Quantitative Assessment of House Price Distributions

This weekend, as I found myself inundated in quantitative finance problem sets, I decided it might be worthwhile to apply some quant methods to real estate. After all, we're in the midst of a recession whose numerous causes - and/or exacerbating factors - include a multi-year decline in median home prices across virtually every geographical market. Furthermore, a larger proportion of Americans own a home than own equity securities. My experiment began with market selection; I wanted to compare two housing markets within relative geographical proximity. I also wanted the comparison to be between markets that have suffered comparably during the recession, and are perceived as good long-term housing bets for reasons such as population and demographic trends, weather etc. After brief deliberation, I decided that tonight's matchup would be between Atlanta and Charlotte.

To begin, I pulled data from the S&P Case-Shiller Home Price Index (monthly) from January 2000 to October 2009. I then converted the index value to a periodic rate of return for each month, using the natural log function. That data was then summarized in histogram format below:

 

The two distributions are somewhat similar at first glance, although Atlanta appears more skewed to the left. Atlanta's most frequently observed interval (bin) of return is also a bit higher than Charlotte's. However, in this instance I'm most interested in providing an investor with a general idea concerning the risk associated with a house purchase in each of these markets. To do so, I computed the mean and standard deviation for each city's returns. Furthermore, I calculated the (theoretical of course) probability that a given month's return would be less than zero for each market:

The Conclusion: Although the monthly return could conceivably be higher for an Atlanta house, there is a 45.75% probability that a given month's return will be less than zero - negative that is. In Charlotte, that figure is only 39.54%. Furthermore, it's important to note that the Atlanta data is characterized by a fatter left tail; that is, Atlanta has experienced multiple months of >2% price declines, while Charlotte's returns all fall above -2%.

Clearly, there are many variables that influence house prices, not all of which are even subject to attempted forecasting. However, I would venture to say that the method above provides a reasonable illustration of the relative risk associated with a real estate investment in the two subject markets.

*no positions in either Charlotte or Atlanta real estate. I am licensed to sell real estate in NC however. Sphere: Related Content

New Home Sales Up 11 Percent; Don't Celebrate Too Long

The Commerce Department this morning announced that sales of new, single family homes for the month of June increased by 11 percent (month to month). Because analysts were expecting a bump of only 2.3%, the news fueled the view - shared by many misunderstood individuals - that the housing market has bottomed, and may even have begun it's first "leg" of recovery. In evaluating this claim, it would be prudent to highlight several facts pertaining to the residential housing market, notably:

• Although the month-to-month comparison is positive 11%, the level of new home sales in June 2009 was 21.3% lower than in June 2008.
• At the current level of new home sales and new home starts, the supply of housing will return to a level of around 6 months worth (considered healthy) of inventory in early 2010. This is good news, however, Housing Starts are the wild card; this data point is heralded as a sign of recovery, yet too many new starts will simply contribute to the backlog of inventory.
• Those "sales" that were logged in June were facilitated by the record low mortgage rates of the April/May time period. There has been some volatility in the average mortgage rate since then - owing to volatile Treasury market conditions - but the overall trend has been towards slightly higher rates.
• The first-time-home buyer-tax credit (a.k.a that 8 grand cash injection) has been cited as an explanation for the uptick in new home sales. Needless to say, the tax credit does not apply to homes purchased after December 1,2009, prompting speculation as to whether the recent uptick in new home sales is even sustainable.

Finally, we would note that new home sales only represent 15% of the US residential market; the other 85% is comprised of existing homes. When you apply a little bit of logic to the situation, it makes perfect sense that new sales would begin ticking back prior to existing sales. The reason: new homes are sold by businesses, and existing homes are sold by individuals. In an inefficient market such as real estate, the price of an individuals home is largely determined by:

1. What he/she thinks the house is worth
2. How bad he/she needs to sell the house

Homeowners are notoriously optimistic concerning the value they attribute to their own residence. Buyers, as it turns out, are not so optimistic. The result is a massive bid/ask spread that exists for any piece of real estate listed on an MLS; with the length of time it takes to sell the asset largely a function of the size of the spread.

New home sales in contrast, are for the most part transactions conducted between a builder and client/customer. The builder has more resources, and is likely more aware of the proper ask price than the individual seller. Additionally, the publicly traded builder can reap a tax benefit by offloading inventory at a price below his basis.

We aren't perma bears by any means; however, evidence of a more sustained and substantive nature is required before we will throw our hat into the "residential recovery" ring. Sphere: Related Content