Abstract
Index-based derivatives markets are fast developing in Europe, the US and Asia. Both valuation based and transactions based indices are used as bases for these derivatives contracts. This paper addresses the issue of revision effects on key index parameters, and their implications for derivatives pricing and questions whether these indices may be suitable for derivatives. More specifically, we address the issue of the robustness of the price level, mean, and volatility estimates for two repeat sales real estate price indices: the classical Weighted Repeat Sales (WRS) method and a Principal Component Analysis (PCA) factorial method, as elaborated in Baroni et al. (J Real Estate Res, 29(2):137–158, 2007). Our work is an extension of Clapham et al. (Real Estate Econ, 34(2):275–302, 2006), with the aim of helping judge the efficiency of such indices in designing real estate derivatives. We use an extensive repeat sales database for the Paris (France) residential market. We describe the dataset used and compute the parameters (index price level, trend and volatility) of the indices produced over the period 1982–2005. We then test the sensitivity of these two indices to revisions due to additional repeat-sales transactions information. Our analysis is conducted on the overall Paris market as well as on sub-markets. Our main conclusion is that even if the revision problem may cause substantial concern for the stability of key parameters that are used as inputs in the pricing of derivatives contracts, the order of magnitude of revision on derivatives pricing is not sufficient to deter market participants when it comes to products such a swap contract or insurance contracts against severe losses. We also show that WRS and PCA react differently to revision. The impact of index revision is non negligible in estimating the index price level for both indices. This result is consistent with existing literature for the US and Swedish markets. Price level revision causes moderate concern when trading products such as index futures or price insurance contracts, but could deter option like products. We show that managing this price level revision risk is similar to delta hedging in standard option pricing theory. We also find that although revision impact on index trend can be important, the WRS method seems more robust than PCA. However, the trend revision impact order of magnitude for contracts such as total return swaps is low. Finally, revision influence on volatility estimates seems to have a modest impact on derivatives, and according to the robustness of the volatility estimate, the PCA factorial index seems to fare relatively better than the WRS index. Hence, our findings show that the factorial index could better sustain volatility based derivatives. We also show that whatever the index, managing this volatility revision risk is similar to vega hedging in option pricing theory.
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Notes
The Chicago Mercantile Exchange (CME) Group began listing housing futures and options based on S&P/Case-Shiller® Home Price Indexes since May 2006 for ten cities in the US. These derivatives have at most an 3 year duration. On Sept 17, 2008 CME listed 4–5 years of housing futures and options trading with contracts that settle in 2009, 2010 and 2011. These contracts will allow investors for the first time to express views on the US housing market using fungible, centrally-cleared contracts for several years forward. This transparency and visibility will create a dynamic, focused trading point for taking positions in US housing. There is also an over-the-counter market for S&P/Case-Shiller® Housing Index derivatives for certain institutional users. The simple fact that 5 year housing price curves are now going to be visible, accessible and tradable will alter the discussion of housing price direction forever. At some point when the discussion of these transparent housing markets becomes mainstream in the capital markets and published in the business pages of newspapers, the housing forward prices may influence the buying and selling behaviour in the spot housing market—the tail wagging the dog. An index description for the S&P/Case-Shiller® Home Price Indices can be found on www2.standardandpoors.com/spf/html/products/url_homeprice.htm.
See Case and Shiller (1987). We should also add here that for the particular case of the Paris housing market, the age of building is not really relevant, as the building depreciation is generally low or even non-existent (this is particularly the case for Haussmannian buildings. Hausmannian buildings are present in a large part of the city. They were built in the late nineteenth century.
Note that by construction we will include a transaction in our analysis only if the sale and resale dates do not belong to the same subperiod.
Transactions i take place over T units of time (weeks, months, quarters...). It is therefore equivalent to either specify the number of periods S or the time length of the period in units (the smallest period being the one contained in the original transactions data).
To the comments made in Footnote 4, one may add that the index also depends on the nature of the returns initially observed or used in the estimate. This has to do with the way one constructs vector R in the model. Based on monthly transactions, one may construct returns for higher periods of time.
Recall \(I_t = \ln \left( {i_t } \right)\).
See for instance Spanos (1999) p. 597–600.
We have to note important features concerning the database’s structure: we only observe those transactions whose second transaction has taken place after 1993. Moreover, the percentage of transactions registered in the database is increasing over time. These two characteristics imply that the number of observations doubles between 2000 and 2005.
The OLAP residential reletting index is based on a large sample of apartments that are regularly surveyed for which new lettings are systematically documented in order to produce the Paris and close suburban areas rent index.
For long-term and short-term interest rates, the series are calculated by applying the rates to a basis of 100 as of January 1982. The applied rate corresponds to the average of the day-to-day rates for the 10-year or 1-year bonds and for a given period (month).
A map of Paris and a short description of each arrondissement is available at: http://www.intransit-international.com/housing_paris_arrondissement_tour.html
For instance, if the dataset ends in December 2005, taking 3 years of revision implies that the estimation period stops in December 2002. So the estimation is realized for observations from 1981 to 2002. Adding one more year leads to the estimation of the 1981–2003 index. From this estimation the 1981–2002 index is extracted. The same method is then used for the other revisions.
Note that the PCA index takes into account all the factors computed by the PCA. We have verified that if only the first factors are used, the impact of revision is higher. In fact, the more factors used, the weaker the cumulative effect.
See http://www.ipd.com/OurProducts/Indices/DerivativesInformation/tabid/485/Default.aspx for more information on IPD derivatives.
For example, for the European call, the range of possible values is [5, 12] when the option is out of the money and becomes [21, 34] when the option is in the money. For the American call, the ranges are respectively [18, 20] and [25, 35]. This leads to a maximal percentage of revision for the option price from more than 50% to 25% for the European call out of the money. At the opposite this maximal percentage varies from 5% to 20% for the American call option. This explains why the relation is inversed.
References
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Acknowledgment
The authors thank the Bureau Van Dijk for graciously providing the database CD-BIEN.
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Baroni, M., Barthélémy, F. & Mokrane, M. Is It Possible to Construct Derivatives for the Paris Residential Market?. J Real Estate Finance Econ 37, 233–264 (2008). https://doi.org/10.1007/s11146-008-9114-6
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DOI: https://doi.org/10.1007/s11146-008-9114-6