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