Kwelia Rent Price Trends vs. The Case-Shiller Home Price Index

Introduction

As Hamlet probably said while perusing Danish real estate: “to rent, or not to rent, that is the question.” Prospective renters (or homeowners) can attest that the decision to buy or to rent involves a complex consideration of a number of factors, including the time horizon for the living arrangement, expected changes in rental and home prices, and mortgage rates (fortunately, both the New York Times and Trulia conveniently provide tools to assist with some of the math). While the market dynamics and personal factors that inform the decision to buy or to rent are complex, we’d like to briefly explore one of the factors mentioned above: the evolution in rental and home prices, and then investigate the relationship between the two.

Background

In order to compare home prices and rental prices, we first need yardsticks for both. For home prices, we used the 20-city indices from the Case-Shiller 20-city composite index, and for rental prices we used our Kwelia data (of course), as well as some nationwide Consumer Price Index (CPI) data for rent of primary residence.

The Case-Shiller Index–Useful for Tracking Home Values

As mentioned last time in our piece about correlations between search interest and rental prices, the Case-Shiller index provides a benchmark measurement for home values in the U.S. There are multiple indices, including the national index (using quarterly single family home values), and the 20 and 10-city composite indices (as well as an index for each of the 20 cities), using monthly home values. The indices use a “repeat-sales” methodology by including homes that have sold at least twice in order to quantify an appreciation in value. Lastly, the Case-Shiller methodology involves measuring changes in price while keeping quality constant, i.e., ignoring physical changes to homes in order to measure the real appreciation in price (for example, a home increasing in price by 20% because an addition was added is not the same as a home gaining 20% in value with no improvements).

Not quite apples-to-apples…apples-to-pears?

For the rental data, we used a monthly average of the weekly median rental prices in the same 20 cities as the Case-Shiller data. However, it should be noted that while the Case-Shiller home price index provides a “real” (i.e., constant quality) measure of housing prices from month to month, the rental data is not quality adjusted. That said, the duration of the comparison for each city is generally one to two years, over which period the impact of quality changes in rental stock should be relatively minor on a city-wide basis.

Are Home Prices and Rental Rates Related?

Note: while others have written in detail about prices and rents, this exploration should be treated as more of a “lab-exercise” to illustrate an effect empirically rather than as a formal study.

The hypothesis (“Here be Economics”)

Purchasing a house or an apartment instead of renting can be a more economical choice depending on the time horizon under consideration. For a very short timespan, it is often cheaper to rent, but for longer timeframes there is a breakeven point (at which you would be indifferent between buying and renting) after which it is cheaper to have purchased the house or apartment rather than renting. For example, it might take a decade for a house to become the cheaper option compared to renting for the same period of time. How long it takes to reach this breakeven point depends on the conditions of the market, including tax rates, interest rates, expected capital returns, the risk premium in the housing market, etc. For instance, low interest rates make ownership more attractive, while a risky housing market and high interest rates incentivize renting instead of purchasing.

Are rental rates and prices related in theory? In a classical frictionless market, the total cost of ownership for a house is comparable to an equivalent rental rate. This is called the owner’s equivalent rent, or the amount which an owner would pay in a competitive rental market to rent his own home. Any home has an associated hypothetical rental value, and any rental has an associated hypothetical purchase value. As such, in a competitive market in the long run, the discounted returns to renting an apartment should be equivalent to the total purchase value.

Therefore, we would hypothesize that rental values and home values are positively correlated (i.e., the two would move in the same direction in general). If rental rates and prices were to deviate too much, then arbitrage opportunities would act to bring the two closer together. For example, if rental rates were very high and housing were very cheap, then one could take advantage of this price difference by buying a house and renting it out. This would have the effect of: 1) Increasing the supply of rentals, bringing down rental rates and 2) Decreasing the supply of houses, increasing the price of purchasing a home. The opposite would also hold true.

However, because there are frictions in the market and buying and selling is expensive, one would not expect complete arbitrage (i.e., price differences would persist). Furthermore, although rental rates and prices are related in theory, there are other independent factors in both the rental and housing markets that determine prices for each. Because of this, we would expect only a moderate positive correlation on average in the long run. Does the data bear this prediction out?

The Results

City

Correlation between monthly Kwelia rent values and Case-Shiller index (r)

t

r-squared

Boston

0.989

16.389

0.978

Denver

0.978

11.395

0.956

Portland

0.963

8.738

0.927

San Diego

0.947

7.246

0.897

Chicago

0.925

5.981

0.856

San Francisco

0.915

7.531

0.838

Los Angeles

0.915

5.547

0.837

Seattle

0.899

5.039

0.809

Miami

0.896

4.947

0.803

Phoenix

0.846

3.883

0.715

Las Vegas

0.826

3.591

0.682

Minneapolis

-0.804

-3.316

0.647

Dallas

0.786

3.115

0.618

Charlotte

-0.634

-2.008

0.402

Atlanta

0.616

2.593

0.379

Cleveland

-0.542

-1.580

0.294

DC

-0.384

-1.610

0.147

Detroit

0.380

1.005

0.144

Tampa

0.289

1.316

0.084

New York

-0.288

-1.345

0.083

From a quick look, we can observe that 15 out of 20 of the cities showed a positive correlation between rental rates and home values. However, by looking at the t-values to determine which of these correlations is significant, we can eliminate the bottom 5 cities (whose correlations are not statistically significant), leaving us with 13 out of 15 correlations both positive and statistically significant. Excellent. Not only are the majority of the correlations positive and significant, but most of them have r-squared values above .6, indicating that a significant amount of the variation in the data is accounted for in the model.

But what about Charlotte and Minneapolis, which both have statistically significant and negative correlations? We thought about this for a while (and welcome any ideas!), and after investigating a few hypotheses, have settled on one theory for now: it’s an accident. The timeframe for the data used in both of those cities is just under a year, which is necessarily a short-run analysis. If rental rates and home values were to drift apart over the course of a year, the market wouldn’t have time to take advantage of the price difference and bring them closer together.

Ok, that sounds fine in theory, but data talks–does this long-term positive correlation between rents and home prices exist? To find out, we compared the 10 and 20-city Case-Shiller composite indices against the Consumer Price Index data for rent of primary residence (which is a real-valued index), from January 1st 2000 until now. Unfortunately, the CPI is not segregated by metropolitan area, but rather an index of national rental values. Nevertheless, as most rentals are in cities, we compared the CPI to the 20 and 10-city composite indices rather than the national Case-Shiller index to get the most fair comparison.

Although one can clearly see the explosion (and subsequent bust) in home values surrounding the mortgage crisis, there is as predicted a moderate (r~.3), statistically significant (t~4), positive correlation between rental values and home values over a long duration. This helps add evidence to our theory that the observed negative correlations were essentially an artifact of the short-run analysis, and that given sufficient long term data, a positive correlation would prevail as prices adjust.

The trend in Denver was positive as well.

Concluding Thoughts

While the evidence from this little experiment suggests that rents and prices are in fact positively correlated, it’s important to remember not to overstate the significance of the result. First, as noted above, the lack of a city by city “real-valued” rental index makes one-to-one comparisons with the Case-Shiller index difficult. Furthermore, the limited timeframe under consideration also prevents one from drawing too strong of a conclusion. Lastly, it is worth mentioning once more that the determinants of prices in both markets are diverse, and that the correlations found here serve more as an illustration of a specific connection between rentals and homes, rather than indicating a strong causal effect in determining prices.

That said, it is still interesting to “verify” these theoretical relationships with some actual data. Those interested in seeing the graphs for the remaining 18 cities can see them below, and those curious should check out some relevant papers at the end of this post. Finally, the scope and depth of our data is constantly growing, so we hope to provide even more robust analyses in the future!

Tampa   

Seattle 

San Francisco 

San Diego

Portland

Miami                    

Los Angeles

Las Vegas

Detroit              

D.C.      

Dallas  

Cleveland        

Chicago 

Charlotte

Atlanta             

Phoenix  

New York

Minneapolis     

Appendix for the curious

Outside Data Sources:

Case-Shiller data:

http://us.spindices.com/indices/real-estate/sp-case-shiller-20-city-composite-home-price-index

Rent CPI data:

http://research.stlouisfed.org/fred2/series/CUUR0000SEHA

Relevant Literature:

“The Long-Run Relationship Between House Prices and Rents,” Joshua Gallin.

http://www.federalreserve.gov/Pubs/FEDS/2004/200450/200450pap.pdf

“Run-up in the House Price-Rent Ratio: How Much Can Be Explained by Fundamentals?,” Kamila Sommer, et al.

http://www.bls.gov/ore/pdf/ec100090.pdf

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