Forecasting Real Estate Prices

Transcription

1 Forecasting Real Estate Prices Stefano Pastore Advanced Financial Econometrics III Winter/Spring 2018

2 Overview Peculiarities of Forecasting Real Estate Prices Real Estate Indices Serial Dependence in Real Estate Returns Predictability based on Valuation Ratios Predictability based on Economic Variables REITs 2

3 Forecasting RE Prices: The general framework Understanding what drives real estate values is crucial from an economic perspective Important issue of data availability Real estate prices are a key driver of the business cycle o Large fluctuations in RE prices can have important consequences on the financial system and the rest of the economy o Variations in RE prices have a significant effect on aggregate consumption dynamics Relevant econometric issues arise when forecasting in a real estate framework o Available data is relatively short in its duration and is observed at a low frequency; this renders estimation and hypothesis testing difficult o Dichotomous variables are very relevant for in-sample fit, but they cannot be sources of predictability o Data availability limits out-of-sample analysis and robustness checks 3

4 Real Estate Indices Since real estate transactions are very infrequent, the literature focuses on the use of indices rather than individual property prices Median Price Indices: Track the price at which the median priced home within a particular area trades in a given period (e.g. Census index) o Ignore potentially important changes in the characteristics of the dwellings being sold o Provide not only a noisy but also a systematically biased estimate of the behavior of home prices Repeat-Sales Indices: Use information about homes that transact at least twice during the sample period to infer marketwide price movements (e.g. Case-Shiller index, HPI index) o Standard modeling approach: pp ii,tt = pp mm,tt + ee ii,tt, where pp ii,tt is the log price of home ii at the end of period tt, pp mm,tt is the aggregate RE index and ee ii,tt is a property-specific mean-zero stochastic drift, i.i.d. across properties, s.t. ee ii,tt = ee ii,tt 1 + εε tt with variance of the error term σσ2 εε 4

5 Real Estate Indices Suppose we have a sample of II properties, and for each of them we have the price of the initial purchase at period tt ii and the price of the sale at period TT ii. Then, we can express the log return during the period as pp ii,ttii +TT ii pp ii,ttii = pp mm,ttii +TT ii pp mm,ttii + tt ii +TT ii ττ=tt ii +1 Various approaches to estimate pp mm o Bailey, Muth and Nourse (1963) estimate via OLS the regression yy ii = ββxx ii + uu ii, where yy ii is the holding period return for home ii, XX ii is a tt house-specific time dummy variable and uu ii = ii +TT ii ττ=ttii +1 εεii,ττ o The Weighted Repeat Sales Method (WRS) of Case and Shiller (1987) extend the model to allow for the presence of noise in individual home prices: pp ii,tt = pp mm,tt + ee ii,tt + nn ii,tt, with nn ii,tt ~NN 0, σσ 2 nn that captures variation in market-wide conditions This indices make use of just a limited number of transactions, those relative to houses that sold twice during the period 5 εε ii,ττ

6 Real Estate Indices Hedonic Indices: Express the price of a property as a function of a set of characteristics which determine its quality and other factors Standard linear specification: pp ii,tt = ββzz ii + δδdd + εε ii,tt where pp ii,tt is the log transaction price of property ii in period tt, ZZ ii is a vector of property attributes (hedonic variables), DD is a vector of time dummies o ββ measure the marginal utility an investor derives from having one additional unit of a characteristic (shadow price) o δδ capture the period-specific change in log price once taking into account the effect of property characteristics Meese and Wallace (1997) show that repeat-sales estimators can be viewed as constrained versions of an hedonic model in which it is assumed that homes that sold twice are representative of the whole market, and the shadow prices of the attributes are constant over time and thus cancel out in the construction of the index. They show that these assumptions are rejected by the data An important issue is the choice of the relevant variables 6

7 Residential Indices 7

8 Forecasting Real Estate Returns General framework: rr tt+1 = αα + ββ XX tt + εε tt+1 XX tt is the vector that includes the variables observable at time tt that could be used to forecast the return in the next period Predictability of future returns might arise because of two distinct economic reasons o Market inefficiency o Time variation in expected returns In order for predictability to be economically meaningful, it should be high enough in order to cover the large transaction costs associated with real estate transactions The predictor XX tt is often persistent, and its innovations are correlated with εε tt+1. This induces bias in the estimation of ββ, an issue that must be taken into account (Stambaugh (1999)) 8

9 Serial Dependence in Real Estate returns The evidence shows that most residential indices exhibit serial correlation; whether this might be exploited is not clear The literature find evidence of short-run momentum and long-run reversal. However the general conclusion is that these patterns are too small to be exploited by trading strategies, given the high transaction costs Schindler (2011) documents instead the presence of exploitable predictability in some markets Regime-Switching models might be able to capture variations in returns due to local specific economic conditions o Model specification: rr tt = cc sstt + φφ sstt rr tt 1 + εε tt, εε tt ~NN(0, σσ sstt 2 ) o Most studies rely on models with two or three regimes Crawford and Fratantoni (2003) find that a two-states regime model display better in-sample properties, while ARMA models have better forecasting performances 9

10 Predictability based on Valuation Ratios Valuation Ratios have a long-standing tradition as predictors of stock returns Analogous ratios have been used in the Real Estate literature The economic reason for the use of ratios as predictors of future returns is based on the assumption that the variables which form the ratios are co-integrated in logs One of the most widely used variables is the rent-price ratio HH tt PP tt. Letting hpp tt ln HH tt ln(pp tt ), we can decompose hpp tt as hpp tt = kk + EE tt ρρ jj rr tt+1+jj EE tt ρρ jj h tt+1+jj jj=0 jj=0 where rr tt+1+jj are the future returns of the properties and h tt+1+jj is the future growth in its rents. Therefore, the rent-price ratio should be able to predict either future returns or future growth in rents (or both) 10

11 Predictability based on Valuation Ratios Starting from the previous decomposition, the literature has tried to investigate predictability of returns in the following framework: rr rr tt+1:tt+tt = ββ rr TT hpp tt + ττ tt+1:tt+tt dd h tt+1:tt+tt = ββ dd TT hpp tt + ττ tt+1:tt+tt where the terms on the LHS represent future log returns and rent growth over a period of length TT Several studies find that the rent-price ratio has a positive relation with future returns and a negative relation with future rent growth rates; however, the statistical significance of the estimate of ββ rr TT is not very high Also more sophisticated models (e.g. VARs) point to the lack of statistical significance of return predictability Note that the above forecasting framework is meaningful under the assumption that the ratio captures all relevant economic information. Otherwise, the model will be misspecified 11

12 Predictability based on Economic Variables Considerable evidence shows that economic variables, other than past returns or valuation ratios, are associated with future appreciations in property values The empirical framework rr tt+1 = αα + ββ XX tt + εε tt+1 is extended in order to include demographic variables, construction costs, tax rates and other variables in the information set XX tt Linneman (1986) tests wether a set of property characteristics are associated with future changes in property values. However, most of the varables in his model are fixed-effects and do not change with time Case and Shiller (1990) test for predictability in excess total returns with a number of conditioning variables. The economic predictors seem to be able to capture a significant fraction of the fluctuations in future real estate returns Specific analyses for various metropolitan areas seem to show that a considerable part of time variations in returns is due to macroeconomic fluctuations and not to local factors 12

13 REITs Real Estate Investment Trusts (REITs) are exchange-traded funds that derive their income from real estate investments REITs are particularly suitable for forecasting tests o They are traded on the US stock exchange, are relatively liquid and have small transaction costs o Data are available at higher frequency and over a longer time period, allowing to obtain better estimates and to perform (pseudo) out-ofsample analysis of the forecasts performance Possible drawbacks o REITs represent a small fraction of the value of the RE market o REITs expose investors to risks inherent in small-cap stocks, and comove more with the stock market rather than the RE market Standard empirical framework: rr tt+1 = μμ rr + ββ rr xx tt + ττ tt+1 dd dd tt+1 = μμ dd + ββ dd xx tt + ττ tt+1 dddd xx tt+1 = μμ xx + φφxx tt + ττ tt+1 where xx tt is usually the log dividend-price ratio rr 13

14 REITs One issue is given by the fact that often xx tt is highly persistent and dddd there is correlation between ττ tt+1 and rr ττtt+1. In this case, the estimator of ββ rr would be biased, thus some small-sample corrections are necessary (e.g. Stambaugh (1999)) The literature documents some degree of predictability for REIT returns, using variables such as the rent-price ratio and T-Bill returns. The degree of predictability found is similar to that for a portfolio of small-cap stocks. Moreover, many authors find that this degree of predictability might be economically meaningful In-sample evidence points to a stronger evidence for rent-growth predictability Campbell and Shiller (1988) and Lettau and Van Nieuwerburgh (2008) derive some economic restrictions on the coefficients of the model that might improve estimation Overall, the evidence for out-of-sample predictability is not strong, even when imposing the economic restrictions 14