posted on 02 January 2016
-- this post authored by David Stiff
The CoreLogic Home Price Index (HPI®) and the CoreLogic Case-Shiller indexes track average home price trends. But every residential property is a unique bundle of physical characteristics (of both the housing structure and the lot) and location (proximity to jobs and schools and the attributes of the surrounding neighborhood).
So the price paths of individual homes will vary significantly from the average path measured by a home price index. The divergence of individual price paths can change over time as well, due to changes in housing market conditions and the shifting preferences of homebuyers.
The dispersion in individual home price appreciation will usually be larger in markets where houses and their locations are more dissimilar. Dispersion also tends to increase during housing market boom and bust periods since homebuyers and sellers have more difficulty pricing properties when there are rapid changes in market-level prices. Increased home price dispersion makes it more difficult to manage home price risk. The CoreLogic HPI and the Case-Shiller indexes are good at tracking market-level home price risk, but ultimately, exposure to home price risk resides in individual properties.
Home price indexes can be combined with measures of price dispersion, however, to better understand exposure to home price risk. Karl Case and Robert Shiller observed that individual home prices are more likely to drift away from the average market trend as the time interval between sales transactions increases.1 TheCase-Shiller implied volatility estimates summarize the dispersion in individual home price appreciation relative to the time interval between sales.
In Chart 1, each grey diamond represents a single residential property that transacted two times in the San Diego Core Based Statistical Area (CBSA). The vertical axis measures the difference in each property's appreciation rate relative to the change in the Case-Shiller index for San Diego. The red lines are the implied volatility estimates for the San Diego Case-Shiller index. The implied volatilities are calculated by regressing the squared differences between the property price changes and the Case-Shiller index changes against the time intervals between the first and second transactions for each property. This means that the implied volatility estimates measure the standard deviation in relative price appreciation by the time interval between sales. Approximately two-thirds of properties will fall within the upper and lower implied volatility lines.
The implied volatility estimates have two, related, limitations: (1) they assume that the degree of property-level price dispersion is constant across housing market cycles, and (2) that price dispersion is symmetric - that is, in all time periods, one-half of properties will have appreciation rates that exceed the market average, while the other half will have rates that underperform the average. These assumptions, in general, are only valid when housing demand and supply are balanced. During market booms and busts, the dispersion in individual home price appreciation usually becomes asymmetric (for properties that transact)2. Larger numbers of properties will appreciate at above-market rates when housing markets are booming, while negative dispersion tends to be larger during housing market crashes.
The Case-Shiller dispersion measures were created to track the asymmetry in price dispersion. But unlike the implied volatility measures, which are defined for the time intervals between sales, the dispersion measures are typically segmented by the second transaction date of properties.3 The dispersion measures are calculated as percentiles of the differences between property price changes and changes in the Case-Shiller index. Since the dispersion measures are non-parametric, unlike the implied volatilities which assume that price dispersion is normally distributed, they can easily capture asymmetries in property-level price appreciation rates.
Chart 2 shows the Case-Shiller dispersion measures for the San Diego CBSA using the same set of single-family properties that appear in Chart 1. The "q90" line measures the 90th-percentile of property-level price appreciation relative to the San Diego Case-Shiller index - 90 percent of properties experienced relative rates of appreciation below the "q90" line. The dispersion measures illustrate the asymmetry in price dispersion that occurs during boom and bust periods. Between 2002 and 2005, more than one-half of properties transacted had appreciation rates that exceeded changes in the Case-Shiller index (which appears as the 0 percent line in the chart). During the housing market boom, many homebuyers were willing to overpay for properties to avoid being priced out of the market, creating positive appreciation asymmetry. But when the market crashed this pattern was reversed -- huge discounts had to be offered to nervous homebuyers to entice them to buy properties, so the price dispersion for transacted properties became negatively skewed.
For organizations exposed to mortgage or residential property price risk, both the implied volatility estimates and the dispersion measures can be used to augment the Case-Shiller indexes to get a finer-grained picture of their exposure. Both sets of price dispersion metrics can be used to measure the spread of individual home price risk around a Case-Shiller index. The dispersion measures also track shifts in home price tail risk which are especially important during periods of housing market stress when market-level measures of home price trends may understate the risk embedded in portfolios of individual properties. Metrics that track the distribution of downside home price are useful for the stress-testing mortgage and investment portfolios and, potentially, for developing hedging strategies to protect financial positions in the event of another regional or national housing market downturn.
 Case, K. and Shiller, R. (1987), "Prices of Single-Family Homes Since 1970: New Indexes for Four Cities,"New England Economic Review, Sept./Oct. 1987, pp. 45-66.
 It is important to emphasize that price dispersion becomes more asymmetric for properties that are bought and sold during the boom and bust periods. Repeat sales indexes, like the CoreLogic and Case-Shiller indexes, track the value of properties across all time periods, regardless of when they transact. This means that it is possible for more than one-half of transacted properties to outperform or underperform the Case-Shiller index even while the index is accurately tracking the average price trend. Over long-time horizons, periods of negative and positive price appreciation asymmetry will tend to balance out.
 The Case-Shiller dispersion measures can be segmented by the second transaction date, by the time interval between sales transactions, or by the year of the first transaction date (vintage) and the second transaction date.
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