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



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

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

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

regulatory trends, and to econ...
standard asset pricing specifications are mainly positive,2 and conclude that managers of

real estate FOFs do add value. ...
inferences. Real estate fund managers’ incremental alphas with respect to those alphas

produced by passive investing stra...
outperform the benchmark only if they have lower amounts of systematic risk than the

NAREIT Equity REIT Index. This fact ...
The study performs two sets of statistical analyses. The first set involves a Monte

Carlo experiment. For each sample fun...
Kallberg, Liu, and Trzcinka 2000; Buttimer, Hyland, and Sanders 2005; Chiang, Lee, and

Wisen 2004, 2005; among many other...
This is a necessary condition; otherwise, investors will be better off by holding passive

portfolios.   As a result, focu...
results. A second, rather puzzling, observation is that the raw return distribution of real

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

yields 14.30, which is statis...
time-series are regressed under the previous specifications. An additional benefit of

applying this robustness check is t...
Overall, the results indicate that our results are not sensitive to the use of the momentum

factor.

Conclusion

        ...
References

Brinson, G.P., L.R. Hood, and G.P. Beebower. 1991. Determinants of Portfolio
Performance II: An Update. Financ...
Table 1 ■ Summary statistics

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

...
Table 3 ■ Time-series regressions

                                          Mean Estimate                         t-Stati...
Table 4 ■ Controlled time-series regressions

                                          Mean Estimate                     ...
Table 5 ■ Calendar-time regressions

                                             Estimate                         t-Stati...
Table 6 ■ Controlled calendar-time regressions

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




                                       ...
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Real Estate Mutual Fund Paper.doc

  1. 1. Further Evidence on the Performance of Funds of Funds: The Case of Real Estate Mutual Funds Kevin C.H. Chiang* College of Business Administration Northern Arizona University Flagstaff, AZ 86011-5066 Kirill Kozhevnikov Lundquist College of Business University of Oregon Eugene, OR 97403 Ming-Long Lee Department of Finance National Yunlin University of Science and Technology Douliou, Yunlin, Taiwan 640 Craig H. Wisen School of Management University 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.
  2. 2. 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. 2
  3. 3. 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 3
  4. 4. 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 4
  5. 5. 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
  6. 6. 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 6
  7. 7. 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 7
  8. 8. 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 = αi + bi Rm,t + εi,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 = αi + bi Rm,t + si SMBt + hi HMLt + εi,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. 8
  9. 9. 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 = (αi − αNAREIT) + (bi − bNAREIT) Rm,t + (εi,t − εNAREIT,t) ≡ ∆αi + ∆bi Rm,t + ei,t Ri,t − RNAREIT,t = (αi − αNAREIT) + (bi − bNAREIT) Rm,t + (si − sNAREIT) SMBt + (hi − hNAREIT) HMLt + (εi,t − εNAREIT,t) ≡ ∆αi + ∆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, ∆αi’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 ∆αi’s to be zero. In contrast, if managers’ active REIT selection adds value to real estate mutual funds, one would expect ∆αi’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. 9
  10. 10. 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 10
  11. 11. 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. 11
  12. 12. 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 12
  13. 13. 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. 13
  14. 14. 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. 14
  15. 15. 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. 15
  16. 16. Table 1 ■ Summary statistics Mean Median Standard Deviation NAREIT Monthly Return (%) 1.11 1.11 3.42 CRSP Stock Monthly Return (%) 1.13 1.50 4.55 SMB Monthly Return (%) 0.00 0.00 3.39 HML Monthly Return (%) 0.42 0.35 3.26 Mutual Fund Monthly Return (%) 1.06 1.18 3.37 Net Assets ($MM) 267.68 105.55 535.10 Expense Ratio (%) 1.26 1.24 0.47 Age (Year) 7.80 6.92 3.54 Note: These summary statistics are based on 55 real estate mutual funds. The sample period is from January 1982 to December 2003. 16
  17. 17. Table 2 ■ Time-series regressions of NAREIT equity REIT returns based on the CAPM and the Fama-French three-factor model Estimate t-Statistic Panel A: The CAPM ai 0.0039 [0.0478] 2.09 bi 0.3727 9.25 R2 (%) 24.60 Panel B: The Fama-French (1993) Three-Factor Model ai 0.0020 [0.0243] 1.20 bi 0.4286 11.11 si 0.3572 6.34 hi 0.3541 7.00 R2 (%) 40.19 Note: The regressions in Panel A are based on the following specification: Ri,t = αi + bi Rm,t + εi,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 = αi + bi Rm,t + si SMBt + hi HMLt + εi,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. 17
  18. 18. Table 3 ■ Time-series regressions Mean Estimate t-Statistic Panel A: The CAPM ai 0.0064 [0.0796] 14.30 (1.65) bi 0.2572 17.08 (3.57) 2 Average R (%) 12.30 Panel B: The Fama-French (1993) Three-Factor Model ai 0.0039 [0.0478] 11.09 (1.12) bi 0.2873 18.01 (4.28) si 0.2801 24.21 (3.16) hi 0.3002 34.13 (4.23) Average R2 (%) 29.93 Note: The regressions in Panel A are based on the following specification: Ri,t = αi + bi Rm,t + εi,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 = αi + bi Rm,t + si SMBt + hi HMLt + εi,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. 18
  19. 19. Table 4 ■ Controlled time-series regressions Mean Estimate t-Statistic Panel A: The CAPM ∆ai 0.0002 [0.0024] 0.91 (0.07) ∆bi 0.0387 2.89 (0.81) 2 Average R (%) 4.60 Panel B: The Fama-French (1993) Three-Factor Model ∆ai 0.0005 [0.0060] 2.23 (0.43) ∆bi 0.0341 2.64 (0.65) ∆si -0.0262 -2.50 (-1.38) ∆hi -0.0388 -5.15 (0.13) Average R2 (%) 13.49 Note: The regressions in Panel A are based on the following specification: Ri,t − RNAREIT,t = ∆αi + ∆bi Rm,t + εi,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 = ∆αi + ∆bi Rm,t + ∆si SMBt + ∆hi HMLt + εi,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. 19
  20. 20. Table 5 ■ Calendar-time regressions Estimate t-Statistic Panel A: The CAPM ai 0.0032 [0.0391] 1.81 bi 0.3951 10.24 R2 (%) 28.57 Panel B: The Fama-French (1993) Three-Factor Model ai 0.0015 [0.0181] 0.92 bi 0.4561 12.04 si 0.2605 4.70 hi 0.3290 6.62 R2 (%) 40.34 Panel C: The Carhart (1997) Four-Factor Model ai -0.0014 [-0.0167] -0.81 bi 0.5242 13.40 si 0.3145 5.78 hi 0.5031 8.36 ui 0.2114 4.76 2 R (%) 45.10 Note: The regression in Panel A is based on the following specification: Ri,t = αi + bi Rm,t + εi,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 = αi + bi Rm,t + si SMBt + hi HMLt + εi,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 = αi + bi Rm,t + si SMBt + hi HMLt + ui UMDt + εi,t. Annual alpha estimates are in brackets. 20
  21. 21. Table 6 ■ Controlled calendar-time regressions Estimate t-Statistic Panel A: The CAPM ∆ai -0.0007 [-0.0084] -0.57 ∆bi 0.0223 0.90 2 R (%) 0.31 Panel B: The Fama-French (1993) Three-Factor Model ∆ai -0.0005 [-0.0060] -0.44 ∆bi 0.0275 1.04 ∆si -0.0967 -2.50 ∆hi -0.0251 -0.72 2 R (%) 2.64 Panel C: The Carhart (1997) Four-Factor Model ∆ai -0.0009 [-0.0107] -0.76 ∆bi 0.0378 1.33 ∆si -0.0885 -2.24 ∆hi 0.0012 0.03 ∆ui 0.0320 0.99 R2 (%) 3.00 Note: The regression in Panel A is based on the following specification: Ri,t − RNAREIT,t = ∆αi + ∆bi Rm,t + εi,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 = ∆αi + ∆bi Rm,t + ∆si SMBt + ∆hi HMLt + εi,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. 21
  22. 22. Figure 1 ■ The distribution of p-values under the null of superior performance 22

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