I recently had an interesting conversation with a Real Estate agent (whom I know for a long time) about local sales and prices. She had seen an increase in total units, but was surprised at the increase in home prices that have been reported. Having sold multiple identical units in the same waterfront condo complex, as well as having sold similar (or sometimes the same exact home) repeatedly, she was not seeing the allegedincrease in prices.

I mentioned Price Dispersion as the likely cause, and she looked at me quizzically. if someone in the industry for 3 decades is unfamiliar with the term, than perhaps a brief explanation and example are in order.

No two homes are truly identical, as they cannot occupy the same physical space. When the NAR or Zillow or RealtyTrack or Case-Shiller report about pricing, they are reporting a series of prices across different regions and neighborhoods, some with better locations and school districts than others. These are different size homes, with different finish quality and amenities

We do not do a particularly great job reporting these differences, other than describing them via price. We could report home sales the way we often do with Commercial Real Estate, on a $ per square footage basis; we mostly don’t.

Instead, we use a form of price dispersion that measures a range of price points. If you have access to the raw data, you can analyze the sale figures by deciles, showing which part of the market is doing better or worse, well or poorly. You could analyze monthly % differences from highest to lowest prices, standard deviation and variance of price distribution, etc.

But we don’t. We simply get a report of median sale price. This turns out to be highly misleading.

Let’s use cars as an example. If you wanted to know whether car prices were going up or down, you could take the average price of all cars sold each month. Or you could take a weighted average, where the greater the number of sale units have a greater impact on final price. We don’t want the 9 Bugatti Veyrons sold at $1.6 million dollars in 2011 skewing the results of 350,0000 Toyota Camrys at $23k.

Now imagine that this year, due to certain outside factors, we could not gain access to a small segment of auto data. No Toyota Yaris or Kia Rio or Ford Fiesta or Nissan Vestra or Chevy Sonic or, well, you get the idea. These are amongst the cheapest cars sold in America.

Imagine for the moment we stop getting the sales data for just these very inexpensive automobiles. What would this do to reported auto prices? Even if every make and manufacturer kept prices flat, it would appear that the median price was rising due to this dispersion.

Yet that is exactly what we have done in the residential real estate price reporting. Due to the voluntary foreclosure abatement, the bottom deciles of home sales appear to have stabilized, when in fact all that has happened is the distressed properties have artificially been kept off of the market.

That variance across sold homes is ending. We know that the foreclosure machinery is cranking up again now that the abatements are over. We should not be surprised if over the next 6 months we see significantly more distressed properties hit the market — and they typically sell at 20-30% discount below comparable non-distressed homes.

Consider how this will impact reported sale prices over the next few quarters. Its hard to make the case for housing turnaround when prices are falling.

Category: Markets, Mathematics, Real Estate

Please use the comments to demonstrate your own ignorance, unfamiliarity with empirical data and lack of respect for scientific knowledge. Be sure to create straw men and argue against things I have neither said nor implied. If you could repeat previously discredited memes or steer the conversation into irrelevant, off topic discussions, it would be appreciated. Lastly, kindly forgo all civility in your discourse . . . you are, after all, anonymous.

15 Responses to “Understanding Price Dispersions”

  1. sailorman says:

    I live in Sarasota and reply to this genre of comment repeatedly. House prices in Sarasota have bottomed and in some areas, risen slightly. Florida has many developments of similar houses, so a reported price per square foot on one of these houses does not suffer from price dispersion.

    Sarasota led the market down and has now bottomed. I have no idea if it will lead the market up, I don’t think so myself. I can only say that many areas of south Florida, like Sarasota, have bottomed. Activity is up substantially and even the distressed sales have higher prices and multiple bids. Time on the market is dropping as well.

    This has a lot to do with the demographic of the country; baby boomers are reaching retirement age and some percentage of them want to move to Florida. Although they can’t get top dollar for their current house, they can still get considerably more than the cost of a house in south Florida.

  2. daykevi says:

    Ummm…. that’s certainly true for NAR’s index of median sales, but Case Shiller is a repeat sales index. They only use sales of the exact same home (which in fact does occupy the same physical space) to calculate the price index (you can look up a description of their methodology on wikipedia or the S&P site). For someone who’s been so astute about the housing markets, I am surprised to see you make this mistake.


    BR: Yah, you are right about CS. I am reviewing the methodology here.

  3. dead hobo says:

    Thanks for reminding me. It’s getting about that time of the year to consider home reappraisals for real estate tax purposes.

  4. urbandigs says:

    Also, serious individual buyers typically do not buy foreclosed homes that typically end up being in worn out, abused shape. Was the house winterized, is the owner still living there, hidden maint issues, will it appraise as typically appraisals come in a bit lower for foreclosed homes than regular existing resales, is the bank desperate to get rid of the home and how long will the process be if the buyer needs a loan?? I must say, its a quality of inventory problem out there right now. There is a lack of quality product that is also priced correctly. We just bought a 2000sft summer house near Woodbury CT after looking at say 30+ properties over a 18 month period and I cant believe the # of shit houses asking $600K and under in both NY and CT. 98% of the stuff we looked at was pure shit whose price was simply wrong. I guess my point is that people think they can get amazing deals for amazing property, I simply dont think that is true on a widespread basis. So yes, foreclosures and the shit properties will bring down prices as they get through the pipeline, but let someone else or a bulk reo team go for those!

  5. AHodge says:

    for serious data geeks
    this problem addressed some with the FHFA repeat sales index
    while it has a lot of other problems it mostly gets away from these “mix” probs you describe
    nonfinance corporate planners actually selling stuff?
    they wrestle with this all the time to describe their own sales trends
    and often use the formula
    revenue gains = price x volume x mix. with “mix being the residual

  6. crease123 says:

    You mentioned that the distressed properties prices are kept intentionally off the market, but what, if I may ask, will be the motives for this? Wouldn’t you want to report include those lower prices as well to give the impression to would-be buyers that the housing market is cheap, enticing them further?

    Also, if they are artificially keeping those numbers off the market, what’s preventing them from continuing to do that forever? Any reason why you are expecting them to come back and be reported on the market within the next 6 months?


    BR: During the robo-signing settlement negotiations, the major mortgage holder banks agreed to stop foreclosing until they cleaned up their process. That took about 14 months, and the abatements are now over.

    See this: Foreclosure machinery creaks back to life

  7. streeteye says:

    Case Shiller does account for this using the repeat sales methodology… but I don’t know if they account for renovations and improvements. One could possibly adjust for this by subtracting GDP residential additions & alterations as a percentage of residential housing stock.

    Would be interesting to look at the hedonic adjustments to owner-occupied housing in CPI… mostly home tech has improved a lot, energy efficiency, fancy high tech fixtures and appliances, but then you also have shoddy new construction, Chinese sheetrock.

  8. wally says:

    The part of the home industry that helps the economy is new home construction. It employs people, it sells materials, helps the transportation and manufacturing sectors… and it is picking up enough now to have a positive effect on the economy.
    That means the housing slump has ended; it is not now a drag on the economy. It isn’t boom times. but we really don’t want those again for a while, do we?

  9. socalguy says:

    My wife works in the RMBS loss mitigation department for a major bond insurer and her view from the trenches indicates that the carrots and sticks that were packaged into the robo-signing settlement to get banks to modify mortgages is working and fewer delinquent loans are heading to the courthouse steps or ending up as short sales. Lower inventory and higher prices may be here to stay. RE Bubble 2.0?

  10. donna says:

    Well the San Diego area is actually starting to recover and we are seeing more homes on the market here and higher prices. We typically lead the housing recovery. I would say the market in such lead areas probably actually is in recovery.

  11. RW says:

    Data dispersion looks like an illustration of Simpson’s Paradox; i.e., aggregating data sets from different sources and/or of different sizes in the presence of an inadequately controlled lurking variable typically produces erroneous results and, not infrequently, results that are diametrically opposed to most or even all of the smaller sets; e.g., Simpsons’s Paradox – When Big Data Sets Go Bad.

    The Stanford Encyclopedia of Philosophy’s discussion of Simpson’s Paradox covers the entire range — history, mathematical foundations, threats to validity and causal relationship, research methods, etc. — but it can be heavy going at times.

    NB: The Wikipedia entry is good but I don’t agree with some parts of their definition; e.g., the paradox does not inevitably result in a ‘reversal’ of correlation between sub-groups and their aggregated whole nor does it necessarily disappear “when causal relations are brought into consideration” (identifying and controlling all lurking variables can be a nontrivial task).

  12. nofoulsontheplayground says:

    Judicial or not, recourse or not; these are big reasons for some regional disparities in supply/pricing. Places like NY State have docket backlogs in the courts that amount to almost 20-years to clear the cases that are working their way through the foreclosure system there.

  13. Giovanni says:

    @crease123 The reason most banks don’t want to report their distressed sales prices is so they don’t have to recognize the losses on loans that FASB accounting fraud allows them to carry at face value. Yes it would help price discovery, clear the market and allow housing to return to driving growth in the economy but it would endanger Wall St. banksters’ bonus pool- and you can’t have that!

  14. Zillow does not report on median sale prices. Instead, we report on the Zillow Home Value Index which is a housing index based on hedonic imputation which fully adjusts for any variances in the mix of sales over time. We agree with Barry that about the best way to misunderstand the real estate market is to look at median sale prices which are measuring mix shifts at least as much as they are measuring price level changes.

    ZHVI methodology: http://www.zillow.com/blog/research/2012/01/21/zillow-home-value-index-methodology

    Why it’s better than median sale price: http://www.zillow.com/blog/2008-03-27/debunking-the-median-sale-price/

    How’s it’s different than repeat sale methodology: http://www.zillow.com/blog/2008-03-18/zillow-home-value-index-compared-to-ofheo-and-case-shiller-indexes/

    Full ZHVI time series for any geography can be downloaded here: http://www.zillow.com/local-info/