Is quality a priced factor in real estate returns?

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University of Amsterdam, Amsterdam Business School

Master in International Finance (MIF)

Master Thesis

Is Quality a Priced Factor in Real Estate Returns?

Sara Kelly Anzinger

Thesis Supervisor: Milena Petrova

Abstract

This paper examines the effect of quality, as defined by Asness et al. (2013), on price and return behavior in U.S. listed real estate from 1999-2013. Quality real estate stocks trade at higher prices. However, similar to findings in the aggregate stock market (Asness et al., 2013), quality in listed real estate is underpriced as evidenced by the limited explanatory power of the price of quality and higher risk adjusted returns to quality. A long quality, short junk portfolio (QMJ) is found to produce average risk adjusted returns of 1.01% per month. QMJ is negatively correlated with the market and size factors (MKT and SMB) and positively correlated with value factor (HML), making it long low beta, big, and value stocks, and short high beta, small and growth stocks. The explanatory power of the Fama-French 3-factor model on REIT (or in this case, all real estate) returns, is found to have declined since the mid 1990s. Adding QMJ to the Fama French 3-factor model, does improve the overall fit of the model on U.S. real estate stocks, but not materially. Removing the market factor from the asset pricing model appears to correct underestimation of alpha in historically low beta real estate stocks. Several anomalies are found during the 5-year period 2004-2008, which encompasses both the height of the U.S. real estate bubble and the subsequent financial crisis.

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Introduction

Two recent papers, Quality Minus Junk (Asness, Frazzini, & Pedersen, 2013), and A Five-Factor Asset Pricing Model (Fama, & French, 2014), examine the quality of firm performance in order to further explain stock returns and adjust for risk within the context of empirical asset pricing models. Both papers begin with an interpretive analysis of the Gordon Growth Model or dividend discount model, which is intuitively interpreted to derive fresh insight into the relationship(s) between variables included (and previously excluded), from asset pricing models.

Fama and French (2014) add profitability and investment variables1_{, which later become}

factors, robust minus weak (RMW) and conservative minus aggressive (CMA), added to the existing Fama-French 3-factor model, creating a new five-factor model. (Momentum is excluded due to variable correlation resulting in poor portfolio diversification.) The major findings of Fama and French (2014) are that the new, 5-factor model still falls short of fully capturing the cross section of expected stock returns, but does explain between 69%-93% of them. HML (high minus low, the Fama-French value factor) becomes redundant in the new model, its returns previously attributed to value, captured by the other four factors.

Asness et al. (2013) constructs a much more comprehensive set of variables built on general accounting data and formulas, separately calculated, then grouped as measures of profitability, growth, safety and payout, the four components it derives from the Gordon Growth Model, which are used to define quality. While both papers link returns to prices through the Gordon Growth Model analysis, only Asness et al. (2013) goes on to empirically test the effects of quality on prices. Asness et al. (2013) clearly lay out and progressively test for quality- its persistence, effect on prices, effect on returns and finally, as a long/short quality portfolio factor, its ability to add to the explanatory power of the 4-factor model (Fama and French, 1993; Carhart, 1997) and its risk adjusted returns. All of these reasons make Asness et al. (2013) a more meaningful choice for repetition and application to the universe of listed real estate.

1_{Profitability is calculated as, OP}_t_{= annual revenues – (cost of goods sold + interest expense + selling +}

general and administrative expenses)/ book equityt-1. Investment is calculated as, Invt= (total assetst-2 – total

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In light of the recent emersion of a quality factor in asset pricing models, this paper seeks to specifically test quality as a factor in real estate returns in the U.S., both the cross section of expected real estate investment trust (REIT) returns and those of all publicly traded real estate operating companies (REOCs). Hoesli and Oikarinen (2012) find that direct and securitized real estate markets are closely connected in the long run, with REITs leading direct real estate. Given this link, the ample data available on publicly traded REITs, and inclusion of all listed real estate investment firms, findings will be applicable to not only the universe of U.S. real estate equities, but also to direct real estate investment.

The central question to be examined in this paper, “Is quality a priced factor in real estate returns?” is supported by a complimentary progression of sub questions, to a great extent, following Asness et al. (2013). Is quality persistent in the cross section of real estate returns? Do higher quality real estate stocks trade at higher prices? What is the price of each component of quality (profitability, growth, safety and payout)? Is quality a priced factor in real estate returns? What level of return is attributed to a long quality, short junk portfolio? Does the inclusion of a quality factor create a superior asset pricing model for real estate returns? How does exclusion of the market factor (MKT) impact alpha?

Theoretical Framework

Background

The universe of U.S. listed real estate consists of real estate investment trusts (REITs) and real estate operating companies (REOCs). The primary business of both REITs and REOCs is investment in real estate (generally commercial, not residential). The primary difference between REITs and REOCs is the dividend or payout required by the Internal Revenue Service (IRS). Qualifying as a REIT is a voluntary declaration, but it demands that a minimum of 90% of the REIT’s taxable income be paid out in dividends. In exchange REITs do not pay corporate income tax on at least 90% of their income. REOCs on the other hand are subject to the same taxation as all other corporations, however, they have greater flexibility, not only in terms of dividend policy, but also in terms of the types of property assets they hold. Interestingly, in 2013 (the last year of this study), the total number of U.S. REITs was approximately the same as in 1999 (the first year of this study), while in

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the interim period, the number of U.S. REITs declined, especially during the financial crisis. Approximately 88% of the companies included in the subject sample are or were designated REITs at time of reporting. In order to capture all real estate, this study includes both REITs and publicly traded REOCs.

Literature Review

This paper is related to a vast literature that encompasses empirical asset pricing models and their attempts to explain the cross section of expected stock returns. More specifically, and most relevant to this paper, is the literature regarding return anomalies, especially those pertaining to qualitative measures of firm performance, and the predictability of cross sectional returns based on these measures.

The traditional, single factor CAPM (Sharpe, 1964; Lintner, 1965; Black, 1972) is the point of departure for numerous subsequent refinements of the market beta pricing model. The size effect, first documented by Banz (1981), indicates an inverse relationship between stock returns and market capitalization. The value effect reveals a positive relationship between returns and the ratio of cash flow, earnings or book value to market value (Basu, 1977; Reinganum, 1981; DeBondt and Thaler, 1985; Fama and French, 1992; Lakonishok, Shleifer, and Vishny, 1994). Both the size and value effect have since been identified in many studies, spanning diverse markets, and time periods. Because the traditional CAPM did not fully capture excess returns with market beta alone, size and value factors were added to create a 3-factor model (Fama & French, 1993). A fourth factor, momentum was later proven to add explanatory power to the 3-factor model (Carhart, 1997; Fama & French, 2011). While allowing for more accurate risk adjustment, in terms of higher R2_{s and lower alphas, the 3}

and 4-factor models have not fully captured excess returns or put an end to return anomalies.

A substantial amount of literature on cross sectional determinants, specific to REIT returns, now exists. Much of it, like this paper, is an extension of research tested on broader, non-REIT stocks, but specifically applied to the universe of real estate stocks and its peculiarities. It has been documented that when applying the Fama-French 3-factor model to REITs, better test specifications are provided and therefore, returns are more accurately captured,

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when REIT-mimicking portfolios are used (Chiang et al., 2006). Chui et al. (2003) and Derwall (2009) apply factor models (Fama & French, 1993; Carhart, 1997) and find that momentum dominates REIT returns. Chiang et al. (2006) shows that when REIT-mimicking portfolios are used to create the Fama-French 3-factors (vs. the original, non-REIT portfolios), the resulting REIT market betas converge to those indicated by the NCREIF Index, which measures returns on direct real estate investment. This is consistent with the presence of a link between REIT returns and an underlying real estate factor (Lee & Mei, 1994; Ziering et al., 1997). Chui et al. (2003) studies all U.S. listed REITs and regresses excess returns using the Fama-French 3-factor model, plus several additional factors, including turnover, volume, analyst coverage and momentum, and finds that turnover and momentum are significant cross sectional determinants of expected REIT returns, while book to market (the value effect), is not. Divergence between REIT and non-REIT stock returns, is evidenced in their differing relationships with the same variables, e.g., book to market and institutional ownership, when impacted by Fed interest rate policy (Goebel et al., 2013), and systematic volatility (or the market factor), which is not priced into REIT returns (DeLisle et al., 2013).

As described by Asness et al. (2013), one theme to emerge in numerous papers dedicated to non-REIT stocks, both recent and dated, is outperformance based on high vs. low quality stocks. Quality is defined by Asness et al. (2013) as stock or company characteristics that an investor is willing to pay more for, ceteris paribus. Examples within the literature include documentation of higher long-run returns associated with stocks that advantageously time repurchases (Baker & Wurgler, 2002), more profitable firms generate higher returns than less profitable firms (Novy-Marx, 2010), greater investment is associated with lower returns (Aharoni et al., 2013), firms with lower leverage have higher alpha (George & Hwang, 2010), and growing firms are associated with better performance than firms with poor growth (Mohanram, 2005).

Perhaps an alternative way to identify quality and differentiate it from the market factor (beta), size factor (market capitalization relative to other stocks), value factor (book to market ratio), and momentum factor (persistence of relatively high returns over the past year), may be as a choice factor. Unlike the other four factors, which, to a great degree are

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determined by larger, uncontrollable market forces, quality (profitability, growth, safety and payout ratio (Asness et al., 2013), can be directly manipulated by corporate management decisions. In fact of the eight documented examples of quality outperformance cited by Asness (2013), only one, low beta associated with high alpha (Frazzini & Pedersen, 2014), is not subject to firm choice, though it is somewhat influenced by industry. While capable of being impacted by exogenous forces, quality, is to a great extent, determined by endogenous forces, or choices made from within the firm.

Finally, literature pertaining to quality measures that serve to predict future returns and fundamentals from the perspective of a discounted (or present value) model is highly relevant, though more limited than the other pertinent literature. Campbell and Shiller (1988) develop a dynamic version of the Gordon Growth Model using a dividend price ratio that predicts future stock returns within the next year, moderately well. Cohen et al. (2009) determine that prices are more relevant than returns in forecasting future expected returns, in cases of long required hold periods (such as with real estate), and that book to market values can be approximated well (without the joint hypothesis problem) when prices rather than returns are used as a basis. Rather than aggregate market returns, returns at the firm level are examined by Fama and French (2006), and Vuolteenaho (2002), and are found to be driven by cash flow news vs. return news (Vuolteenaho, 2002).

Asness et al. (2013) adds to this literature by testing a very large sample of U.S. and international stocks and examining: the effects of quality on stock prices, the changes in the price of quality over time, the ability of the price of quality to predict future returns to quality, a unifying quality factor and its explanatory power for excess returns. As far as known, quality, as defined here, after Asness et al. (2013), is a variable that has not yet been tested on real estate returns as an additional factor in an asset pricing model.

Design & Hypotheses

This research is structured around six questions that all relate to the central question, “Is real estate a priced factor in real estate returns?” The empirical approach, presentation and analysis of results, are designed around these six questions and the hypotheses developed for each of them, as follows:

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Is quality persistent in the cross section of real estate returns? In order to establish whether quality can be predicted, and therefore relied upon as a determinant in stock picking, first the predictability of quality over time, or quality persistence, is analyzed. Similar to the results from the overall stock market (Asness et al., 2013), quality persistence is anticipated in listed real estate. As a less liquid asset class, real estate has a relatively long-term investment horizon associated with it. Further, long-term leases characterize much of the cash flow generated by investment grade real estate, and matching these term assets with long-term liabilities (often fixed rate debt), is common practice. It is therefore expected that the subject sample will have, on average, more stable profitability, growth and safety measures than that found within the overall U.S. stock market. Further, the payout component of quality is expected to be the most predictable due to the high proportion of REITs contained within the sample and their dividend requirements.

Do higher quality real estate stocks trade at higher prices? And what is the price of each component of quality (profitability, growth, safety and payout)? Based on the efficient market hypothesis and risk-return trade-off, higher quality implies lower risk, resulting in a lower return and corresponding higher price. Since investors are expected to be willing to pay more for less risk, known as quality herein, higher quality real estate stocks are expected to command higher market prices, ceteris paribus (Asness et al., 2013).

Is quality a priced factor in real estate returns? Real estate investors are likely to be especially focused on quality, and therefore, to value it properly. At the property level, investment grade real estate already represents the highest quality real estate stock. Long-term hold periods and capital intensiveness require a high level of expertise and delivery of profitability, growth, and safety, for sustained success in real estate investment2_{. Quality is thus expected}

to be a priced factor in real estate returns and reflected by flat risk adjusted returns across all levels of quality.

What level of return is attributed to a long quality, short junk portfolio? Empirical results on quality returns to non-real estate stocks found that high quality had less exposure to the

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market factor, resulting in risk adjusted returns that were higher than excess returns in a long quality, short junk portfolio (Asness et al., 2013). In the subject sample of U.S. real estate stocks, this anomaly is expected to strengthen, rather than be corrected. Though driven by their underlying real estate exposure, which might sound risky, REITs, have a low historic beta of less than 1.0, most recently, 0.78 (NYU Stern School of Business, 2014). High quality real estate stocks are therefore likely to have, on average, lower than mean REIT beta. Therefore, risk adjusted returns are anticipated to be higher than excess returns to a quality minus junk portfolio (QMJ).

Does the inclusion of a quality factor create a superior asset pricing model for real estate returns? Given a long quality, short junk portfolio (QMJ) is anticipated to produce positive alpha, the addition of QMJ as a fourth factor in a modified asset pricing model, is expected to further explain the cross section of real estate returns, which should result in a higher R2

than that seen in the 3-factor model.

How does exclusion of the market factor (MKT) impact alpha? Removal of the market factor from the modified 4-factor model is expected to increase the constant or alpha reported. Rather than correcting for the high quality, high risk adjusted return anomaly, stronger outperformance of risk adjusted returns is anticipated. If this hypothesis is proven true, it will imply that the market factor underestimates alpha derived from investment in U.S. listed real estate due to the low beta characteristics and limited market exposure associated with these assets.

Research & Results

Data and manipulations

The sample consists of all U.S. listed real estate from January 1999 to December 2013, totaling 438 companies (387 of which are REITs and 51 of which are REOCs), as reported by SNL Financial. (Real estate subcategories, such as homebuilder and gaming, are excluded from the sample.) Monthly stock prices and returns, as well as accounting data are from SNL Financial. Prices are represented as market to book, or price as a percent of book value per share. Monthly total returns include price appreciation and reinvestment of dividends,

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and have been transformed into excess returns by calculating monthly log returns, net of the 1-month U.S. Treasury bill rate (Ibbotson and Associates, Inc., as cited by Kenneth R. French Data Library, 2014). Outliers have been addressed by imputing the 5th_{and 95}th

percentile return values for those that fall below or above this range, respectively. Additional information on panel formation and selection is outlined in the section titled, Robustness Checks.

Quality Metric

Quality measures are based on quarterly accounting values after Altman (1968), Ang, Hodrick, Xing, and Zhang (2006), Daniel and Titman (2006), Penman, Richardson, and Tuna (2007), Campbell, Hilscher, and Szilagyi (2008), Chen, Novy-Marx and Zhang (2011), Novy-Marx (2012), Frazzini and Pedersen (2013) and Asness and Frazzini (2013), as cited in Asness et al., 2013). Some modifications have been made to adapt the metrics to the particulars of real estate specific companies’ accounting data and to more accurately reflect their intention. For example, since real estate is the primary asset of the firms in the sample, depreciation levels are material and therefore need to be excluded to avoid skewing of profitability measures. In this case, funds from operations (FFO) is a more meaningful measure than earnings before interest, taxes, depreciation and amortization (EBITDA). Each subcategory of quality (profitability, growth, safety and payout) is measured by three variables.

Profitability is measured by funds from operations over total assets (ROA), funds from operations over book equity (ROE), and cash flow from operating activities over total assets (CFOA). Book equity is defined as tangible common equity.

Each variable is then converted to a standardized z score. An overall profitability measure is calculated by averaging these three individual component z-scores.

Profitability = (z_ROA + z_ROE+ z_CFOA)/3

Growth is measured as the prior three-year change in the profitability variables by subtracting the three-year lag from the numerator and dividing by the three-year lag in the

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denominator. For example, change or growth in ROA is calculated as funds from operations in year t, minus funds from operations in year 3, divided by total assets in year t-3 (FFOt-FFOt-3 / TotAsstst-3).

As with profitability, individual z-scores are averaged to compute an overall growth measure.

Growth = (zΔROA + zΔROE + zΔCFOA)/3

Safety is measured by leverage, volatility and bankruptcy risk. Leverage (LEV) is calculated as negative total debt divided by total assets (-TotDebt/TotAssts). Volatility (VOL) is derived from the 3-year standard deviation of ROE (funds from operations divided by book equity (FFO/BkEq).3_{Bankruptcy risk (AZ) is assessed using a variation of the Altman}

Z-score, a weighted average of working capital (WC), retained earnings (RetEarns), earnings before interest taxes depreciation and amortization (EBITDA), market equity (MktCap) and sales. Given real estate companies report sales inconsistently, total revenue (TotRev) is used as a proxy for sales. Working Capital is generally calculated as current assets minus current liabilities. However, given these aggregate values were not available through the data provider, working capital is calculated as: cash plus account receivables, plus trading account securities, plus available for sale securities, plus current inventory, minus short term debt (Cash + ARs + TAS + AFSS + Cinv) – STD. Further, given the inconsistent reporting of working capital among real estate companies, missing values were replaced with values reported in the previous quarter. AZ = (1.2*WC + 1.4* RetEarns + 3.3* EBITDA+ 0.6* MktCap + TotRev)/TotAssts.

A safety z-score is computed by averaging the z-scores of leverage (LEV), volatility (VOL) and bankruptcy risk (AZ).

Safety = (zLEV + zVOL + zAZ)/3

3_{The 1-year standard deviation of ROE was also calculated for comparison and indicated an aggregate mean of}

less than half that of the 3-year. However, once incorporated into the overall safety score and used in

regressions, the resulting safety coefficients were not substantially different from those associated with the 3-yr standard deviation.

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Payout is measured by funds from operations payout (FFOP), dividend payout (DIVP) and dividend yield (DY).

Payout = (zFFOP + zDIVP + zDY)/3

The overall quality score, for each company, in each month, is the sum of the total profitability, growth, safety and payout z-scores:

Quality = z (Profitability + Growth + Safety + Payout). Z-score Methodology

Following Asness et al. (2013), variables are converted to z-scores using a methodology of ranking. Each month, variables are ranked, creating a vector of ranks (r). The cross sectional mean (µ) of the vector of ranks is calculated, as is the cross sectional standard deviation (σ) of the vector of ranks (r). For example, using the payout variable FFOP, zFFOP = (rFFOP - µFFOP )/σFFOP .. Again, using payout as an example, the same method is

employed for variables, DIVP and DY. The total payout score for each company, in each month, is the average of all three z-scores.

Factors

The market factor (MKT), size factor, small minus big (SMB), and value factor, high minus low (HML), are based on the 3-factor model (Fama and French, 1993), and are taken from Kenneth R. French’s Data Library (2014). The quality minus junk factor (QMJ) is described in detail on page 20.

Quality Portfolios

Quality portfolios are based on Asness et al. (2013). Each month, stocks are sorted by quality. Quality is then categorized into ten deciles (P1 being the lowest and P10 the highest). Stocks are assigned to one of these ten quality portfolios on a monthly basis. In keeping with the relative homogeneity of the sample, value weighting is not employed.

Approach & Results by Research Question

1. Is quality a persistent characteristic in the cross section of real estate stocks?

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average of cross sectional means is reported month end, at time of portfolio creation and every 5-years thereafter, for fifteen years. Standard errors are adjusted for heteroskedasticity and autocorrelation. In the same manner, the persistence of each of the four components of quality (profitability, growth, safety and payout) is calculated.

Table I summarizes quality persistence by reporting cumulative average quality scores at time t (January 1999), t+60 months (December 2003), t+120 months (December 2008) and t+180 months (December 2013). The spread between the highest and lowest quality portfolios is indicated by P10 – P1 in the far right column. Standard errors for the final period, t +180, are shown in parentheses beneath relevant quality scores. The results indicate that quality and its components are stable over time, especially from t+ 60M (December 2003) to t + 180-months. All mean quality scores for the full period, t+ 180 months, were statistically significant at 99%. Therefore, the null hypothesis, that quality scores from t to t + 180 months are not different from 0, may be rejected.

Table II shows the quality persistence results in contrast with those presented by Asness et al. (2013) on the overall U.S. stock market. By looking at the standard deviation of the spread between highest and lowest quality scored portfolios (from portfolio creation (t) to ten years out (t+ 120M)), it is clear that the U.S. real estate sample has lower standard deviations across the board, and therefore, stronger persistence on average than that of the aggregate U.S. stock market (Asness et al., 2013). This is indicative of the homogenous real estate sample relative to the heterogeneous sample used by Asness et al. (2013), and agrees with the hypothesis that quality persistence in real estate is stronger on average than that of the overall U.S. stock market. Payout, which is the least persistent quality characteristic in the Asness et al. (2013) sample (based on its standard deviation over ten years), is the most persistent characteristic in this study’s real estate sample. The higher persistence of payout in real estate, relative to both Asness et al. (2013) and to other quality characteristics within the subject sample, alludes to the influence of REITs and their 90% payout requirement.

The results reflected in tables III and IV support the hypothesis that quality is a predictable characteristic in real estate stocks, as tested in the U.S. market from 1999-2013. In contrast with results reported by Asness et al. (2013), all components of quality (profitability, growth,

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safety and payout) appear to be more stable characteristics in U.S. listed real estate than in the aggregate U.S. stock market, which further supports the hypothesis that quality is especially relevant in real estate investment. The finding that payout is the most stable of the four components of quality confirms the hypothesis that payout is the most persistent quality characteristic for real estate stocks, many of which are REITs and adhere to the high dividend requirements established by the IRS.

2. Do higher quality real estate stocks trade at higher prices? And what is the price of each component of quality?

Since quality has been established as a predictable characteristic in listed real estate, it is logical to next consider how quality is priced, beginning with the question: Do higher quality real estate stocks trade at higher prices than low quality real estate stocks? The following cross sectional regression is employed in order to answer this question.

Pi,t = α + βQuality,i,t + εj,t (1)

P is the price of each individual firm’s stock (i) in market price to book value ratio at the end of each month (t). Quality is the overall quality score for each individual firm (i) at the end of each month (t). The scaled price of each firm is regressed on its overall quality score per monthly observation. Standard errors are corrected for heteroskedasticity and autocorrelation. Given quality measures are z-scores, the interpretation follows that if quality improves by one standard deviation, the price to book ratio increases by x percent.

First, regression (1) is run on quality alone. Then, in order to further determine the explanatory power of quality on prices, market capitalization and lagged 12-month returns are added to control for size and momentum, respectively, and time dummies are employed to control for market conditions. Market capitalization is in millions of dollars (U.S.) and lagged 12-month returns are in log percent form.

Table III shows that the price of quality is positive and statistically significant. Column 1 reveals that for every one standard deviation increase in quality, price to book increases by 4.67% and is statistically significant at the 99% confidence level. The effect of quality on

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scaled prices increases slightly to 4.86% once controls for size, momentum and market environment are added (column (2)).

Next, the cross sectional regression of price to book on each component of quality is executed in univariate and multivariate form, later, adding controls for size, momentum and market conditions, as done with the overall quality measure.

Pi,t = α + β1Profitabilityi,t + β2Growthi,t + β3Safetyi,t + β4Payouti,t + εj,t (2)

Table III shows that in breaking out the individual components of quality, two components, profitability and growth, are significantly positive in univariate regression, 18.25% and 5.65%, respectively, but only profitability remains positive in the multivariate regression of prices on all components of quality (column (7)). Paying more for profitability and growth makes sense. However, the negative price of safety is especially surprising given its magnitude and significance, -17.3% with a p-value of less than 0.01% (univariate) which only becomes larger in the multivariate regression (-28.07%).

Asness et al. (2013), which finds similar results on the negative price of safety, attribute a low price of safety to a flat security market line (Black, Jensen, & Scholes, 1972; Frazzini & Pedersen, 2013) and its consistency with the theory of leverage constraints (Black, 1972; Frazzini & Pedersen, 2013), which argues that when leverage is constrained, investors seek risker (higher beta) assets, resulting in higher prices for risky assets and lower prices for low risk assets. This is a plausible explanation in the U.S. real estate sample, especially given that, historically, REIT betas are reported as relatively low, or less than 1.0. If high quality real estate stocks are low risk assets, then leverage would generally be employed to realize higher risk adjusted returns. However, since in reality, investors do not have access to unlimited borrowing, they may be more likely to invest in lower quality real estate stocks to achieve high risk adjusted returns without leverage, and thereby drive up the price of low quality real estate and drive down the price of high quality real estate.

Other explanations for the negative price of safety are that bankruptcy risk (as captured by a variation of Altman’s Z (variable, AZ)), may be overestimated due to the use of total revenue as a proxy for sales, as well as the use of EBITDA vs. FFO. Further, REITs in particular are

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more likely to be dependent upon debt for growth and acquisition of new properties, given they are required to pay out 90% of net income in dividends. Because of this, declining leverage (increasing safety) may be seen as a negative signal to the market.

As for payout, it was not expected to be a differentiating variable in the price of listed real estate, given the 90% net income payout requirement for REITs. Since payout is a known factor among the REITs in the sample, it is possible that the payout requirement stands as a benchmark norm and that those REITs paying more in dividends than required (and thereby retaining less cash than their REIT peers), are penalized with a lower priced stock.

Robustness checks on price regressions are conducted by breaking out the price of quality by 5-year increments, by firm size, and also by isolating the financial crisis. Given the sample encompasses 2007-2008, controlling for the market environment is critical to obtaining results not skewed by the crisis. Table VIII shows price regressions on quality during each five-year time period within the sample. From 1999-2003, a one standard deviation increase in quality is reported as equivalent to a 4.37% increase in scaled prices, at 99% significance. This is similar to the price of quality for the overall sample period, 1999-2013. From 2009-2013, the price of quality is still positive, though not significant. However, during the five-year period 2004-2008, which encompasses both the height of the U.S. real estate bubble and the subsequent financial crisis, the price of quality is negative.

To achieve greater understanding of what is happening during the tumultuous period of 2004-2008, year by year regressions are run on quality and controlled for size, momentum and market conditions. Table IX, shows the annual regression results and reveals a negative price of quality during the real estate boom, leading up to the financial crisis (2004, 2005, 2006), followed by a significant and positive price, of 3.09% in scaled prices, once the financial crisis begins in 2007. Interestingly, the price of quality does not remain positive in the second year of the crisis, but rather, returns to a significant negative of -2.58%.

Table X shows the pricing of quality for small and big stocks defined by the median market capitalization of the sample. For the overall sample period (1999-2013), quality is positively priced for both small and big stocks, though quality has a greater and more significant

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impact on the price of small stocks (columns (1) and (2)). During the crisis, the reverse prevails. Quality has a greater impact on the price of big stocks. In 2007, there is a significantly positive price of quality for big stocks, 7.15%,. In 2008 the price of quality turns negative, but it is big stocks that are hit hardest, though the quality coefficients are insignificant, and therefore we cannot reject the null that the price of quality is different from 0 in 2008.

Quality is clearly a significant determinant of scaled prices. While the price of quality varies over time, it is especially volatile during the five-year period that encompasses the real estate bubble and financial crisis (2004-2008). However, for the overall sample period, 1999-2013, the null hypothesis, that the quality coefficient is not significantly different from 0 can be rejected based on a p-value of 0.01% (table III). Interestingly though, the explanatory power of quality is fairly low at 11.5% R2_{. Of the seven scaled price regressions presented in table}

III, the highest R2 _{of 24.4% is reflected in column (7), which includes all components of}

quality together with controls for size, momentum and dummies for quarterly market conditions. The low overall fit of the model means that the majority of the cross section of real estate prices is unexplained.

The results discussed above support the hypothesis that higher prices are associated with quality in the cross section of U.S. real estate stocks for the sample period 1999-2013. On average and over time, investors appear to be willing to pay more for quality (ceteris paribus). Though overall results show positive pricing of quality, this is clearly not the case all the time, as evidenced by the negative price of quality in the years leading up to the financial crisis.

3. Is quality a priced factor in real estate returns?

Since higher prices are associated with quality at highly significant levels, as reported in table III, it would be logical to assume that quality is priced in real estate returns. In order to test this hypothesis, excess returns (over 1-month U.S. Treasury bill yields) and risk adjusted returns, or alphas, are analyzed by quality portfolio. First, stocks are monthly sorted by quality score and ten decile portfolios are created. Then stocks are assigned monthly to one of the ten portfolios by quality score. The time series mean excess return is calculated for each quality portfolio. Second, cross sectional regression (3) is run, first, using only the market factor, MKT, based on the CAPM 1-factor model, and then adding size and value

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factors SMB and HML (Fama & French, 1993). Standard errors are adjusted for heteroskedasticity and autocorrelation.

Rt = α + βMKT MKTt + βSMB SMBt + βHML HMLt + εt (3)

Initially the 4-factor model including momentum (Jegadeesh & Titman, 1993; Asness, 1994; Carhart, 1997) was also applied to risk adjust returns. However, across all quality levels, the 4-factor alphas were consistently larger (more positive or less negative) than 3-factor alphas, and did not add to the objective of risk adjustment. These results imply that real estate stocks move in opposition to stock market momentum. Therefore, the 4-factor model has been excluded from the final presentation of results.

Table IV reports excess returns and alphas with robust standard errors in parentheses beneath. The far right column reports the difference or spread between the combined returns from high quality portfolios 9 and 10 and those from low quality portfolios 1 and 2. (This is also the basis of the quality minus junk (QMJ) factor, which will be described in greater detail later on.) Returns and alphas in bold print are those that are statistically significant at 90% or higher (p- values less than 0.1%).

While average excess returns do not increase monotonically as quality increases, there is a general positive trend as quality goes up, and the positive difference in the far right column indicates that high quality stocks have higher average excess returns than low quality or junk stocks. Over the sample period 1999-2013, high quality real estate stocks outperformed low quality real estate stocks by 0.99% per month.

Adjusting for systematic risk with the CAPM model, we see that across all quality portfolios, CAPM alphas are lower than excess returns, but still result in quality outperformance of 0.585% per month. 3-factor alphas increase the outperformance of high quality real estate to 0.93% per month, implying high quality listed real estate has less exposure to size (SMB) and value (HML) factors than low quality real estate. In other words, there appears to be a positive link between quality and big stocks and quality and growth stocks. We can reject the null hypothesis that there is no difference in average returns among excess returns and

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CAPM adjusted alphas. The null for 3-factor alphas cannot be rejected, as only portfolios 1 and 7 have p-values less than 0.1% (denoted in bold print in table IV).

Robustness checks on returns are conducted through closer examination in 5-year increments and isolation of the financial crisis from 2007-2008. Table XI reports excess returns and 3-factor alphas from 1999-2003, 2004-2008 (2007-2008), and 2009-2013. From 1999-2003, high quality outperformed junk by 1.927% per month in excess returns and 1.674% on a risk adjusted basis (3-factor alphas). Quality outperformance declines dramatically in 2004-2008, with 0.211% and 0.124% in excess returns and 3-factor alphas, respectively. From 2009-2013, quality outperformance increases to 0.63% per month in excess returns and 0.748% per month in 3-factor alphas.

In order to achieve a better understanding of return behavior during the five-year period that encompasses the height of the real estate bubble and the subsequent financial crisis, returns to quality are broken out annually for 2004-2008 and summarized in table XII. During the three years leading up to the financial crisis 2004-2006, quality underperforms on a risk adjusted basis, as indicated by the negative 3-factor spreads in the far right columns of table XII. In 2005 and 2006, quality also underperforms without adjustment for risk, as illustrated by the negative excess return spreads in the far right columns of table XII. In 2007, average risk adjusted returns are still negative, but unadjusted returns are positive. And by 2008, quality is outperforming significantly on both an unadjusted and adjusted basis, of 2.12% per month and 3.97% per month, respectively. The trend of higher risk adjusted returns seen for the first time in 2008, continues in the following five-year period, 2009-2013.

Contrary to the hypothesis that quality is a priced factor in real estate returns, the results of this analysis indicate that quality is not fully priced in real estate returns, and suggest that real estate investors are not any more capable of accurately pricing quality than the average equity investor. While returns do not increase monotonically as quality increases, there is a clear trend in higher returns to higher quality as reflected in positive spreads (P9+P10 – P1+P2). This implies limited market efficiency and quality underpricing in listed real estate.

Beyond quality return performance, what is also observed in tables XI and XII is a trend toward improving R-squared or increasing explanatory power of the Fama-French 3-factor

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model on real estate returns. From 1999-2003, the average R2 _{resulting from 3-factor risk}

adjustment is 9.6%. From 2004-2008 and 2009-2013, this increases to 23.8% and 29.9%, respectively. When looking at the annual break out of returns from 2004-2008, fairly flat average R2_{is seen during the boom of 2004-2006 (reflecting a low of 14.4% in 2006),}

followed by dramatic increases during the financial crisis to 24.1% in 2007 and 38.1% in 2008. These results imply that listed real estate moves more closely with the market (and other control factors) in times of crisis, as MKT, SMB and HML capture more of the cross section of listed real estate returns than prior to the crisis.

4. What level of return is attributed to a long quality, short junk portfolio?

In order to better assess the ability of quality to outperform, we construct a long high quality, short low quality (junk) portfolio. The quality minus junk factor (QMJ) is constructed by first, subtracting the excess returns from the two lowest quality portfolios (P1 and P2) from those of the two highest portfolios (P9 and P10), for every monthly observation, ((i),(t)). The time series average cross sectional mean is then calculated in order to arrive at monthly excess returns to QMJ.

QMJ = (rP9+ rP10) – (rP1 + rP2) (4)

Given the actual QMJ portfolio will be the time series average of monthly cross sectional high quality/low quality return differences, the crude spread ((P9 + P10) – (P1 + P2)) calculated in the previous section and reported in tables IV, XII and XII, will serve only as an approximation.

This simplified portfolio construction, or spread, does not follow in the same fashion as Fama & French (1992, 1993 & 1996) and Asness & Frazzini (2013). The reason for this divergence is specific to the listed real estate sample. Unlike an aggregate stock market study, in which the individual stocks are heterogeneous in size, industry, and even country, the subject real estate sample is relatively homogenous. All firms operate in the same industry and country and are relatively similar in size. Compared to all firms listed on the New York Stock Exchange (NYSE), whose median market capitalization is 21.3% of its average, the subject real estate sample has a median market capitalization of 40.4% of its average, and the

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75th_{percentile is only 107.8% of its average market cap.}4_{Given the relative homogeneity of}

the sample, sorting by size and value weighting is superfluous. Further, since the study examines returns to ten quality portfolios, the simplified construction is also more appropriate in reflecting consistency between returns to quality and returns to a long quality, short junk investment strategy. Given the actual QMJ portfolio will be the time series average of monthly cross sectional high quality, low quality return differences, the crude spread ((P9 + P10) – (P1 + P2)) calculated in the previous section and reported in tables IV, XII and XII, will serve only as an approximation.

In the same manner as QMJ, portfolios are also constructed for each of the four components of quality (profitability, growth, safety and payout). Profitable minus unprofitable (PMU), growing minus mature (GMM), safe minus volatile (SMV) and high payout minus low payout (HpMLp), reflect more granular information on returns to long/short investment strategies focused on individual aspects of quality.

Table V reports average, monthly excess returns and alphas to long/short portfolio QMJ and its components, PMU, GMM, SMV and HpMLp. Standard errors are corrected for heteroskedasticity and autocorrelation and statistical significance at 90% or higher is denoted by bold print. Over the sample period 1999-2013, QMJ earns average monthly returns of 0.97%. Average risk adjusted returns are indeed higher at 1.01% per month, and support the hypothesis. In keeping with higher risk adjusted returns, we see negative average market and size factor loadings of -0.041 and -0.168, respectively. However, QMJ has a positive average value factor loading of 0.176, which implies a link between quality stocks and value stocks, concurring with the quality metric construction, but contrasting with the expectation that value stocks will be quality stocks, which will have higher prices and therefore, lower returns. This positive factor loading for HML contrasts with the positive loading seen in Asness et al. (2013), and may be caused by the negative price of quality in the real estate bubble leading up to the crisis, as well as the negative price of quality seen in 2008, suggesting quality is more underpriced in real estate stocks than in the aggregate stock market, and resulting in a an HML loading that is sensitive to the lower price (higher returns) of quality (in this case,

4_{The NYSE’s average and median market capitalizations are $8.9 billion and $1.9 billion, respectively (NYSE, 2014). In}

contrast, the sample has an average and median market capitalization of $1.867 billion and $755 million, respectively, with a 75th_{percentile of $2 billion.}

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low book to market stocks). As for QMJ’s negative exposure to SMB, implying small stocks are junk stocks, Asness et al. (2013) find similar results in the aggregate stock market, but upon closer examination, find continued support for the size effect, as big stocks, though more likely to be quality stocks, actually underperform small quality stocks. In other words, when comparing stocks of similar quality, smaller stocks significantly outperform larger ones on average, which corresponds to our finding in the price space that larger firms are more expensive.

Among the other long/short portfolios, all return positive average risk adjusted returns, with the exception of HpMLp. PMU has the highest average monthly alpha of 1.53% (3-factor) followed by GMM with 1.20%. While PMU and SMV move with the market, GMM and HpMLp, move against it. Only HpMLp has positive exposure to small stocks, as reflected in its average monthly SMB coefficient. Only GMM has negative exposure to value stocks, as reflected in its average monthly HML coefficient.

Table VI shows the correlation of excess returns for each long/short portfolio. Only SMV is negatively correlated with the QMJ factor. This result agrees with the large and significant negative price of safety reported in table III. All other portfolios are positively correlated with QMJ. A trade-off between safety and growth is implied in the negative correlation between GMM and SMV, suggesting that greater leverage or less than ideal retained earnings accompany growth. Similarly, there is an implied trade-off between safety and payout as seen in the negative relationship between SMV and HpMLp, which may suggest higher dividends contribute to greater financial risk for REITs and/or REOCs.

Robustness checks are reported in Table XIII, which breaks out returns and alphas to QMJ in every five-year period, and isolates the 2007-2008 financial crisis. Once again, robust standard errors are reported beneath returns and alphas and bold print denotes those with statistical significance at 90% or higher confidence levels. The first five years of the sample period (1999-2003) produce the highest average monthly returns to QMJ at 1.9%, which concurs with returns by portfolio as shown in table XI. Average monthly 3-factor alpha is minimally lower, 1.8% for the same period. In the five-years that encompass the real estate boom and financial crisis (2004-2008), average returns to QMJ are much lower, though still

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positive, at an average of 0.19% per month. Risk adjusted returns of 0.22% are higher than excess returns in this period. Upon further investigation of 2007-2008, defined by the financial crisis, returns to QMJ, and to a greater extent, QMJ alphas, are found to be very strong, averaging 1.37% and 1.56% per month, respectively. Most recently, from 2009-2013, alphas remained higher than returns, though the size of both, 0.58%, and 0.71%, respectively, is substantially reduced from the levels seen during the financial crisis. In every period after 2003, QMJ appears to act as a hedge to market, size and value factors.

Overall results for the sample period 1999-2013 support the hypothesis that QMJ risk adjusted returns outperform its unadjusted returns. As such QMJ is shown to be a good hedge against the market, with its best performance seen in the 2007-2008 financial crisis. Since QMJ is a long quality, short junk portfolio, these results also support the hypothesis that high quality real estate stocks, are low beta stocks.

5. Does the inclusion of a quality factor create a superior asset pricing model for real estate stocks?

Given the positive alpha generated by QMJ, its inclusion as a regressor in the asset pricing model is expected to further explain the cross section of real estate returns. In order to determine whether this is the case, first, the cross sectional regression below is employed to ascertain the explanatory power of the existing 3-factor model.5

Rt = α + βMKT MKTt + βSMB SMBt + βHML HMLt +εt (5)

Excess returns are regressed monthly on the market, size and value factors. Table VII shows the regression results in column (1), which indicate R2_of_{20.0%. This means that only}

20% of the cross section of returns is explained by the 3-factor model. Why is the explanatory power of the Fama-French 3-factor model so low when applied to real estate returns?

5_{The 4-factor model including momentum (Carhart, 1997; Fama & French, 2011) is not applied here. While}

momentum has been shown to have a major impact on the cross section of REIT returns (Chiang, 2006); Chui, 2003), this is true of industry specific momentum or REIT specific momentum, not of the momentum factor for the aggregate stock market. Since the creation of a real estate specific momentum portfolio is beyond the scope of this paper, the Fama French 3-factor model is utilized for this analysis.

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Previous studies provide some insight. In order to develop a real estate factor for testing on the common stock market, Hsieh and Peterson (2000) apply the Fama-French 3-factor model on equity REIT returns from 1972-1995, and find average factor loadings for MKT, SMB and HML of 0.60, 0.50, and 0.34, respectively, resulting in explanatory power (or R2_{) of}

0.50. Chiang, et al. (2006), help to further explain the relatively low explanatory power of the Fama-French 3-factor model. First they regress the 3-factors on REIT returns from 1993-2003, resulting in average factor loadings of 0.36, 0.46 and 0.40 for market beta, size and value factors, respectively, and an overall model fit or R2_{40.1%. Chiang et al. (2006)}

report that by creating analogous factor portfolios, using only firms from the REIT industry as components (not all common stocks), REIT alphas from 1993-2003 are reduced and the regression using the REIT mimicking portfolios provides twice the explanatory power of the traditional Fama-French factors. Using these REIT mimicking portfolio factors, Chiang et al. (2006) obtain new results for the same period, 1993-2003, of 0.03, -0.58, and 0.26 for market beta, size and value factor loadings, respectively. R2_{increases from 40.1% to 78.62%. Zhou}

and Ziobrowksi (2009), examining the performance persistence of REITs, specifically look at equity REITs from 1994-2006, sorting them into deciles by lagged one-year excess returns, and applying a 4-factor model (Fama & French, 1993; Carhart, 1997), finding average MKT, SMB and HML factor loadings of 0.41, 0.42, and 0.52, respectively. The resulting R2 is 32%.

In contrast with previous studies, this paper regresses the Fama-French 3-factors (MKT, SMB and HML) on excess real estate returns from 1999-2013, resulting in factor loadings of 0.55, 0.36 and 0.60 for market beta, size and value factors, respectively. As previously reported, the related R2_{is 20%. While the above referenced studies are not identical (Zhou}

& Ziobrowski, 2009, include momentum as a 4th_{factor; Anzinger (2014) includes REOCs as}

well as REITs in data sample), they provide an approximate basis for comparison and inference.

Study Hsieh & Peterson (2000) Chiang et al. (2006) Zhou & Ziobrowski (2009) Anzinger (2014) Sample REIT Data 1972-1995 1993-2003 1994-2006 1999-2013

Model 3-factor 3-factor 4-factor 3-factor

MKT 0.60 0.36 0.41 0.55

SMB 0.50 0.46 0.42 0.36

HML 0.34 0.40 0.52 0.60

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Chronological trends reflect REIT exposure to the market factor has increased since the mid 1990s, after dropping considerably prior to that. It is possible that the 2007-2008 financial crisis is responsible for driving REIT returns more in line with the overall stock market, however, the increasing beta trend, though smaller in magnitude, began prior to the crisis. REIT exposure to size minus big factor (SMB), declines monotonically over time, and REIT exposure to high minus low (HML) has increased since the mid 1990s, indicating the link between value stocks and REIT performance has strengthened over time. Simultaneously, the explanatory power of the Fama-French 3-factor model appears to have declined precipitously since the 1990s. These results stand in opposition to Chiang et al. (2006), who attribute the decline in R2 _{to a decline in REIT return sensitivity to the market. Clearly, the}

subject results indicate that R2_{is declining while market beta is increasing. Clayton &}

Mackinnon (2003) suggest that the sensitivity of REIT returns to large cap stocks declined over time while its sensitivity to small cap stocks increased (as cited by Chiang et al., 2008). This argument supports the above results for HML, but not SMB exposure. Overall, the explanatory power of the Fama-French 3-factor model on REIT returns appears to decline over time, at least since the 1990s, as suggested by the results from this study and those contrasted above.

Now that a basis for comparison exists, the QMJ factor is added to the right hand side of the equation in the following cross sectional regression.

Rt = α + βMKT MKTt + βSMB SMBt + βHML HMLt + βQMJ QMJt +εt (6)

Excess returns are regressed monthly on the market, size and value factors, as well as quality minus junk. Table VII, column (2) reports the results, which indicate an R2_{of 20.6%. The}

overall fit of the 4-factor model using QMJ as a regressor is only slightly better than that of the 3-factor model. In light of the low R2_{resulting from the 3-factor model, and the}

possibility of omitted variable bias (e.g., due to not capturing the real estate factor (Lee & Mei, 1994) or real estate momentum factor (Goebel, 2013)), the level of improvement may be more significant than realized.

The results presented above technically support the hypothesis that inclusion of a quality factor (QMJ) will improve the overall fit of the asset pricing model. Yet the degree of

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improvement as measured by R2 _{is immaterial. Given the potential for omitted variable bias}

and the use of Fama-French factors on a real estate specific sample, the interpretation of the significance of improvement is ambiguous.

6. How does exclusion of the market factor (MKT) impact alpha?

Empirical evidence suggests that the market factor is an inefficient predictor of expected returns, overestimating the market premium for high beta stocks and underestimating it for low beta stocks (Black, Jensen, & Scholes, 1972; Fama & MacBeth, 1973; Fama & French, 1992; Frazzini & Pedersen, 2013). Historically, REITs are low beta stocks (less than 1.0). Further, as reflected in its higher risk adjusted returns and negative average MKT coefficient, the QMJ factor is long low beta stocks and short high beta stocks, implying that high quality real estate stocks are low beta stocks. So are the 3-factor (and 4-factor model including QMJ), accurately predicting alpha in real estate stocks?

Fama and French (2014) propose that by assuming all stocks have a beta of 1.0, and removing the MKT factor from the right hand side of the regression equation, a better estimate of alpha is achieved. Following this technique, the asset pricing model is revised as follows:

r_t = α + βSMB _SMB

t + βHML HMLt + βQMJ QMJt +εt (6)

Table VII, column (3) reports the results of the above regression. But first, the constant or alpha associated with the first two models is reviewed. Prior to inclusion of the QMJ factor, the 3-factor model predicted risk adjusted returns of -0.024% per month, as reported in column (1). With the addition of QMJ, the 4-factor alpha becomes increasingly negative, reported at -0.148%. By removing the market factor from the right hand side, alpha increases significantly to a positive .04% per month (column (3)). However the null, that this constant is not significantly different from 0, cannot be rejected, as its p-value is greater than 0.1%, and therefore not statistically significant at 90% or higher. As expected, the overall fit of the modified model declines from 20.6% to 8.9% due to exclusion of the market factor.

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Robustness checks are executed by separately running regression equations (5) and (6) for each five-year period within the sample, and results are reported in table XIV. In both 1999-2003 and 2009-2013, alpha increases with the removal of the market factor as a regressor. However, during the five-year period from 2004-2008, exclusion of the market factor results in a lower or more negative alpha. Isolating the financial crisis, 2007-2008, and running the regressions again, the reversal in alpha is even greater, starting with -0.66% in the 4-factor model, and declining to -2.13% per month absent the market factor, with significance at 99%. It appears that the crisis is strongly influencing the reversal in alpha seen in 2004-2008. The null hypothesis, that alpha is not significantly different from 0, can be rejected in every period, except 1999-2003.

For the overall sample period 1999-2013, the results presented above support the hypothesis that real estate stocks are low beta stocks and that removal of the market factor in a risk adjusting asset pricing model corrects the underestimation of the premium associated with U.S. real estate stocks, as evidenced in the constant, which increases in every period, with the exception of 2007-2008.

Discussion

Overall Analysis

Based on the results analyzed above, quality is a persistent and therefore, predictable characteristic in U.S. real estate. From 1999-2013, its components, profitability, growth, safety and payout are all found to be more persistent within listed real estate than in the aggregate stock market, based on contrasting study conducted by Asness et al. (2013). Payout is the most predictable component, which is indicative of the 90% payout requirement imposed on REITs by the IRS.

Though clearly a significant determinant of price, quality’s explanatory power on price is limited to 11.5%. Asness et al. (2013) find a similar low R2 _{in their quality regression results}

for the aggregate stock market, and suggest three possible causes: a) limited market efficiency, which implies the underpricing of quality and anticipates high quality stocks will have higher risk adjusted returns, b) an inadequate quality measure that does not capture quality as the

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market does, implying no relationship between returns and quality as measured by Asness et al. (2013), or c) an inadequate quality measure that does not capture risk(s) associated with quality, implying that once returns are properly risk adjusted, the impact of quality will be immaterial.

Examination of returns to quality real estate reveals higher risk adjusted returns for high quality stocks and lower returns for low quality or junk stocks. Reasons b and c, proposed by Asness et al. (2013), can therefore be rejected, as there is a clear relationship between sample returns and quality, and after risk adjustment of returns, using the Fama-French 3-factor model, the relationship between quality and higher returns strengthens in 2008 and 2009-2013. Even in periods when risk adjusted returns are not higher than excess returns, the difference between alphas on high quality and low quality, remains positive, indicating quality outperformance. It is therefore likely that reason a, limited market efficiency is responsible for the limited explanatory power of quality on returns. Quality is therefore, not fully priced in U.S. listed real estate for the sample period 1999-2013.

On average, there is a significant positive price associated with quality, as investors are willing to pay more for quality in real estate stocks. This was especially true in the financial crisis (2007), which supports the theory of flight to security. However, during the boom years of 2004-2006, which led up to the crisis, and encompassed the height of the U.S. real estate bubble, quality is negatively, priced. This suggests that quality is less valued in a boom, especially one characterized by a real estate bubble, in which all real estate, on average, is overpriced. Asness et al. (2013) find similar results for the low price of quality in the period prior to the 2007 Global Financial Crisis. Historical support for the low pricing of quality in periods preceding downturns, include February 2000, the height of the internet bubble and just before the 1987 stock market crash (as cited in Asness et al., 2013). The price of quality in small real estate stocks is greater than in big real estate stocks during the sample period. However, during the financial crisis, this trend reverses, and the price of quality in big stocks becomes greater, supporting flight to security.

As previously mentioned, the price of quality jumps from -1.97% in 2006 to 3.09% with significance at 95% in 2007. But surprisingly, the price declines drastically in 2008, to

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-2.58%. Given the ongoing financial crisis, this is unexpected. However, the low price of quality in 2008 may show that after the rational, initial flight to security, further information about the extent to which all real estate was overpriced (including high quality listed real estate) was integrated into the market, and resulted in a pull back or partial reverse in the previous year’s quality price gains.

The natural, inverse relationship between prices and returns is observed from one year to the next in the annual break out of the period 2004-2008. For example, the average monthly price of quality increases from 2004 to 2005 while simultaneously, returns to quality decrease from one year to the next. From 2005 to 2006, the price of quality decreases and returns increase, and so on through 2008. Given the contention previously made that quality is underpriced during the boom leading up to the crisis, high quality stocks are expected to have higher risk adjusted returns or alphas, than low quality stocks. Yet, from 2004–2007, high quality stocks have lower alphas than low quality stocks. At first glance this appears to disprove the contention that limited market efficiency is resulting in quality underpricing. However, the years 2004-2007 also coincide with a real estate bubble in which, on average, all real estate, regardless of quality, is overpriced. It is possible that low quality real estate stocks are outperforming due to the overheated real estate market, while at the same time, high quality real estate stocks are underpriced relative to low quality stocks. The trend for low quality to outperform high quality gradually reverses as the boom gives way to the crisis. High quality excess returns outperform low quality excess returns in 2007, and both high quality excess returns and risk adjusted returns outperform low quality in 2008.

Returns to QMJ are significant across time period and are highest during the financial crisis. This is shown on both the left hand side and right hand side of the regression equation. On the left hand side, risk adjusted returns are higher than excess returns to QMJ in 2007-2008, as illustrated in table XIII. (This continues to be the case in the period 2009-2013, and may be a carry over of the financial crisis into the beginning of this period.) On the right hand side, as reflected in table XIV, returns to QMJ, as a regressor, are significant across all time periods within the sample, with the highest returns seen during the 2007-2008 crisis.

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Given the significant alpha associated with QMJ, its addition to the 3-factor asset pricing model was expected to significantly improve the overall fit of the model, which explained 20% of the cross section of real estate stock returns during the period 1999-2013. The low R2_{is supported by previous studies that similarly apply the Fama-French 3-factor model to}

REIT returns. The explanatory power of the Fama-French 3-factors appears to have been declining since the mid 1990s.

Upon inclusion of QMJ as a regressor, R2_{increased to 20.6%, as reported in table VII. QMJ}

is identified as statistically significant at the 99% confidence level, yet average monthly returns attributed to the factor (its coefficient) are smaller than that of all other control variables, and as previously mentioned, the overall fit of the model improves by only 0.6%, still leaving the vast majority of the cross section of U.S. listed real estate returns, unexplained. Similar to the limited explanatory power of quality on price, the addition of quality as a risk adjusting variable also provides limited improvement. Technically, the 4-factor model including QMJ is a superior model to the Fama French 3-4-factor model. However, materially, this does not appear to be the case.

It is possible that other shortcomings within the applied factor model exist and distort the true impact of the addition of a QMJ factor. For example, REIT momentum, which is not included, has been found to dominate as a determinant of REIT returns (Goebel, 2013). In assessing REIT performance, use of the CAPM and Fama-French 3-factor models, have been found to lead to Type I errors, with better specification achieved when mimicking portfolios are constructed using REITs, not all firms from the aggregate stock market (Chiang, 2006). Further, the real estate factor, which drives not only direct real estate, but also listed real estate (Lee & Mei, 1994), is not captured by the 3-factor model or the additional QMJ factor. Any one of the omitted variables mentioned or not mentioned, could limit the explanatory power of the 4-factor model used herein.

In an attempt to potentially improve the fit of the asset pricing model used for real estate stocks, the market factor issue was addressed. Empirical evidence suggesting that the market factor is an inefficient predictor of expected returns, overestimating the market premium for high beta stocks and underestimating it for low beta stocks (Black, Jensen, & Scholes, 1972;