MARKET HETEROGENEITY AND INVESTMENT RISK – APPLYING QUANTILE REGRESSION TO THE PARIS APARTMENT MARKET, FABRICE BARTHÉLÉMY, UNIV. DE VERSAILLES ST QUENTIN, FRANCE CHARLES-OLIVIER AMÉDÉE-MANESME, LAVAL UNIVERSITY, CANADA FRANÇOIS DES ROSIERS, LAVAL UNIVERSITY, CANADA MICHEL BARONI, ESSEC, FRANCE

OBJECTIVE AND CONTEXT OF RESEARCH This study aims at addressing the heterogeneity of the Paris apartment market with regard to investment risk; The complexity of metropolitan residential markets makes it most relevant to assume that hedonic prices are not homogeneous over time, space and types of assets; Based on previous research, there is evidence that various submarkets may be defined for selected housing attributes, among which price indices; House price evolution, hence returns and volatility, may follow dissimilar patterns depending on location but also on other structural dimensions and, in particular, the price quantile they belong to; Resorting to quantile regression enables us to determine optimal portfolio allocation according to the quantile and to the area;

LITERATURE REVIEW – MARKET SEGMENTATION AND HOUSE PRICE APPRECIATION Several authors have investigated the heterogeneity-of- attributes and market segmentation issues (Bajic, 1985; Can & Megbolugbe, 1997; Goodman & Thibodeau, 1998 and 2003; Thériault et al., 2003; Bourassa, Hoesli & Peng, 2003; Des Rosiers et al., 2007) as they affect the shaping and interpretation of hedonic prices (HP) and question a major assumption of the HP model (Rosen, 1974); As a corollary, the price appreciation issue has been extensively addressed (Case & Quigley, 1991; Quigley, 1995; Knight, Dombrow and Sirmans, 1995; Meese & Wallace, 2003, for Paris dataset; Bourassa, Hoesli & Sun, 2006; Bourassa, Cantoni & Hoesli, 2007; Bourassa et al., 2009).

LITERATURE REVIEW – MARKET SEGMENTATION AND HOUSE PRICE APPRECIATION Past research suggests that…: Hedonic prices of housing attributes may vary over space and time according to submarket specifics and structure as well as to property buyers’ profiles; Houses will appreciate at different rates depending on property characteristics, the relative bargaining power of agents and the strength of the local submarket; Reliable estimates of the willingness-to-pay for housing attributes may be derived from the hedonic price (HP) framework in spite of the heterogeneity problem.

LITERATURE REVIEW – REAL ESTATE PORTFOLIO ALLOCATION Real estate portfolio allocation has fed a large area of research since the seminal works of Markowitz. Researches have focused on the role of real estate in a multi- asset portfolio (Chaudhry, Myer and Webb, 1999; Ziobrowski and Ziobrowski, 1997; Hoesli, Lekander and Witkiewicz, 2004, Oikarinen, Hoesli and Serrano, 2011); and on the way to diversify within real estate (Eichholtz, Hoesli, MacGregor and Nanthakumaran, 1995; Hartzell, Shulman and Wurtzebach, 1996; Seiler, Webb, Myer, 1999; Viezer, 2000; Byrne and Lee, 1997, 2003, 2011 and Lee, 2001);

LITERATURE REVIEW – REAL ESTATE PORTFOLIO ALLOCATION Past research suggests that…: Real estate is a good portfolio diversifier and should be included in every diversified portfolio; Real estate portfolio can be diversified by region, by property types or by size; Diversification within real estate involves the most complicated diversification strategy;

OVERALL ANALYTICAL APPROACH Step 1: A global hedonic price model is built for Paris as a whole, with a focus on the marginal contribution of time (Price Index), living area, building period and location on values; Step 2: Quantile regression is applied on selected price segments (deciles 1 through 9) for testing the homogeneity of price index estimates relative to location (2 groups of districts – Central and Peripheral - are created) and real estate cycles (slump, recovery and boom); Step 3: Based on research findings, evidence of heterogeneity is demonstrated and optimal portfolio mix are suggested for various periods.

THE TWENTY PARIS « ARRONDISSEMENTS » Paris “Arrondissements” are structured according to a clockwise, spiral design starting in the central core of the city, on the north (right) bank of the River Seine (Arr. 1) and ending up with Arr. 20, in the north-east area. In this research, we differentiate between Central districts (Group C: 1 to 9) and Peripheral districts (Group P: 10 to 20)

THE DATABASE The database is provided by the Chambre des Notaires de France (French Notary’s association) and includes, after filtering, some 252,700 apartment sales spread over a 17-year period, that is from 1990 to Housing descriptors include, among other things: Building age (construction period); Apartment size and number of rooms; Floor location in building; Number of bathrooms; Presence of a garage; Type of street and access to building (blvd, square, alley, etc.); Location dummy variables standing for the 20 “arrondissements” and 80 “neighbourhoods” (“quartiers”); Time dummy variables for sale year and month. Centiles below 1% and above 99% have been excluded from the analysis. 9 quantiles are thus computed on a quarterly basis from 10% (Q01) to 90%(Q09)

MAIN REGRESSION FINDINGS: GLOBAL MODEL / PRICE INDEX YEAR (1990 = ref.) Parameter estimates P value < < < < < < < < < < < < < < <.0001 Number of Obs.: 252,772Dep. Variable: Ln Sale Price R-Square: Mean Sale Price: 172,270 Eur. SLUMP (P 1 ) RECOVERY (P 2 ) BOOM (P 3 )

RESORTING TO QUANTILE REGRESSION FOR SORTING OUT SPECIFIC RESIDENTIAL SUBMARKETS Whereas the OLS method results in estimates that approximate the conditional mean of the response variable given certain values of the predictor variables, quantile regression (Koenker & Hallock, 2001; Koenker, 2005) results in estimates approximating either the median or other quantiles of the response variable. While resorting to quantile regression will result in more robust hedonic price estimates in response to large outliers, it also allows for estimating hedonic prices that are specific to any quantile. This is a major advantage where hedonic prices are assumed to differ substantially among quantiles, defined as submarkets.

MAIN REGRESSION FINDINGS: PRICE INDEX PER QUANTILE PARIS GLOBAL Typical hedonic housing price indices are computed based on median quantile Results are similar to the one obtained with the OLS procedure (Barthélémy et al. 2013)

MAIN REGRESSION FINDINGS: PRICE INDEX PER QUANTILE PARIS GLOBAL The graph shows differences among quantiles: Lowest quantiles representing the cheapest apartments show a slightly better resilience during downturn. Overall they exhibit better returns; Upper quantiles exhibit better returns during the early quarters of the upturn.

MAIN REGRESSION FINDINGS: PRICE INDEX PER QUANTILE - PARIS, CENTRAL AND PERIPHERAL DISTRICTS Central and Peripheral districts somehow display similar median indices, with the latter prices though experiencing a slower pace of growth during recovery and a higher one over the boom period; Patterns are roughly the same as the one obtained for global Paris;

MAIN REGRESSION FINDINGS: PRICE INDEX PER QUANTILE - PARIS, CENTRAL AND PERIPHERAL DISTRICTS Lowest quantiles, both Central and Peripheral, exhibit a slightly better resilience during downturn; Overall, lowest quantile for the Central districts show a better performance;

MAIN REGRESSION FINDINGS: PRICE INDEX PER QUANTILE - PARIS, CENTRAL AND PERIPHERAL DISTRICTS The graph shows differences among groups: Central district indices display higher heterogeneity among quantiles than Peripheral ones; Index ordering is similar for both central and peripheral districts with cheaper units displaying the highest return over the whole period ( );

QUANTILE RISK/RETURNS: Overall, Central and Peripheral districts yield roughly similar returns, with lower volatility though for peripheral ones

Returns systematically decrease with quantile but discrepancies are much more pronounced for Central districts; Lowest quantile are much more volatile; QUANTILE RISK/RETURNS:

Volatility is substantially higher for Central districts than for the Peripheral ones; Lower quantiles exhibit higher performance over the whole period. QUANTILE RISK/RETURNS: Decreasing volatility with decile Decreasing return with decile

QUANTILE RISK/RETURNS (CRISIS) During decline : The most expensive apartments show lower returns than the least expensive ones; Except for the lowest decile, all Peripheral apartments underperform the Central ones.

QUANTILE RISK/RETURNS (CRISIS) During decline : Central districts exhibit higher risk than the Peripheral ones, except for the lowest decile; Globally, Peripheral districts suffer more from the crisis;

QUANTILE RISK/RETURNS (RECOVERY AND BOOM) During recovery and boom : Highest returns are experienced for cheapest apartments in Central locations; The cheapest, Central apartments also display highest risk Upper-price, centrally located units yield lowest returns

CONCLUDING COMMENTS AND SUGGESTIONS FOR FURTHER RESEARCH Considering that apartment prices tend to reflect socio-economic differences, sorting out housing submarkets using quantile regression emerges as a convenient device toward an optimal management of investment risk and return as it brings out the investor’s adversity to risk; Findings suggest that optimal portfolio may be obtained through a mix of central and peripheral district assets:  During critical times, the most expensive apartments show the worst performance, even more so in Peripheral districts;  During recovery and boom periods, highest returns are experienced for cheapest apartments while upper-price, centrally located units yield lowest returns;  Overall, Central districts exhibit higher volatility; Further research on Paris includes: (i) computing confidence intervals on price indices; (ii) looking for optimal portfolio by combining groups of “arrondissements” or submarkets in order to improve the efficient frontier; (iii) Sharpe ratios should be computed; Finally, the analytical approach used for Paris could be extended for others urban areas worldwide.

QUANTILE CAPITAL RETURNS FOR PARIS At the early stage of the crisis, the upper quantile is the first to decrease while it recovers more quickly at the end of the crisis. The lowest quantile performs better in the last years and especially in