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An analysis of relative return behavior: REITs vs. stocks.

ABSTRACT

Given the ongoing changes in the REIT industry, we have analyzed the return behavior of the equity REIT, mortgage REIT, and S&P 500 indices using monthly data for the period of 19722001, to see if previously identified return patterns still hold for REITs relative to stocks. Following a large monthly gain, investors can benefit by adopting a momentum buying strategy for stocks or mortgage REITs, but not for equity REITs. Investors can also profitably employ a mean reversion strategy for any of the three indices. Indications for the existence of exploitable calendar effects were found all three markets indices. While the general pattern of seasonality effects differs across indices, a positive January effect, negative August and October effect were found in all index return series for several subperiods. Our findings also suggest that both equity REITS and mortgage REITS can enhance the risk/return relationship of a general stock portfolio. However, equity REITs clearly dominate mortgage REITs on a risk-return basis and compare favorably with stocks. The correlation coefficients between all three asset classes are similar, but the relationship between stocks and equity REITs has lessened over time.

INTRODUCTION

A sizeable body of literature has developed that examines the behavior of real estate investment trust (REIT) returns relative to those of common stocks. In this paper, we analyze the return behavior of REITs and stocks using monthly data for the period of 1972-2001 to determine whether investors should consider adding REITs to traditional stock and bond portfolios. We examine returns for equity and mortgage REIT indices and for the Standard and Poor's 500 stock index (S&P 500) to address three issues that have been subject to controversy in the literature.

First, there has been some debate over whether stocks and REITs exhibit momentum, mean reversion, or both types of behavior. To investigate this issue, we identify the twenty-four largest monthly increases and decreases for the equity REIT, mortgage REIT, and S&P 500 indices--similar to the selection procedure employed by Seligman (2001). Then, we apply the event study methodology to measure the subsequent response to these events to determine whether momentum or mean reversion is prevalent for each index and whether REITs behave differently than stocks during these periods. Our findings suggest a buy and hold strategy after a large decline for all three indices and a momentum buying strategy for stocks and mortgage REITs only.

A second area of focus is to investigate calendar effects across our three asset classes. As seasonalities for each asset class are documented and become widely known, they are subject to short-term trading activities designed to exploit inefficiencies. Thus, testing for the persistence of monthly calendar effects is also a test of market efficiency for each type of financial asset. We find calendar effects in several subperiods across all three indices. Positive January and negative October effects are most pronounced in the REITs indices, weak complementing evidence is also found in the S&P 500 stock index. The time varying nature suggests that investors may have already incorporated this knowledge into their trading strategies as would be consistent with the Efficient Market Hypothesis.

The third objective of this paper is to identify the degree of correlation between equity REITs, mortgage REITs and stock returns. If REITs are not highly correlated with stocks, or if this correlation has been declining over time, REITs can enhance the risk/return relationship of a general stock portfolio. With the structural changes initiated in January 1993, more institutional investors entered and more analysts covered the REITs market (Chan, Leung, and Wang 1998). To further investigate this issue, we examine correlations between the three asset classes for the pre-1993 period, the years 1993-1999, and for 2000-2001, which represents the recent bear market for stocks. We find diversification benefits from the inclusion of real estate related securities into a general stock portfolio to have increased over time and that equity REITs, based on a superior risk/return relationship, are to be preferred over mortgage REITs.

LITERATURE REVIEW

An important theme in many studies has been whether REITs are sufficiently different from stocks to provide diversification benefits or enhance portfolio returns. While Chen, Hsieh, and Jordan (1997) find superior financial performance for equity REITs during the period 1980-1985, Chen and Peiser (1999) show that REITs, as a separate asset class, under perform both bonds and stocks on a risk-return basis over the 1987-2000 period, and conclude that real estate has "no role in a very highly risk-tolerant portfolio". Yet, Ibbotson Associates (2002) indicate that inclusion of REITs into a well-diversified stock and bond portfolio could have enhanced returns by up to 0.8% annually over the period 1972-2001 and by 1.3% annually for the years 1992-2001. The methodology varies between these three studies, but the apparently conflicting results may arise primarily from differences in time periods considered.

Liao and Mei (1998) find the risk premiums of real estate related securities to vary significantly over time and stress the importance of market timing. Using monthly return data for the S&P 500 index, Seligman (2000) explains that only a few extraordinarily good months account for a large portion of the entire holding period's return. The biggest gains were concentrated in months following large declines, directly supporting the mean reversion argument. Jegadeesh and Titman (1993, 2001) have documented the success of momentum strategies using portfolios of individual stocks for time horizons of generally three to six months. Similarly, Chui, Titman, and Wei (2001) find momentum effects in REIT portfolios over six-month holding periods that are even stronger than the momentum effects for stocks. And while Glascock (2004) reveals that REITs momentum return are less during bear markets, Chui and Titman (2003) finds momentum effects to be positive related to REIT size.

The tests conducted by Chui, Titman, and Wei (2001) can serve as a framework to determine whether monthly effects contribute to either momentum profits or mean reversion. Evidence of a January effect in equity securities is abundant and not limited to the US [see e.g., Rozeff and Kinney (1976), Reinganum (1983), and Keim (1983)]. Also, Ma and Goebel (1991) observe the January effect in securitized mortgage markets, while Colwell and Park (1990) and McIntosh, Liang, and Tompkins (1991) document calendar effects in REIT returns.

The combination of the look through provision, which allowed pension funds to invest in REITs (January 1, 1993) and the liquidity crisis and recapitalization of commercial real estate, led to the REIT boom of 1993-1997. While Mull and Soenen (1997) reveal the existence of large temporal differences in REIT efficiency as a stock portfolio component, Clayton and MacKinnon (2001) discuss the time-varying nature of the link between REIT, stock, and bond returns and point out that return relationships underwent a structural change, leaving REITs to be a different type of investment than they were in earlier years. Given the recent changes in the REIT industry, it may be useful to revisit the risk-return characteristics of REITs to see if previously identified return patterns still hold for REITs relative to stocks. While Paladino and Mayo (1998) and Capozza and Seguin (1999) conclude that REITs do not provide diversification benefits to a stock portfolio, Hudson-Wilson (2001) suggests that a declining correlation of REITs and stocks can enhance the risk/return relationship of a general stock portfolio. As more institutional investors entered and more analysts covered the REITs market subsequent to the structural changes initiated in January 1993 (Chan, Leung, and Wang 1998), REITs could become more like stocks. However, recent work by Clayton and MacKinnon (2001) and Chui, Titman, and Wei (2001) suggests that the opposite may have happened in recent years and Lee and Stevenson (2005) conclude that the attractiveness of REITs as a diversification asset increases as the holding period increases. To further investigate this issue, we examine correlations between the three asset classes for the pre-1993 period, the years 1993-1999, and for 2000-2001, which represents the recent bear market for stocks.

DATA AND METHODOLOGY

The data set of monthly REIT returns for January 1972 to December 2001 is calculated from monthly index prices of equity REITs (ERI) and mortgage REITs (MRI) available on the National Association of Real Estate Investment Trusts website. Monthly returns for the S&P 500 index and Academy of Accounting and Financial Studies Journal, Volume 9, Number 2, 2005 returns on Treasury bills are obtained from Pinnacle Data Corporation. These data are used to analyze the return behavior of REITs relative to stocks (S&P 500), and as discussed earlier, the empirical analysis focuses on three major issues.

MEAN REVERSION OR MOMENTUM?

METHODOLOGY

Monthly returns on the ERI, MRI, and S&P 500 index are ranked in order of decreasing (increasing) abnormal returns. This formulation modifies and extends ideas presented in Seligman (2001), who looks at the 41 largest return months for the S&P 500 and discovers that they occur primarily after the months of largest declines for the S&P 500. Two samples are formed for each index, consisting of the 24 best and 24 worst months. These 48 top or bottom performing months are labeled "event month". Event study methodology was used to determine abnormal returns subsequent to a significant up or down move. Abnormal index returns are measured over a ten month event window that includes the three months prior to the event, [t.sub.-3] to [t.sub.-1], the event day t = 0, and the subsequent six months of returns [t.sub.+1] to [t.sub.+6.] Abnormal returns are calculated as the difference between actual return and expected return, the monthly return average for the previous 12 months ([t.sub.-15] to [t.sub.-4]):

[AR.sub.it] = [R.sub.it] - E([R.sub.it]), Formula (1)

where:

[R.sub.it] = the actual rate of return on index i for the event month t,

E([R.sub.it]) = the expected rate of return on event month t.

For a sample of N events (24 in our analysis), an average abnormal return ([AAR.sub.t]) for each event month is computed as:

[AAR.sub.t] = (1/N) Sum ([AR.sub.it]) Formula (2)

The cumulative average abnormal return ([CAAR.sub.t]) for any event month j within the 10-month window from [t.sub.-3] to [t.sub.+6] is computed as:

[CAAR.sub.t] = Sum ([AAR.sub.t]) Formula (3)

EMPIRICAL RESULTS

As shown in Exhibit 1, the S&P 500's best 24 months are preceded by two months of negative returns with a CAAR of -3.53%. The average abnormal return of the event month [t.sub.0] is 8.85%. With AARs for the following six months [t.sub.+1] to [t.sub.+6] all being positive (ranging from 0.32% to 1.23%), the S&P 500 index clearly displays momentum behavior following large gains. An investor, who benefited from the high returns of an event month, would not have to suffer from the negative consequences of a severe market reaction, due to the lack of a mean reverting tendency. Even more interesting is the finding that an investor could have earned a modest abnormal return simply by investing in the S&P 500 immediately after a significant upturn. The result would have been a positive CAAR of 3.91% for the period of [t.sub.+1] to [t.sub.+6].

[GRAPHIC 1 OMITTED]

The S&P 500's worst 24 months generated an AAR of-9.72%. As shown in Exhibit 1, monthly AARs range from 0.15 to 0.99% for the subsequent 6-months period and CAAR = 3.96%, indicating that it is beneficial to invest in the S&P 500 index right after a huge downturn to capture the subsequent impact of mean reversion.

[GRAPHIC 2 OMITTED]

The return analysis of the ERI reveals a picture somewhat different from that of the S&P 500 index (Exhibit 2). Both the upswings and especially the downswings of the ERI are less pronounced. The 24 best (worst) months produce average abnormal returns of 8.03% (-8.15%). Following the best months, the AARs for [t.sub.+1] to [t.sub.+4] are negative, indicating some profit taking and minor evidence of mean reversion. Consequently, following a major up move, investors should retire from the equity REITs markets for a period of four to six months to avoid the negative impact of what technical analysts would describe as a market reaction. Following months with unusually high negative returns, the ERI recovers less quickly than the S&P 500 index. While the S&P 500 index generates positive AAR in the month immediately following a large downturn, AAR for [t.sub.+1] is still negative (1.69%) for the ERI and becomes positive only in the months [t.sub.+2] to [t.sub.+5], with averages ranging from 1.10% to 1.86% for the former. The ERI displays continued negative momentum in the month following a large decline and then finally mean reversion sets in and CAAR increases by 5.38% from periods [t.sub.+1] to [t.sub.+6].

As shown in Table 1, the MRI is more volatile than both the ERI and the S&P 500 index. Its standard deviation is 5.77% per month over the period 1972-2001, versus 3.92% and 4.50% for ERI and S&P 500, respectively. In addition, the mean monthly return of .44% per month is noticeably smaller than the .98% and .95% monthly returns for ERI and the S&P 500. On a pure risk-return basis, mortgage REITs may not make sense for inclusion in investment portfolios. The best (worst) 24 months AAR for the MRI on event days is 12.57% (-11.69%). This compares with 8.03% (-8.10%) and 8.85% (-9.72%) for the ERI and the S&P 500 index (Exhibit 3). Surprisingly, the MRI behaves more like the S&P 500 index than like the ERI. CAAR for the three months preceding the event month is -4.13%, compared to -3.53% for the S&P 500 index. Beginning with the event month rather than month [t.sub.-3], CAAR cumulates to 19.72% by month [t.sub.+6] and CAAR for months [t.sub.+1] to [t.sub.+6] is 7.15%. Both the S&P 500 and mortgage REITs display continuation of momentum in the months following a large gain, but the momentum effect is considerably more pronounced for mortgage REITs.

The mean reverting tendency of the MRI following the 24 worst months is also more pronounced than that of the ERI and the S&P 500 index. The ERI displayed positive AARs prior to the event month, AAR = -11.69% for t = 0, and CAAR of 9.80% over months [t.sub.+1] to [t.sub.+6]. This compares to values of 5.38% and 3.91% for mean reversion on the ERI and S&P 500 indices over the same period.

[GRAPHIC 3 OMITTED]

CALENDAR EFFECTS

METHODOLOGY

To assess possible calendar effects, each of the three market indices (ERI, MRI, and S&P 500) is regressed on a set of 12 monthly dummy variables:

[R.sub.i] = [a.sub.i] + Sum ([b.sub.im][TD.sub.m]), with Sum ([b.sub.im]) = 0 Formula (4)

where:

[R.sub.i] = the monthly return on the market index i

[a.sub.i] = the intercept term

[b.sub.im] = the slope coefficient associated with the time dummy variables

[T.sub.dm] = the time dummy variable, equal to one if the index return was generated in month m; zero otherwise

Instead of regressing the index return on a set of eleven time dummy variables, leaving an arbitrarily chosen month, e.g., January, to become the intercept term, with the [b.sub.im] coefficients measuring the pairwise difference between the average return in January and each of the other months (see for example Friday and Peterson (1997) or Redman, Manakyan, and Liano (1997)), the [b.sub.im] coefficients in equation (4) represent the pair-wise difference between the average monthly across all 12 months and the average return in each of the months--January through December. Since the average month's effect is zero, a set of unique values of the coefficients can be obtained. (1) The least squares estimate of the intercept term, [a.sub.i], is equal to the average monthly return on the market index i, since the average residual is zero in every month. (2) Thus, the calendar effects are estimated net of the average monthly index returns for any given period.

EMPIRICAL RESULTS

We found significant, non-stationary calendar effects for all three indices. The pattern of these effects differs somewhat across the indices. For the entire 30-year period, the most significant calendar effects experienced by the ERI were positive in January and negative in October. While the positive January effect was mirrored in the MRI, the negative October effect was replaced by a negative August effect. In contrast, the only evidence of a full period calendar effect in the S&P 500 index was found in September (negative at the 10%-level).

For all three indices, Tables 2-4 provide a detailed account of the time varying pattern of the calendar effects by 5-year subperiods. For example, some of the calendar effects displayed by the ERI and MRI can also be found in the returns of the S&P 500 index: the positive January effect during 1972-1976 and the negative effects in August and October during 1997-2001 and 1987-1991, respectively. Similar to the MRI, a negative effect was found during 1977-1981 for the month of October. Resembling the ERI, a negative effect was found during 1982-1986 for the month of July. Other calendar effects significant only to the S&P 500 index were found for August (positive during 1982-1986), September (negative during 1982-1986), October (positive during 1972-1976), and November (positive during 1977-1981). Contrary to the ERI and MRI, no significant calendar effects were found for stocks for the subperiod of 1992-1996.

Our results provide evidence for the existence of calendar effects across all three asset classes. These effects may play some role in momentum (positive Decembers and Januaries), but seasonality does not seem to explain the differential behavior of equity REITs relative to mortgage REITs and stocks after a large up move in the index. Also, given the time varying nature of the monthly effects, seasonality does not seem to explain either momentum or mean reversion in index returns. The non-stationarity of monthly effects itself, however, could be explained by the Efficient Market Hypothesis, that is, as investors incorporate the anticipation of these calendar effects into their trading strategies, they cause them to disappear.

The fact that calendar effects differ across the three market indices suggests differences in market return behavior and may indicate potential benefits from diversifying across asset classes. Several authors have focused on these return differences. Hudson-Wilson (2001) points out that a partial investment in REITs can enhance the risk/return relationship of the portfolio. Booth, Cashdan and Graff (1989) conclude that investors should differentiate between equity REITs and mortgage REITs, as the former behave more similar to equity while the latter is closer related to fixed-income debt securities. However, the poor risk-return results for mortgage REITs may not make them suitable replacements for bonds, or as desirable as equity REITs. Subsequently, we will analyze the return correlation between the three market indices in search for possible changes in the relationship that occurred over time.

MARKET CORRELATIONS

METHODOLOGY

The correlation coefficients are computed pairwise for the ERI, MRI, and the S&P 500 index on a 24-month rolling basis. The resulting correlation coefficients are regressed on constant, a trend variable that increases by one with each monthly observation, and two dummy variables that indicate how the trend changes between time periods. The intercept shows the estimated general correlation coefficient at the beginning of 1972 and the [b.sub.1] coefficient shows the monthly trend over the 1972-1992 period (the trend dummy is one for all years, but when additional trend subperiod dummies are added, it then captures the trend in the first subperiod). The dummy variables [TD.sub.2] and [TD.sub.3] for the years 1993-2001 and 2000-2001 reflect the period after the elimination of the pension fund barrier for investing in REITs, and the recent bear market in stock returns. The [b.sub.2] coefficient actually measure trend changes for 1993-1999 relative to 1972-1992, while the [b.sub.3] coefficient to capture any additional trend changes for 2000-2001 relative to the second subperiod. The regression equation is:

[rho.sub.ij,t] = [a.sub.t] + [b.sub.1t][Trend.sub.ij] + [b.sub.2t][Trend.sub.ij] * [TD.sub.1] + [b.sub.3t][Trend.sub.ij] * [TD.sub.2] + [e.sub.ij] Formula (5)

where: [rhoi.sub.j,t] = the correlation coefficient between market index i and j at time t

[a.sub.t] = the intercept term

[b.sub.1t-3t] = the slope coefficient associated with each independent variable

[Trend.sub.ij] = trend variable, indicating the change in the correlation coefficient over the entire 1972-2001 period.

[TD.sub.1] = the time dummy variables equal to one starting January 1993; zero otherwise.

[TD.sub.2] = the time dummy variables equal to one starting January 2000; zero otherwise.

[e.sub.ij] = the random error term

EMPIRICAL RESULTS

The time trend analysis of the market index correlation coefficients reveals that ERI and MRI behave quite similarly (Table 5 shows a = .75, or a high initial degree of correlation starting in 1972). The negative coefficients [b.sub.1] and [b.sub.2] associated with the variables Trend and [TD.sub.2], respectively, indicate a slight reduction of rho over time in general and after January 1993 in particular (at the 5% and 10%-level, respectively). This finding is surprising in light of the notion that equity REITs behave more like stocks and mortgage REITs behave more like bonds, e.g., see Hudson-Wilson (2001), but confirms Clayton and MacKinnon (2001) who found the sensitivity of REIT returns to large cap stock returns declining over time and updates He (1998) who found stable long-run linear relationship between the equity and mortgage REITs.

The base correlation coefficient (the a portion of rho) is .66 between the ERI and the S&P 500 and .68 between the MRI and the S&P 500. Although Peterson and Hsieh (1997) already hinted on mortgage REIT returns being related to three stock market factors, it is surprisingly that mortgage REITs and stock returns are more closely related than are equity REITs and stock returns, though the level is decreasing over time, especially in the recent bear market, as indicated by the negative [b.sub.1] and [b.sub.3] coefficients (significant at the 5% and 10%-level, respectively). The negative [b.sub.2] coefficient indicates an increasing level of "disconnect" between ERI and the S&P 500 index after 1993 (significant at the 1%-level). Our findings suggest that (1) equity investors can reduce portfolio risk by including REITs in the portfolio, (2) the diversification effect of including REITs in the portfolio has increased over time, and (3) since mortgage REITs are actually more correlated with the S&P 500 than are equity REITs and provide lower returns at higher risk, there is little reason to include mortgage REITs in an equity portfolio. (3) In light of the findings of Howe and Jain (2004), who document a significant decline in the systematic risk of REITs subsequent to the REIT Modernization Act of 1999 (RMA), it seems reasonable to assume that the introduction of the RMA was a contributing factor to the decline in REITs and stock market correlation in the latest subperiod.

Equity REITs can enhance the risk/return relationship of a general stock portfolio and long-term investors, aiming for a well balanced portfolio, should monitor any changes in the relative return behavior of asset classes and, from time to time, adjust the portfolio weights if necessary.

CONCLUSIONS

We have analyzed the return behavior of the equity REIT, mortgage REIT, and S&P 500 indices using monthly data for the period 1972-2001. A major goal was to identify recurring return patterns in each index that could be exploited by either momentum or mean reversion trading strategies. Our results differ across markets. Investors can obtain positive abnormal returns from a momentum strategy that buys either the mortgage REIT or the S&P 500 index immediately after the index has experienced a significant up move. The equity REITs market should be avoided for about four months after a large monthly gain due to its mean reversion tendencies. For all three assets classes, investors can earn above average returns from buying and holding the index for the six month period immediately following a large monthly decline. Both stocks and REITs display mean reversion after large declines, confirming the often repeated investment advice to avoid selling immediately after a large decline in asset value.

Significant calendar effects were found for both REIT and stock indices, although the general pattern for monthly effects differs across asset classes. While the positive January and negative October effects were most pronounced in the REITs indices, weak complementing evidence was also found in the S&P 500 stock index. The non-stationarity of these effects suggests that investors may have already incorporated this knowledge into their trading strategies as would be consistent with the Efficient Market Hypothesis. We also examined correlation and changes in correlation between asset classes over the period 1972-2001. Both mortgage and equity REITs have become less correlated with the S&P 500 index from 1972 to 2001, but the difference has become greater for equity REITs than for mortgage REITs. Equity REITs also provide a more favorable risk-return ratio than mortgage REITs. Our findings suggest that equity REITs can enhance the risk-return relationship of a general stock portfolio and probably should be added to many investors' stock and bond portfolios. Mortgage REITs may be useful for diversification, but greater benefits are obtained by adding equity REITs to a portfolio.

REFERENCES

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Jorg Bley, American University of Sharjah

Dennis Olson, American University of Sharjah

ENDNOTES

(1) See also Suits (1984) and Kennedy (1986) for a detailed discussion

(2) By construction, in OLS estimation of a regression the estimated disturbances are orthogonal to all months.

(3) "Some authors, e.g., Liang and McIntosh (1998) and Chen and Peiser (1999), have suggested using the S&P mid-cap 400 index as a stock market proxy. This index was introduced in September 1991. Given the 30-year data window of this study, the inclusion of the mid-cap index would be of limited use for the first and second part of the analysis. However, the inclusion of the S&P mid-cap 400 index in our market correlation analysis confirms our findings for the S&P 500 index. In fact, the lower correlation coefficient of the S&P mid-cap 400 index with equity REITs indicates an even greater potential for diversification benefits from the inclusion of equity REITs in a stock portfolio than suggested by the S&P 500 index."
Table 1: Descriptive statistics

The table presents descriptive statistics for the 360 monthly
return observations (in%) for the period of 1972-2001, and each of
the six 5-year subperiods for the ERI, MRI, and SP500 index.
CV is the coefficient of variation, showing risk per unit of return.
Low CV values are preferred to higher values.

 Std.
Period: 1972-2001 Minimum Maximum Mean Dev. CV

Equity REITS -16.53 13.17 0.98 3.91 3.99
Mortgage REITS -24.58 32.49 0.44 5.77 13.11
SP500 Index -24.23 15.51 0.95 4.49 4.73

 Std.
Period: 1997-2001 Minimum Maximum Mean Dev. CV

Equity REITS -09.91 9.07 0.06 3.74 62.33
Mortgage REITS -23.14 13.25 1.04 7.38 7.10
SP500 Index -15.59 9.33 1.08 5.21 4.82

 Std.
Period: 1992-1996 Minimum Maximum Mean Dev. CV

Equity REITS -5.58 9.89 1.32 3.10 2.35
Mortgage REITS -08.09 11.82 1.30 2.98 2.29
SP500 Index -04.50 7.24 1.18 2.81 2.38

 Std.
Period: 1987-1991 Minimum Maximum Mean Dev. CV

Equity REITS -16.53 10.38 0.52 3.89 7.48
Mortgage REITS -10.84 8.96 -0.33 3.83 -11.61
SP500 Index -24.23 12.63 1.19 5.49 4.61

 Std.
Period: 1982-1986 Minimum Maximum Mean Dev. CV

Equity REITS -3.84 9.64 1.67 2.82 1.69
Mortgage REITS -11.08 13.41 1.24 3.87 3.12
SP500 Index -8.64 11.44 1.50 4.13 2.75

 Std.
Period: 1977-1981 Minimum Maximum Mean Dev. CV

Equity REITS -12.96 11.87 1.47 4.41 3.00
Mortgage REITS -12.69 15.86 0.73 5.18 7.10
SP500 Index -10.24 10.12 0.64 4.20 6.56

 Std.
Period: 1972-1976 Minimum Maximum Mean Dev. CV

Equity REITS -15.09 13.18 0.39 5.08 13.03
Mortgage REITS -24.58 32.49 -0.30 8.51 -28.37
SP500 Index -12.23 15.51 0.39 4.92 12.62

Table 2: Calendar Effects, Equity REITs Index

Calendar effects are measured by regressing monthly returns
on the market index i over the period 1972-2001 on a complete
set of 12 time dummy variables. The results are reported for
the full 30-year period and each of the six 5-year subperiods.
The least squares estimate of the intercept is equal to the
subperiod's average monthly return.

Ri = ai + Sum (bimTDm), with Sum (bim) = 0

Month 1972- 2001 1972- 1976 1977- 1981 1982- 1986

January 2.25 *** 6.01 *** 1.81 1.58
February -0.03 1.10 -0.17 -1.10
March 0.28 0.22 -1.11 1.44
April -0.06 -0.82 -0.17 0.56
May -1.10 -5.23 ** -1.28 -1.55
June 1.34 * 4.24 ** 2.78 -0.69
July -0.07 0.03 1.42 -2.14 *
August -1.05 -2.77 1.61 -0.03
September -0.57 0.42 -3.50 * -0.21
October -1.86 *** -0.10 -2.37 2.33 *
November -0.47 -3.78 * 1.06 -0.35
December 1.33 * 0.68 -0.10 0.16
Mean 0.98 0.31 1.47 1.67

Month 1987- 1991 1992- 1996 1997- 2001

January 3.30 ** 1.34 -0.55
February 1.09 0.82 -1.94
March 1.57 -0.97 0.55
April 0.08 -1.86 1.85
May -0.58 1.00 1.03
June 0.87 -0.78 1.62
July 0.63 0.27 -0.62
August -2.49 0.30 -2.91 *
September -1.74 0.35 1.26
October -5.35 *** -2.28 * -3.40 **
November 0.71 -1.64 1.20
December 1.89 3.46 ** 1.91
Mean 0.52 1.32 0.52

where:

Ri = the monthly return on the market index i

ai = the intercept term

bim = the slope coefficient associated with the time dummy variables

TDm = the time dummy variable, equal to one if the index return was
generated in month m; zero otherwise *, **, and *** indicate
statistical significance at the 10%, 5%, and 1%-level, respectively.

Table 3: Calendar Effects, Mortgage REITs Index

Calendar effects are measured by regressing monthly returns on
the market index i over the period 1972-2001 on a complete set
of 12 time dummy variables. The results are reported for the
full 30-year period and each of the six 5-year subperiods. The
least squares estimate of the intercept is equal to the subperiod's
average monthly return.

Ri = ai + Sum (bimTDm), with Sum (bim) = 0

Month 1972-2001 1972-1976 1977-1981 1982-1986

January 4.26 *** 10.28 *** 1.62 1.62
February -0.91 -0.47 -2.27 -1.05
March -0.37 0.94 -1.55 -0.57
April 0.16 -5.54 4.09 * 0.94
May 0.29 -1.94 -0.26 -1.55
June 0.69 -0.85 3.58 -1.50
July 0.45 2.28 1.55 -0.71
August -2.37 ** -6.30 * 0.82 0.56
September 0.05 3.40 -3.37 -0.74
October -0.82 3.54 -4.38 ** 4.09 **
November -0.60 -4.40 3.04 -0.17
December -0.83 -0.93 -3.25 -0.92
Mean 0.44 -0.30 0.73 1.24

Month 1987-1991 1992-1996 1997-2001

January 3.12 * 4.78 *** 3.75
February -0.53 -0.46 -0.67
March 0.75 -1.57 -0.22
April -0.89 -2.15 4.49
May 1.75 1.15 2.61
June 0.61 -0.73 3.05
July 0.79 0.20 -1.38
August -0.42 0.75 -9.66 ***
September -2.06 -0.04 3.13
October -3.47 ** -0.77 -3.96
November 0.50 -1.34 -1.21
December -0.14 0.18 0.06
Mean -0.33 1.30 0.02

where:

Ri = the monthly return on the market index i

ai = the intercept term

bim = the slope coefficient associated with the time dummy variables

TDm = the time dummy variable, equal to one if the index return was
generated in month m; zero otherwise *, **, and *** indicate
statistical significance at the 10%, 5%, and 1%-level, respectively.

Table 4: Calendar Effects, SP 500 Index

Calendar effects are measured by regressing monthly returns
on the market index i over the period 1972-2001 on a complete set
of 12 time dummy variables. The results are reported for the full
30-year period and each of the six 5-year subperiods. The least
squares estimate of the intercept is equal to the subperiod's
average monthly return.

Ri = ai + Sum (bimTDm), with Sum (bim) = 0

Month 1972-2001 1972-1976 1977-1981 1982-1986

January 1.25 4.27 * -1.41 0.47
February -0.17 0.50 -1.89 -1.24
March -0.03 0.55 -0.37 0.56
April 0.11 -0.94 1.80 0.83
May 0.35 -0.24 -0.28 -1.36
June 0.47 0.70 1.39 0.02
July -0.50 -2.48 1.88 -3.90 **
August -0.76 -2.56 -0.27 4.43 **
September -1.46 * -2.17 -1.02 -3.35 *
October -0.61 3.85 * -3.16 * 2.54
November 0.55 -2.36 4.15 ** 1.28
December 0.80 0.88 -0.83 -0.28
Mean 0.95 0.39 0.64 1.50

Month 1987-1991 1992-1996 1997-2001

January 3.13 0.55 0.51
February 1.52 -0.32 0.38
March 0.26 -1.26 0.06
April -0.51 0.13 -0.61
May 2.48 0.92 0.58
June -0.45 -1.37 2.54
July 2.38 0.02 -0.94
August -2.30 0.34 -4.21 *
September -2.19 0.32 -0.34
October -5.70 ** 0.29 -1.51
November -2.46 0.79 1.94
December 3.83 -0.41 1.59
Mean 1.19 1.18 0.83

where:

Ri = the monthly return on the market index i

ai = the intercept term

bim = the slope coefficient associated with the time dummy
variables

TDm = the time dummy variable, equal to one if the index
return was generated in month m; zero otherwise *, **, and
*** indicate statistical significance at the 10%, 5%, and
1%-level, respectively.

Table 5: Market Correlations

The correlation coefficients are computed pairwise for the equity
Reits index (ERI), the mortgage Reits index (MRI), and the SP500
index on a 24-month rolling basis. Subsequently, the correlation
coefficients are regressed on a "trend" variable, which increases
by one with every monthly observation, and two time dummy variables.
The intercept shows the estimated general correlation at the 1972-2001
period. The trend varible indicates the change in the correlation
coefficient over the entire 1972-1992 period. The time dummy variables
TD2 and TD3 indicate additional trend changes between periods.
TD2 is equal to one starting January 1993, TD3 is equal to one staring
January 2000; zero otherwise. The covariance estimator is consistent
in the presence of both heteroscedasticity and autocorrelation
of unknown form, according to Newey and West (1987).

Market Correlation Intercept t-stat. b1 Trend t-stat.
between 1976-
 2001

ERI and MRI 0.7517 23.89 *** -0.0005 -1.98 **
ERI and SP500 0.6627 18.18 *** 0.0001 0.19
MRI and SP500 0.6831 13.50 *** -0.0008 -2.35 **
ERI and SP mid-cap 4001 0.5703 5.18 *** 0.0024 2.91 ***
MRI and SP mid-cap 4001 0.6661 11.82 *** -0.0037 -4.12 ***

Market Correlation b2 Trend t-stat. b3 Trend t-stat.
between * TD2 * TD3
 1993- 2000-
 2001 2001

ERI and MRI -0.0004 -1.93 * 0.0002 0.85
ERI and SP500 -0.0011 -5.44 *** -0.0005 -1.51
MRI and SP500 0.0001 0.15 -0.0005 -1.93 *
ERI and SP mid-cap 4001 n/a n/a -0.0027 -5.41 ***
MRI and SP mid-cap 4001 n/a n/a 0.0007 0.13

(1) The SP mid-cap 400 data range is limited to 1992-2001 but, for
comparison purposes, was included in the analysis as a
stock index alternative to the SP500.

*, **, and *** indicate statistical significance at the 10%, 5%,
and 1%-level, respectively.
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Author:Bley, Jorg; Olson, Dennis
Publication:Academy of Accounting and Financial Studies Journal
Date:May 1, 2005
Words:6950
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