Configurations study for the Banzhaf and the Shapley-Shubik indices of power

How can we count and list all the Banzhaf or Shapley-Shubik index of power configurations for a given number of players? There is no formula in the literature that may give the cardinal of such a set, and moreover, even if this formula had existed, there is no formula which gives the configuration vectors. Even if we do not present such a formula, we present a methodology which enables to determine the set of configurations and its cardinality.

A comparison between the methods of apportionment using power indices: the case of the U.S. presidential election

In this paper, we compare the five more famous methods of apportionment, the methods of Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known Banzhaf power index. The populations are the ones of the different States of the U.S. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population: this ensures that every citizen in the country gets the same power. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results.Banzhaf index, methods of apportionment, distances, balance population-power.

Optimal Time to Sell in Real Estate Portfolio Management

This paper examines the properties of optimal times to sell a diversified real estate portfolio. The portfolio value is supposed to be the sum of the discounted free cash flows and the discounted terminal value (the discounted selling price). According to Baroni et al. (2007b), we assume that the terminal value corresponds to the real estate index. The optimization problem corresponds to the maximization of a quasi-linear utility function. We consider three cases. The first one assumes that the investor knows the probability distribution of the real estate index. However, at the initial time, he has to choose one deterministic optimal time to sell. The second one considers an investor who is perfectly informed about the market dynamics. Whatever the random event that generates the path, he knows the entire path from the beginning. Then, given the realization of the random variable, the path is deterministic for this investor. Therefore, at the initial time, he can determine the optimal time to sell for each path of the index. Finally, the last case is devoted to the analysis of the intertemporal optimization, based on the American option approach. We compute the optimal solution for each of these three cases and compare their properties. The comparison is also made with the buy-and-hold strategy.Real estate portfolio, Optimal holding period, American option.

On the performance of the Shapley Shubik and Banzhaf power indices for the allocations of mandates

A classical problem in the power index literature is to design a voting mechanism such as the distribution of power of the different players is equal (or closer) to a pre established target. This tradition is especially popular when considering two tiers voting mechanisms: each player votes in his own jurisdiction to designate a delegate for the upper tier; and the question is to assign a certain number of mandates for each delegate according the population of the jurisdiction he or she represents. Unfortunately, there exist several measures of power, which in turn imply different distributions of the mandates for the same pre established target. The purposes of this paper are twofold: first, we calculate the probability that the two most important power indices, the Banzhaf index and the Shapley-Shubik index, lead to the same voting rule when the target is the same. Secondly, we determine which index on average comes closer to the pre established target.Banzhaf, Shapley-Shubik, power indices

The Paris Residential Market: Driving Factors and Market Behaviour 1973-2001

In this paper we investigate the driving factors associated with the Paris apartment market. We explore a database of nearly 230 000 transactions for residential properties in the Paris area over the 1973 – 2001 period. We develop a factorial model that may capture the systematic link between residential prices and a set of predefined economic variables or a linear combination of these economic variables. We assume that capital growth rates in real estate are related to the variables we defined in the last paragraph. We measure this link which underlines the ‘true path’ of the real estate market: in that way we can develop an index as a function of many other indices. The methodology we develop, based on a multifactor approach to apartment price movements in the long run, has two main advantages over traditional indices. Firstly, we are able to identify the main driving factors for the Paris residential market. And secondly, the factors thus derived can be used to generate a “factor model” useful in comparison to existing capital growth indices and that provides valuable intuition for forecasting residential prices.Real estate indexes; Repeat sales; Risk factors

A repeat sales index robust to small datasets

As suggested by D. Geltner, commercial properties indices have to be built using repeat sales instead of hedonic indices. The repeat sales method is a means of constructing real estate price indices based on a repeated observation of property transactions. These indices may be used as benchmarks for real estate portfolio managers. But the investors in general are also interested in introducing real estate performance in their portfolio to enhance the efficient frontier. Thus, expected return and volatility are the two key parameters. To create and to improve contracts on real estate indices, trend and volatility of these indices must be robust regarding to the periodicity of the index and the volume of transactions. This paper aims to test the robustness of the trend and volatility estimations for two indices: the classical Weighted Repeat Sales (Case & Shiller 1987) and a PCA factorial index (Baroni, Barthélémy and Mokrane 2007). The estimations are computed from a dataset of Paris commercial properties. The main findings are the trend and volatility estimates are biased for the WRS index and not for the PCA factorial index when the periodicity increases. Consequently, the level of the index at the end of the computing period is significantly different for various periodicities in the case of the WRS index. Globally, the PCA factorial seems to be more robust to the number of transactions. Firstly, we present the two methodologies and then the dataset. Finally we test the impact of the number of transactions per period on the trend and volatility estimates for each index and we give an interpretation of the results.Repeat sales indices, Index estimations, Transactions volume

A PCA Factor Repeat Sales Index (1973-2001) To Forecast Apartment Prices in Paris (France)

In this paper we address the issue of building a repeat sales index, based on factors. This is an extension of a companion paper, Baroni, Barthélémy and Mokrane (2001, BBM) in which we had built a factorial index as a selected linear function of existing economics and financial variables. Here we offer a more general and robust model based on a Principal Components Analysis (PCA). We apply this methodology to the Paris residential market. We use the CD-BIEN database that contains more than 220 000 repeat sales transactions for residential apartments in the Paris area covering the period 1973-2001 period. Our PCA index for the Paris and close surrounding area is estimated and its characteristics and robustness are analysed depending on: estimation period, choice of observations, periodicity and reversibility. We then compare it to the traditional WRS repeat sales index developed by Case & Shiller (1987). Finally we show that contrary to the WRS index, our index can be used to forecast apartment prices.Real estate indices; Repeat sales; Factors; PCA; Index forecasting

A Repeat Sales Index Robust to Small Datasets

As suggested by D. Geltner, commercial properties indices have to be built using repeat sales instead of hedonic indices. The repeat sales method is a means of constructing real estate price indices based on a repeated observation of property transactions. These indices may be used as benchmarks for real estate portfolio managers. But the investors in general are also interested in introducing real estate performance in their portfolio to enhance the efficient frontier. Thus, expected return and volatility are the two key parameters. To create and to improve contracts on real estate indices, trend and volatility of these indices must be robust regarding to the periodicity of the index and the volume of transactions. This paper aims to test the robustness of the trend and volatility estimations for two indices: the classical Weighted Repeat Sales (Case & Shiller 1987) and a PCA factorial index (Baroni, Barthélémy and Mokrane 2007). The estimations are computed from a dataset of Paris commercial properties. The main findings are the trend and volatility estimates are biased for the WRS index and not for the PCA factorial index when the periodicity increases. Consequently, the level of the index at the end of the computing period is significantly different for various periodicities in the case of the WRS index. Globally, the PCA factorial seems to be more robust to the number of transactions. Firstly, we present the two methodologies and then the dataset. Finally we test the impact of the number of transactions per period on the trend and volatility estimates for each index and we give an interpretation of the results.Index Estimations ; Property Transactions Volume ; Repeat Sales Indices

Optimal holding period In Real Estate Portfolio

This paper considers the use of simulated cash flows to determine the optimal holding period in real estate portfolio to maximize its present value. The traditional DCF approach with an estimation of the resale value through a growth rate of the future cash flow does not let appear this optimum. However, if the terminal value is calculated from the trend of a diffusion process of the price, an optimum may appear under certain conditions. Finally we consider the sensitivity of the optimal holding period to the different parameters involved in the cash flow estimations. This methodology may be applied in commercial valuation and enables to get an optimal holding period for a given portfolio.valuation, DCF, optimal holding period, commercial property

Is it possible to construct derivatives for the Paris residential market?

In this paper we address the issue of the robustness of the price level, mean, and variance estimates for two sets of repeat sales real estate price indices: the classical WRS method and a PCA factorial method, as elaborated in Baroni, Barthélémy and Mokrane (2007). Our work can be seen as an extension of Clapham, Englund, Quigley and Redfearn (2006), with the aim of helping to judge of the efficiency of such indices in designing real estate derivatives contracts. We use an extensive repeat sales database for the Paris (France) residential market. We describe the dataset used and compute the parameters (drift and volatility) of the indices produced over the period 1982- 2005. The aim here is to test the sensitivity of these two indices to revision due to additional repeat-sales transactions information. Our analysis is conducted on the global Paris market and on submarkets. Our main conclusion is that the revision problem may cause serious concern for the stability of key parameters that are used as inputs in the pricing of derivatives contracts. The impact of index revision is important on the estimate of the index price level. This result is consistent with the finding of the existing literature for the US and Swedish markets. We also find that although the revision impact on the trend estimate can be important, the WRS method seems more robust and derivatives contracts such as swaps may be based on such indices. Finally, and this is probably the most promising result, revision influence on volatility estimates seems to be less stringent, and according to the robustness of the volatility estimate, the BBM factorial index seems to fare relatively better than the WRS index. Hence, we find that the factorial index could better sustain volatility based derivatives such as call or put options.