Site News  |   Monitor Keywords  |   Monitor Archive  |   Organizer  |   Account Info  |

Price indexing

This application is a continuation in part of and claims the benefit of priority from U.S. application Ser. No. 11/620,417 filed Jan. 5, 2007, the entire disclosure of which is incorporated here by reference.

This description relates to price indexing.

A wide variety of real estate indexing methods exist, for example. Summary indexes report simple statistics (mean or median) of current transactions. Total return indexes like the NCREIF NPI report returns on capital using properties' appraised values and cash flows. Hedonic indices control for quality by using data on particular attributes of the underlying property. Hybrid methods also exist.

Repeat sales methods, which are widely used, have also attracted analysis. Various refinements yield different portfolio weightings or measures of appreciation (e.g. arithmetic vs. geometric), improve robustness, and weight to correct for data quality. A variety of potential issues have been noted, particularly sample reduction, non-random sampling, revision bias or volatility, uncorrected quality change (e.g. depreciation in excess of maintenance), and bias from cross-sectional heteroskedasticity. Hedonic and hybrid methods avoid the nonrandom sampling problems inherent in repeat sales, but have strong data requirements that in practice impose similar sample size reductions and as a result limit the potential temporal resolution of the index to monthly or quarterly in practice.

Power laws have been widely observed in nature, and particularly in such phenomena as financial market movements and income distribution. Pareto's Law in particular was proposed as an empirical description of an apparent “80/20” distribution of wealth. In real estate, Kaizoji & Kaizoji observe power law behavior in the right tail of the real estate price distribution in Japan, and propose that real estate bubbles burst when the slope of the tail is such that the mean price diverges. Kaizoji observes similar power law behavior in the right tail of assessed real estate values and asymmetric upper and lower power law tails in relative price movements. A variety of generative models have been proposed for power law and lognormal distributions of income and property values, many of which are discussed by Mitzenracher. In particular, double-tailed power law distributions can arise as the result of random stopping or “killing” of exponentially growing processes. Andersson et al. develop a scale-free network model of urban real estate prices, and observe double-tailed power law behavior in simulations and data for Sweden.

In a somewhat different vein, Sornette et al. explain financial bubbles in terms of power law acceleration of growth, and observe the super-exponential growth characteristic of bubbles in some real estate markets.

Real estate transaction data generally is available infrequently, tending to be published monthly, quarterly or semi-annually. Sales transaction volumes fluctuate over time, may be subject to seasonal effects, and vary across geographical areas. Each property is unique, and not necessarily comparable to other individual properties within a market or within other geographic areas. Public source records have inconsistencies due to the many local jurisdictions involved and their varying data processing standards.

Additional information about the use of indexes of real estate values in connection with trading instruments is set forth in United States patent publications 20040267657, published on Dec. 30, 2004, and 20060100950, published on May 11, 2006, and in international patent publications WO 2005/003908, published on Jan. 15, 2005, and WO 2006/043918, published on Apr. 27, 2006, all of the texts of which are incorporated here by reference.

In general, in an aspect, transactions involving assets (for example, real estate assets) that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points. The probability density function for at least one of the components comprises a power law. The parameters do not include an offset parameter representing possible shifts in the value spectrum over time. An index is formed of values associated with the assets using at least one of the determined parameters.

Implementations may include one or more of the following features. The data points that are excluded are associated with values that are outside defined cutoffs. The defined cutoffs include a lower cutoff that is a function of a minimum value of any of the data points. The defined cutoffs include an upper cutoff that corresponds to a maximum value of any of the data points.

In general, in an aspect, transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points. The probability density function for at least one of the components comprises a power law. A median derived from the fitted probability density function is provided as an index of values associated with the assets using at least one of the determined parameters.

In general, in an aspect, representing transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points. The probability density function for at least one of the components comprises a power law. The parameters are separated into parameters that characterize a shape of the probability density function but not its position and at least one parameter that characterizes its position but not its shape. An index of values associated with the assets is formed using at least one of the determined parameters.

Implementations may include one or more of the following features. A single parameter characterizes the position of the probability distribution function. The shape parameters are fit using data for many days, and the single position parameter is fit using data for a single day.

In general, in an aspect, transactions that involve assets that share a common characteristic are represented as a set of respective data points associated with values of the assets, the data points including transaction value information. The set of data points suffices to form an index of the values of the assets, using parameters that are determined by fitting probability density functions to at least one component of a value spectrum of the data points, the parameters including at least one shape parameter determined by fitting data over multiple days and at least one position parameter determined by fitting data either over a single day or multiple days, the probability density function for at least one of the components comprising a power law. A subindex is formed of values of the assets that are associated with a subset of fewer than all of the data points of the set, the subset being selected to represent a range of one or more of a demographic, geographic, value, or other attribute of the transactions.

Implementations may include one or more of the following features. Parameters are determined that fit probability density functions to at least one component of a value spectrum of a subset of the data points. The subindex is formed by determining parameters that fit probability density functions to at least one component of a value spectrum of the subset of data points. The subindex comprises an approximation based on scaling the index of the set by a ratio of medians of, respectively, the subset of values associated with the subindex and the set of values associated with the index. The subindex comprises an approximation based on scaling the index of the set by a ratio of the means of, respectively, the subset of values associated with the subindex and the set of values associated with the index.

These and other aspects and features, and combinations of them, can be expressed as methods, apparatus, program products, means for performing functions, systems, and in other ways.

Other aspects and features will become apparent from the following description and from the claims.