Further Evidence on the Performance of Funds of Funds: The Case of Real Estate Mutual Funds

Kevin C.H. Chiang*

College of Business AdministrationNorthern Arizona University

Flagstaff, AZ 86011-5066

Kirill Kozhevnikov

Lundquist College of BusinessUniversity of OregonEugene, OR 97403

Ming-Long Lee

Department of FinanceNational Yunlin University of Science and Technology

Douliou, Yunlin, Taiwan 640

Craig H. Wisen

School of ManagementUniversity of Alaska Fairbanks

Fairbanks, AK 99775

2nd round with Real Estate Economics

Key Words: REIT, performance evaluation, mutual funds

* Correspondence: Kevin C.H. Chiang, College of Business Administration, Northern Arizona University, Flagstaff, AZ 86011-5066. Phone: (928) 523-4586, Fax: (928) 523-7331, E-mail: Kevin.Chiang@nau.edu.

The authors thank three anonymous referees and David Ling (the editor) for their helpful suggestions. The authors also thank Kenneth French for providing factor return series.

Further Evidence on the Performance of Funds of Funds: The Case of Real Estate Mutual Funds

Abstract

Funds of funds (FOFs) are created when investment companies invest in other investment

companies. Although the additional layer of fees incurred by FOFs has a negative effect

on returns, there is empirical evidence that real estate FOFs generate superior

performance net of fees and risk adjustments. The evidence is inconsistent with a

growing consensus that most actively managed mutual funds do not, on average, generate

excess returns after adjusting for fees and risk. This study explains this apparent

contradiction and finds that most real estate FOFs do not outperform their benchmarks

under alternative risk adjustment specifications.

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Further Evidence on the Performance of Funds of Funds: The Case of Real Estate Mutual Funds

Introduction

Funds of funds (FOFs) are generally defined as investment companies that hold

shares of other investment companies. This framework separates the task of managing

securities from that of managing investment companies, and it suggests that some

investors may benefit from the specialization of professional management, enhanced

diversification, and the economies of scale. The separation of fund selection from

security selection has been a common practice among institutional investors and

retirement plan participants for decades.

In the U.S., FOFs have come in and out of vogue twice over the last century.

After a period of popularity in the first quarter of the century, public perception of FOFs

reached a low point in the 1930s when some of them were associated with extreme

leverage, market manipulation, and pyramid schemes. Such behavior led in part to

passage of the Investment Company Act of 1940. Public perception of FOFs rebounded

over the next few decades, but reached a second low point in the early 1970s when

Investors Overseas Services imploded under the management of Bernie Cornfeld and

Robert Vesco.

Since then, FOFs have regained some of their popularity. Based on 2003 market

values, they held approximately 3% of long-term mutual fund assets that year.1 In

January 2006, approximately 9% of the 6,200 unique mutual fund portfolios listed in the

Morningstar Principia database were classified as FOFs. Although explaining the market

share of FOFs is outside the scope of the present analysis, casual observation suggests

1 Stategic Insight FRC Report dated September 30, 2003

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that it is likely to be related to growth in the number and complexity of mutual funds, to

regulatory trends, and to economies of scale as it relates to investments that would

typically be closed to new investors.

In spite of (or perhaps, because of) the renewed popularity of FOFs, the Securities

and Exchange Commission (SEC) recently proposed several rules that would affect FOFs

operating under the Investment Company Act of 1940. One major effect would be

requirements for enhanced disclosure; i.e., an increase in the transparency and clarity of

fees incurred by FOFs. Enhanced disclosure is important because FOFs generally charge

a management fee when portfolio holdings include shares of investment companies that

are not issued by the FOF’s family of funds. This management fee is in addition to the

fees incurred by each position within the FOF portfolio.

The degree to which the mutual fund industry is competitive plays an important

role in motivating traditional empirical studies of mutual fund performance. Although

individual studies reach different conclusions, there appears to be a growing consensus

that most mutual funds do not, on average, generate excess returns after adjusting for fees

and risk. It is therefore puzzling to find that this consensus has not been reached among

studies that focus on the performance of real estate FOFs. Real estate mutual funds are

specialized funds that invest primarily in real estate investment trusts (REITs). Kallberg,

Liu, and Trzcinka (2000) classify real estate mutual funds as FOFs because a REIT acts

like an investment manager of a portfolio of individual real estate investments.

The present study addresses the apparent contradiction in consensus by analyzing

the performance of real estate funds during the sample period, December 1986 to June

1998. Kallberg et al. (2000) find that the alphas of their sample of FOF returns under

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standard asset pricing specifications are mainly positive,2 and conclude that managers of

real estate FOFs do add value. The authors estimate the incremental annual return to be

approximately 2% relative to passive benchmarks, despite the additional layer of fees.

The present analysis starts with a simple question: Do real estate funds, on

average, produce a higher raw return than that produced by a strategy based on a random

selection of available REITs? The answer is important for two reasons. First, without an

accurate description of risk-return tradeoff for real estate securities, it is beneficial to

have several methods to evaluate the robustness of individual test results.3 This line of

reasoning is abundant in the literature of hedge funds (Lo 2001). Second, Kallberg et al.

show that real estate fund managers produce superior performance by investing in illiquid

REITs, which typically have small market capitalizations. Fund managers who invest in

this segment of REITs are hypothesized to have information advantages. This strategy

involves a higher level of risk than investing in more liquid REITs with larger market

capitalizations; consequently, one would expect that real estate mutual funds should, on

average, produce higher returns than those generated by passively selected benchmarks.

Surprisingly, this study finds the opposite to be the case.

The present analysis also examines the performance of real estate funds under the

CAPM and the Fama-French (1993) three-factor model. This study uses additional

control mechanisms because the two standard asset-pricing models do not yield unbiased

2 Lin and Yung (2004) examine the performance of real estate mutual funds during the sample period of 1993 to 2001. Although Lin and Yung’s sample is largely overlapped with that of Kallberg, Liu, and Trzcinka (2000), they reach the opposite conclusion, and argue that real estate mutual fund managers do not add value. This study performs some of Lin and Yung’s analyses and finds that their alpha estimates appear to be systematically too low. For example, for their eighth sample fund, Alpine International Real Estate, Y has an intercept of -0.40 under the CAPM with the use of the CRSP and the Morningstar Principia; yet, Lin and Yung’s result is -0.80. This inconsistency is likely due to Lin’s and Yung’s use of daily return data from Yahoo, which is likely to be less reliable than data extracted from the CRSP.3 As we will show in the following analyses, traditional stock-based asset pricing models do not provide unbiased inferences. The passive National Association of Real Estate Investment Trusts (NAREIT) Equity REIT Index does not yield zero alphas under traditional specifications.

5

inferences. Real estate fund managers’ incremental alphas with respect to those alphas

produced by passive investing strategies are estimated under the two specifications. With

the inclusion of this control mechanism, the results suggest that the environment in which

real estate funds compete is competitive in that the funds do not add value net of fees and

risk adjustments.

Data

This study uses the January 2004 edition of the Morningstar Principia database to

identify real estate mutual funds. The analysis focuses on the subset of real estate mutual

funds that satisfied the following criteria: (1) is classified by the Morningstar as a real

estate fund, (2) has a fund portfolio allocation to bonds and other asset classes of less

than 10%, and (3) has a return history of at least two years. Since a fund with a

successful return history is more likely to issue multiple-share classes representing

different fee structures, we selected the oldest share class for the analysis. By excluding

multiple-share classes, we avoided introducing a positive performance bias into the

results. We then retrieved monthly returns of sample funds from the Center for Research

in Security Prices (CRSP) mutual fund database to the end of 2003. Merging the data

from the two databases resulted in the final set of 55 real estate FOFs.

Table 1 reports summary statistics. During the sample period, January 1982 to

December 2003, the average monthly return on the National Association of Real Estate

Investment Trusts (NAREIT) Equity REIT Index is 1.11%. Based on monthly returns,

the standard deviation is 3.42%. The 55 sample funds yield slightly lower returns -- on

average, 1.06% per month. The standard deviation is 3.37%. Because real estate FOFs

tend to yield lower returns than the NAREIT Equity REIT Index, real estate funds can

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outperform the benchmark only if they have lower amounts of systematic risk than the

NAREIT Equity REIT Index. This fact seems to be inconsistent with the notion that real

estate fund managers produce superior performance by investing in small, illiquid REITs

that typically have higher amounts of systematic risk.

During the sample period, January 1982 to December 2003, U.S. stocks have a

slightly higher average monthly return, 1.13%, and a higher standard deviation, 4.55%.

The hedging strategy of buying small stocks and selling big stocks (SMB) yields zero

return. The strategy of buying high BE/ME (book-to-market ratio) stocks and selling low

BE/ME stocks yields an average return of 0.42% per month. As of December 2003, the

average real estate FOFs held approximately $268 million in assets and had an average

expense ratio of 1.26%. According to the CRSP mutual fund database, the expense ratio

for domestic stock mutual funds is approximately 0.60%. The relatively high expense

structure of real estate FOFs suggests that, holding other factors constant, it is relatively

difficult for these FOFs to outperform their benchmarks.

The identification of the sample from the 2003 Morningstar database imparts a

survivorship bias. This bias inflates performance metrics because funds with poor

performance records have a higher probability of being terminated and not being included

in our sample. In the presence of survivorship bias, the alpha estimates of the current

study are inflated upward by the absence of terminated funds. This should make the

notion that real estate FOFs do not outperform the market a more conservative

conclusion.

Statistical Methods

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The study performs two sets of statistical analyses. The first set involves a Monte

Carlo experiment. For each sample fund, this experiment compares the accumulated

return of the fund during its sample period with a large number of accumulated returns

that are based on a strategy of randomly selecting REITs. This strategy takes equally

weighted positions in the portfolio and rebalances the positions on a monthly basis. The

naïve strategy randomly selects one-half of all REIT returns available for that month in

the CRSP stock file.4 Portfolio positions are equal-weighted because this study is

interested in the question of whether real estate mutual fund managers on average

outperform their benchmarks. The Monte Carlo experiment is repeated 1,000 times.

Since the empirical distribution of accumulated returns is obtained through the

experiments, statistical inferences can be conducted in the usual manner.

The second set of analyses involves time-series regressions based on two

specifications. The first specification is based on the CAPM:

Ri,t = i + bi Rm,t + i,t

where Ri,t is the excess return on sample fund i net of one-month T-Bill rate and Rm,t is the

excess return on the CRSP value-weighted portfolio net of one-month T-Bill rate.

The second specification uses the Fama-French three-factor model:

Ri,t = i + bi Rm,t + si SMBt + hi HMLt + i,t

where SMB is the difference between the returns on portfolios of small and big stocks,

and HML is the difference between the returns on portfolios of high- and low-BE/ME

(book-to-market ratio) stocks. These two models are used in this study because they have

been widely used in REIT and real estate mutual fund studies (Peterson and Hsieh 1997;

4 The study also experiments with the strategies of randomly investing in one-quarter, one-third, two-third, and three-quarter of available REITs. The results are qualitatively similar.

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Kallberg, Liu, and Trzcinka 2000; Buttimer, Hyland, and Sanders 2005; Chiang, Lee, and

Wisen 2004, 2005; among many others).

Although performance evaluation is more meaningful when it is done on a risk-

adjusted basis, performance evaluation models are nevertheless subject to the bad model

problem (Fama 1998). This caveat is particularly important for real estate funds because

the asset pricing of REITs is still in its nascent stage and industry-specific factors may

exist (Downs 2000). Because of this concern, this study proposes the following

robustness checks:

Ri,t − RNAREIT,t = (i − NAREIT) + (bi − bNAREIT) Rm,t + (i,t − NAREIT,t)

i + bi Rm,t + ei,t

Ri,t − RNAREIT,t = (i − NAREIT) + (bi − bNAREIT) Rm,t + (si − sNAREIT) SMBt + (hi − hNAREIT) HMLt

+ (i,t − NAREIT,t)

i + bi Rm,t + si SMBt + hi HMLt + ei,t

where RNAREIT,t is the excess return on the NAREIT Equity REIT Index net of one-month

T-Bill rate. Thus, the dependent series are active (incremental) returns with respect to the

passive NAREIT equity REIT returns. Under these two specifications, i’s measure the

incremental alphas due to active selection of REITs. That is, if managers passively

manage their funds and produce alphas that are no different from that of the passive

benchmark, one would expect i’s to be zero. In contrast, if managers’ active REIT

selection adds value to real estate mutual funds, one would expect i’s to be positive

after risk adjustments.5 Active management adds value only if incremental returns have

positive alphas because benchmark returns have zero alphas under well-specified models.

5 Note that this control mechanism is, at best, a weak one. One would prefer to evaluate real estate mutual funds’ performance directly under a well-specified model but as of yet this model does not appear to exist.

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This is a necessary condition; otherwise, investors will be better off by holding passive

portfolios. As a result, focusing on the performance of active returns provides an

alternative way to check the robustness of performance tests.

This control mechanism is similar to the one used in Chordia and Swaminathan

(2000). The difference between these authors’ research design and ours is that they use

incremental beta to infer differential speed of price discovery, whereas we use

incremental alpha to infer managerial ability. Because the risk exposures of the passive

NAREIT Equity REIT Index are subtracted from those of real estate FOFs, the fit of the

above specifications is, by construction, reduced to reflect the importance of investment

styles on mutual fund performance (Brinson, Hood, and Beebower 1991).

Empirical Results

Monte Carlo results based on accumulated raw returns are depicted in Figure 1.

The histogram of p-values under the null of superior performance shows that 37 and 43

out of 55 sample funds are rejected at the 5% and the 10% level, respectively. That is,

the majority of real estate mutual funds yield returns that are no better than a simple

strategy of randomly investing in a large number of REITs. There are only three real

estate mutual funds that show consistently superior raw returns at the 5% level.

This result is quite surprising. Kallberg et al. find that real estate mutual fund

managers add value under standard asset pricing specifications by investing in small,

illiquid REITs. Given this finding, in equilibrium one would expect that real estate

mutual funds would produce higher average returns than those produced by passively

selected benchmarks because illiquid securities with small market capitalizations should

be compensated with higher returns. This expectation stands in contrast to the empirical

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results. A second, rather puzzling, observation is that the raw return distribution of real

estate mutual funds is polarized. There are only a few real estate mutual funds that yield

returns that are approximately on par with randomly selected benchmarks. The majority

of real estate mutual funds yield lower returns than the benchmark and only a few of

them generated higher returns than the benchmark.

It is important to highlight that the ability of the CAPM or the Fama-French

model to describe REIT returns is rather low. Table 2 reports the monthly time-series

regression results of NAREIT equity REIT returns based on the two specifications.6

During the sample period, January 1982 to December 2003, the alphas for the passive

portfolios are 4.78% and 2.42% per annum under the CAPM and the Fama-French three-

factor model, respectively. The corresponding t-statistics are 2.09 and 1.20. These

alphas are economically significant and their magnitudes are in line with Kallberg et al’s

estimates that used active real estate mutual fund returns. The R-squared values under

the two specifications are 24.60% and 40.19%, respectively.

The test results suggest that control mechanisms are needed to mitigate the

positive alpha bias under the two standard asset-pricing models. The reason for this is

that, if no control mechanisms are used, inactive managers can simply mimic the

NAREIT Equity REIT Index and produce seemingly positive alphas and values under

standard asset-pricing models.

Table 3 summarizes the regression results for each real estate mutual fund under

the CAPM and the Fama-French three-factor model. As expected, without any control

mechanism, the average alpha is positive and large, and has a value of 7.96% per annum.

6 Monthly regressions are used because high-frequency tests yield more powerful results. Alpha estimates are reported at both monthly and annual frequencies because annual alpha presentation is more intuitive.

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The average t–statistic is 1.65. A t-test for a population mean on these 55 alpha estimates

yields 14.30, which is statistically significant at the 1% level. These results indicate that

real estate funds have statistically superior performance under the CAPM.

The average alpha is 4.78% per annum under the Fama-French three-factor

model. The average t–statistic is 1.12. A t-test for a population mean on these 55 alpha

estimates yields a test static of 11.09, which is statistically significant at the 1% level.

The average R–squared is 29.93%. The estimates overall are quite close to those results

in Kallberg et al.

Table 4 reports the regression results with the proposed control mechanisms.

The average incremental alphas due to active selection of REITs are 0.24% and 0.60%

per annum under the CAPM and the Fama-French three-factor model, respectively. The

average t-statistics of these incremental alphas are 0.07 and 0.43, respectively. The t-

statistics for testing a population mean are 0.91 and 2.23, respectively. Overall, there

appears no superior performance from real estate mutual fund managers’ active REIT

selection once control mechanisms are used.

The performance distribution shown in Figure 1 suggests that there could be a few

funds with stellar records that skew average incremental alpha estimates. An

examination of the 55 incremental three-factor alphas indicates that the largest three

incremental alphas are 12.68%, 7.31%, and 3.66% per annum.

Further Checks

A standard robustness check for time-series regressions is to evaluate calendar-

time regressions. Sample fund returns are aggregated into a portfolio, and the monthly

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time-series are regressed under the previous specifications. An additional benefit of

applying this robustness check is that it accounts for the cross-correlation in alphas.

The test results for the portfolio of aggregated real estate funds under the CAPM

and the Fama-French three-factor model are reported in Table 5. The results are similar

to those reported in Table 3. The average alphas under the CAPM and the Fama-French

three-factor model are 3.91% and 1.81% per annum, respectively. The t-statistics for

testing a population mean are 1.81 and 0.92 for the two specifications, and neither is

statistically significant at conventional levels. The R-squared values from the two

specifications are 28.57% and 40.34%, respectively.

Table 6 reports the calendar-time regressions with the control mechanisms. The

incremental alphas under the CAPM and the Fama-French three-factor model become

negative, and are -0.84% and -0.60% per annum. Their t-statistics of -0.57 and -0.44

suggest that the skills of real estate mutual fund managers are not statistically different

from zero.

Another usual robustness test involves the inclusion of the Carhart (1997)

momentum factor; i.e., the up-minus-down (UMD) strategy of buying winner stocks and

shorting loser stocks.7 The test results are shown in the last panels of Tables 5 and 6.

Real estate FOFs exhibit positive exposures to the momentum factor. The t-statistic is

4.76, which is statistically significant at the 1% level. This lowers the alpha to -0.14%

per month, indicating that our baseline result of no superior performance appears to be

robust. When the control mechanism is used, the incremental alpha is -0.09% per month.

7 Details of the factor formation process and the factor returns are available on Kenneth French’s website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

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Overall, the results indicate that our results are not sensitive to the use of the momentum

factor.

Conclusion

The study finds that the prior evidence of superior performance of real estate

mutual funds is quite sensitive to model specification. Monte Carlo simulations indicate

that the vast majority of real estate FOFs performs no better than a strategy of randomly

investing in REITs. The study also finds the hypothesis that real estate FOF managers

invest in illiquid REITs with small market capitalizations to create superior performance

is unlikely to be true.

The biased ability of the CAPM and the Fama-French three-factor model to

describe REIT returns calls into question prior studies that found that real estate FOFs

produced superior performance. Under additional performance evaluation specifications,

this study shows that real estate mutual funds do not produce abnormal returns. These

results are consistent with the mutual fund literature that finds that fund managers, on

average, do not outperform their benchmarks.

Mutual funds that specialize in managing REITs provide administrative and

monitoring services and offer additional diversification benefits to investors. Their

economic functions are also important for promoting real estate securitization. Real

estate FOFs have generated higher returns than other mutual fund categories during the

last two decades; however, the risk-adjusted performance of real estate mutual funds

using a variety of performance metrics and control procedures suggests that their

performance is consistent with an equilibrium in which competition drives away

abnormal returns.

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References

Brinson, G.P., L.R. Hood, and G.P. Beebower. 1991. Determinants of Portfolio Performance II: An Update. Financial Analysts Journal 47: 40-48.

Buttimer, R.J., D.C. Hyland, and A.B. Sanders. 2005. REITs, IPO Waves, and Long Run Performance. Real Estate Economics 33(1): 51-88.

Carhart, M.M. 1997. On Persistence in Mutual Fund Performance. Journal of Finance 52(1): 57-82.

Chiang, K., K. Kozhevnikov, M. Lee, and C. Wisen. 2004. Another Look at the Asymmetric REIT-Beta Puzzle. Journal of Real Estate Research 26(1): 25-42.

Chiang, K., M. Lee, and C. Wisen. 2005. On the Time-Series Properties of Real Estate Investment Trust Betas. Real Estate Economics 33(2): 381-396.

Chordia, T., and B. Swaminathan. 2000. Trading Volume and Cross-Autocorrelations in Stock Returns. Journal of Finance 55(2): 913-935.

Downs, D.H. 2000. Assessing the Real Estate Pricing Puzzle: A Diagnostic Application of the Stochastic Discounting Factor to the Distribution of REIT Returns. Journal of Real Estate Finance and Economics 20(2): 155-175.

Fama, E.F. 1998. Market Efficiency, Long-Term Returns, and Behavioral Finance. Journal of Financial Economics 49: 283-306.

Fama, E.F., and K.R. French. 1993. Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics 33: 3-56.

Kallberg, J.G., C.L. Liu, and C. Trzcinka. 2000. The Value Added from Investment Managers: An Examination of Funds of REITs. Journal of Financial and Quantitative Analysis 35: 387-408.

Lin, C.Y., and K. Yung. 2001. Real Estate Mutual Funds: Performance and Persistence. Journal of Real Estate Research 26(1): 69-95.

Lo, A. 2001. Risk Management for Hedge Funds: Introduction and Overview. Financial Analysts Journal 57: 16-33.

Peterson, J. and C. Hsieh. 1997. Do Common Risk Factors in the Returns on Stocks and Bonds Explain Returns on REITs? Real Estate Economics 25(2): 321-345.

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Table 1 ■ Summary statistics

Mean Median Standard Deviation

NAREIT Monthly Return (%) 1.11 1.11 3.42CRSP Stock Monthly Return (%) 1.13 1.50 4.55SMB Monthly Return (%) 0.00 0.00 3.39HML Monthly Return (%) 0.42 0.35 3.26Mutual Fund Monthly Return (%) 1.06 1.18 3.37Net Assets ($MM) 267.68 105.55 535.10Expense Ratio (%) 1.26 1.24 0.47Age (Year) 7.80 6.92 3.54Note: These summary statistics are based on 55 real estate mutual funds. The sample period is from January 1982 to December 2003.

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Table 2 ■ Time-series regressions of NAREIT equity REIT returns based on the CAPM and the Fama-French three-factor model

Estimate t-StatisticPanel A: The CAPMai 0.0039 [0.0478] 2.09bi 0.3727 9.25R2 (%) 24.60Panel B: The Fama-French (1993) Three-Factor Modelai 0.0020 [0.0243] 1.20bi 0.4286 11.11si 0.3572 6.34hi 0.3541 7.00R2 (%) 40.19Note: The regressions in Panel A are based on the following specification: Ri,t = i + bi Rm,t + i,t, where the dependent series is the excess return of NAREIT equity index net of one-month T-Bill rate. The independent variable is the CRSP value-weight stock market excess return net of one-month T-bill rate. The regressions in Panel B are based on the following specification: Ri,t = i + bi Rm,t + si SMBt + hi HMLt + i,t. Explanatory factors consist of the market excess return net of one-month T-bill rate, and the SMB and the HML factors of Fama and French (1993). Annual alpha estimates are in brackets.

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Table 3 ■ Time-series regressions

Mean Estimate t-StatisticPanel A: The CAPMai 0.0064 [0.0796]

(1.65)14.30

bi 0.2572(3.57)

17.08

Average R2 (%) 12.30Panel B: The Fama-French (1993) Three-Factor Modelai 0.0039 [0.0478]

(1.12)11.09

bi 0.2873(4.28)

18.01

si 0.2801(3.16)

24.21

hi 0.3002(4.23)

34.13

Average R2 (%) 29.93Note: The regressions in Panel A are based on the following specification: Ri,t = i + bi Rm,t + i,t, where the dependent series are the excess returns of 55 real estate mutual funds net of one-month T-Bill rate. The independent variable is the market excess return net of one-month T-bill rate. Average t-statistics from the 55 regressions are in parentheses. The regressions in Panel B are based on the following specification: Ri,t = i + bi Rm,t + si SMBt + hi HMLt + i,t. Explanatory factors consist of the market excess return net of one-month T-bill rate, and the SMB and the HML factors of Fama and French (1993). The last column reports t-statistics for one population mean based on the 55 sets of point estimates. Annual alpha estimates are in brackets.

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Table 4 ■ Controlled time-series regressions

Mean Estimate t-StatisticPanel A: The CAPMai 0.0002 [0.0024]

(0.07)0.91

bi 0.0387(0.81)

2.89

Average R2 (%) 4.60Panel B: The Fama-French (1993) Three-Factor Modelai 0.0005 [0.0060]

(0.43)2.23

bi 0.0341(0.65)

2.64

si -0.0262(-1.38)

-2.50

hi -0.0388(0.13)

-5.15

Average R2 (%) 13.49Note: The regressions in Panel A are based on the following specification: Ri,t − RNAREIT,t = i + bi Rm,t + i,t, where the dependent series are the differences between the excess returns of 55 real estate mutual funds and the excess returns of the NAREIT equity REIT returns. The independent variable is the market excess return net of one-month T-bill rate. Average t-statistics from the 55 regressions are in parentheses. The regressions in Panel B are based on the following specification: Ri,t − RNAREIT,t = i + bi Rm,t + si SMBt + hi HMLt + i,t. Explanatory factors consist of the market excess return net of one-month T-bill rate, and the SMB and the HML factors of Fama and French (1993). The last column reports t-statistics for one population mean based on the 55 sets of point estimates. Annual alpha estimates are in brackets.

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Table 5 ■ Calendar-time regressions

Estimate t-StatisticPanel A: The CAPMai 0.0032 [0.0391] 1.81bi 0.3951 10.24R2 (%) 28.57Panel B: The Fama-French (1993) Three-Factor Modelai 0.0015 [0.0181] 0.92bi 0.4561 12.04si 0.2605 4.70hi 0.3290 6.62R2 (%) 40.34Panel C: The Carhart (1997) Four-Factor Modelai -0.0014 [-0.0167] -0.81bi 0.5242 13.40si 0.3145 5.78hi 0.5031 8.36ui 0.2114 4.76R2 (%) 45.10Note: The regression in Panel A is based on the following specification: Ri,t = i + bi Rm,t + i,t, where the dependent series is the excess return of the equal-weight portfolio of real estate mutual funds net of one-month T-Bill rate. The independent variable is the market excess return net of one-month T-bill rate. The regression in Panel B is based on the following specification: Ri,t = i

+ bi Rm,t + si SMBt + hi HMLt + i,t. Explanatory factors consist of the market excess return net of one-month T-bill rate, and the SMB and the HML factors of Fama and French (1993). The regression in Panel C is further augmented by the inclusion of the Carhart (1997) momentum (UMD) factor: Ri,t = i + bi Rm,t + si SMBt + hi HMLt + ui UMDt + i,t. Annual alpha estimates are in brackets.

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Table 6 ■ Controlled calendar-time regressions

Estimate t-StatisticPanel A: The CAPMai -0.0007 [-0.0084] -0.57bi 0.0223 0.90R2 (%) 0.31Panel B: The Fama-French (1993) Three-Factor Modelai -0.0005 [-0.0060] -0.44bi 0.0275 1.04si -0.0967 -2.50hi -0.0251 -0.72R2 (%) 2.64Panel C: The Carhart (1997) Four-Factor Modelai -0.0009 [-0.0107] -0.76bi 0.0378 1.33si -0.0885 -2.24hi 0.0012 0.03ui 0.0320 0.99R2 (%) 3.00Note: The regression in Panel A is based on the following specification: Ri,t − RNAREIT,t = i + bi

Rm,t + i,t, where the dependent series is the difference between the excess return of the equal-weight portfolio of real estate mutual funds and the excess return of the NAREIT equity REIT returns. The independent variable is the market excess return net of one-month T-bill rate. The regression in Panel B is based on the following specification: Ri,t − RNAREIT,t = i + bi Rm,t + si

SMBt + hi HMLt + i,t. Explanatory factors consist of the market excess return net of one-month T-bill rate, and the SMB and the HML factors of Fama and French (1993). The regression in Panel C is augmented by the inclusion of the Carhart (1997) momentum factor. Annual alpha estimates are in brackets.

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Figure 1 ■ The distribution of p-values under the null of superior performance

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