Is There A Functional Relation Between The Repeat-Sales Index And The Median Index?

Based on the repeat-sales theory, this article tries to give an answer to the following question: Is it possible to find a functional relation between a flow index, whose values at time t are calculated only with the transactions observed at this moment (like the median or the hedonic index) and the Case-Shiller index? The main result of this paper establishes that the monoperiodic growth rates of the repeat-sales index can be calculated directly from the mean rates realised by the investors, applying them an informational matrix. And as these mean rates can be expressed, in a simplified context, as a function of the flow index values, the relation between these two indexes exists. Simultaneously this theoretical issue generates, as a by-product, a data analysis methodology more thorough than the single value of the index. Indeed, the computation of the repeat-sales index can be realised decomposing it in elementary blocks which can be easily interpreted and handled. It allows a better exploitation of the information embedded in a dataset, gathering in a unified framework several concepts (instantaneous and mean rates, levels of liquidity for the buy-side and for the sell-side, length of the holding periods, quantity of information provided by a trade Ö) whose evolutions can be observed jointly. In order to develop the practical consequences of theses formulas a benchmark sample is presented and its properties are analysed in a detailed manner. The survival rates are modelized using an exponential distribution. It provides an interesting and simple reference which can be used when analysing a real and more complex dataset. Its use is illustrated with a synthetic sample associated to a simple economic scenario.