«Nina Rogers Tarleton State University Imre Karafiath University of North Texas Margie Tieslau University of North Texas INTRODUCTION Since Jensen‟s ...»
Significant Alphas in Real Estate Funds: Do Fund Managers Add Value?
Tarleton State University
University of North Texas
University of North Texas
Since Jensen‟s 1967 study, the majority of academic research has supported
the efficient market hypothesis, which implies that fund managers cannot routinely over
time „beat the market‟ with superior risk adjusted returns (Fama and French (2010)).
However, sector fund managers may have access to informational asymmetries about their area that enable superior risk adjusted returns (Dellva, DeMaskey and Smith (2001)). In this environment, real estate fund management has presented a conundrum, with several studies reporting positive and significant alphas1 for real estate funds (Cici, Corgel and Gibson (2011), Kallberg, Liu, Trzcinka (2000), Gallo, Lockwood and Rutherford (2000)). Other researchers report real estate fund managers do not outperform the market on a risk-adjusted basis, taking into account differing benchmarks, bootstrap methodology, control factors or test periods (Lin and Yung (2004), Rodriquez (2007), and Chiang, Kozhevnikov, Lee and Wisen (2008), Kaushik and Pennathur (2013)).
We evaluate two issues regarding Jensen‟s alpha as a measure of superior risk adjusted returns to real estate mutual funds. First, are the test statistics sensitive to alternative estimates of the standard errors that take heteroskedasticity into account? 2 Second, are the estimates of Jensen‟s alpha sensitive to specification error in the Jensen‟s alpha is used to evaluate a fund manager‟s ability to provide superior risk-adjusted returns.
The Morningstar Box Score Report, http://global.morningstar.com/US/documents/Indexes/MorningstarBoxScoreReport2H09.pdf (accessed October 2013 Real estate returns have been noted for heteroskedasticity (Young (2008), Cheng (2005), Yang and Chen (2009)).
model, i.e., is the apparent significance of alpha attributable to the pricing of factors other than “the” market return?
In in order to address the first issue, we evaluate the significance of Jensen‟s alpha in real estate returns using several robust (i.e., heteroskedastic-consistent) estimators including the variants of the White (1980) estimator present by MacKinnon and White (1985), the Newey-West (1987) heteroskedastic-autocorrelation-consistent [HAC] estimator, and the „wild‟ bootstrap suggested by Davidson and Flachaire (2008).3 In order to address the second issue, we estimate regression models that include innovations in the default spread, credit spread, market skewness and change industrial production growth as explanatory variables.
Additionally, three indexes as benchmarks are used in evaluating significant alphas in real estate returns. The Wilshire 5000 Index provides a total market benchmark, the Wilshire Real Estate Index provides a general real estate benchmark, and the NAREIT Index provides a REIT benchmark.
We compare the frequency of significant alphas obtained from OLS regression with OLS standard errors to the results obtained from three heteroskedastic-consistent [HC] estimators, the Newey-West (1987) standard errors, and a wild bootstrap applied to one of the HC estimators4. Examining several contiguous sub periods over the interval from 1990 to 2012, we find that the heteroskedastic-consistent standard errors reduced the number of significant alphas exhibited by real estate mutual funds.
We are not aware of any other study of Jensen‟s alpha that relies on a wild bootstrap.
More specifically, we apply the wild bootstrap to the HC standard error designated HC3 by MacKinnon and White (1985); HC3 is an exact equivalent to the „delete-one‟ jackknife. Since HC3 is more conservative (less likely to reject the null) than other HC standard errors, our goal is to establish whether bootstrapping can further reduce the frequency of significant alpha.
Implementing a wild bootstrap consistently provides the most conservative result.
Similar results were obtained with real estate investment trusts. [REITs] Contrary to expectations, the HAC (Newey-West) standard error increased the per cent of REITs that exhibit significant alphas. For most of the time periods studied (regardless of benchmark) the number of REITs that exhibit significant alphas based on Newey-West standard errors was greater than any other estimator.
In general, adding explanatory variables to the regression failed to systematically attenuate the frequency of significant alphas in real estate fund returns.
However, using the nominal 5% critical values, the inclusion of the short-run volatility proxy reduced the per cent of real estate mutual funds that exhibit significant alphas from 14% to 8% over the 2005 to 2012 period. A further reduction occurred with the wild bootstrap. This result suggests that financial constraints (proxied by market skewness) may be a factor in the pricing of real estate mutual funds returns during some time periods.
For the REIT sample, short- and long-run volatility proxies attenuated the frequency of significant alphas from 9% to 7% over the 1996 to 2012 period using OLS standard errors. When the REIT sample is examined with the wild bootstrap applied to heteroskedastic consistent standard errors, the proportion of REITs that exhibit significant alphas is reduced to less than 4% in most periods, i.e. less than the nominal significance level of the test.
The addition of innovations from the change in default and term spread had a minimal effect on explanatory power as measured by the adjusted R2. Our proxies for short and long-run volatility increased the explanatory power only in the 1990 to 2012 sample for real estate mutual funds.
Our results suggest the potential for erroneous interpretation of significance of variables when the standard errors are not adjusted for heteroskedasticity. Tabulating critical values of the empirical distribution using a wild bootstrap provided the most conservative result regarding the frequency of real estate funds with significant alphas.
The remainder is organized as follows: Section 2 describes the methodology, Section 3 the data, Section 4 and 5 provides empirical results and concluding comments.
Section 2 Methodology Jensen‟s alpha measures fund performance using the single index version of the capital-asset pricing model (CAPM). The model assumes that realized returns on the security or portfolio are expressed as a linear function of its systematic risk, the realized returns on the market portfolio, the risk-free rate and a random error. Following
Gallo et. al. (2002), our first model specification is based on the CAPM:
t net of the change in the monthly return on the Citi 3-month Treasury Bill5 in month t.
Alternative proxies for Rm,t are the excess return on the Wilshire Real Estate Index, the NAREIT Index, or the Wilshire 5000 Index.
Citi 3-month Treasury Bill was used by Gallo, Lockwood and Rutherford (2000) in their study.
Following Hahn and Lee (2006) our second model includes innovations from
the default spread and the term spread:
Where Ri,t, αi, and Rm,t are as previously defined and the ∆defaultt is the white noise innovations from deft – deft-1 and ∆termt is the white noise innovation from termt – termt-1, and deft and termt are the default spread and term spread at time t.
Following Adrian and Rosenberg (2008), our third model is an attempt to improve explanatory power by including market skewness and the change in growth in
industrial production as proxies for short-and long-term volatility:
Where Ri,t, αi, and Rm,t are as previously defined and the market skewness variable and the change in industrial production are included in the model. Adrian and Rosenberg (2008) found that adding short- and long-run volatility components achieved lower pricing errors, as measured by the root-mean-squared pricing error, than the market model with size and book-to-value factors. The third specification of the model includes innovations from market skewness and the change in industrial production.6 To evaluate whether fund managers can add value (as measured by Jensen‟s alpha, i.e., ̂ in equations 1-3) we evaluate the standard error of the estimate with several robust (i.e., heteroskedastic-consistent) estimators. Following MacKinnon and To explain the short-run volatility factor, Adrian and Rosenberg (2008) posit that „negative shocks to the market return increase short-run volatility more than positive shocks to the market‟. This relationship is reflected in the „strong positive correlation in the market risk premia of short-run volatility and skewness‟ White (1985) we tabulate test statistics and empirical rejection rates for the null
from the following variants of the White (1980) standard error:
HC1 is the White (1980) estimator adjusted for degrees of freedom.
HC2 is the leverage-adjusted heteroskedastic-consistent estimator.
HC3 is an exact equivalence to the delete-one jackknife.
Following Davidson and Flachaire (2008), we also evaluate HC3 with a „wild‟ bootstrap.7 The empirical distribution of the test statistic is tabulated from 10,000 iterations of the bootstrap; the critical value for the test is determined by the 5 % tail of the empirical (bootstrapped) distribution after sorting the test statistic from high to low.
Section 3 DATA Real Estate Mutual Funds Domestic fund data available on Morningstar8 from January 1990 to December 2012 comprises the real estate mutual fund sample in this study. Funds with a „successful return history tend to issue multiple-share classes‟ (Chiang, Kozhevnikov, Lee and Wisen (2008)). By excluding all but a single fund from the multiple-share classes, „positive performance bias‟ is avoided (Chiang, Kozhevnikov, Lee and Wisen (2008)). Therefore, funds with multiple share classes are limited to a one-time inclusion in the study. This criterion eliminated 269 funds. A minimum of 36 consecutive months of data is also required for inclusion in the sample which eliminated an additional 15 funds. The final sample contains 80 funds, with five of the 80 funds active from 1990 to 2012.
In accordance with Davidson and Flachaire (2008) we select the Radermacher distribution for the auxiliary random variable.
Morningstar Inc, provided monthly and daily return data for real estate mutual funds.
The number of real estate mutual funds from the Morningstar dataset increased from five funds in 1990 to a peak of seventy-two funds in 2007. The summary statistics for each period under study are listed in Table 1. The first period, 1991 to 1997, corresponds to the time period studied by Gallo, Lockwood and Rutherford (2000).
Subsequent seven-year periods, an eight-year period and the full period of 1990 to 2012 follow the initial seven-year analysis.
There are 84 months in the first and second study periods, with an average number of 53 and 76 observations. The third period included eight years or 96 months with an average of 85 data points per fund. The entire study included 12,000 observations from 1990 to 2012.
Table 1 Real Estate Mutual Fund Summary Statistics
The null hypothesis of no autoregressive conditional heteroskedasticity was rejected for 37 of the 80 real estate mutual funds on the basis of Engle‟s ARCH test at the 5% level. The Breusch-Godfrey test for serial correlation was rejected for 15 funds.10 Forty-one funds exhibited serial correlation or heteroskedasticity.
The significance level for the Breusch-Godfrey test was 5%.
A two-step process developed by Lee, Strazicich, and Meng (2012) is used to test for structural breaks in the mutual fund return series.11 The majority of the breaks in the real estate funds were during the financial crisis period of 2008 and 2009.
REITs Monthly returns of REITs was collected from the Center for Research in Security Prices (CRSP) database from 1990 to 2012 specifying security characteristic line (SCL) 18, which identified 363 REITs. The REIT sample includes equity, mortgage and hybrid REITS listed on the NYSE, AMEX and NASDAQ.12 The initial sample is filtered further by requiring 36 months of continuous returns, which eliminated 60 firms.
The final REIT sample consists of 33,120 firm-month observations and 313 REITs.
The null hypothesis of no heteroskedasticity was rejected for thirty per cent of the 313 REITs in the study sample with Engle‟s ARCH test at a 5% significance level.
Additionally, twenty-eight per cent of the REITs rejected the null hypothesis of no serial Each data series is jointly tested for a structural break by an endogenous trend-break LaGrange Multiplier unit root 2-step procedure. If multiple breaks are detected within a six month interval these are considered a single structural break. If no trend (slope) breaks are identified, the data is tested for breaks in level (intercept) with the Lee and Strazicich (2003) method. If no level breaks are identified, the series is analyzed for stationarity by the Schmidt and Phillips (1992) technique.
Hybrid REITs invest in equity and mortgage trusts.
correlation at the 5% level for with the Breusch-Godfrey test for serial correlation. Fortythree per cent of the REITs displayed serial correlation or heteroskedasticity, while fifteen per cent of the firms exhibited both serial correlation and heteroskedasticity.
Benchmarks Three benchmarks were employed in the single-index model of each period: the Wilshire Real Estate Index, the NAREIT Index and the Wilshire 5000 Index. The Wilshire Real Estate Index (RESI) is a „market capitalization-weighted index of publicly traded securities including REITs and real estate operating companies‟ formed by Wilshire Associates to serve as „proxies for direct real estate investment by institutions‟13.