Excess returns of industrial stocks and the real estate factor.

He, Ling T.

Ling T. He (*)

In order to identify the major risk factors in pricing industrial stocks, this study estimates different models based on six explanatory factors: the overall stock market, size, book-to-market equity ratio, the term structure, default risk, and the unsecuritized real estate market. The results of this study indicate that the real estate factor plays an important role in explaining excess returns on industrial stocks, along with other risk factors. The coefficient of the stock market factor declines when the real estate market factor is included in the model. Therefore, the large coefficient in the single-factor (stock market) model probably results from covariation between the overall stock market factor and the real estate factor. Results for subperiods indicate that the effects of the real estate factor are quite stable and second only to the overall stock market factor.

1. Introduction

For more than three decades, numerous studies have been devoted to capital asset pricing issues. Identifying key factors influencing returns on capital assets remains the major focus of the studies. According to the first important asset pricing theory, the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), there is a positive linear relationship between expected stock returns and market betas. This single-factor model is theoretically challenged by the arbitrage pricing theory (APT) developed by Ross (1976). The APT provides a theoretical framework to identify more macro factors that have significant explanatory power for stock returns (Roll and Ross 1980; Chen 1983; Bower, Bower, and Logue 1984; and Chen, Roll, and Ross 1986). In order to be included in a multifactor model, a factor must represent a source of nondiversifiable or systematic risk. In addition to theoretical challenges, the evidence of many empirical studies casts doubts on the adequacy of the long-existing CAPM. For examp le, the findings of Fama and French (1996) suggest that [beta]s alone cannot explain expected returns on common stocks. Meantime, other macro factors related to the bond market, such as unanticipated changes in the term structure (Chen, Roll, and Ross 1986), are used to explain stock returns.

In recent years, more risk factors have been suggested in the literature. For example, in their time-series study about common risk factors in the returns on common stocks, Fama and French (1993) argue that there are three stock market factors, an overall market factor, a size factor (stock price times number of shares), and a book-to-market equity factor, that have a significant impact on stock returns. In addition, two bond market factors, the term structure and default risk factors, can capture common variation in stock and bond returns (Fama and French 1993).

Similar to Fama and French's (1993) multifactor models, the present study uses all three stock market factors (an overall stock market factor, a size factor, and a book-to-market equity factor), two bond market factors related to maturity and default risks, and a real estate market factor. The reason for introducing a new risk factor, real estate market factor, although not so obvious, is engendered by the theoretical spirit of the APT. Real estate is a major asset class, and as almost all firms have operating expenses under this category, it does not matter if the properties are acquired or rented. According to Zeckhauser and Silverman (1983), a significant portion of corporate assets, on average as high as 25%, is real estate related. Changes in real estate market value, therefore, potentially have a direct impact on the value of corporate assets and operating expenditures. If this impact is significant, as are other systematic risk factors, the real estate market factor must play an important role in stock pricing. In addition, the real estate market risk is a macro factor. Therefore, results about this factor do not have any interpretation problems that are associated with firm-specific variables.

In order to identify significant factors in explaining returns for industrial stocks, this study estimates various models based on the following six risk factors: an overall stock market factor, a size factor, a book-to-market equity factor, a term structure factor, a default risk factor, and an unsecuritized real estate market factor. Results of this study provide some empirical evidence about the significance of the six risk factors on excess returns for industrial stocks. In addition, this study also investigates how the inclusion of additional risk factors, for example, the inclusion of the bond market factors or the real estate market factor in the single market-factor model, increases the explanatory power of the model.

The remainder of this study is organized as follows. Section 2 describes the data and methodology; section 3 presents the empirical results; and section 4 contains the conclusions.

2. Data and Methodology

This study uses time series data that covers the period of January 1963-December 1997. There is no specific reason, other than the availability of data, for the selected sample period. The data set includes the following monthly return indices:

NAN = the monthly returns on the NYSE/ASE/NASDAQ value-weighted index (CRSP Stock Files).

SMB (small minus big) the monthly returns on the mimicking portfolio for the common size factor in stock returns. This is the difference between the simple averages of the percentage returns on the three small-stock and the three big-stock portfolios with similar average book-to-market ratios. See Fama and French (1993) for a detailed discussion of the construction of the series.

HML (high minus low) = the monthly returns on the mimicking portfolio for the common book-to-market equity factor in stock returns. This is the difference between the simple averages of the percentage returns on the two high and two low book-to-market equity portfolios with similar average size. See Fama and French (1993) for a detailed discussion of the construction of the series.

LONG = the monthly returns on long-term U.S. government bonds (Stocks, Bonds, Bills, and Inflation 1998 Yearbook, Ibbotson Associates).

CORP = the monthly returns on long-term corporate bonds (Stocks, Bonds, Bills, and Inflation 1998 Yearbook, Ibbotson Associates).

SHORT = the monthly returns on three-month treasury bills (Economic Database, St. Louis Federal Reserve Bank).

RLES = the monthly percentage changes in the median sales price index of new houses sold. The price reflects changing proportions of different sizes, locations, etc., as well as changes in the prices of houses with identical characteristics. The sales price includes the land (U.S. Bureau of the Census).

SPIND = the monthly returns on the S&P Industrial Stock Value-Weighted Index. The index consists of 86 industrial groups or 376 companies as of December 1997. The largest company's market value is $26 billion, the smallest company's market value is $370 million, and the mean market value is $15 billion.

In order to examine whether the six risk factors are driving forces of industrial stock returns, this study extends Fama and French's (1993) five-factor excess stock return model as follows:

[R.sub.J] = [[beta].sub.J] + [[beta].sub.M]MKT + [[beta].sub.S]SMB + [[beta].sub.H]HML + [[beta].sub.T]TERM + [[beta].sub.D]DEF + [[beta].sub.R]HPRICE + [[member of].sub.J], (1)

where [R.sub.J] SPIND - SHORT, MKT = NAN - SHORT, TERM = LONG - SHORT, DEF = LONG - CORP. HPRICE = RLES - SHORT, and [[member of].sub.J] = an error term.

One possible concern is the proxy for the real estate market factor in Equation 1. The stock returns on real estate investment trusts (REITs) are widely used as the proxy for real estate in the literature. For example, in their study about the sensitivity of bank stock returns to real estate, He, Myer, and Webb (1996) used stock returns on all REITs, equity REITs, and mortgage REITs, respectively, as the real estate proxy. However, REITs are real estate-backed stocks, and returns to REITs are essentially returns on a particular group of stocks with investments concentrated on real estate or real estate-related assets. In order to examine the effect of real estate on stock pricing, a proxy for the unsecuritized real estate market should be used. In this study, the real estate proxy is the median sales price index for new houses (residential properties) sold. The ideal proxy for the real estate market would be the sales price index for the overall real estate market. Unfortunately, such information is not avail able. Giliberto (1990) used the Russell-NCREIF (National Council of Real Estate Investment Fiduciaries) property index in this regard. But this index does not reflect changes in the overall real estate market. The properties included in the index are primarily commercial. In addition, the index, started in 1978, is an appraisal-based return index and contains only quarterly information. Myer and Webb (1993) find that returns of equity REITs Granger cause unsecuritized and appraisal-based real estate returns (the Russell-NCREIF property indices). As the purpose of this study is to examine the impact of unsecuritized real estate on stock returns, therefore, an appraisal-based real estate return index is obviously not an ideal proxy for real estate. Gyourko and Keim (1992) report that equity RUT returns are contemporaneously correlated with the quarterly home appreciation rate from the existing homes price series of the National Association of Realtors. Therefore, the use of the monthly median sales price index for new houses sold, a transactions-based return index, although less than ideal, should not create any serious problems. Price changes in residential and nonresidential real estate markets cannot deviate very far from each other despite the fact that there are some different demand and supply functions for residential and nonresidential properties. The major cost components of these two types of properties are the same, such as land cost, construction material prices, labor cost, etc. Therefore, overall, it seems reasonable to assume that price changes in both residential and nonresidential real estate markets are in the same direction and close in magnitude. Nevertheless, the Russell-NCREIF property total return index is also used in this study.

In order to examine if the inclusion of additional risk factors significantly enhances the explanatory power of the model, the F-statistic for testing the regression relationship (Kmenta 1986) is calculated as

([SSR.sub.Q]/SST) - ([SSR.sub.K]/SST)/1 - ([SSR.sub.Q]/SST)[n - Q/Q - K] = [F.sub.(Q-K,n-Q)], (2)

where SSR = regression sum of squares, SST = total sum of squares, n = number of observations, K = number of explanatory variables plus a constant term, Q = number of explanatory variables plus a constant term, and Q > K.

3. Empirical Results

Description of Variables

The descriptive statistics for the seven variables during February 1963-December 1997 are summarized in Table 1. The size of monthly average excess returns for the overall stock market factor (MKT) is the highest, 0.70%. The default risk factor (DEF) has the lowest mean, 0.03%. The magnitude of monthly average excess returns for the real estate market factor (HPRICE) is approximately 0.27%. Three measures are used to examine the instabilities of the six risk factors. The real estate market factor has the largest range, 74.36%, while the default risk factor (DEF) has the smallest, 9.37%. The standard deviation for DEE, again, is the smallest, 1.19%, while the overall stock market factor has the greatest standard deviation, 8.26%. However, the coefficient of variation indicates that the default risk factor is the most unstable risk factor and the book-to-market equity factor is the least unstable. The real estate market factor has the second highest coefficient of variation.

Excess returns on industrial stocks (IND) have a very high correlation with MKT (0.92) and lower correlations with TERM (0.37) and HPRICE (0.73). Relationships between these market factors are also quite close. The correlation between HPRICE and MKT is the highest (0.69), between TERM and MKT medium (0.47), and between TERM and HPRJCE the lowest (0.30). These results clearly indicate that the three factors may be relevant in explaining variation in the excess returns for industrial stocks (Table 1). The correlation between IND and SMB is 0.25. SMB has a similar correlation with MKT (0.21) and much lower correlations with HPRICE (0.07). The correlation between IND and HML, -0.03, and between IND and DEE is as small as -0.02. Both HML and DEF have very low correlations with all other factors.

Various diagnostic tests are also performed to examine if any statistical problems are contained in the data. The following are the major test results. The Dickey-Fuller (Dickey and Fuller 1981) unit root test indicates that the data do not have any significant nonstationary problems. Results of principal components and factor analysis do not suggest any significant multicollinearity difficulties in the five risk factors. For example, for the period of 1963-1997, the highest condition index is only 6.05. However, the data do have serious first-order autocorrelation problems. The Lagrange multiplier statistic is about 5.08% for the five-factor model and the Durbin-Watson statistic is 2.48. In addition, results of the Breusch-Pagan-Godfrey test (Godfrey 1978; Breusch and Pagan 1979), the ARCH test (Engle 1982), and the Glejser test (Glejser 1969) suggest serious heteroscedasticity problems. Therefore, this study uses the heteroscedasticity-consistent covariance matrix and autocorrelation-consistent matrix with order = 1 by the Newey-West correction method (Newey and West 1987) in the ordinary least squares (OLS) estimation for all models.

Results Based on Monthly Data

In order to examine the impact of including additional independent variables into a regression model on its explanatory power, this study estimates the following eight different models containing different independent variables: (1) the overall stock market factor; (2) the overall stock market and two bond market factors; (3) the overall stock market and real estate market factors; (4) the overall stock market, bond market, and real estate market factors; (5) the overall stock market, size, and book-to-market equity factors; (6) the overall stock market, size, book-to-market, and bond market factors; (7) the overall stock market, size, book-to-market, and real estate market factors; and (8) the overall stock market, size, book-to-market, bond market, and real estate market factors. In addition, a single real estate factor model is estimated in order to examine the pure impact of the real estate market factor on industrial stock returns. Table 2 presents the OLS regression results with corrections for autocorr elation and heteroscedasticity for industrial stocks.

The single-factor (stock market) excess return model (2.1) is essentially the capital asset pricing model (CAPM). It has an [R.sup.2] as high as 84.6%. The coefficient of MKT is large (0.84), with a very high t-value (37.61). This indicates that the sensitivity of excess returns on industrial stocks to the overall stock market factor is positive and very significant. Changes in MKT can explain most of the variation in excess returns on industrial stocks. The constant term is small (-0.19).

Nevertheless, when two bond market factors, TERM and DEF, are added to the single-factor model, its explanatory power increases significantly (the [R.sup.2] for model 2.2 is 85%). This addition has an F-statistic of 5.54. The coefficients of MKT and TERM are both significant at the 1% level, although with different signs. The coefficient of DEF is only marginally significant. The less important explanatory role played by DEF is also indicated by Fama and French's results (1993). The overall results of model 2.2 suggest that excess returns on industrial stocks are very sensitive to changes in both MKT and TERM and that model 2.2 is better specified than model 2.1.

The [R.sup.2] increases to 86.1% when the real estate market factor, HPRICE, is added to model 2.1. The F-statistic for the addition is 44.89. Both factors have highly significant coefficients. The constant term in model 2.3 is insignificantly different from zero. The stock pricing model improves even further when MKT, TERM, DEF, and HPRICE are all included in the model. First, the [R.sup.2] for the four-index model further increases to 86.4% (model 2.4) from 85% (model 2.2) and 86.1% (model 2.3). Although the magnitude of increase is very small, it represents a significant (at the 1% level) increase in the explanatory power of the model. The F-statistics are 42.72 and 4.73, respectively. Second, the constant term remains small and insignificant. Third, coefficients of MKT, HPRICE, and TERM are significant at the 1% level. This means that these three risk factors have important effects on the size of excess returns on industrial stocks and play crucial roles in explaining variations in excess returns for indu strial stocks. More importantly, the results unambiguously indicate that the real estate market factor captures shared variation in excess returns of industrial stocks, related to the real estate market, that is missed by the overall stock market and bond market factors. Therefore, the real estate market factor is relevant and important in explaining excess returns for industrial stocks.

Does the real estate market factor truly represent a systematic risk or is it simply a proxy for the size and book-to-market equity factors? Results of models 2.5-2.8 provide some useful clues to the question. Model 2.5 includes the three factors MKT, SMB, and HML. All three coefficients are significant at the 1% level. The [R.sup.2] (85.3%) is significantly higher (with an F-statistic of 9.90) than model 2.1. With the inclusion of TERM and DEF, the explanatory power of model 2.6 further increases to 85.7%. The F-statistic for the increment is 5.79.

In model 2.7, TERM and DEF are replaced with HPRICE. All four coefficients are significant. The result clearly indicates that the real estate market factor indeed represents a systematic risk that cannot be measured by the overall stock market, the size, and the book-to-market equity factors. The [R.sup.2] for the model has a significant increase (at the 1% level) compared with the [R.sup.2] for model 2.5.

The addition of HPRICE to the five-factor model (2.6) substantially, with an F-statistic of 37.83, increases the explanatory power of the model to 86.9% (model 2.8). The coefficients of HPRICE and their significance are very stable in different models (2.3, 2.4, 2.7, and 2.8). On the other hand, the inclusion of TERM and DEF in model 2.7 can only marginally enhance the model's explanatory power. The F-statistic for the [R.sup.2] increase is 3.15. Although the bond market factors play a less important role than the stock and real estate market factors in explaining stock returns, TERM is apparently more important than DEF in explaining returns for industrial stocks. This result is in line with Fama and French's (1993) results. In model 2.8, the coefficient of MKT is 0.76 (with a t-value of 20.21) compared with 0.84 (with a t-value of 37.61) in the single-factor model (2.1). This suggests that the highly powerful explanatory effect of MKT in the single-factor model may largely result from covariation between th e overall stock market factor and other factors. These results indicate that the stock market, real estate market, book-to-market, size, and maturity factors capture the strong variation in excess returns for industrial stocks.

Does the real estate market factor still have a significant impact on returns of industrial stocks when the encompassing stock market factor along with other factors, is omitted? The answer provided by model 2.9 is positive. The coefficient of HPRICE increases to 0.74 with a t-value of 8.77; the constant term is small and insignificantly different from zero.

Results Based on Quarterly Data

HPRICE is essentially an index for residential real estate. In order to examine effects of commercial real estate on industrial stock returns, this study also uses the Russell-NCREIF property total return index (NCR) as the proxy for real estate. However, it is necessary to point out some facts that are associated with the index. First, it is a quarterly index. In order to use NCR, all other monthly indices, except for HPRICE, are compounded into quarterly series. Compared with a monthly index, less information is contained in a quarterly index, given the same sample period. Therefore, results based on quarterly data may differ from that from monthly data. Second, NCR is an appraisal-based return index, which may not fully reflect changes in market value for commercial real estate. Finally, since NCR started in 1978, fewer observations can be used.

Results in Table 3 clearly suggest that NCR plays an important role in explaining returns of industrial stocks. When NCR is used as the only explanatory variable, it has a very significant coefficient, with a t-value of 17.10 (model 3.9). If NCR is added to the single-market factor model (3.1), it can increase the explanatory power of the model greatly. The [R.sup.2] rises from 97.74% (model 3.1) to 97.91% (model 3.3). The F-statistic for the change is 6.26 and significant at the 5% level. Even when NCR is included in model 3.2 with the overall market and two bond market factors, the [R.sup.2] obtains an important increase (with an F-statistic of 6.24), from 97.89% (model 3.2) to 98.05% (model 3.4). However, when NCR is added to models containing SMB and HML, [R.sup.2]'s get only minimal increases. For example, the [R.sup.2] of 97.87% for model 3.5 to 97.89% for model 3.7 and 98.05% (model 3.6) to 98.06% (model 3.8). In fact, the addition of NCR to models 3.5 and 3.6 reduces the size and significance of coeff icients of HML. This result may reflect that the economic stress factor (HML) and the commercial real estate index (NCR) have similar responses (covariation) to economic changes.

The quarterly data used in this study reduce the explanatory power of TERM, DEF, SMB, and HML greatly. Both bond market factors, TERM and DEF, do not have any significant coefficients in various models (3.2, 3.4, 3.6, and 3.8). SMB becomes an unimportant explanatory variable also. Coefficients of HML in models 3.5 and 3.6 are much smaller than that in models 2.5 and 2.6, although they are significant at the 5% level.

MKT and NCR are only two variables that have coefficients significant at the 1% level. Coefficients for MKT are always highly significant and are therefore more stable than NCR.

Monthly Results in Subperiods

Results in Tables 4 through 6 indicate stability of coefficients over subperiods (five-year intervals) from 1963 to 1997. The following four real estate-related models with different independent variables are estimated in each of seven subperiods: (1) the real estate market factor; (2) the overall stock market and the real estate market factors; (3) the overall stock market, size, book-to-market, and real estate market factors; and (4) the overall stock market, size, book-to-market, bond market, and real estate market factors.

In the first subperiod of 1963-1967, only two variables, MKT and HPRICE, have important effects on returns of industrial stocks. Coefficients of SMB, HML, TERM, and DEF are statistically insignificant (Table 4).

All four models are well specified for the subperiod of 1968-1972 (Table 4). All coefficients, except for HML in model 4.32, are significant at the 5 and 1% levels, and four constant terms are insignificantly different from zero.

The results in the third subperiod (1973-1977) show significant coefficients for MKT, HPRICE, TERM, and DEF (Table 4). Nevertheless, both SMB and HML cannot exercise an important influence on determining returns for industrial stocks. Constant terms are all significant.

In addition to significant coefficients for MKT and HML, results in the subperiod of 1978-1982 show mixed coefficients for HPRICE (Table 5). HPRICE has significant coefficients in the single-factor model (5.11) and two-factor model (5.21), while coefficients of HPRICE in the other models (5.31 and 5.41) are insignificant.

The mixed results for HPRICE appear again in the following subperiod (1983-1987). The coefficient of HPRICE in the single-factor model (5.12) is significant at the 1% level. However, in models 5.22-5.42, only MKT has significant coefficients (Table 5).

HPRICE plays a very important explanatory role in the next five-year period (1988-1992). Coefficients of HPRICE in all four models are significant at the 1% level, like MKT. In addition, both bond market factors (TERM and DEF), along with SMB, have significant coefficients (Table 6).

Similar results are presented in Table 6 for the last subperiod (1993-1997). HPRICE has significant coefficients in all four models, as MKT does. Coefficients for SMB are also significant. However, HML has only one significant coefficient in model 6.42. Coefficients for TERM and DEF are not significant at all.

Overall, HPRICE has quite stable significant coefficients in all four models except for two subperiods, 1978-1987. The stability is only second to coefficients for MKT.

4. Concluding Comments

In order to identify major risk factors in pricing industrial stocks, the present study estimates different models based on six explanatory variables: an overall stock market factor, a size factor, a book-to-market equity factor, a term structure factor, a default risk factor, and an unsecuritized real estate market factor proxied by either monthly percentage changes in the median sales price index of new houses sold or quarterly percentage changes in the Russell-NCREIF property total return index.

Monthly results in this study indicate that excess returns of industrial stocks are very sensitive to changes in the unsecuritized real estate market factor proxied by the median sales price index of new houses sold. The coefficients of the real estate market factor are always significantly different from zero in all relevant models. In addition, the inclusion of the real estate market factor in a model can significantly raise its explanatory power. Therefore, the results clearly suggest that the real estate market factor indeed represents a systematic risk and plays an important role in explaining excess returns on industrial stocks.

Results of various models suggest that the overall stock market factor, the size factor, and the bond-to-market factor are all important in terms of explaining variation in excess returns for industrial stocks. Coefficients of these factors are always significant and [R.sup.2]'s are high when these factors are included in regression models. The coefficient of the stock market factor declines when the real estate market factor is included in the model. Therefore, the large coefficient in the single-factor (stock market) model presumably results from covariation between the overall stock market factor and the real estate market factor.

When the maturity and default risk measures are used as the bond market factors, only the maturity risk factor has significant explanatory power regarding industrial stock returns. Nevertheless, the significant influence of the real estate factor on excess returns of industrial stocks is not affected by the inclusion of the maturity and default risk measures as bond market factors.

Once again, quarterly results suggest that a significant part of variation on excess returns of industrial stocks may be explained by changes in unsecuritized commercial real estate proxied by the Russell-NCREIF property return index. However, results also indicate that the economic stress factor (HML) and the commercial real estate index (NCR) may have similar responses (covariation) to economic changes. That is, when HML and NCR are both included in a model, neither one has a significant coefficient. The size factor and two bond market factors do not have important explanatory power in various models based on quarterly data.

Evidence about stability of coefficients is provided by monthly results in seven five-year subperiods. The results suggest that the overall stock market factor is the most stable factor. It has highly significant coefficients in all relevant models in all subperiods. The second most stable variable is the real estate market factor. It has quite stable significant coefficients in all four models, except for two subperiods, 1978-1987. During this 10-year period, coefficients of the real estate factor are not significant in some multifactor models. The next stable variable is the book-to-market equity factor, followed by the size factor and two bond market factors.

(*.) Department of Economics and Finance, University of Central Arkansas, Conway, AR 72035, USA; E-mail linghe@mail.uca.edu.

The author is sincerely grateful to Eugene F. Fama for providing the SMB and HML series. Thanks go to two anonymous referees for helpful comments and suggestions.

Received August 2000; accepted June 2001.

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Table 1

Summary Statisties for the Monthly returns (in Percent), February
1963-December 1997

 Correlations
Variable Mean Std. Dev. C.V. Range IND

IND 0.40 7.53 18.84 67.01 1.00
MKT 0.70 8.26 11.82 71.23 0.92
SMB 0.20 2.84 14.34 20.56 0.25
HML 0.46 2.52 5.52 19.33 -0.03
TERM 0.19 2.89 15.21 23.01 0.37
DEF 0.03 1.19 45.87 9.37 -0.02
HPRICE 0.27 7.36 27.03 74.36 0.73

 Correlations
Variable MKT SMB HML TERM DEF HPRICE

IND
MKT 1.00
SMB 0.21 1.00
HML -0.11 -0.13 1.00
TERM 0.47 -0.12 -0.02 1.00
DEF -0.02 0.14 0.07 -0.46 1.00
HPRICE 0.69 0.07 0.10 0.30 -0.05 1.00

IND = (monthly value-weighted returns for industrial stocks) -
(treasury-bill return rate); MKT = NYSE/ASE/NASDAQ monthly
value-weighted returns) - (treasury-bill return rate); SMB (small minus
big) = monthly retuns on the mimicking porfolio for the common size
factor; HML (high minus low) = monthly return on the mimicking porfolio
for the common book-to-market equity factor; TERM = (monthly returns on
long-term government bonds) - (treasury-bill return rate); DEF =
(monthly returns on long-term corporate bonds) - (monthly returns on
long-term government bonds); HPRICE = (monthly percentage changes in the
median sales price index of new houses sold) - (treasury-bill return
rate); C.V. = coefficient of variation.
Table 2

OLS Regression of Excess Returns of Industrial Stocks (IND) on Risk
Factors with Corrections for Autocorrelation and Heteroscedasticity,
February 1963- December 1997 (Monthly Data) (a)

Model Constant MKT SMB HML

2.1 -0.19 0.84
 (l.68) (*) (37.61) (***)
2.2 -0.18 0.88
 (-1.64) (34.38) (***)
2.3 -0.16 0.73
 (-1.15) (31.64) (***)
2.4 -0.15 0.77
 (-1.44) (23.40) (***)
2.5 -0.32 0.83 0.17 0.22
 (-2.62) (***) (37.92) (2.57) (***) (3.25) (***)
2.6 -0.31 0.87 0.14 0.24
 (-2.63) (***) (32.45) (***) (2.07) (**) (3.57) (***)
2.7 -0.25 0.72 0.20 0.14
 (-2.11) (**) (20.85) (***) (3.15) (***) (2.05) (**)
2.8 -0.25 0.76 0.17 0.15
 (-2.12) (**) (20.21) (***) (2.58) (***) (2.29) (**)
2.9 0.20
 (0.79)

Model TERM DEF HPRICE [R.sup.2]

2.1 0.846

2.2 -0.23 -0.23 0.850
 (-3.11) (***) (-1.18) (*)
2.3 0.18 0.861
 (4.47) (***)
2.4 -0.21 -0.17 0.17 0.864
 (-3.08) (***) (-0.91) (4.40) (***)
2.5 0.853

2.6 -0.22 -0.30 0.857
 (-2.90) (***) (-1.67) (*)
2.7 0.17 0.867
 (3.98) (***)
2.8 -0.18 -0.22 0.16 0.869
 (-2.56) (***) (-1.27) (3.86) (***)
2.9 0.74 0.527
 (8.77) (***)

(a)(***)represents the 1% significance level;

(**)represents the 5% level; and

(*)represents the 10% level.

IND = (monthly value-weighted returns for industrial stocks) -
(treasury-bill return rate); MKT = (NYSE/ASE/NASDAQ monthly value-
weighted returns) - (treasury- bill return rate); SMB (small minus big)
= monthly returns on the mimicking portfolio for the common size factor;
HML (high minus low) = monthly returns on the mimicking portfolio for
the common book-to-market equity factor; TERM = (monthly returns on
long-term government bonds) - (treasury-bill return rate); DEF =
(returns on long-term corporate bonds) - (returns on long-term
government bonds); HPRICE = (monthly percentage changes in the median
sales price index of new houses sold) - (treasury-bill return rate);
t-values are in parentheses.
Table 3

OLS Regression of Excess Returns Industrial Stocks (IND) on Risk Factors
Using Quarterly Data (1978-1997) (a)

Model Constant MKT SMB HML TERM

3.1 -0.01 0.93
 (-1.85) (*) (58.47) (***)
3.2 -0.01 0.95 -0.08
 (-1.99) (**) (40.23) (***) (-0.97)
3.3 -0.00 0.85
 (-1.31) (26.83) (***)
3.4 -0.00 0.88 -0.08
 (-1.45) (24.99) (***) (-1.05)
3.5 -0.01 0.94 -0.06 0.13
 (-2.27) (**) (59.76) (***) (-0.92) (2.19) (**)
3.6 -0.01 0.97 -0.11 0.11 -0.12
 (-2.37) (**) (41.37) (***) (-1.68) (*) (1.99) (**) (-1.51)
3.7 -0.01 0.88 -0.02 0.07
 (-1.62) (21.28) (***) (-0.44) (1.11)
3.8 -0.01 0.93 -0.08 0.07 -0.11
 (-1.81) (*) (20.07) (***) (-1.13) (1.11) (-1.36)
3.9 0.02
 (2.11) (**)

Model DEF NCR [R.sup.2]

3.1 0.977

3.2 0.37 0.979
 (1.48)
3.3 0.12) 0.979
 (2.71) (***)
3.4 0.33 0.11 0.981
 (1.40) (2.68) (***)
3.5 0.979

3.6 0.31 0.981
 (1.28)
3.7 0.08 0.979
 (1.38)
3.8 0.32 0.06 0.981
 (1.30) (1.06)
3.9 1.14 0.787
 (17.10) (***)

(a)(***)represents the 1% significance level;

(**)represents the 5% level, and

(*)represents the 10% level. IND = (value-weighted returns for
industrial stocks) - (treasury- bill return rate); MKT = (NYSE/
ASE/NASDAQ value-weighted returns) - (treasury-bill return rate); SMB
(small minus big) = returns on the mimicking portfolio for the common
size factor; HML (high minus low) = returns on the mimicking portfolio
for the common book-to- market equity factor; TERM = (return on
long-term government bonds) - (treasury-bill return rate); DEF =
(Returns on long-term corporate bonds) - (returns on long-term
government bonds). NCR = (percentage changes in the Russell-NCREIF
property total return index) - (treasury-bill return rate); t-values are
in parentheses.
Table 4

OLS Estimates of Risk Factors with Corrections for Autocorrelation and
Heteroscedasticity in Subperiods (1) (a)

Model Constant MKT SMB

February 1963-December 1967

4.11 0.07
 (0.13)
4.21 -0.19 0.81
 (-0.86) (11.03) (***)
4.31 -0.20 0.81 0.07
 (-0.79) (10.95) (***) (0.68)
4.41 -0.39 0.86 0.05
 (-1.52) (12.18) (***) (0.55)

January 1968-December 1972

4.12 -0.08
 (-0.13)
4.22 -0.15 0.73
 (-0.58) (10.14) (***)
4.32 -0.12 0.67 0.29
 (-0.48) (9.14) (***) (2.32) (**)
4.42 -0.11 0.74 0.33
 (-0.43) (9.67) (***) (2.67) (***)

January 1973-December 1977

4.13 -1.33
 (-2.13) (**)
4.23 -0.66 0.69
 (- 1.87) (*) (8.59) (***)
4.33 -0.85 0.64 0.22
 (-1.81) (*) (8.24) (***) (1.57)
4.43 -0.80 0.68 0.21
 (-1.76) (*) (8.31) (***) (1.39)

Model HML TERM DEF

February 1963-December 1967

4.11

4.21

4.31 -0.17
 (-0.97)
4.41 -0.07 -0.54 -0.44
 (-0.44) (-1.76) (-1.02)

January 1968-December 1972

4.12

4.22

4.32 0.12
 (0.79)
4.42 0.29 -0.44 -0.74
 (2.03) (**) (-2.69) (***) (-2.39) (**)

January 1973-December 1977

4.13

4.23

4.33 0.07
 (0.34)
4.43 0.09 -0.04 -0.42
 (0.44) (-0.04) (***) (-0.95) (**)

Model HPRICE [R.sup.2]

February 1963-December 1967

4.11 0.63 0.437
 (6.69) (***)
4.21 0.17 0.835
 (2.31) (**)
4.31 0.15 0.834
 (2.09) (**)
4.41 0.13 0.841
 (2.25) (**)

January 1968-December 1972

4.12 0.88 0.614
 (13.56) (***)
4.22 0.20 0.873
 (2.36) (**)
4.32 0.22 0.878
 (2.77) (***)
4.42 0.17 0.890
 (2.19) (**)

January 1973-December 1977

4.13 1.06 0.700
 (10.21) (***)
4.23 0.23 0.878
 (2.30) (**)
4.33 0.29 0.881
 (2.84) (***)
4.43 0.24 0.880
 (2.52) (**)

(a)(***)represents the 1% significance level

(**)represents the 5% level

(*)represents the 10% level.

IND = (monthly value-weighted returns for industustrial stocks) -
(treasury-bill return rate)

MKT = (NYSE/ASE/NASDAQ monthly value-weighted returns) - (treasury-bill
return rate)

SMB (small minus big) = monthly returns on the mimicking portfolio for
the common size factor

HML (high minus low) = monthly returns on the mimicking portfolio for
the common book-to-market equity factor

TERM = (monthly returns on long-term government bonds) - (treasury-bill
return rate)

DEF = (returns on long-term corporate bonds) - (returns on long-term
government bonds)

HPRICE = (monthly percentage changes in the median sales price index of
new houses sold) - (treasury-bill return rate)

t-values are in parentheses.
Table 5

OLS Estimates of Risk Factors with Corrections for Autocorrelation and
Heteroscedasticity in Subperiods (2) (a)

Model Constant MKT SMB HML

January 1978-December 1982

5.11 -0.08
 (-0.09)
5.21 -0.47 0.77
 (-1.36) (10.09) (***)
5.31 -0.59 0.79 0.08 0.28
 (-1.51) (11.14) (***) (0.31) (2.52) (**)
5.41 -0.63 0.82 0.07 0.25
 (-1.65) (10.15) (***) (0.27) (2.15) (**)

January 1983-December 1987

5.12 0.98
 (1.62)
5.22 0.21 0.65
 (0.71) (12.87) (***)
5.32 0.15 0.67 0.17 0.13
 (0.44) (11.35) (***) (0.80) (1.02)
5.42 0.18 0.68 0.15 0.14
 (0.35) (9.57) (***) (0.65) (1.08)

Model TERM DEF HPRICE [R.sup.2]

January 1978-December 1982

5.11 0.73 0.616
 (3.77)
5.21 0.15 0.904
 (1.74)
5.31 0.12 0.905
 (1.56)
5.41 -0.16 0.30 0.12 0.906
 (-1.24) (0.96) (1.53)

January 1983-December 1987

5.12 0.43 0.216
 (2.88)
5.22 0.15 0.726
 (1.59)
5.32 0.13 0.722
 (1.30)
5.42 -0.10 -0.23 0.14 0.715
 (-0.78) (-0.67) (1.41)

(a)(***) represents the 1% significance level

(**)represents the 5% level

(*)represents the 10% level

IND = (monthly value-weighted returns (monthly value-weighted for
industrial stocks) - (treasury-bill return rate); MKT = (NYSE/ASE/NASDAQ
monthly value- weighted returns) - (treasury-bill return rate); SMB
(small minus big) = monthly returns on the mimicking portfolio for the
common size factor; HML (high minus low) = monthly returns on the
mimicking portfolio for the common book-to- market equity factor; TERM =
(monthly returns on long-term government bonds) - (treasury-bill return
rate); DEF = (returns on long-term corporate bonds) - (returns on
long-term government bonds); HPRICE = (monthly percentage changes in the
median sales price index of new houses sold) - (treasury-bill return
rate); t-values are in parentheses.
Table 6

OLS Estimates of Risk Factors with Corrections for Autocorrelation and
Heteroscedasticity in Subperiods (3) (a)

Model Constant MKT SMB

January 1988-December 1992

6.11 1.34
 (2.28) (***)
6.21 0.24 0.69
 (0.80) (11.08) (***)
6.31 0.19 0.71 0.43
 (0.63) (12.55) (***) (3.58) (***)
6.41 -0.10 0.68 0.30
 (-0.32) (10.99) (***) (2.87) (***)

January 1993-December 1997

6.12 0.81
 (1.71) (*)
6.22 0.13 0.72
 (0.61) (11.03) (***)
6.32 0.07 0.72 0.33
 (0.28) (12.56) (***) (2.55) (***)
6.42 0.08 0.77 0.26
 (0.38) (11.12) (***) (1.67) (*)

Model HML TERM DEF

January 1988-December 1992

6.11

6.21

6.31 0.25
 (1.60)
6.41 0.21 0.44 2.26
 (1.35) (2.14) (**) (2.87) (***)

January 1993-December 1997

6.12

6.22

6.32 0.19
 (1.51)
6.42 0.24 -0.17 0.08
 (1.96) (*) (-0.76) (0.11)

Model HPRICE [R.sup.2]

January 1988-December 1992

6.11 0.51 0.244
 (4.59) (***)
6.21 0.18 0.742
 (3.30) (***)
6.31 0.19 0.791
 (3.97) (***)
6.41 0.24 0.803
 (4.43) (***)

January 1993-December 1997

6.12 0.59 0.334
 (4.95) (***)
6.22 0.19 0.779
 (2.52) (**)
6.32 0.17 0.801
 (2.23) (**)
6.42 0.15 0.800
 (2.06) (**)

(a)(***)represents the 1% significance level

(**)represents the 5% level; and

(*)represents the 10% level.

IND = (monthly value-weighted returns for industrial stocks) -
(treasury-bill return rate); MKT = (NYSE/ASE/NASDAQ monthly value-
weighted returns) - (treasury-bill return rate); SMB (small minus big) =
monthly returns on the mimicking portfolio for the common size factor;
HML (high minus low) = monthly returns on the mimicking portfolio for
the common book-to- market equity factor; TERM = (monthly returns on
long-term government bonds) - (treasury-bill return rate); DEF =
(returns on long-term corporate bonds) - (returns on long-term
government bonds); HPRICE = (monthly percentage changes in the median
sales price index of new house sold) - (treasury-bill return rate);
t-values are in parentheses.