase a home while rates are low?

Preconceived notions regarding the housing market have proven to be disastrous in the past. With historically low interest rates homes are flying off the market, often going well above their asking price as buyers attempt to outbid one another. This can lead to borrowers spending more than the perceived market value of the home. As of August 2020, median home price listings are up 10.1% year over year, which is the fastest growth in list price since January 2018 [2].

It’s never been more relevant to understand how interest rates can shift the housing market in both the short and long term. By taking advantage of data science techniques this problem can be answered in new ways.

Phase 1 Deliverable

This presentation covers an introduction to my capstone project, information about datasets utilized, research regarding similar projects, and how that research can be built upon. The full deck can be found on my GitHub Repository.

Figure 1In the past 20 years there are three periods of significant rate cuts. In the early 2000's when GDP growth was slowing to prevent a recession, in 2008 to combat the housing crisis, and now in 2020 to mitigate economic harm caused by COVID-19. These rates are charted against the rolling year over year rate at which homes are appreciating (or depreciating) above.

Hypothesis

Falling interest rates will lead to spikes in demand for homes, temporarily raising home values and create less favorable market conditions for buyers.

Goals

1. Discover relationships between interest rate fluctuation and housing market metrics

2. Build models to forecast market reaction to rate changes, I plan to start with developing Autoregression models

3. Utilize models to determine optimal buyer and seller conditions

Datasets

Home Price Index (HPI) Data (2.1MB – 57.4MB)

- - HPI Data ranging from 1975 to the present
  - Sourced from the Federal Housing Finance Agency, Case-Schiller HPI Index, and Zillow Home Value Index data
  - Data covers national, state, metro, division, zip code, and county level regions

Zillow Inventory and Sales Data (23KB – 166KB)

- Contains new metrics to gage the market at metro and national levels
  - Total for sale inventory
  - Newly pending listings
  - Mean days to pending sale
  - Median list price
  - Median sale price
  - Share of listings with a price cut
  - Mean/Median price cut %

Historical Interest Rate Data (13kb – 2.1MB)

- Fed fund rate history
- Prime rate history

Literature Review

During my literature review I discovered the Monetary and Economic Department of the Bank for International Settlements (BIS) conducted a great study called “Interest Rates and house prices in the United States and around the world” [3]. The study looked at house price series data from the United States and 47 other advanced emerging markets through 2015 compared against rate changes.

The study concluded that short-term interest rates play an important role in home prices, especially in countries where securitization of home mortgages is less prevalent. In most cases there appeared to be a statistically significant negative correlation between rate changes and home prices. They noted modest cuts to policy are not likely to fuel fast increases in home prices, but rather that home prices build inertia over time, suggesting a Bayesian estimate relying on random walk prior modeling (a specific type of autoregression model that assumes each step in a time series takes a random step away from the previous data point) would underestimate interest rate impact. BIS opted to model the relationship using a single regression equation.

In addition, the New York Fed produced a paper in 2014 titled “The Sensitivity of Housing Demand to Financing Conditions: Evidence from a Survey” [4]. This study used a “strategic survey” to gauge sensitivity of housing demand based on changes to interest rates, down payment constraints and shock in non-housing wealth.

The survey proposed four scenarios to gauge what impacted a buyer’s willingness to pay (WTP) for a home if they were moving today to a house similar to their own. The four scenarios proposed are:

1. Down payment amount is constant, but some respondents received a 4.5% interest rate, and others a 6.0% interest rate
2. Rate remains the same as scenario one, but now respondents must choose a down payment at least 5% of what they’re willing to pay (to examine sensitivity of WTP to down payment constraints)
3. Interest rates are swapped from scenario 1 (examine sensitivity of WTP and down payments on rates)
4. Buyer inherits large some of cash

The paper concludes that a borrower’s willingness to pay for a home was not impacted significantly by potential mortgage rates. The New York Fed noted influence of mortgage rates in their study was lower than what most user cost models predict, suggesting those models could be overstating sensitivity of home prices to mortgage rates.

Even though the New York Fed’s study resulted in an opinion on the question I’m studying, the approach to get there was completely different. There’s more overlap with the BIS study to my approach. My project will differentiate itself from theirs by focusing on a more concentrated geographical location and by incorporating additional market data beyond national level macroeconomic performance. By incorporating regional data and additional metrics I hope to paint a less broad picture of how rates are impacting the housing market.

Phase 2 Deliverable

This presentation covers an overview of data exploration, EDA, and some high level preliminary model output for this project. It also covers next steps leading into the final phase of the project. The full deck and jupyter notebook can be found in my GitHub repository.

Figure 2Key variables that indicate whether or not market conditions favor buyers are compared in a correlogram at the national level.

Relationships between key variables

There's mixed evidenced as to whether or not interest rates are negatively correlated with favorable buyer conditions. Figure 2 illustrates that the fed fund rate is negatively correlated with change in month over month HPI and median list price, but positively correlated with percent of homes on the market with a price cut and mean sale price. The negative correlation with home price is consistent with the study produced by the Monetary and Economic Department of the Bank for International Settlements. All values represent nation level figures.

Modeling Assumptions

One key assumption made while creating autoregression models is that data used to train the model is stationary. A stationary dataset has consistent mean, autocorrelation, and variance throughout time. The decomposition of the original month over month change in HPI shows a trend of an increasing rate of change up until the housing crisis of the late 2000's, in which there's a downward trend before bouncing back around 2014 and stabilizing up to the present.

M/M HPI Seasonal Decomposition

Figure 3A comparison of the seasonal decomposition before and after adjusting the month over month change in HPI by the rolling 12-month average rate shows more stationary data after the transformation. All data is at the national level.

Adjusted M/M HPI Seasonal Decomposition

To test whether or not the data was stationary I ran a Dicky-Fuller test over the dataset. The significance value of the test was 12.5% indicating the data is not stationary, the test also identified an 11-month seasonality within the dataset. The seasonality appears to be additive because the rate of increase is not increasing each cycle.

I decided to adjust the data by subtracting the rolling 12-month average from each data point. The seasonal decomposition of the adjusted data can be seen on the right in figure 3. The trend appears to be more stable. To test this, I reran the Dicky-Fuller test over the adjusted data which produced a significance value of 0.01%, indicating the data was now stationary.

To start with model construction, I chose to train the autoregression model on 10-years of data (~1992 - 2002) to compare the forecast against actual performance, which is shown below. These results will need to be transformed back to their original state.

This was only done using national level metrics, however in the final stage of the project I plan to develop models for more specific regions and include more variables, while also investigating implementing additional modeling types depending on performance.

Preliminary Model Output

Figure 4Autoregression model forecast based on 10-years of training data can be found on the left. The correlation of residuals for the model again indicates a negative relationship between the fed fund rate and home prices. The actual adjusted HPI data is on the right for comparison.

Phase 3 Deliverable

The final presentation covers model methodology, project results, conclusions, and next steps/future work.

Figure 5 Mapping the relationship between the correlation matrix of residuals shows a stronger negative correlation between rates and home prices in the midwest than costal states over the model training timeframe

Figure 6Example of building out an autoregression model in python, full notebook can be found on my GitHub Repository

Figure 7An example of national level model output against actual seasonally adjusted rate of home price change shows that the model was unable to capture variation in price, and under predicted overall trend

Conclusions

Autoregression models were created for all 50 states and the District of Columbia. Most models were unable forecast variation in home price after a few periods and regressed to a mostly linear trend. Although this was disappointing looking at the correlation matrix of residuals in the models is insightful and shows that there is a visible relationship between how home prices and interest rates shift geographically.

In general, there appears to be a negative correlation between interest rates and home prices in the short term. This is especially true in the Midwest over the time period I trained the models. The correlation becomes weaker in coastal states, and in some cases, there is a positive correlation between interest rates and home prices.

This suggests you could be saving money on principal if you purchase while interest rates are rising in certain areas, but that doesn’t necessarily mean it’s the correct time to purchase a home. It’s important to note that the Fed manipulates rates to offset potential economic distress. The relationship between rates and home prices are compounded by many other factors.

Home prices have historically increased at a fairly stable rate over long periods of time, so now might always be the best time to buy. There’s always the option of refinancing your mortgage when interest rates do start falling if you happen to buy when rates are high.

Explore Market Trends In Tableau

Relationships between housing market data and interest rates can be explored for yourself using the following Tableau dashboard:

Tableau Dashboard

Potential Next Steps

Control for compounding factors such as general economic growth or decay that impact both home prices and interest rates
Re-think modeling approach to produce more accurate forecasts
Refresh dashboard to reflect additional metrics and keep data up to date
Develop an application that could factor potential home appreciation into determining what a borrower should be willing pay

References:

Delmar. "White Houses Minimal Art 4k". Nov. 2019. https://hdqwalls.com/white-houses-minimal-art-4k-wallpaper. Accessed September 2020.
Passy. "Mortgage rates are going back up - just as home prices begin to skyrocket". Market Watch, Aug. 2020. https://www.marketwatch.com/story/mortgage-rates-are-going-back-up-just-as-home-prices-begin-to-skyrocket-2020-08-20. Accessed September 2020.
Sutton, Mihaljek, Subelyte. “Interest rates and house prices in the United States and around the world”, Bank For International Settlements, Oct. 2017, https://www.bis.org/publ/work665.pdf. Accessed September 2020.
Fuster, Basit. “Demand to Financing Conditions: Evidence from a Survey”, Federal Reserve Bank of New York, Aug. 2015,https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr702.pdf. Accessed September 2020.
Alam, Mahbubul. "Multivariate time series forecasting". towards data science. April 2020. https://towardsdatascience.com/multivariate-time-series-forecasting-653372b3db36. Accessed October 2020.

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