Abstract
Based on behavioral finance and economics literature, we construct a theoretical framework in which consumers of newly constructed housing units perceive prices to follow a stochastic mean reversion pattern. Given this belief and the high carrying cost maintained by real estate developers, potential buyers opt to either exercise immediately or defer the purchase. We simulate the model within a real option framework by which we show that the optimal time to wait before exercising a purchase is positively related to the price level; hence, a negative (positive) correlation between transaction volume and price level (yield) emerges. Observing data on housing prices and new construction sales in Israel for the years 1998–2007, we apply an adaptive expectation regression model to test consumers’ belief in both mean reversion and momentum price patterns. The empirical evidence shows that while consumers’ demand pattern is simultaneously consistent with the belief in both momentum and mean reversion processes, the effect of the latter generally dominates. Moreover, while the data does not allow for testing the volume and pricelevel correlation, it does provide support to the positive volumeprice yield correlation.
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Notes
 1.
This evidence stands in contrast to the efficient market and rational expectation theory [see, among others, Lucas (1978), Case and Shiller (1989) and Poterba et al. (1991)]. For further empirical documentation of the positive pricevolume correlation in real estate markets, see, among others, OrtaloMagne and Rady (1998), Leung et al. (2002), and Chu and Sing (2005).
 2.
This explanation, which is empirically supported by Genesove and Mayer (1997), may hold, of course, only if the illiquidity constraint is sufficiently substantial in the market.
 3.
Also see the asymmetric information motivation for the positive pricevolume correlation in Berkovec and Goodman (1996).
 4.
For more on loss aversion and prospect theory, see Kahneman and Tversky (1979).
 5.
The longterm mean price may either be constant or experience a drift (see further details in the empirical section).
 6.
In our model, potential consumers face developers as those, unlike potential sellers in the secondary market, face substantial carrying costs and, thus, are generally willing to sell their housing stock at the current market price. In contrast, sellers of secondhand assets generally maintain the same level of flexibility (to either rush or delay the transaction) as that of buyers and may thus choose to delay (rush) the sale if the current price terms favor the buyers (sellers), given the belief in the mean reverting price process. This zerosum game situation between buyers and sellers in the secondary market limits the applicability of our theory to the market segment of new housing units.
 7.
 8.
Representativeness is further related to the recency bias and the “hot hand” effect, i.e., the expectation for the prevalence of the recent trend [see, Gilovich et al. (1985)]. The latter implies that people may detect price patterns even when prices do, in fact, follow a random walk. DeBondt and Thaler (1985) argue that, by violating basic statistical rules, the representativeness heuristic may lead to price overreaction, that is, people’s expectation for positive autocorrelation in price patterns. Also, note that the representativeness heuristic further includes the frequency bias; the tendency to judge predictive relationships according to frequency as opposed to relative frequency [see, for example, Tversky and Kahneman (1973) and Estes (1976)].
 9.
Momentum trading and positive feedback trading are interchangeably used to term the trendchasing trading strategy.
 10.
While some of these studies use a varianceratio test, others apply the habit persistence model. As will be clarified later, we are not interested in directly testing for the prevalence of momentum and mean reversion price patterns but rather in exploring whether the transactions are based on consumers’ belief regarding these patterns. We thus apply the adaptive expectation model (see the next section). On the differences and similarities between the models see, for example, the discussion in Kmenta (1997).
 11.
 12.
Conservatism is the tendency of individuals to slowly adjust to new information.
 13.
Note that, in contrast to shares of common stock, autocorrelation in real estate prices in the short run does not immediately imply an arbitrage opportunity since there is no direct market in which one may shortsale real estate assets.
 14.
 15.
Firsttime home buyers, rather than repeat buyers, are considered in the model as the former are not likely to maintain a hedge on the amount invested in the real estate asset. The model may also include repeat buyers as long as the price correlations among the segments of the real estate market are low. Also, note that the carrying costs borne by the developers specifically include substantial financing cost. However, they may further include maintenance cost, guarding and supervision cost, etc. In contrast, the carrying cost on the part of buyers is mainly the alternative rental cost.
 16.
Expiration date is exogenous in the model. Realistically, one can view T as the final period in which the buyer must purchase the property for an idiosyncratic cause such as an expected change in the size of the household (due to marriage, divorce, newborn child, etc.) or any other exogenous event that induces the purchase.
 17.
For more on similar processes, see Schwartz (1997), for example. Also, note that while the results of the model depend on a mean reverting price process, they do not depend on the particular form of the process that is presented in Eq. (1). Finally, note that we focus on a partial equilibrium established in the short run. We do not consider the longrun equilibrium in which price reversals may occur. For the latter, see, for example, Barberis et al. (1998) and DeLong et al. (1990).
 18.
Equation (4) is the solution to the differential equation in (1), derived by using Maple software package.
 19.
See, for example, Kmenta (1997).
 20.
The data is available from the Central Bureau of Statistics in Israel (www.cbs.gov.il/reader/?MIval=cw_usr_view_Folder&ID=141).
 21.
Our tests show that both series (price levels and transaction volume) display a randomwalk pattern. In order to encompass the limitations imposed by the presence of a unit root in our time series data, we transform the series into a difference form for which the unitroot hypothesis is generally rejected. The results of the unit root tests may be received from the authors upon request.
 22.
These returns could be computed in either nominal or real terms as well as in terms of premium over the return on the riskfree asset. Genesove and Mayer (2001), for example, provide evidence that supports the nominal terms approach, which we later assume for our test.
 23.
This specification is referred to as adaptive expectation model as the expectations are constantly modified with the new coming information [see Kmenta (1997)].
 24.
Note that if 0 ≤ λ < 1, then the termλ ^{∞} Δ _{ k } X _{t−∞} ^{*}, which approaches zero, could be omitted.
 25.
Note that the equation derived in (8a) is, in fact, similar to a VAR model with infinite lags. Unlike the VAR model, however, (8a) includes the current return, Δ _{ k } X _{ t } and, therefore, when λ=0, the coefficient β directly estimates the correlation betweenΔ _{ k } Y _{ t } and Δ _{ k } X _{ t }. Furthermore, (8a) does not contain lagged dependent variables on the righthand side and thus we avoid the problem of biased estimators in small samples [see, for example, Ramanathan, (2002)].
 26.
In order to estimate Equation (9) we must require that t≥ 3; otherwise, the degrees of freedom do not suffice for the estimation of the model. We therefore add additional observations of the housing price index for the last two months of the year 1997. Also, note that the procedure that is suggested in (9) and (10) potentially allows the perceived longterm mean price to be nonconstant (i.e., to experience either a positive or a negative trend).
 27.
In most cases the estimated λ in Table 2 are different from the corresponding estimates obtained in Table 1. In fact, substitution of the λ obtained from Table 1 as an initial value yields a local maximum. This might be the outcome of the high multicolinearity between Δ _{ k } x _{ t } and the dummy variable NEG with R ^{2} = 0.59.
 28.
 29.
We generate the confidence interval for category (2) in the following way: We define a new parameter ψ _{2} for category (2) such that β _{0} + β _{1} = ψ ^{.}_{2} We then substitute β _{1} = ψ _{2} − β _{0} into Equation (11b) yielding
(11b*)
β = β_{0}(1 − BM) + ψ_{2}BM + β_{2}NEG + β_{3}BM × NEG.
Reestimation of (8d) under the restriction of (11b*) allows a direct ttest of ψ _{2} and the derivation of the confidence interval. We can further use this concept to derive the confidence interval for the estimated β under categories (3) and (4) [For more on this method see, for example, Ramanathan, (2002)].
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Acknowledgments
We would like to thank Smadar Shatz for her invaluable assistance. We also thank Daniel Baraz, Jacob Boudoukh, Daniel Czamanski, Saggi Katz, Melissa Porras Prado, Zvi Wiener, and the participants of the AmsterdamCambridgeUNC Charlotte Symposium, Netherlands 2008, the TechnionTAUUBCUCLA Symposium, Israel 2008, the Weimer School of Advanced Studies in Real Estate and Land Economics, Florida 2009, and the department seminar at the Hebrew University of Jerusalem for helpful comments.
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Appendix
Appendix
Simulation:

Step 1:
Following Eq. (2), for a given x _{0}, generate N×(T+1) matrix of ask prices x _{ n,t }, n=1,2,…,N, and t=0,1,…,T, where N and T denote the number of paths and number of periods, respectively.

Step 2:
Compute c _{n,T−1} = x _{n,T} e ^{−r}

Step 3:
Regress c _{n,T−1} = b _{0} + b _{1} x _{n,T−1} + b _{2} x _{n,T−1} ^{2} + u _{n,T−1} applying an ordinary LeastSquares procedure. Then, compute z _{n,T−1} = b _{0} + b _{1} x _{m,T−1} + b _{2} x _{m,T−1} ^{2}.

Step 4:
Note that if x _{n,T−1} ≤ z _{n,T−1}, then the buyer should exercise the option to purchase at time T1 along path n. If, however, x _{n,T−1} > z _{n,T−1}, then the buyer is better off with the option alive. Denote the transaction price at time t along path n by p _{ n,t }. Then, if x _{n,T−1} ≤ z _{n,T−1}, set p _{ n,T }=0 (zero denotes no transaction) and p _{n,T1}=x _{n,T1}. Otherwise (that is, if x _{n,T−1} > z _{n,T−1}), then set p _{ n,T }=x _{ n,T } and p _{n,T1}=0.

Step 5:
Compute c _{n,T−2} = Min(p _{n,T} × e ^{−2r}, p _{n,T−1} × e ^{−r}).

Step 6:
Regress c _{n,T−2} = b _{0} + b _{1} x _{n,T−2} + b _{2} x _{n,T−2} ^{2} + u _{n,T−2} applying an ordinary LeastSquares procedure. Then, compute z _{n,T−2} = b _{0} + b _{1} x _{n,T−2} + b _{2} x _{n,T−2} ^{2}.

Step 7:
If x _{n,T−2} ≤ z _{n,T−2}, set p _{ n,T }=p _{ n,T1 }=0 (zero denotes no transaction) and p _{n,T2}=x _{n,T2;} and if x _{n,T−2} > z _{n,T−2}, then set p _{n,T2}=0 and maintain the results previously obtained for p _{ n,T1 } and p _{ n,T }.

Step 8:
Recursively repeat steps 6–8 for all n and t=1,…,T3. That is, compute c _{n,t} = Min[p _{n,T} e ^{−r(T−t)}, …, p _{n,t+1} e ^{−r}]. Regress c _{n,t} = b _{0} + b _{1} x _{n,t} + b _{2} x _{n,t} ^{2} + u _{n,t} applying an ordinary LeastSquares procedure. Then, compute z _{n,t} = b _{0} + b _{1} x _{n,t} + b _{2} x _{n,t} ^{2}. Finally, If x _{n,t} ≤ z _{n,t}, set p _{ n,T }=...=p _{n,t+1}=0 and p _{ n,t }=x _{ n,t } and if x _{n,t} > z _{n,t}, then set p _{ n,t }=0 and maintain the results previously obtained for p _{n,t+1,…}, p _{ n,T }.

Step 9:
Along each path n denote the period t at which p _{ n,t }>0 by t*_{ n }. Then, compute the optimal stopping time, t*, by averaging t* _{ n } across all paths. That is, \( t * = \frac{1}{N}\sum\limits_n {t *_n } \).
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Arbel, Y., BenShahar, D. & Sulganik, E. Mean Reversion and Momentum: Another Look at the PriceVolume Correlation in the Real Estate Market. J Real Estate Finan Econ 39, 316–335 (2009). https://doi.org/10.1007/s1114600991804
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Keywords
 Mean reversion
 Momentum
 Pricevolume
 Real estate
 Real option
 Geometricallag