Further Evidence on the Performance of Funds of Funds: The Case of Real Estate Mutual Funds Kevin C.H. Chiang* School of Management University of Alaska Fairbanks Fairbanks, AK 99775 Kirill Kozhevnikov Lundquist College of Business University of Oregon Eugene, OR 97403 Ming-Long Lee Department of Finance National Yulin University of Science and Technology Touliu, Yulin, Taiwan 640 Craig H. Wisen School of Management University of Alaska Fairbanks Fairbanks, AK 99775 Key Words: REIT, performance evaluation, mutual funds * Correspondence: Kevin C.H. Chiang, School of Management, University of Alaska Fairbanks, Fairbanks, AK 99775. Phone: (907) 474-7049, Fax: (907) 474-5219, E-mail: ffkcc@uaf.edu. The authors thank Kenneth French for providing the three-factor return series.
Further Evidence on the Performance of Funds of Funds: The Case of Real Estate Mutual Funds Abstract The investors of Funds of funds (FOFs) incur double fees. This fee structure has a negative effect on the performance of FOFs. Nevertheless, there is empirical evidence that real estate mutual funds are able to overcome this disadvantage and add value to their investors by holding shares of real estate investment trusts. This study resolves this puzzle. Under a variety of specifications, the study finds that, consistent with the mutual fund literature, most real estate mutual funds do not outperform their benchmarks. 2
Further Evidence on the Performance of Funds of Funds: The Case of Real Estate Mutual Funds Funds of funds (FOFs) are investment companies that hold shares in other investment companies. The existence of FOFs suggests that they provide investors with superior information, professional oversights, and further diversification because FOF investments incur double fees at the level of individual funds and the level of FOFs. Furthermore, in a competitive market one would expect the marginal benefits from investing in FOFs to be equal to the incremental costs. 1 This study finds that real estate mutual fund industry is indeed quite competitive, and most real estate mutual funds do not outperform their benchmarks. A real estate mutual fund is a specialized mutual fund that invests primarily in real estate investment trusts (REITs). A real estate mutual fund is a FOF because an REIT is a fund of real estate properties. Kallberg, Liu, and Trzcinka (2000) take on this view and examine whether there is value added from real estate mutual fund managers. The authors find that during the sample period of December 1986 to June 1998, the alphas associated with real estate mutual funds under the standard asset pricing specifications are mostly positive. 2 They conclude that real estate mutual fund managers add value of an incremental annual return of about 2% relative to passive benchmarks. 1 There is even evidence from the sector of hedge funds that FOF investors may pay too much for the incremental services (Brown, Goetzmann, and Liang 2003). Nevertheless, the incentive structure in the hedge fund industry is quite different from that in the mutual fund industry. 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 Lin and Yung s alpha estimates appear to be systematically too low. For example, 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 3
This paper adopts a different approach to the performance evaluation of real estate mutual funds. The reason for this is that the study of REIT pricing is still in its nascent stage. Using the most recent five years return data, most of standard, stock-based asset pricing models, e.g., the Capital Asset Pricing Model (CAPM) and the Fama-French (1993) three-factor model, produce only about 10-30% of R-squared on REIT indices. Our understanding on pricing real estate securities is actually no better than that on pricing hedge funds. Motivated by this observation, this study asks a simple question: Does a real estate mutual fund on average produce a higher raw return than a randomly selected REIT portfolio? Answering this question is important for two reasons. First, without an accurate description of risk-return tradeoff for real estate securities, it is beneficial to have multiple evaluation mechanisms to ensure the robustness of empirical results. This line of reasoning is abundant in the literature of hedge funds (Lo 2001). Second, Kallberg et al. show that real estate mutual fund managers add value by investing in small, illiquid REITs in which they have informational advantages. Because of the riskiness of this strategy, one would expect that real estate mutual funds should on average produce higher returns than passively selected benchmarks. Surprisingly, this study finds the opposite. This paper also examines the performance of real estate mutual funds under the CAPM and the Fama-French three-factor model. Nevertheless, because these standard asset pricing models provide limited description of REIT returns, this study adopts a different testing design. Specifically, this study estimates real estate fund managers incremental alphas with respect to those alphas produced by passive investing strategies Principia. Yet Lin and Yung s result is -0.80. This inconsistency is likely due to the use of a less reliable source of daily return data from Yahoo by Lin and Yung. 4
under the two specifications. The notion is that one is more confident about managers performance if they are able to add alphas (value) even under parsimonious specifications. With this control mechanism, our results suggest that the real estate mutual fund industry is quite competitive in that real estate mutual funds do not add alphas. Data The study employs the 2003 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) classified by the Morningstar as a real estate fund, (2) fund portfolio allocation to bonds and other asset classes less than 10%, and (3) return history of at least two years. Funds with successful return histories are more likely to issue multiple share classes representing different fee structures. To prevent multiple share classes from affecting the results the fund s oldest share class is used for the analysis. Monthly returns on these sample funds are then retrieved from the Center for Research in Security Prices (CRSP) mutual fund database to the end of 2003. The merger of the data based on the two databases resulted in the final set of 55 sample funds. Table 1 reports summary statistics. During the sample period of 01/1982-12/2003, the 55 sample funds on average yield 1.05% monthly return. Their returns are stable over this time period, evident by the low monthly standard deviation of 0.26%. As of 12/2003, our sample funds have average net assets of $267.68 million. The average expense ratio is 1.26%. The average age of these funds is 7.8 years. We do not have access to every quarterly Morningstar file from 1987 to the present. Using the 2003 file, our dataset is subject to survivorship bias. Fortunately, 5
although the size of the bias is unknown, it is positive because funds with poor performance records tend to fail. The bias is in fact against our investigation that shows no value added on the part of real estate mutual funds, and makes our results more conservative. Statistical Methods The study performs two sets of statistical analyses. The first set involves Monte Carlo experiment. For each sample fund, this experiment compares the accumulated return of the fund during its sample period to a large number of accumulated returns that are based on a monthly rebalanced strategy of randomly investing in a portfolio of available REITs. Specifically, for each of the fund s available monthly returns the study randomly selects one-half of all REIT returns available for that month in the CRSP stock file and forms an equal-weight monthly return for the purpose of benchmarking. 3 Equal weighting is used throughout the paper because we are interested in the question of whether real estate mutual fund managers on average outperform their benchmarks. This experiment is then repeated for 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 the CAPM: R i,t = α i + b i R m,t + ε i,t where R i,t is the excess return on sample fund i net of one-month T-Bill rate and R m,t is the excess return on the CRSP value-weighted portfolio net of one-month T-Bill rate. 3 The study also tries strategies of investing in one-quarter, one-third, two-third, and three-quarter of available REITs. The results are not sensitive to these variations. 6
The second specification is the Fama-French three-factor model: R i,t = α i + b i R m,t + s i SMB t + h i HML t + ε 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; Kallberg, Liu, and Trzcinka 2000; Buttimer, Hyland, and Sanders 2005; Chiang, Lee, and Wisen 2004, 2005; among many others). Although performance evaluation is meaningful only when it is done on a riskadjusted basis, performance evaluation models are subject to the bad model problem (Fama 1998). This is particularly so for real estate mutual funds because the asset pricing of REITs is still in its nascent stage. To mitigate the inaccuracy associated with the CAPM and the Fama-French three-factor model, this study examines the following two specifications that subtract the regression counterparts on the National Association of Real Estate Investment Trusts (NAREIT) equity REIT returns: R i,t R NAREIT,t = α i + b i R m,t + s i SMB,t + h i HML,t + (ε i,t ε NAREIT,t ) R i,t R NAREIT,t = α i + b i R m,t + s i SMB REIT,t + h i HML REIT,t + (ε i,t ε NAREIT,t ) Under these two specifications, α i s measure the incremental alphas due to active selection of REITs. If managers active REIT selection adds value to real estate mutual funds, one would expect α i s to be positive. 4 4 Note that this control mechanism is, at best, a weak one. We would prefer to evaluate real estate mutual funds performance directly under a well-specified model. But, the reality is that we do not have one yet. 7
Empirical Results Based on the metric of accumulated raw returns, our Monte Carlo results 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. One would expect that real estate mutual funds should on average produce higher returns than passively selected benchmarks because in equilibrium small, illiquid investments should be compensated with higher returns. But this is not what the data shows. Another interesting observation is that the raw return performance of real estate mutual funds appears to be 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; a few of them generate higher returns. Before applying the CAPM and the Fama-French three-factor model to real estate mutual funds, it is important to highlight the fact that their descriptions of REIT returns are far from perfect. Table 2 reports the time-series regression results of NAREIT equity REIT returns based on the two specifications. During the sample period of 01/1982 to 12/2003, the R-squared values under the two specifications are 24.60% and 40.19%. The 8
alphas for this investing in this passive portfolio 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 with the use of active real estate mutual fund returns. It is clear that testing control mechanisms are needed to mitigate the positive alpha bias under the two 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. The average t statistic is 1.65. A t-test for a population mean on these 55 alpha estimates yield a statistic of 14.30, which is statistically significant at the 1% level. The testing result shows that real estate mutual 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 yield a static of 11.09, which is statistically significant at the 1% level. The average R squared is 29.93%. Overall, these estimates are quite close to those in Kallberg et al. Table 4 reports the regression results with the proposed control mechanisms. The 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 9
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. Another interesting result is that the differential loading on the SMB REIT factor is positive and has a value of 0.576. The sign indeed indicates that real estate mutual funds tend to invest more in small, illiquid REITs. This result, together with the performance distribution shown in Figure 1, suggests that there might be a few strong performers that might skew those average incremental alpha estimates. While not plotted, an examination of the 55 incremental three-factor alphas shows that the top 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 run calendar-time regressions. That is, for each month available sample fund returns are aggregated into a portfolio return. Then, the time-series of these portfolio returns are regressed under the previous specifications. An additional benefit for running such regressions is that the cross-correlation in alphas is statistically accounted for. The testing results for the equal-weight, monthly rebalanced portfolio of real estate mutual funds under the CAPM and the Fama-French three-factor model are reported in Table 5. The testing 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 both are not statistically significant at any conventional level. The R-squared values from the two specifications are 28.57% and 40.34%, respectively. 10
Table 6 reports the calendar-time regressions with 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. Conclusion The study finds that the previously documented value added for investing in real estate mutual funds is specification dependent. Using raw returns, the study shows that the usual strategy of investing in small, illiquid REITs employed by real estate mutual fund managers does not lead to superior performance because the funds raw returns are on average no better than those generated from our passive experiments. Under another two performance evaluation specifications, the study also shows that there is no abnormal returns for investing in active real estate mutual funds. Our results are consistent with the mutual fund literature that fund managers on average do not outperform their benchmarks. As FOFs, real estate mutual funds provide administrative services and additional diversification benefits. Their economic functions are important for promoting real estate securitization, and their economic roles are unique. Our findings on real estate mutual funds performance during the past two decades represent an equilibrium result in which competition drives away abnormal returns. 11
References Brown, S.J., W.N. Goetzmann, and B. Liang. 2003. Fees on Fees in Funds of Funds. Working paper, New York University. Buttimer, R.J., D.C. Hyland, and A.B. Sanders. 2005. REITs, IPO Waves, and Long Run Performance. Real Estate Economics, forthcoming. Chiang, K., K. Kozhevnikov, M. Lee, and C. Wisen. 2004. Another Look at the Asymmetric REIT-Beta Puzzle. Journal of Real Estate Research, vol. 26, no. 1(January-March): 25-42. Chiang, K., K. Kozhevnikov, M. Lee, and C. Wisen. 2005. On the Time-Series Properties of Real Estate Investment Trust Betas. Real Estate Economics, forthcoming. Fama, E.F. 1998. Market Efficiency, Long-Term Returns, and Behavioral Finance. Journal of Financial Economics, vol. 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, vol. 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, vol. 35: 387-408. Lin, C.Y., and K. Yung. 2001. Real Estate Mutual Funds: Performance and Persistence. Journal of Real Estate Research, vol. 26, no. 1 (January-March): 69-95. Lo, A. 2001. Risk Management for Hedge Funds: Introduction and Overview. Financial Analysts Journal, vol. 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, vol. 25, no. 2 (Summer): 321-345. 12
Table 1.Summary Statistics Mean Median Standard Deviation Monthly Return (%) 1.05 1.01 0.26 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 base on 55 real estate mutual funds. The sample period is from 01/1982 to 12/2003. 13
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 a i 0.0039 2.09 b i 0.3727 9.25 R 2 (%) 24.60 Panel B: The Fama-French (1993) Three-Factor Model a i 0.0020 1.20 b i 0.4286 11.11 s i 0.3572 6.34 h i 0.3541 7.00 R 2 (%) 40.19 Note: The regressions in Panel A are based on the following specification: R i,t = α i + b i R m,t + ε 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 market excess return net of one-month T-bill rate. The regressions in Panel B are based on the following specification: R i,t = α i + b i R m,t + s i SMB t + h i HML t + ε 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). 14
Table 3. Time-Series Regressions Mean Estimate t-statistic Panel A: The CAPM a i 0.0064 14.30 (1.65) b i 0.2572 17.08 (3.57) Average R 2 (%) 12.30 Panel B: The Fama-French (1993) Three-Factor Model a i 0.0039 11.09 (1.12) b i 0.2873 18.01 (4.28) s i 0.2801 24.21 (3.16) h i 0.3002 34.13 (4.23) Average R 2 (%) 29.93 The regressions in Panel A are based on the following specification: R i,t = α i + b i R m,t + ε 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: R i,t = α i + b i R m,t + s i SMB t + h i HML t + ε 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. 15
Table 4. Controlled Time-Series Regressions Mean Estimate t-statistic Panel A: The CAPM a i 0.0002 0.91 (0.07) b i 0.0387 2.89 (0.81) Average R 2 (%) 4.60 Panel B: The Fama-French (1993) Three-Factor Model a i 0.0005 2.23 (0.43) b i 0.0341 2.64 (0.65) s i -0.0262-2.50 (-1.38) h i -0.0388-5.15 (0.13) Average R 2 (%) 13.49 Note: The regressions in Panel A are based on the following specification: R i,t R NAREIT,t = α i + b i R m,t + (ε i,t ε NAREIT,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: R i,t R NAREIT,t = α i + b i R m,t + s i SMB t + h i HML t + (ε i,t ε NAREIT,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. 16
Table 5. Calendar-Time Regressions Estimate t-statistic Panel A: The CAPM a i 0.0032 1.81 b i 0.3951 10.24 R 2 (%) 28.57 Panel B: The Fama-French (1993) Three-Factor Model a i 0.0015 0.92 b i 0.4561 12.04 s i 0.2605 4.70 h i 0.3290 6.62 R 2 (%) 40.34 Note: The regressions in Panel A are based on the following specification: R i,t = α i + b i R m,t + ε 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 regressions in Panel B are based on the following specification: R i,t = α i + b i R m,t + s i SMB t + h i HML t + ε 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). 17
Table 6. Controlled Calendar-Time Regressions Estimate t-statistic Panel A: The CAPM a i -0.0007-0.57 b i 0.0223 0.90 R 2 (%) 3.06 Panel B: The Fama-French (1993) Three-Factor Model a i -0.0005-0.44 b i 0.0275 1.04 s i -0.0967-2.50 h i -0.0251-0.72 R 2 (%) 2.64 Note: The regressions in Panel A are based on the following specification: R i,t R NAREIT,t = α i + b i R m,t + (ε i,t ε NAREIT,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 regressions in Panel B are based on the following specification: R i,t R NAREIT,t = α i + b i R m,t + s i SMB t + h i HML t + (ε i,t ε NAREIT,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). 18
Figure 1. The Distribution of p-values under the Null of Superior Performance 19