The securitized or public real estate

MARTIN HOESLI is a professor at the University of Geneva s Finance Research Institute and Swiss Finance Institute in Geneva, Switzerland, and a member of the faculties at the Business School at the University of Aberdeen in Scotland, U.K. and the Kedge Business School in Talence cedex, France. martin.hoesli@unige.ch ELIAS OIKARINEN is an Academy Research Fellow at the School of Economics at the University of Turku in Turku, Finland. elias.oikarinen@utu.fi CAMILO SERRANO is head of analytics at IAZI AG CIFI SA in Zurich, Switzerland. camilo.serrano@iazi.ch Do Public Real Estate Returns Really Lead Private Returns? MARTIN HOESLI, ELIAS OIKARINEN, AND CAMILO SERRANO The securitized or public real estate market is generally assumed to be more informationally efficient than the direct or private market. This is due to the greater liquidity, larger number of market participants, lower transaction costs, and existence of a public market place for real estate securities. Therefore, securitized real estate prices are expected to react faster to shocks in the fundamentals than direct real estate prices. In line with this hypothesis, empirical evidence suggests that public market returns lead direct market returns (Barkham and Geltner [1995]; Oikarinen et al. [2011]; Yunus et al. [2012]; Ling and Naranjo [2015]) and, hence, that there is a price discovery mechanism between public and private real estate markets that can have important predictability and portfolio allocation implications. However, the reported lead lag relationship could in some cases be biased due to data complications. These complications include the use of appraisal-based data to measure direct market capital values, the different property-type mixes of securitized and direct real estate indexes, and the fact that public real estate returns are leveraged whereas direct returns are not. A number of studies (Geltner and Kluger [1998]; Li et al. [2009]; Yavas and Yildirim [2011]; Hoesli and Oikarinen [2012]; Ling and Naranjo [2015]) have addressed some or all of the aforementioned data complications and suggest that securitized returns lead their direct counterparts even after controlling for these data problems. However, there is one remaining data issue that has not been considered previously: the escrow lag in the recording of direct market transaction prices. In indexes that track direct real estate market performance, the recorded price might represent the agreed-upon price based on the meeting of minds that occurred a few weeks prior to recording. This delay, which could potentially explain the lead lag relationship observed in the literature, is commonly referred to as the escrow period, during which the due diligence process takes place. We contribute to the literature by providing a clearer picture of the dynamic relationships between public and private real estate returns by accounting for all the aforementioned data complications, including the escrow lag issue. We also make a further contribution to the literature. While previous research finds that REIT (real estate investment trust) returns react faster than private market returns to fundamentals (Ling and Naranjo [2015]), thus creating a lead lag relationship between the markets, this is the first analysis to derive impulse responses of real estate returns to shocks in the fundamentals to specifically examine the factors behind the lead lag relationships between the securitized and direct markets. IT IS ILLEGAL TO REPRODUCE THIS ARTICLE IN ANY FORMAT THE JOURNAL OF PORTFOLIO MANAGEMENT 105 Copyright 2015

We use sector level REIT and transaction-based direct real estate total return data for the United States to study the reaction patterns of public and private real estate returns to economic shocks and to examine the lead lag relationships between the public and private real estate markets. Unlevered data are used to avoid the potential influence of leverage in the REIT data on our conclusions. We add economic fundamentals in the analysis to allow for the influence of fundamentals on real estate market dynamics. Moreover, we lag the direct market data to take the escrow lag into account; market price levels will thus more accurately reflect those that prevailed at the time of the meetings of minds. We find tight long-term relationships in terms of cointegration in all four sectors. Based on the impulse responses derived from the estimated vector error-correction models, the results show that REIT returns lead private real estate returns in the office and retail sectors even after accounting for leverage, the inf luence of fundamentals, and a 90-day escrow lag. The lead lag relationships are due to the slow reaction of private market returns to shocks in REIT returns, the risk premium, and consumer sentiment. In the industrial sector, in contrast, the lead lag relationship goes from the direct market to REITs if a 90-day escrow lag is assumed. For the apartment market, we do not find clear-cut evidence of a lead lag relationship going either way. Overall, the findings suggest that a universal lead lag relationship going from the public to the private real estate market is not as evident as has generally been thought. The findings have several practical implications. REIT returns can be used to predict direct real estate returns in all four sectors, because even in the industrial and apartment markets the direct real estate prices react to deviation from the long-term relationships despite not observing a leading role of REITs in those two sectors. More unexpectedly, REIT returns, too, have predictable components. Furthermore, over the long horizon, the co-movement between securitized and direct real estate markets is substantially stronger than suggested by the quarterly correlation coefficients. Importantly, as the observed direct returns include a recording lag due to the escrow period, the perceived contemporaneous correlation between REIT and direct index returns can be notably lower than the actual co-movement even in the short horizon. Therefore, the benefits of including securitized real estate in a portfolio containing direct real estate (or vice versa) are more limited than what is often thought. The findings further suggest that the implications in the literature that during crisis periods, one should sell direct real estate and buy REITs, rather than the other way round (Hoesli and Oikarinen [2012]) hold even when accounting for the escrow lag and for the time-varying liquidity in the private market. Our results also show that there are notable differences across real estate sectors with respect to the return dynamics; it is thus desirable to use sector level data when evaluating the return and price dynamics of REITs and direct real estate and when making forecasts concerning future price developments on those markets. DATA DESCRIPTION Although REIT returns include the impact of leverage, available direct real estate market benchmarks reflect the performance of unleveraged properties. The magnitude of leverage naturally affects the mean and volatility of returns. Moreover, time variation in the leverage may hinder the cointegration tests and distort the estimated long-run parameters. In addition, there can be notable differences in the dynamics across real estate sectors so that the aggregate indexes can mask valuable sector-specific information and could lead to erroneous conclusions being drawn (Yavas and Yildirim [2011]; Hoesli and Oikarinen [2012]). Therefore, we use the sector-level unlevered U.S. equity REIT data presented in Ling and Naranjo [2015]). The Ling Naranjo REIT data, in which REIT returns are unlevered at the firm level, are based on the CRSP-Ziman and CRSP/Compustat databases and include separate series for the office, apartment, retail, and industrial sectors. For direct real estate, we use the sector-level transaction-based NCREIF indexes (TBI). These indexes are available for the same four sectors. The sample period, 1994Q1 2010Q4, is limited by the availability of the hedonic TBI indexes. 1 All indexes are total return indexes. The TBI and REIT indexes may also exhibit differences with respect to the geographic distribution of the properties. We performed Granger causality tests across the four TBI regions (East, West, South, and Midwest) and found no evidence of lead lag relationships. Thus, differences in the geographical distribution of the properties, at least at the four-region level, are unlikely to have a notable influence on our findings. Locational differences may, of course, be more subtle than portfolio 106 DO PUBLIC REAL ESTATE RETURNS REALLY LEAD PRIVATE RETURNS?

composition dissimilarities across broadly defined geographical areas. For instance, there may be differences between REIT and institutional investors with respect to the quality and size of the cities in which they invest. Empirical evidence by Malpezzi and Shilling [2000] suggests that private investor holdings are more heavily tilted toward high-quality metropolitan areas and toward areas with greater density, higher average human capital accumulation, and less stringently regulated real estate markets than those of public investors. Given that such metro areas should react relatively fast to changes in fundamentals (Capozza et al. [2004]), such effects may make it easier to reject the existence of lead lag relationships between public and private real estate returns. In addition to the real estate data, the analysis includes several variables that may affect significantly the real estate returns according to theory and previous empirical evidence (Karolyi and Sanders [1998]; Ewing and Payne [2005]; Hoesli and Oikarinen [2012]; Ling et al. [2014]). These variables concern economic growth, general price levels, short-term interest rates, the term structure of interest rates, the default risk premium, and consumer sentiment. We measure economic growth with the change in U.S. GDP (GDP). Changes in the consumer price index are used to track movements in the general price level (INF), while the three month T-bill rate and the spread between the 10-year government Treasury bond yield and the three month T-bill rate measure the short-term interest rates (IR) and the term structure of interest rates (S), respectively. The spread between low-grade corporate bond (Baa, Moody s) and the 10-year government Treasury bond yields is used as the measure for the default risk premium (D). Finally, we capture the sentiment (SE) using the University of Michigan Consumer Sentiment Index (UMCI) regarding the five-year economic outlook. The UMCI is a survey gauging how consumers foresee changes in the economic environment and is an official component of the U.S. Index of Leading Economic Indicators (i.e., an indicator providing information regarding future economic growth). A number of studies (e.g., Carroll et al. [1994]; Lemmon and Portniaguina [2006]) showed that the consumer confidence measured by the UMCI predicts future economic activity. 2 The sentiment component of the UMCI index can be regarded as the component that is unrelated to prevailing economic fundamentals. Hence, following Lemmon and Portniaguina [2006] and Ling et al. [2014], we regress UMCI on the economic fundamentals included in our study and use the residual series of this OLS regression as the sentiment measure. SE, GDP, and INF stand in for the expectations concerning real cash flow growth, whereas the other fundamentals in the model (and the inflation rate, to some extent) represent the current and expected future movements in the discount factor. The data are sourced from Thomson Datastream. In the econometric analysis, we use real indexes for NAREIT, TBI, and GDP. The series are deflated using the CPI and used in the natural log form. The short-term interest rate is also deflated using the CPI. Exhibit 1 shows that the REIT and TBI indexes generally track each other closely. An exception is the apartment sector, where the TBI index outperformed the unlevered REIT index, especially during the early sample period. Also, the global financial crisis of 2008 induced divergences between the public and private markets. A major complication when studying the dynamics between public and private real estate markets is that the recorded prices for direct real estate might represent the agreed-upon prices based on the meeting of minds that occurred a few weeks prior to recording. This delay is commonly referred to as the escrow period or escrow lag, during which the due diligence process takes place. The duration of the escrow period can vary across property types as highlighted by Crosby and McAllister [2004] in their analysis of U.K. commercial real estate. They reported median escrow lags of approximately 80 days for the industrial sector, 50 days for offices, and 90 days for retail property. Unfortunately, there is no study reporting corresponding values for the United States. According to several U.S. expert opinions, however, the escrow period can be as long as 90 days for apartments and up to 180 days for the other property types. The average escrow periods are shorter than these maximum values, however, and in some cases, the price is renegotiated during the due diligence process. Given the expert opinions, our best estimate for the escrow lag in TBI indexes is 90 days, and we use this escrow lag assumption in our baseline estimations in the econometric analysis. 3 As the REIT index values are beginning-ofquarter values, they reflect the 45-day escrow lag case. This is because the TBI indexes show average quarterly values by construction (i.e., they are based on all transactions that took place during a given quarter). For the THE JOURNAL OF PORTFOLIO MANAGEMENT 107

E XHIBIT 1 Sector Level (unlevered) NAREIT and TBI Total Return Indexes, 1994Q1 2010Q4 purposes of the baseline 90-day escrow lag analysis, we first compute a REIT index that better corresponds to the nature of the TBI: For a given quarter, the index value is calculated as the average of beginning and end of quarter values in the REIT data. If the escrow lag is 90 days, the TBI index return for quarter t actually reflects the direct market price change that took place during quarter t 1. Therefore, we lag the nominal TBI indexes by one quarter, deflate these indexes by the CPI, and study these TBI index returns together with the modified REIT index returns to study the baseline 90-day escrow case. The escrow lag is of course potentially time varying. In particular, the lag might have become shorter over the sample period due to advances in information technology. However, our diagnostic checks show that the estimated model parameters are stable over the sample period, suggesting that the potential time variation in the escrow lag should not have notable effects on our findings. The escrow period can also vary with location and size of the property. Thus, we explore the robustness of our findings to the escrow lag length assumption by considering 45-day and 135-day escrow periods. Exhibit 2 presents descriptive statistics for the unlevered office (Off_TBI, Off_REIT), apartment (Apt_TBI, Apt_REIT), retail (Ret_TBI, Ret_REIT), and industrial (Ind_TBI, Ind_REIT) sector total returns and the fundamental variables. The means (ranging from 6.2% to 7.6%) and volatilities (from 7.1% to 11.0%) are quite similar across unlevered public and private market returns and across sectors. The industrial sector is the most volatile one. Exhibit 2 also reports the contemporaneous quarterly correlations of REIT returns with TBI returns. The reported correlations are based both on the original series and on the series adjusted for the 90-day escrow lag assumption (TBIe). For all sectors except industrials, the correlation is greater when the escrow period is accounted for than when it is not. The within-sector escrow lag adjusted correlations are between 0.24 108 DO PUBLIC REAL ESTATE RETURNS REALLY LEAD PRIVATE RETURNS?

E XHIBIT 2 Descriptive Statistics of Differenced Variables, Unit Root Test Results, and Correlations of Real Estate Returns, 1994Q1 2010Q4 Notes: Within-sector correlations are bolded. The number of lags included in the DF-GLS tests is decided based on the Akaike information criterion (AIC). A constant term (c) is included in the DF-GLS test if the series clearly seem to be trending or if the test results without the constant term suggests that the series are exploding. s indicates the inclusion of seasonal dummies in the test. For the sentiment factor, the statistics are in index points, not in percentages. *and **denote statistical significance at the 5% and 1% levels, respectively, in the DF-GLS unit root test and in the correlation analysis. (apartments) and 0.47 (offices) and statistically significant for all sectors. Based on the DF-GLS unit root test, all return indexes are non-stationary in levels but stationary in differences, as expected, and the fundamental variables, too, are I(1). An exception to this is the sentiment variable, which is stationary. ECONOMETRIC METHODOLOGY There are sound a priori theoretical reasons to expect that securitized and direct real estate total return indexes should be cointegrated (Oikarinen et al. [2011]). Because a cointegrating relationship can be an important force driving the short-term return dynamics and hence can substantially affect the lead lag relationships, we test for cointegrating relations and estimate such longterm relationships, as a preliminary step, employing the Johansen [1996] maximum likelihood technique and the small-sample corrected trace test (Johansen [2002]). The trace test provides evidence of cointegration for all the sectors. 4 Hence, the deviations of private return indexes from these long-term relationships are included in the vector error-correction models (VECMs) that are estimated to study the dynamics of real estate returns: ΔX t = μ + Γ 1 ΔX t-1 + + Γ k-1 ΔX t-l + α(tbi t-1 TBI * ) + ε t-1 t where ΔX t is X t X t-1, X t is an eight-dimensional vector including both the return index values and the fundamentals in period t, μ is an eight-dimensional vector of drift terms, Γ i is an 8 8 matrix of coefficients for the lagged differences of the stochastic variables at lag i, 5 and ε is an eight-dimensional vector of white noise error terms. α(tbi t-1 TBI * ) forms the error-correction t-1 mechanism, where α is a vector of the speed of adjustment parameters and TBI t-1 TBI * is the deviation of t-1 the TBI value from its cointegrating relation (TBI * ) with the REIT index in period t 1. Because only the THE JOURNAL OF PORTFOLIO MANAGEMENT 109

real estate indexes can be assumed to adjust toward a cointegrating relation between those indexes, the alpha is restricted to equal zero in the equations for the fundamentals. Real estate returns are allowed to influence the economic fundamentals through the short-term dynamics, however. In addition to the multiple variable models including the fundamentals, we estimate a pairwise model for each sector. The lag length in the models is decided by the Schwarz information criterion (SIC). The direction of the possible Granger causality is tested using a standard F-test (equivalent to a t-test if the lag length is 1) to examine the existence of a lead lag relationship between the assets. The multiple variable models are also used to derive the impulse responses of real estate returns to unanticipated changes in the fundamentals and in the real estate returns themselves. We use the generalized impulse response functions (GIRFs) developed by Pesaran and Shin [1998]. The GIRFs do not require orthogonalization of shocks and are invariant to the ordering of the variables in the VECM. EMPIRICAL RESULTS In our baseline estimations, we assume that the escrow lag is 90 days. The Granger causality (GC) test results are provided in Exhibit 3. The test statistics from the pairwise models show whether there are lead lag relationships between the two series, while the statistics from the multiple variable models indicate whether the lead lag relationships are due to differences in the reaction speeds to changes in the fundamentals and/or in the returns in the other real estate market. In particular, if GC disappears when fundamentals are added to the model, then the perceived lead lag relationship observed in the pairwise model is likely due to differences in reaction speed to shocks in the fundamentals. For the office sector, REIT returns lead direct real estate returns, with the lead lag relationship taking place through both the long-run relationship and the short-run dynamics. The GC analysis does not provide clear-cut evidence of lead lag relationships for the other three sectors, even though REIT returns Granger cause private market returns directly and through the deviation from the long-term relationship. The mixed evidence for those three sectors is because REITs also react to deviations from the long-run equilibrium. The inclusion of the fundamentals alters the statistical significances to some extent but does not change the main conclusions. The GC tests indicate that the returns on REITs, too, contain predictable elements. In addition to the predictability through the deviation from the long-term relationship, Exhibit 3 shows that REIT returns are predictable by their past values and by the economic fundamentals. 6 The GC tests examine the predictability of and the lead lag relationship between securitized and direct real estate returns. However, they do not provide details about the reaction patterns and adjustment speeds of real estate prices to various shocks. For instance, the GC statistics only show the statistical significance of the adjustment speeds toward the long-run relation (alphas), although the size of the alphas also influences the dynamics and possible lead lag relationships: Other things being equal, the greater the alpha, the greater the lagged response of private (public) returns to a shock in the public (private) market returns. The adjustment toward the long-run relations is relatively slow, and with the exception of the industrial sector, alpha is greater for direct real estate than for REITs. The private market alpha in the multiple variable models is 0.19 for offices (versus 0.04 and not statistically significant for REITs), 0.23 for apartments (0.13 for REITs), 0.19 for retail (0.08 and not statistically significant for REITs), and 0.21 for industrial (0.28 for REITs). To shed more light on the dynamics, we derive impulse responses of the returns to shocks in the fundamentals and in the returns themselves. These impulse responses are based on the same multiple variable models as the GC tests. 7 The GIRFs up to 10 quarters from the shocks are shown in Exhibits 4 7. These impulse responses correspond to shocks that are one standard error in magnitude. Therefore, the estimated responses show the economic significance of the shocks. In the graphs, the horizontal axis shows the time from the shock, while the vertical axis indicates the influence of the shock on the returns in each period from the contemporaneous influence up to that taking place 10 quarters after the shock. The estimated reactions are sensible and have the expected signs, with the exception of the reaction to an inflation rate shock. While the empirical literature presents mixed results regarding the inflation hedging qualities of direct real estate, empirical evidence has generally suggested that securitized real estate does 110 DO PUBLIC REAL ESTATE RETURNS REALLY LEAD PRIVATE RETURNS?

E XHIBIT 3 F-test statistics in the Granger Causality Tests, 1994Q1 2010Q4 Notes: The null hypothesis in the tests is that of no Granger causality. The models include one lag except for the office market pairwise model, which includes two lags. To fulfill the assumption of normally distributed residuals, most of the models also contain one or more point dummy variables that take the value of 1 in one period and of zero otherwise. The inclusion of these dummies does not notably affect the test statistics. The homoskedasticity of the residuals can be accepted in all the models based on the ARCH(4) test. *and **denote statistical significance at the 10% and 5% levels, respectively. not provide a hedge against inflation (see Hoesli et al. [2008] for a review of the inflation hedging literature). The impulse responses graphed in Exhibits 4 7 suggest that inflation rate shocks induce money flows into both private and public real estate markets, thereby having a positive (typically lagged) impact on the returns. A possible explanation is that real estate generally is viewed as providing relatively good inflation hedging effectiveness; increased flows into the asset class will occur at times of higher expected inflation or greater inflation uncertainty. As expected, the impacts of shocks in economic growth and sentiment are positive. Both of these shocks imply larger cash flows for real estate investments. The positive impact on real estate returns of improved sentiment indicates that real estate prices embody forwardlooking components concerning economic growth. An increase of the risk premium increases the discount factor for risky investments and thereby decreases asset prices, as would be expected. Although the results by Ewing and Payne [2005] suggest flight to safety (from risky bonds to REITs; it is, of course, highly questionable whether REITs are safe), our results suggest that an THE JOURNAL OF PORTFOLIO MANAGEMENT 111

E XHIBIT 4 Reactions of Public (REIT) and Private (TBI) Real Estate Returns to Shocks in the Fundamentals: Office Sector E XHIBIT 5 Reactions of Public (REIT) and Private (TBI) Real Estate Returns to Shocks in the Fundamentals: Retail Sector increase in the risk perceived by investors lowers REIT prices via an increase in the discount factor. Expectedly, we observe a negative impact of interest rate and term spread shocks on real estate returns. Of particular interest are whether the reactions to shocks notably differ between the private and public markets and whether and how quickly the REIT and direct markets react to shocks occurring in the market for the other type of real estate. The GIRFs provide evidence on these questions. Importantly, the upper-left panels of Exhibits 4 7 show that the TBI reaction to REIT shocks is lagged that is, the direct returns react slowly to innovations in REIT returns. In the retail and office sectors, the TBI response peaks one quarter after the shock, and the shock notably influences the TBI returns even with longer lags. The lagged response of the private market is even more pronounced in the apartment sector, where the TBI reaction peaks three 112 DO PUBLIC REAL ESTATE RETURNS REALLY LEAD PRIVATE RETURNS?

E XHIBIT 6 Reactions of Public (REIT) and Private (TBI) Real Estate Returns to Shocks in the Fundamentals: Apartment Sector E XHIBIT 7 Reactions of Public (REIT) and Private (TBI) Real Estate Returns to Shocks in the Fundamentals: Industrial Sector quarters after the shock. In the industrial sector, TBI reacts notably quicker than in the other sectors. Interestingly, the REIT market shows similar lagged reaction to direct market shocks in the apartment and industrial sectors, as indicated by the lowerleft panels of Exhibits 6 and 7. The lag is particularly prominent in the apartment sector, where the REIT reaction peaks two quarters from the shock. In the office and retail sectors, the impact of a TBI shock on REITs is much milder. The impulse responses also suggest that it generally takes a while before real estate prices fully absorb new information regarding the fundamentals, because the response curves converge to zero only slowly. This THE JOURNAL OF PORTFOLIO MANAGEMENT 113

may generate further predictability in real estate returns in both public and private markets. The exhibits clearly indicate that direct market prices react more sluggishly than REIT prices to risk premium and sentiment shocks (an exception to this is the industrial sector s responses to a shock in D). While the instantaneous reaction of REITs to the shocks is notable and the impact on REIT returns diminishes rapidly, the initial TBI reaction is small or even has the wrong sign and the influence of the shock on TBI lasts for several quarters. On the other hand, the GIRFs show evidence of REITs adjusting more sluggishly than TBI to shocks in the term spread. In sum, the impulse responses confirm that REIT returns lead TBI returns in the office sector and provide stronger evidence of REIT returns leading TBI returns in the retail sector than provided by the GC test results. The differences across property sectors could be due to varying levels of uncertainty in pricing across sectors, with public markets adjusting more quickly to the uncertainty than private markets. Cannon and Cole [2011] showed that the average absolute percentage difference between appraised value and transaction price is lower for multifamily properties than for offices. Plazzi et al. [2010] reported that transaction-based cap rates for offices are not able to capture the time variation in expected returns, providing further evidence of the uncertainty in pricing office properties. Wheaton [1999], in turn, documented the complexity of the office and retail sectors in that there is a lag between employment growth and construction activity that does not exist for the multifamily and industrial sectors. We also conducted robustness checks for the real estate market dynamics. First, we tested the robustness of our findings to two alternative escrow lag lengths (45 and 135 days). 8 Then, we used the TBI demand or constant-liquidity indexes developed by Fisher et al. [2003] and Fisher et al. [2007] to test whether the lead lag relationships found in the baseline models could be explained by the time-varying liquidity of direct real estate. 9 The results support the hypothesis that REIT returns lead direct real estate returns in the office and retail sectors. For the industrial sector, direct market returns no longer lead REIT returns if the escrow lag is 45 days, but there is no evidence of a lead lag relationship going in the opposite direction either. In the apartment sector, there is no clear evidence of a lead lag relationship at any of the assumed escrow lags. The results that are based on the demand indexes generally are in line with the baseline findings. SUMMARY AND PRACTICAL IMPLICATIONS This article is the first that explicitly considers the impacts of escrow lags on the reported lead lag relationships between the securitized and direct real estate markets. Our findings show that REIT returns lead private real estate returns in the office and retail sectors even after factoring for leverage and a 90-day escrow lag. For the industrial sector, in contrast, the lead lag relationship goes from the direct market to REITs after adjusting the data for a 90-day escrow period. For the apartment market, we do not find clear-cut evidence of a lead lag relationship going either way. Our findings thus suggest that a universal lead lag relationship going from the public to the private real estate market is not as evident as has generally been thought. Although direct market prices respond sluggishly to the information that is revealed by REIT price movements even in the industrial sector the REIT market reaction, too, is clearly lagged with respect to direct market shocks in the apartment and industrial sectors, taking account of the escrow lag. We also find that, in the office and retail sectors, REIT returns lead even the constant-liquidity private market returns. The results entail several implications for investors, analysts, and fund managers. First, the results indicate that REIT return data can be used to predict direct real estate returns in all the four sectors even when factoring in the escrow lag. A more unexpected finding is that the REIT market can be slow to respond to information coming from the direct market: Private real estate data include predictive power with respect to REIT performance in all the sectors except for offices if timely data on private market returns are available without a notable lag. That is, the results overall indicate that REIT and direct real estate markets absorb only sluggishly the information that is revealed by unexpected price movements in the other market. Regarding the REIT market reaction, this may be a consequence of the data on direct real estate performance not being available or appearing with a notable lag only. Nevertheless, a well-informed investor or fund manager may be able to take advantage of such predictability in REIT prices, at least in the apartment and industrial sectors. 114 DO PUBLIC REAL ESTATE RETURNS REALLY LEAD PRIVATE RETURNS?

Second, our results provide one more piece of evidence showing that the co-movement between securitized and direct real estate markets over the long horizon is substantially stronger than suggested by the contemporaneous quarterly correlation coefficients. Therefore, from a long-term investor s viewpoint, public and private real estate are better substitutes for each other than implied by the contemporaneous correlations, and the benefits of including public real estate in a portfolio containing private real estate (or vice versa) are more limited than what is suggested by quarterly correlations. Third, the results are of importance concerning the recommended shifts in allocations between private and public real estate during crisis periods. Recent empirical literature suggests that one should sell direct real estate and buy REITs, rather than the other way around, during crisis periods (Hoesli and Oikarinen [2012]). Based on the GIRFs, this implication still holds when considering the escrow lag issue and using the constant-liquidity indexes. In particular, even when accounting for the escrow lag and time-varying liquidity of direct real estate, the direct market prices react notably slower than REIT prices to sentiment and risk premium shocks shocks in variables that generally react the quickest and strongest to a financial crisis. That is, whenever REIT prices have notably dropped due to a large jump in the sentiment or the risk premium, or both, it is not advisable to shift the allocation from REITs to direct real estate, but rather it is recommended to proceed the other way around. For instance, if a notable sentiment shock has occurred some 45 days ago causing 30% lower REIT prices today, our estimations suggest that direct market prices are expected to decrease relative to REIT prices by approximately 10% in the office sector, 35% in the apartment and industrial sectors, and 50% in the retail sector within the next one-and-a-half years (90-day escrow lag assumed). Corresponding values for a risk premium shock that has induced a 30% REIT price drop are 15% (industrial), 20% (office), 25% (retail), and 35% (apartments). Finally, our results show that there are significant differences across real estate sectors with respect to the return dynamics. These differences can considerably influence the extent of the aforementioned practical implications. In particular, the predictability implications, including the proposed portfolio allocation shifts during crisis periods, vary across sectors. Therefore, it is desirable to use sector-level data when evaluating the return and price dynamics for REIT and direct real estate markets, when making forecasts concerning future price developments on those markets, and when considering the asset allocation between the markets. Many observers believe that the private market has become more efficient over time for various reasons. This would mean that the lag between private and public real estate returns has diminished. Although we do not focus on investigating the potential temporal changes in the dynamics, we do not detect instability in the model parameter estimates suggesting that no significant change has occurred during the sample period. ENDNOTES We are grateful to Greg MacKinnon and Jim Clayton for many constructive comments and to David Ling and Andy Naranjo for providing us with their REIT data used in this article. Elias Oikarinen is grateful for financial support received from the OP-Pohjola Group Research Foundation. 1 Using these indexes yields more reliable conclusions regarding the lead lag relationships than using the new simplified TBI indexes that are likely to suffer from substantially greater short-term measurement error than the ones based on the hedonic methodology. For instance, the new TBI indexes generally show negative autocorrelation at the one-quarter lag and positive autocorrelation only from twoquarters onwards. This is most likely due to measurement error in the indexes and would bias the analysis on lead lag relationships. 2 The UMCI covers a range of various forecast horizons. The five-year outlook is selected here based on the Akaike information criterion. 3 For apartments, the lag is likely somewhat shorter. 4 Based on a recursive test, the stability of the long-run relationship is not rejected for any of the sectors. 5 An exception is the sentiment, which is included in the dynamics in levels as it is a stationary variable. 6 For further evidence on the predictability of REIT returns by using their past values, see, for example, Serrano and Hoesli [2010]. 7 The alpha for office REITs is restricted to equal zero, as in this sector the REIT returns do not react significantly to deviations from the long-run relationship. In the retail sector, we allow REIT returns to react to deviations from the long-run relationship, although the alpha in the multiplevariable model is a borderline case regarding statistical significance. Based on the Hansen stability test, the stability of THE JOURNAL OF PORTFOLIO MANAGEMENT 115

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