Economic Risk Factors and Commercial Real Estate Returns

Transcription

1 Journal of Real Estate Finance and Economics, 15: 3, 283±307 (1997) # 1997 Kluwer Academic Publishers Economic Risk Factors and Commercial Real Estate Returns DAVID C. LING AND ANDY NARANJO Department of Finance, Insurance and Real Estate, Graduate School of Business Administration, University of Florida, Gainesville, FL Abstract A great deal of research has focused on the links between stock and bond market returns and macroeconomic events such as uctuations in interest rates, in ation rates, and industrial production. Although the comovements of real estate and other asset prices suggests that these same systematic risk factors are likely to be priced in real estate markets, no study has formally addressed this issue. This study identi es the growth rate in real per capita consumption, the real T-bill rate, the term structure of interest rates, and unexpected in ation as fundamental drivers or ``state variables'' that systematically affect real estate returns. The nding of a consistently signi cant risk premium on consumption has important rami cations for the vast literature that has examined the (riskadjusted) performance of real estate, for it suggests that prior ndings of signi cant abnormal returns (either positive or negative) that have ignored consumption are potentially biased by an omitted variables problem. The results also have important implications for dynamic asset allocation strategies that involve the predictability of real estate returns using economic data. Key Words: real estate returns, asset pricing, economic risk factors, risk premiums, multibeta asset pricing model, systematic risk 1. Introduction Theoretical and empirical work linking the macroeconomy to real estate returns is extremely limited and focused primarily on the question of whether real estate returns are ``sensitive'' to various economic events or factors, especially unanticipated in ation. These sensitivities are estimated by regressing ex post real estate returns on a prespeci ed set of explanatory variables (e.g., Gyourko and Linneman, 1988; Liu and Mei, 1992; and Park, Mullineaux, and Chew, 1990). Sensitivity (or risk ``exposure'') is measured by each variable's beta coef cient. Statistical signi cance of a coef cient in these ex post return regressions indicates exposure, but it does not tell us whether a risk factor is ``priced'' ex ante (i.e., bears a premium) or whether the factor's in uence changes over time. Financial theory suggests that a factor will be priced ex ante only if the factor has a ``systematic'' in uence on asset returns, in which case there is a marketwide price of risk measured in the form of an increment to the expected return (a risk premium) per unit of beta. 1 This can be seen in the CAPM (one factor) framework, which posits that an ex ante risk premium is paid to a particular asset in proportion to the beta coef cient (or ``loading'') on the market portfolio. Empirically, considerable evidence indicates that state variables such as the slope of the

2 284 LING AND NARANJO term structure, expected and unexpected in ation, industrial production, and the spread between high-grade and low-grade bonds proxy for economic risk factors that are rewarded, ex ante, in the stock market (e.g., Chen, Roll, and Ross, 1986; Chan, Chen, and Hsieh, 1985; and Ferson and Harvey, 1991). Although the comovements of real estate and other asset prices suggest that these same systematic risk factors are likely to be priced in real estate markets, no study has formally addressed this issue. 2 The purpose of this study is to identify the fundamental macroeconomic drivers or ``state variables'' that systematically affect real estate returns. The study covers the 1978± 1994 time period. Real estate return portfolios are formed using both appraisal-based returns and stock market-based REIT returns. Using the time-series regression techniques suggested by Geltner (1991) and Fisher, Geltner, and Webb (1994), the (NCREIF) appraisal-based returns are ``unsmoothed'' to account for the well-known appraisalinduced smoothing bias. In addition to the ve macroeconomic risk factors proposed by Chen et al. (1986), other macroeconomic risk factors such as the real Treasury bill rate and the growth rate of real per capita consumption are employed as risk factors. To overcome some of the econometric problems encountered in previous research, this study uses nonlinear multivariate regression techniques to estimate the risk factor sensitivities and return premia. In particular, a system of equations with cross-equation and within-equation restrictions is estimated jointly using Gallant's (1975) nonlinear seemingly unrelated regression technique. This xed-coef cient method of estimation eliminates the generated regressors problems from using the two-pass regression technique, although the risk sensitivities and risk premia are constrained to be time invarying. 3 In response to evidence in the literature that the xed-coef cient model may be overly restrictive (Ferson and Harvey, 1991), we also use the Fama-Macbeth (1973) methodology to estimate complete time-varying risk sensitivities and premia. 4 Estimates of the xed-coef cient model show that the growth rate in real per capita consumption and the real T-bill rate are priced consistently across our four real estate portfolio groups. The term structure of interest rates and unexpected in ation do not carry statistically signi cant risk premia in the xed-coef cient model but are signi cant when sensitivities and risk premia are allowed to vary over time. The nding of a consistently signi cant risk premium on consumption differs from previous studies of stock and bond returns, which have found mixed evidence on the role of consumption in explaining ex ante returns. However, this result is consistent with Geltner's (1989) nding that real estate returns are sensitive to national consumption. The nding of a signi cant premium on consumption also has important rami cations for the vast literature that has examined the (risk-adjusted) performance of real estate, for it suggests that prior ndings of signi cant abnormal returns (either positive or negative) that have ignored consumption are potentially biased by an omitted variables problem. The results also have important implications for dynamic asset allocation strategies that involve the predictability of real estate returns using economic data. The remainder of the paper is organized as follows. Section 2 presents our multifactor asset pricing model and our empirical implementation of the model. Section 3 describes the data, while the results appear in section 4. The last section offers some concluding remarks.

3 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS The Theoretical Model 2.1. The Multifactor Asset Pricing Model We use a standard multifactor asset pricing model (MAP), which assumes that there are several sources of risk, usually called factors, and that large subsets of assets respond to their uctuations. For some factors, the resulting risk exposure cannot be diversi ed away. The pricing of assets that carry this nondiversi able risk incorporates a risk premium proportional to the risk exposure (beta) of the asset. Furthermore, the literature has found that certain predetermined variables help to explain asset returns. The multifactor asset pricing model that we examine is consistent with a class of linear asset pricing models that include the capital asset pricing model (Sharpe, 1964; Lintner, 1965; and Mossin, 1966), the intertemporal capital asset pricing model (Merton, 1973), the consumption-based capital asset pricing model (Breeden, 1979), and the arbitrage pricing model (Ross, 1976). These asset pricing models all maintain that a small number of risk factors govern the behavior of asset returns. A useful way to interpret multifactor models is that the risk factors are unanticipated components of state variables correlated with the aggregate marginal utility of consumption (Ferson and Harvey, 1991). By recasting the standard returns generating equation and asset pricing equation, the MAP model can be written as 5 ~r it ˆ l 0t XK kˆ1 b ikt l kt XK kˆ1 b ikt ~F kt E t 1 F kt Š ~e it 1 where the tilde () denotes a time t random variable and r it is the excess return for the ith asset (the return in excess of the risk-free rate), l 0t is the zero-beta excess rate of return (i.e., the rate in excess of the risk-free rate), E t 1 z t is the expected value of z t, F kt is the kth of the K risk factors at time t, b ikt is the possibly time-varying sensitivity of the ith asset to the kth risk factor, l kt is the risk premium ( price of risk) corresponding to the kth risk factor, is a disturbance idiosyncratic to the ith asset. E it We refer to l* kt l kt E t 1 F kt as the gross risk premium. The compensation in the form of additional excess return for bearing the risk associated with the kth risk factor is equal to the risk premium on the kth factor times the sensitivity of the ith asset to the kth risk factor, or l kt b ikt. Note that the price of risk, l kt, which we also refer to as the risk premium, is assumed to be constant across the various assets. To control for potential misspeci cation, we also include several predetermined variables that have been found to help predict returns. These predetermined variables can be viewed as additional control variables in our analysis. 6

4 286 LING AND NARANJO 2.2. Empirical Implementation of the Model To implement the model, we estimate factor risk premia for each macroeconomic factor. We rst estimate a xed-coef cient version of the model shown in equation (1). To estimate the factor risk premia (l k ) in equation (1), it is necessary to simultaneously estimate pricing equations for at least as many portfolios as there are factors. The xedcoef cient model can be written as ~r it ˆ l 0 XK b ik l k E F kt Š XK kˆ1 kˆ1 b ik ~F kt b im l m E r mt Š b mk ~r mt ~e it 2 where r m is the excess return to the market portfolio. In equation (2), l m E r mt ˆ l 0 because the relation must hold for the market portfolio as well. Thus, the system of equations to be estimated reduces to ~r it ˆ l 0 1 b im XK kˆ1 b ik l k E F kt Š XK kˆ1 b ik ~F kt b im ~r mt ~e it 3 Equation (3) shows that the risk premium for the market portfolio cannot be estimated. 7 The only available estimate of the market premium is the sample mean excess return (see Sweeney and Warga, 1986). The remaining gross risk premia, l* k, can be estimated using Gallant's (1975) nonlinear seemingly unrelated regression technique (NLSUR). 8 In addition to the nonlinear multivariate regression approach, we use a version of the two-pass regression technique by Fama and MacBeth (1973) to obtain time-varying risk premia estimates. The Fama±Macbeth two-pass procedure is used for this task because it allows for unrestricted variation of the risk premia. 9 The rst pass of the two-pass approach is a time-series t, while the second pass is a cross-sectional t. 10 For the rst pass, we use only past data to form rolling estimates of the betas for each portfolio, for each factor. After some experimentation, we decided to follow the traditional procedure of using a ve-year window. 11 In the second pass, we estimate the gross risk premia for each factor and each time period. This procedure is applied to each of the real estate return portfolio groups separately. The cross-sectional regression equation is given by equation (4) for I portfolios: ~r i ˆ l 0 ~r mt l 0 b ~ im XK l* k ~F kt Š b ~ ik ~Z i i ˆ 1;...;I; 8t kˆ1 4 where ^b ik is the rst-pass estimate of the beta of the ith portfolio for the kth factor and l* k is the gross risk premium for the kth factor.

5 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 287 It is important to point out that the time series variables ~r mt and ~F kt must be included in the cross-sectional regressions, even though their values do not vary in each crosssectional period. To avoid misspeci cation, it is necessary to include these variables in the estimation, because the coef cients associated with them vary across the i assets, and the single regression constant cannot absorb their impact. 3. The Data We use quarterly data from the rst quarter of 1978 through the fourth quarter of The availability of appraisal-based, time-series data for commercial real estate returns dictates the time interval evaluated. A brief description of the data follows. The appendix provides a detailed description of all the variables and their construction Portfolio Returns We create four separate real estate portfolio groups to assess the robustness of our results with respect to portfolio formation. In particular, we use (1) stock market return data on REITs and other real estate related industries from the Center for Research in Security Prices (CRSP), (2) appraisal-based returns by geographical division from the National Council of Real Estate Investment Fiduciaries (NCREIF), (3) NCREIF return data disaggregated both by region and property type, and (4) a combination of division NCREIF data and regional capitalization rate data from the American Council of Life Insurance Companies (ACLI). 12 Excess quarterly returns on each of the portfolios are calculated by subtracting the known beginning of quarter returns on three-month Treasury bills from the realized portfolio returns. The three-month Treasury bill rates are from the CRSP risk-free rates le. A brief description of the four portfolio groups follows. We restrict our analysis to real estate portfolio returns, because we want to assess the signi cance of macroeconomic risk factors in real estate markets. The inclusion of other asset classes as dependent variables, such as stocks and bonds, may increase the precision of the risk premia estimates by adding more cross-sectional variation to the returns. However, the addition of other asset classes in the estimation requires that the premia estimates be restricted to be equal across the various asset classes for there to be an increase in the precision of the estimates. Although it is clear that multibeta models can be used to price all the assets in the world, the imposition of equal prices of risk across all asset classes may not necessarily be valid. In fact, evidence supports the hypothesis that segmentation does exist between real estate markets and capital markets (see, for example, Liu, Hartzell, Greig, and Grissom, 1990 and Ling and Naranjo, 1997). Therefore, any potential ef ciency gains from including other asset classes in the analysis may be offset by the imposition of invalid equality constraints on the prices of risk.

6 288 LING AND NARANJO CRSP Real Estate Related Industries Returns Portfolios We form value-weighted portfolios for ve real estate related industries from the CRSP NYSE, AMEX, and NASDAQ les. The portfolios are created by grouping common stock data from all three exchanges into the following real estate related industries: REITs, Building Construction, Real Estate Owner Operators, Hotels and Motels, and Real Estate Related Services. 13 The ve industry portfolios of common stocks are grouped on the basis of their four-digit Standard Industrial Classi cation (SIC) code. Each of the ve portfolios in the CRSP portfolio group is value weighted. The appendix presents details on the fourdigit SIC industry groups NCREIF Division and Property Type by Region Returns Portfolios The NCREIF property index is a widely used benchmark of commercial real estate returns based on the reported net operating incomes (NOIs) and appraised values of unlevered properties held for institutional investors in the portfolios of the member rms of NCREIF. Quarterly returns are available beginning in the rst quarter of The total return is divided into its income and appreciation (or depreciation) components. The income component measures the portion of the total return attributable to each property's NOI, with each property weighted by its market value. At the end of 1994, the NCREIF Total Index included 1558 properties appraised at $25.5 billion. NCREIF disaggregates its Total Index by property type ( ve categories), by geographical region (four categories), by subregion or ``division'' (eight categories), and by region and property type (20 categories). These disaggregated index returns are used to create eight unsmoothed division portfolios and 20 unsmoothed property type by region portfolios. 14 The unsmoothed NCREIF returns are simulated historical returns, based on the individual subindices but corrected for smoothing in the second moments (i.e., inertia and appraisal lags are removed). The simulation approach we use is similar to that employed by Geltner (1989, 1991) and Ross and Zisler (1991) ACLI Transactions-Based Returns Portfolios Eight portfolio returns also are computed with imputed sale prices by combining NCREIF divisional NOI data with comparable ACLI data on capitalization rates. The capitalization rate for a sold property is de ned as the net operating income divided by its selling price. Quarterly cap rates for each division are gathered by survey and published in the ACLI publication Mortgage Commitments on Multifamily and Nonresidential Properties. The ACLI imputed price index is constructed by dividing the NCREIF income component of the total quarterly return for each division by the ACLI transactions-based cap rate for each comparable region. Eight regional return portfolios are then calculated from these transactions-based price indices. The estimated prices that result from dividing NCREIF NOI data by ACLI capitalization rates do not represent speci c market transactions.

7 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 289 However, Liu et al. (1990), Fisher et al. (1994), and others have argued that, because the ACLI cap rates are averages computed from speci c market transactions, they provide an indicator of variations in actual sale prices over time Economic Risk Variables and Conditioning Variables Considerable empirical evidence indicates that state variables such as unexpected in ation, industrial production growth, real short-term interest rates, yield spreads between low-grade and high-grade bonds, and yield spreads between long-term and shortterm government bonds are important in explaining asset pricing equilibriums. For practical purposes, we consider these economic risk factors, as well as others that have a precedent in the literature. Economic justi cation for our macroeconomic risk variables can be found in Chen et al. (1986), Chan et al. (1985), and Ferson and Harvey (1991), among others. We do not claim that the variables considered uniquely capture all relevant economic risks. However, these variables can jointly act as a proxy for a set of latent variables that determine asset returns. The economic risk factors that we consider in this study are MKT (the market portfolio), PREM (the bond default premium), TERM (the term structure premium), RLTBL (the real three-month Treasury bill return), GCONSUM (the real per capita growth rate of nondurable goods and services), GIP (the growth rate of industrial production), UI (unanticipated in ation), EI (expected in ation), and CHGEI (the change in expected in ation). The market portfolio is the excess return on a value-weighted portfolio of NYSE, AMEX, and NASDAQ stocks (MKT). 15 The bond default premium, (PREM) is the difference between the quarterly yield on a portfolio of bonds rated Baa by Moody's Investor Services and a portfolio of long-term U.S. government bonds. The term structure premium (TERM) is de ned as the change in the difference between the quarterly yield of a 10-year Treasury bond and a 3-month Treasury bill. The real Treasury bill (RLTBL) is the return on a three-month Treasury bill less the quarterly in ation rate as measured by CPI. The growth rate of industrial production (GIP) is de ned as the percent of quarterly change in industrial production. Since the growth rate of industrial production measures the change in industrial production lagged by at least a partial quarter, this variable is led by one quarter relative to its coincident level (see Chen et al., 1986). GCONSUM is de ned as the quarterly real per capita growth of personal consumption expenditures for nondurable goods and services. Unexpected in ation (UI) is the difference between the realized in ation rate during period t and the expected in ation rate at the beginning of the same period t. The realized in ation rate is the rst-order log relative of the CPI for all urban consumers. Unexpected in ation is calculated by the Fama and Gibbons (1984) method, which uses the Fisher equation and time-series analysis to derive UI. We also examine the residuals from an ARIMA (0, 1, 1) model of the in ation rate (CPI-U). EI and CHGEI (expected in ation

8 290 LING AND NARANJO and the change in expected in ation, respectively) also are derived from the Fisher equation and time-series analysis as in Fama and Gibbons. Drawing from recent results in the literature, we also consider several predetermined variables: the quarterly dividend yield on the value-weighted NYSE index (DIVP), the quarterly income yield on the total NCREIF index (RNYLD), and the logarithm of the lagged market value of the market portfolio (SIZE). These predetermined variables have been found to predict ex ante returns, and therefore are necessary to avoid misspeci cation of the asset pricing model. Descriptive statistics for the economic risk factors over our sample period are contained in the appendix. 4. Results After an extensive preliminary analysis of the pricing of each of the economic risk factors just discussed, we eliminated those factors that were not consistently priced across the various portfolio groups. An economic factor was considered to be priced if it was signi cant at the 10% level in at least two of the portfolio groups. In particular, we eliminated the default premium, the growth rate of industrial production, expected in ation, and the change in expected in ation. 17 In the nal analysis reported here, we retain the real per capita growth rate of consumption expenditures (GCONSUM), the real Treasury bill (RLTBL), the term structure premium (TERM), and unanticipated in ation (UI) as measured by the residuals from the ARIMA (0, 1, 1) model. The market portfolio also was retained because it can serve as a portmanteau variable that captures the effects of all unspeci ed or omitted risk factors (Sweeney and Warga, 1986). As part of the preliminary analysis, principal components analysis also was used to extract the common factors from each portfolio group; and we interpret those factors in light of the economic risk factors. The results are remarkably similar for the various portfolio groups. On average, over 90% of the variation in the portfolio groups can be explained by ve factors. 18 Similarly, in all cases, the majority of the variation is explained by the rst three factors. In terms of the economic risk factors, the consumption factor on average is most highly correlated with the rst principal component, which explains the greatest amount of variation. The real T-bill rate on average is most highly correlated with the second principal component, while the market portfolio on average is most highly correlated with the third principal component. These results are consistent with the pricing analysis presented below. In section 4.1, we present the results from estimating the xed-coef cient risk premium model (represented by equation (3)), using our nal set of risk factors and our four portfolio groups. To examine the effects of constraining the risk premia to be constant, results with time-varying risk premia and betas are presented in section 4.2.

9 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 291 Table 1. Estimates of constant factor risk premia (1978:1±1994:4; n ˆ 68 : No. of Zero- Portfolio group portfolios beta GCONSUM RLTBL TERM UI CRSP: Real estate related industries ** 0.621** (1.332) (0.136) (0.265) (0.703) (0.754) ACLI: Divisions *** 0.067* (4.914) (0.026) (0.036) (0.457) (0.269) NCREIF: a Divisions * 0.356* (4.840) (0.415) (0.185) (0.626) (0.272) NCREIF: a Property types by region * 0.572* (1.452) (0.243) (0.353) (0.326) (0.549) Note: Estimates of the zero-beta excess rate of return and factor risk premia are obtained by estimating each of the portfolio equations within each portfolio group simultaneously, using iterated nonlinear seemingly unrelated regression procedures. The number of equations in each estimation corresponds to the number of portfolios in each portfolio group. The system of equations estimated is ~r it ˆ l 0 1 b im XK b ik l k E F kt Š XK b ik ~F kt b im ~r mt ~e it kˆ1 kˆ1 where r it and b im are the ith portfolio's excess return and its sensitivity to the ``market portfolio,'' respectively. l k is the risk premium corresponding to factor k. The risk factors F 1 through F 4 are the real per capita growth rate of consumption expenditures (GCONSUM), the real Treasury bill (RLTBL), the term structure premium (TERM), and unanticipated in ation (UI), respectively. We also consider several predetermined variables: the quarterly dividend yield on the value-weighted NYSE index (DIVP), the quarterly income yield on the total NCREIF index (RNYLD), and the logarithm of the lagged market value of the market portfolio (SIZE). *, **, *** are 10, 5, and 1% signi cance levels, heteroscedastic-consistent (robust-white) standard errors are in parentheses. The NCREIF return series begin in 1979:1, because four quarters are lost in the unsmoothing process Constant Risk Premia Table 1 summarizes the results of separately estimating the system of equation (3) for each of the four portfolio groups. The rst column contains the portfolio group used in the estimation, while the second column contains the number of portfolios within each portfolio group. The remaining columns contain the risk premia estimates and their heteroscedastic-consistent standard errors (robust-white) obtained by simultaneously estimating all of the portfolios within each of the portfolio groups using the NLSUR technique. 19 The risk premia for each factor are constrained to be the same within each portfolio group, while the betas are allowed to vary across each portfolio within the group; this allows us to obtain risk premia estimates for each portfolio group. The risk premia estimates in table 1, as well as the estimates of the underlying betas and conditioning variable coef cients are encouraging. The risk premia for GCONSUM and RLTBL are signi cant at conventional levels and robust across the four portfolio groups. The zero-beta estimates are all insigni cantly different from 0, which is consistent with the riskless rate version of the model. The risk premia estimates for both TERM and UI are

10 292 LING AND NARANJO insigni cant for each portfolio group. However, as is shown in the following section with the time-varying estimates, the premia on TERM and UI become signi cant in subperiod tests. The estimates of the risk premia reveal the economic signi cance of these risk factors. For instance, the estimate of the risk premium for GCONSUM in the CRSP row suggests that an asset whose GCONSUM beta is 1.00, earns a premium of 0.298% per quarter (1.19%/year). The standard error suggests that this risk premium is between 0.104%/year and 2.28%/year with 95% con dence. The premia estimates for each factor also are relatively close to each other across the four portfolio groups. In fact, the risk premia estimates for each factor are not different from one another at the 95% con dence level. This result is encouraging because it demonstrates that the risk premia estimates using exchange traded real estate (the CRSP portfolio group) are consistent with the results obtained using (unsmoothed) appraisal-based NCREIF returns Time-Varying Risk Premia This section presents the two-pass results that allow for time-variation in the risk premia. In the rst pass, the factor betas for all the portfolios within each of the four groups are computed using ve-year rolling regressions. This produces a quarterly time series of betas for each factor of each portfolio. In the second pass, the factor risk premia for quarter t are estimated with a crosssectional regression that has a transformation of the portfolio returns on the left-hand side and the estimates of the betas from the rst pass on the right-hand side for that quarter. 20 The estimated cross-sectional regression is a transformation of equation (4): r* i ˆ a 0 l 0 1 ^b im XK kˆ1 l* k^bik ~Z i 5 i ˆ 1;...;I; 8t where r* i ~r i ^b im ~r mt P K kˆ1 ^b ik ~F kt ; a 0 is a regression constant; and l* k l k E F kt. The results of these separate cross-sectional pricing regressions can be linked to create a time series of risk premia for each factor, for each of the portfolio groups. Table 2 provides overall statistics for the factor risk premia for each of the four portfolio groups. The standard errors reported in the table are averages of the standard errors from the 48 quarterly cross-sectional regressions. 21 The proportion of quarters in which the premia are signi cant varies between 19 and 60%, an impressive performance, considering that there are few degrees of freedom in these cross-sectional regressions. 22 All the risk premia have roughly the same proportions of signi cance, in contrast to the xed-coef cient case, where the coef cients on TERM and UI were never signi cant. The increase in the number of signi cant risk premia is consistent with evidence in the

11 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 293 Table 2. Summary statistics for the quarterly varying risk premia (1983:1±1994:4; n ˆ 48). No. of Zero- Portfolio group portfolios beta GCONSUM RLTBL TERM UI CRSP: Real estate related industries Mean a Standard error (1.161) (4.044) (2.299) (0.313) (0.273) % Signi cant 21.8% 37.5% 27.1% 43.8% 37.5% ACLI: Divisions Mean Standard error (0.975) (1.219) (1.662) (0.870) (0.625) % Signi cant 39.6% 50.0% 47.9% 60.4% 54.2% NCREIF: Divisions Mean Standard error (0.948) (0.887) (0.818) (1.145) (0.743) % Signi cant 41.7% 50.0% 58.3% 47.9% 50.0% NCREIF: Property types by region Mean Standard error (0.782) (0.616) (0.563) (0.806) (0.571) % Signi cant 14.6% 29.2% 33.3% 18.8% 18.8% Note: The sample starts in 1983, because the rst ve years are used up in the estimation of the initial betas. a The means and standard errors reported in this table are averages of the risk premia and their heteroscedastic-consistent standard errors from the quarterly cross-sectional regressions. % signi cant reports the proportion of quarters that the risk premia were statistically signi cant at the 5% level. literature that the xed-coef cient model may be overly restrictive (Ferson and Harvey, 1991). On average, the ACLI and NCREIF Division portfolios have the most signi cant risk premia estimates and the NCREIF Property Type by Region portfolio estimates are the least signi cant. The consumption premia are signi cant most often (on average, 41.68%), while the excess zero-beta rates are the least signi cant (on average, 29.43%). Finally, the average values of the premia estimates from the time-varying model reported in table 2 are not statistically different from the xed premia estimates shown in table 1. The consistent signi cance of GCONSUM across model speci cations and portfolio groups is noteworthy, given the mixed evidence on the role of consumption in ex ante common stock returns. Table 3 provides summary statistics for the portfolio betas generated with the ve-year rolling regressions. 23 This information is important, because the quality of the risk premia estimates in table 2 depends, in part, on the precision with which the betas are estimated. If the betas are estimated poorly in the rst pass, the errors-in-variables problem associated with the two-pass estimation procedure is exacerbated, and the premia estimates are less reliable. Table 3 shows the proportion of betas that are signi cant at the 5% level. On average, 75.9% of the beta estimates are signi cant and more than 82% of the consumption betas are signi cant. Equally important is that the factor betas are uniformly signi cant across the portfolio groups. Overall, table 3 suggests that the pricing tests

12 294 LING AND NARANJO Table 3. Summary statistics for the betas of the quarterly-varying risk premia (1983:1±1994:4; n ˆ 48). No. of Portfolio group portfolios GCONSUM RLTBL TERM UI CRSP: Real estate related industries Mean a Standard deviation (0.525) (4.563) (1.822) (3.957) % Signi cant 72.9% 83.3% 47.9% 58.3% ACLI: Divisions Mean Standard deviation (2.973) (3.967) (2.586) (5.126) % Signi cant 83.3% 39.6% 79.2% 72.9% NCREIF: Divisions Mean Standard deviation (0.692) (1.765) (0.810) (1.401) % Signi cant 77.1% 66.7% 77.1% 75.0% NCREIF: Property types by region Mean Standard deviation (0.541) (1.322) (0.730) (1.112) % Signi cant 97.9% 91.7% 93.8% 97.9% Note: The sample starts in 1983, because the rst ve years are used up in the estimation of the initial betas. a The means and standard deviations reported in this table are from the averages of the factor betas from each portfolio. The betas are estimated using rolling, ve-year time-series regressions. % Signi cant reports the proportion of quarters in which at least one of the beta estimates from at least one of the portfolios was statistically signi cant at the 5% level. reported in table 2 are unlikely to be seriously affected by a lack of precision in the beta estimates. Table 4 summarizes some relevant time series statistics for the factor premia. These statistics have several interesting features. The largest average standard errors for GCONSUM and RLTBL come from the CRSP portfolio group; whereas for TERM and UI, the largest average standard errors come from the NCREIF Division portfolio group. In all cases, the premia estimates exhibit a great deal of volatility. The w 2 tests of the equality of the variances of the premia across the portfolio groups reject that they are equal in several cases. The strongest rejection occurs for GCONSUM. However, the average values of the premia estimates across each of the portfolio groups are not statistically different from one another. The estimated risk premia also are not highly autocorrelated and very few are statistically different from Conclusion Considerable empirical evidence indicates that state variables such as the slope of the term structure, expected and unexpected in ation, industrial production, and the spread between high-grade and low-grade bonds act as a proxy for economic risk factors that are rewarded, ex ante, in the stock market. Although the comovements of real estate and other

13 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 295 Table 4. Statistical properties of the quarterly-varying factor risk premia. Return series CRSP NCREIF ACLI NCREIF DIV NCREIF PT/R GCONSUM Mean Max Min Sample std Average std % Signi cant Autocorrelations Lag Lag Lag RLTBL Mean Max Min Sample std Average std % Signi cant Autocorrelations Lag Lag Lag TERM Mean Max Min Sample std Average std % Signi cant Autocorrelations Lag Lag Lag UI Mean Max Min Sample std Average std % Signi cant Autocorrelations Lag Lag Lag Note: Sample std is the standard deviation of the time series of the premia. Average std is the average standard deviation of the estimates (reported in Table 2 and repeated here for convenience).

14 296 LING AND NARANJO asset prices suggest that these same systematic risk factors are likely to be priced in real estate markets, no study has formally addressed this issue. The purpose of this study is to identify the fundamental macroeconomic drivers or ``state variables'' that systematically affect real estate returns. To overcome some of the econometric problems encountered in previous research, we use nonlinear multivariate regression techniques to jointly estimate the risk factor sensitivities and return premia. In response to evidence in the literature that the xed-coef cient model may be overly restrictive, because risk sensitivities and risk premia are constrained to be time invariant, we also use the Fama±Macbeth (1973) two-pass methodology to estimate complete timevarying risk sensitivities and premia. To assess the robustness of our results with respect to our measure of real estate returns, we created four separate real estate portfolio groups. In particular, we use (1) stock market return data on REITs and other real estate related industries from the Center for Research in Security Prices, (2) unsmoothed appraisal-based returns by geographical division from the National Council of Real Estate Investment Fiduciaries, (3) unsmoothed NCREIF return data disaggregated by both region and property type, and (4) a combination of regional NCREIF data and regional capitalization rate data from the American Council of Life Insurance Companies. Estimates of the xed-coef cient model show that the growth rate in real per capita consumption and the real T-bill rate are consistently priced across our four real estate portfolio groups. The term structure of interest rates and unexpected in ation do not carry statistically signi cant risk premiums in the xed-coef cient model but are signi cant when sensitivities and risk premia are allowed to vary over time. The nding of a consistently signi cant risk premium on consumption differs from previous studies of stock and bond returns, which have found mixed evidence on the role of consumption in explaining ex ante returns. However, this result is consistent with Geltner's (1989) nding that real estate returns are exposed to consumption risk. The nding of a signi cant premium on consumption also has important rami cations for the vast literature that has examined the (risk-adjusted) performance of real estate, for it suggests that prior ndings of signi cant abnormal returns (either positive or negative) that have ignored consumption are potentially biased by an omitted variables problem. The results also have important implications for dynamic asset allocation strategies that involve the predictability of real estate returns using economic data. Appendix A.1. Estimating Risk Premia Consider the returns generating equation for a standard MFAPM with three factors, the last of which is the Market Portfolio: r it ˆ E r it b im r m E r m Š b i1 F 1 E F 1 Š b i2 F 2 E F 2 Š e it 6

15 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 297 The expected returns are given by E r it ˆl 0 b im l m b i1 l 1 b i2 l 2 7 Since equations (6) and (7) price all assets, they must price the market portfolio as well. This gives E r mt ˆl 0 l m b i1 l 1 b i2 l 2 8 It is clear from equation (8) that l m ˆ E r mt l 0 ; and 9 b mk 0; 8k 10 Substituting equation (9) into equation (7), we get E r it ˆl 0 1 b im b im E r m b i1 l 1 b i2 l 2 11 In its estimated form, the returns equation for the ith asset now becomes r it ˆ l 0 1 b im b i1 l 1 E F 1 Š b i2 l 2 E F 2 Š b im r m b i1 F 1 b i2 F 2 e it 12 It is clear from this proof that the market risk premium drops out of the equation. This is true whether or not we know the population mean. A.2. Data Sources and De nitions The rst part of this section describes the various real estate return series used as the dependent variable. The remainder of the section provides a detailed description of all the independent variables and their construction. A.2.1. Dependent Variables Three sources of data are used to construct real estate portfolio returns: (1) stock market return data on REITs and other real estate related industries from the Center for Research in Security Prices, (2) appraisal-based returns from the National Council of Real Estate Investment Fiduciaries, and (3) regional capitalization rate data from the American Council of Life Insurance Companies. A Real Estate Related Industries Returns. Real estate related stock data are gathered from the CRSP database compiled at the University of Chicago. The range for the data selected are from January 1978 through December These dates correspond to

16 298 LING AND NARANJO Table 5. CRSP real estate related industries portfolios. Portfolio number Four-digit SIC codes Industry ±1549 Building Construction ±6515 and 6552±6553 Real Estate Operators ±6799 REITs Hotels and Motels , 6519, 6531, 6541, and 7340±7349 Real Estate Services the beginning date for NCREIF and ACLI data, while the end-date corresponds to the latest available data in the CRSP les at the time the data were collected. From the individual equities trading on the NYSE, AMEX, and NASDAQ, we create ve value-weighted real estate related industries portfolios on the basis of each rm's four-digit standard industrial classi cation. Table 5 presents the four-digit SIC mappings into each of the real estate related industries portfolios. The SIC codes and industry descriptions can be found in the Standard Industrial Classi cation Manual (1987) compiled by the U.S. government Of ce of Management and Budget. The daily returns from the CRSP tapes were compounded into quarterly returns, and these quarterly returns were used to form the ve value-weighted portfolios. Quarterly returns are used because the NCREIF and ACLI data are available only on a quarterly basis. Each portfolio return is calculated as the value-weighted average of the returns for the individual stocks in that portfolio: R t ˆ X N w it r it iˆ1 X N w it iˆ1 where R t is the return on a particular portfolio in quarter t, r it is the return on rm i in quarter t, and w it is the weight given to a rm's return in time period t. Each quarter, the relative market value is used to weight the individual security returns in a given portfolio. The market value (w it ) of a particular security is de ned as the product of its price ( p t 1 ) and number of shares outstanding (s t 1 ). The total market value ( P w it ) of a particular portfolio in a given quarter is de ned as the sum of the individual security market values. Excess portfolio returns are constructed by subtracting the known beginning of quarter returns on three month U.S. Treasury bills from the realized portfolio returns. The nominal three-month Treasury bill rates that we use were obtained from the CRSP risk-free le. Because the yields in this le are annualized rates, a geometric average is used to convert them to quarterly rates.

17 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 299 A NCREIF Returns. Appraisal-based returns from the NCREIF property indices, formerly known as the Russell-NCREIF indices, are used to create two additional portfolio groups. In particular, we use the NCREIF Division subindices and the Property Type by Region subindices to create 8 unsmoothed Division subindices and 20 unsmoothed Property Type by Region subindices. The NCREIF Region (four categories) and Property Type indices ( ve categories) cannot be used because, with the ve-factor model, we need greater than ve observations (portfolios) per quarter to impose the cross-equation constraints. We are able to avoid this problem with the ve CRSP Real Estate related industries portfolios because we can use monthly data, giving 15 observations per quarter. To unsmooth the NCREIF Division and Property Type by Region subindices, we use the simulation approach employed by Geltner (1989, 1991), Ross and Zisler (1991), and Fisher et al. (1994). Excess portfolio returns are constructed by subtracting the known beginning of quarter returns on three-month U.S. Treasury bills from the realized portfolio returns. The nominal three-month Treasury bill rates that we use were obtained from the CRSP risk-free le. Since the yields in this le are annualized rates, we use a geometric average to convert them to quarterly rates. A ACLI Transaction-Based Returns. We also use NCREIF Division NOI data with comparable ACLI data on capitalization rates to create eight transactions-based returns portfolios. The NOI value index is created by multiplying the NCREIF Division income return indices by their corresponding total value levels from the previous period. The resulting NOI series is then normalized to 100 for the rst quarter of The ACLI imputed price index is then constructed by dividing the eight NCREIF Division quarterly NOIs by comparable division ACLI transactions-based capitalization rates from the previous period. The previous period is used because ACLI cap rates are de ned as the NOI for properties in the upcoming year divided by the current price. Eight transactionsbased return series are then created by dividing the NCREIF income return by the corresponding ACLI capitalization rate. Total returns for each NCREIF division are then computed by summing the NCREIF income return and the price appreciation calculated from the imputed price index. Excess portfolio returns are constructed by subtracting the known beginning of quarter returns on three month U.S. Treasury bills from the realized portfolio returns. A.2.2. Independent Variables: Economic Risk Factors This section provides a description of all explanatory variables and their construction. A Market Portfolio: MKT. The proxy used for the market portfolio is a CRSP value-weighted portfolio of NYSE, AMEX, and NASDAQ stocks. This market proxy also is used by Fama and French (1992). We create this market proxy by combining the CRSP value-weighted NYSE/ANIEX portfolio returns (including all distributions) with the CRSP value-weighted NASDAQ portfolio returns (including all distributions). The excess

18 300 LING AND NARANJO market portfolio returns are generated by subtracting the returns on three-month U.S. Treasury bills from the quarterly portfolio returns. A Corporate Default Premium: PREM. We use the end of quarter difference in the annualized yield between a portfolio of corporate bonds rated Baa by Moody's Investor Services and a portfolio of long-term U.S. Treasury bonds to capture changes in corporate default risk. Thus, the corporate default premium, PREM, is equal to PREM ˆ Baa corporate bond portfolio long-term Treasury bond portfolio The Baa corporate bond portfolio and the long-term Treasury bond portfolio were obtained from the Citibase database. A Term Structure Premium: TERM. The end of quarter change in the slope of the yield curve is used to capture the term structure risk. The slope of the yield curve is measured as the difference between the annualized yield of a 10-year Treasury bond and a 3-month Treasury bill or TERM ˆ D 10-year Treasury bond 3-month Treasury bill The 10-year Treasury bond and 3-month Treasury bill were obtained from the Citibase database. A Real Treasury Bill: RLTBL. The real Treasury bill rate (RLTBL) is measured as the end of quarter difference between the annualized yield on a three-month Treasury bill and the general in ation rate as measured by the consumer price index. Thus, RLTBL ˆ Treasury bill yield inflation rate The Treasury bill data are obtained from the CRSP bond les and the CPI data are obtained from the Citibase database. A Real per Capita Consumption Growth: GCONSUM. We use the end of quarter consumer expenditures for nondurable goods and services to calculate the consumption variable. In particular, the real per capita growth of consumption (GCONSUM) is constructed as the ratio of period t consumption divided by period t 1 consumption minus 1 or GCONSUM ˆ CONSUM t CONSUM t 1 1 The consumption series is seasonally adjusted and de ated by its own price de ator. We also separately examined the real per capita growth of consumption expenditures for

19 ECONOMIC RISK FACTORS AND COMMERCIAL REAL ESTATE RETURNS 301 durable goods, nondurable goods, and services. The consumption, price de ator, and population series were obtained from the Citibase database. A Industrial Production Growth: GIP. production (GIP) is constructed as The end of quarter growth rate of industrial GIP ˆ IP t IP t 1 1 Because GIP measures the change in industrial production lagged by at least a partial quarter, we lead this variable by one quarter (see Chen et al., 1986). The industrial production index was obtained from the Citibase database. A Unexpected In ation and Change in Expected In ation: UI and CEI. We use the Fama and Gibbons (1984) methodology to derive the in ation variables. The unexpected in ation rate (UI) is de ned as the difference between the realized (ex post) in ation rate (as measured by the consumer price index) and the expected in ation rate. That is, UI t ˆ p t E p t jt 1 where p t ˆ log CPI t log CPI t 1 and E p t jt 1 is equal to the expected in ation rate at the beginning of period t. Fama and Gibbons (1984) use the Fisher equation and time-series analysis to estimate real returns for Treasury bills. From the Fisher equation, the difference between the Treasury bill rate and the tted expected real return provides a measure of the expected in ation rate. The difference between the expected in ation rate and the realized in ation rate is the unexpected in ation rate. Using Box±Jenkins analysis, the realized real return can be represented as an integrated rst-order MA process: where r t t 1 r t 1 t 2 ˆ i t 1 p t i t 2 p t 1 ˆu t yu t 1 rt 1 t ˆ realized real returns from time t 1 to time t, i t 1 ˆ nominal rate from time t 1 to time t, p t ˆ realized in ation rate from time t 1 to time t, u t ˆ forecast errors for the MA(1) process, y ˆ MA parameter The estimates are