A Dual Interpretation of the Case-Shiller Index and Its Implications to Home Appraisals

The S&P/Case-Shiller® Home Price Indices are designed to measure change in the total value of all existing single-family housing stocks. This paper utilizes duality in linear programming to explore a close connection between the methodology of the indices and the classic no-arbitrage (NA) condition in financial markets. In essence, the interpretation of the NA is the “dual” problem to the primal minimization problem by which a regression is used to estimate the indices. The variables of the duality of the NA maximization problem present a term structure of discount factors, the reciprocal of which are backward-looking indices. The insight induces a new methodology for appraising single-family housing and exposes its connection to the commonly-used appraisal method. It is well known that the pricing of derivative securities is based on arbitrage arguments. In view of the index family being the underlying asset of the recent home price derivatives, the intimate connection between its estimation methodology and the classical definition of the NA condition is a point of interest.