pricing of volatility risk in reitsidiosyncratic volatility sorted long-short portfolios of...

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P r i c i n g o f Vo l a t i l i t y R i s k i n R E I Ts

A u t h o r s R. Jared DeLisle , S. McKay Price, and

C.F. Sirmans

A b s t r a c t We examine the pricing of volatility risk in the cross-section ofequity real estate investment trust (REIT) stock returns over the1996 to 2010 period. We consider both aggregate (systematic)volatility and firm-specific (idiosyncratic) volatility. In contrastto the negative and significant price of systematic volatility riskfor non-REIT equities, we find that systematic volatility is notpriced in REIT returns. Idiosyncratic volatility, estimated usingthe Fama and French (1993) three-factor model, is negativelypriced in the cross-section and is largely independent of non-REIT idiosyncratic volatility. Within the total volatility riskprofile, idiosyncratic volatility dominates aggregate volatility inREIT pricing.

Risk can be defined as the likelihood that an asset’s realized returns will differfrom that which is expected. According to asset pricing theory, investors requirea reward for bearing the portion of an asset’s risk that cannot be diversified away.Thus, when decomposing risk into aggregate (or systematic) and firm-specific (oridiosyncratic) volatility, only the volatility that can be explained by systematicfactors should be priced. We examine the pricing of systematic and idiosyncraticvolatility risk in equity real estate investment trusts (REITs).

Studying the pricing of systematic and idiosyncratic volatility in REIT returns isimportant for several reasons. First, it has long been debated whether REIT sharesbehave like typical stocks or the underlying real estate assets they own (e.g., Wang,Erickson, and Chan, 1995; Ghosh and Sirmans, 1996; Chan, Erickson, and Wang,2003). The answer to this debate has direct implications for portfolio formationand the hedging properties of REITs. Literature in this area tends to focus oneither the degree of REIT and stock market integration or the stability of REITbetas over time (e.g., Ling and Naranjo, 1999; Glascock, Lu, and So, 2000;Chiang, Lee, and Wisen, 2005; Fei, Ding, and Deng, 2010; Liow and Addae-Dapaah, 2010), with mixed results. To date, the extent of potential connectionsbetween REIT returns and the general stock market have not been decided throughanalysis that relies heavily on time series correlations and/or market beta.Moreover, market beta is a fairly limited proxy for systematic risk that does notdirectly include aggregate stochastic volatility as a state variable.1 Simply put, wedo not know if REIT exposure to aggregate market volatility is priced in the cross-section of REIT returns.

2 2 4 � D e L i s l e , P r i c e , a n d S i r m a n s

Second, while aggregate volatility is important in understanding risk and returnrelations in a portfolio context, distinct REIT characteristics render anunderstanding of idiosyncratic risk to be of great importance (Chaudhry,Maheshwari, and Webb, 2004). Most prominently, REIT assets are all unique withrespect to locational attributes. Ooi, Wang, and Webb (hereafter OWW) (2009)state that the inherently localized and segmented nature of real estate markets hasled to wide acceptance of the idea that real estate assets and property-related stocksmay be more exposed to idiosyncratic risk than typical equities. Despite itsimportance, REIT idiosyncratic risk has only recently attracted the attention ofreal estate researchers, with OWW being among the first papers to explicitly studyfirm-specific volatility in REIT pricing. Overall, the literature is inconclusive withrespect to the sign and significance of REIT idiosyncratic volatility.

OWW (2009) find that idiosyncratic risk not only matters in REIT pricing, butthat idiosyncratic risk is positively priced and dominates market beta in explainingREIT returns. For firm-specific volatility, OWW use exponential generalized auto-regressive conditional heteroscedasticity (EGARCH) models in their estimation ofidiosyncratic risk, which unintentionally introduces a look-ahead bias in thecomputation of idiosyncratic volatility (Guo, Kassa, and Ferguson, 2013). Sun andYung (2009) do not use EGARCH in their estimation of REIT idiosyncraticvolatility and initially find a positive relation with expected returns, although oncethey incorporate various controls the positive relation loses its significance.Chiang, Jiang, and Lee (2009) study the time series relation between REIT returnsand idiosyncratic volatility, without EGARCH, and find a positive relation in thevintage REIT era (pre-1992) and a negative relation during the modern REIT era(post-1992).

We examine the pricing of systematic volatility risk, and revisit the pricing ofidiosyncratic volatility risk, in equity REIT stocks. We avoid the limitations ofmarket beta by utilizing several measures of aggregate volatility, which draw uponoptions data and/or broad, market-wide returns innovations. We also avoidpotential EGARCH bias issues by following the idiosyncratic volatility estimationmethods of Ang, Hodrick, Xing, and Zhang (hereafter AHXZ) (2006, 2009). Ouranalysis examines each component of volatility risk to determine whether it ispriced in the cross-section of REIT returns, and, if so, the magnitude and natureof the price. We also compare the two components in a multivariate frameworkto determine the relative importance of each factor. Ultimately, we are able todetermine whether variation in the measurement of aggregate and firm-specificrisk can improve our understanding of the fundamental REIT risk/return relationand its implications on optimal portfolio formation.

For proxies of expected aggregate market volatility, we follow AHXZ (2006),Bakshi, Kapadia, and Madan (hereafter BKM) (2003), and Da and Schaumburg(hereafter DS) (2011). In order to assess whether aggregate market volatility is astate variable, AHXZ estimate stock sensitivity to changes in the Chicago BoardOptions Exchange’s (CBOE) market volatility index (VIX). VIX is constructedusing implied volatilities from call and put options on the S&P 500 Index and

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relies on a limited set of at-the-money and out-of-the-money options.2 AHXZ(2006) show that sensitivity to VIX is a priced risk-factor in the cross-section ofnon-REIT stock returns. Specifically, they find that stocks with high sensitivity tochanges in VIX underperform stocks with low sensitivity to such changes. Thisnegative price of risk is commonly referred to as the negative volatility riskpremium.

While AHXZ (2006) focus exclusively on VIX, we employ the techniques ofBKM (2003) to derive additional implied market volatility measures using the fullset of tradable S&P 500 and Russell 2000 options data. The latter index allowsus to examine whether REITs, which are typically smaller firms than thoseincluded in the S&P 500, are more sensitive to aggregate volatility in the returnsof small stocks. By following BKM, we are also able to compute the highermoments of the returns distribution and control for the effects of implied marketskewness. Without controlling for skewness, potentially fat tails in the returndistribution can be misinterpreted as increased volatility. Incorporating skewnessallows us to more accurately estimate the shape of the market’s return distribution(e.g., BKM, 2003; DeLisle, Doran, and Peterson, 2011; Chabi-Yo, 2012; Chang,Christoffersen, and Jacobs, 2013).

We also incorporate the market volatility factor of DS (2011) as an alternativemeasure that uses monthly, rather than daily, volatility innovations. DS show thataugmenting the CAPM by a measure of innovations in market-wide volatilityyields a two-factor model that performs well in explaining the cross-section ofreturns on securities in several asset classes. They construct the volatility factorby extracting the first principal component from the broad cross-section ofindividual monthly stock volatility innovations. Consistent with what AHXZ(2006) find using implied market volatility, DS find a negative and highlysignificant aggregate volatility risk premium using the principal factor in Famaand MacBeth (1973) pricing regressions.

We compute idiosyncratic volatility for each REIT using the Fama and French(1993) three-factor model in a manner widely used in the extant literature. AHXZ(2006, 2009) provide evidence, using non-REIT U.S. and international stocks, thatidiosyncratic volatility calculated in this way is negatively priced in the cross-section of stock returns. In contrast, OWW (2009) find a positive relation betweenidiosyncratic volatility and the cross-section of REIT returns by incorporatingEGARCH adjustments in their estimation of idiosyncratic volatility. This result isconsistent with economic theories that suggest that idiosyncratic volatility andexpected returns should be positively related if investors demand a premium forthe inability to fully diversify risk (e.g., Merton, 1987; Malkiel and Xu, 2002).However, Fink, Fink, and He (2012) and Guo, Kassa, and Ferguson (2013) show,analytically and empirically, that this fairly new estimation strategy inadvertentlyintroduces a look-ahead bias into recursive volatility forecasts by including thecontemporaneous stock return in the estimation of month t EGARCH idiosyncraticvolatility. Where, in reality, an investor would not have the benefit of knowingmonth t returns when estimating month t idiosyncratic volatility. Both papers find


that without controlling for this EGARCH flaw, idiosyncratic volatility can showup significantly positively related to returns, as in Fu (2009). They further showthat EGARCH idiosyncratic volatility can strongly depend on contemporaneousreturns in relatively small sample periods, to the point where it affects statisticalinference.3

Our analysis is conducted in the cross-section of REIT returns at both theportfolio- and firm-level over the 1996–2010 period. Our results show thataggregate volatility risk is not priced in REIT returns. REITs do not appear to besensitive to innovations in implied market volatility using VIX or the full set oftradable options on the S&P 500 and Russell 2000 indices, even when controllingfor implied market skewness. Moreover, REITs do not appear to be sensitive tothe market volatility factor of DS (2011). These results are strikingly differentthan the negative and significant relation AHXZ (2006) and DS (2011) findbetween non-REIT stocks and aggregate volatility risk. For example, AHXZ findthe non-REIT price of aggregate volatility risk to be approximately �1% perannum, while we find the corresponding REIT price to not be significantlydifferent from zero.

In contrast to the cross-sectional REIT results of OWW (2009), but consistentwith the cross-sectional non-REIT results of AHXZ (2006, 2009), we find thatidiosyncratic volatility risk is negatively priced in the cross-section of REITreturns.4 AHXZ (2006) find a difference of �1.06% per month between theaverage returns to stocks sorted into high and low idiosyncratic volatility quintileportfolios for non-REIT U.S. equities.5 We find remarkably similar prices of�1.14% and �0.98% per month for equity REITs in portfolio-level and firm-leveltests, respectively. Furthermore, we find that idiosyncratic volatility risk pricingremains negative and significant after controlling for various measures ofaggregate volatility risk. These results hold after controlling for various factorsknown to affect returns including idiosyncratic skewness, firm size, book-to-market equity, momentum, institutional ownership, and liquidity.

Moreover, we find that REIT idiosyncratic volatility is largely independent ofnon-REIT idiosyncratic volatility. AHXZ (2009) find that excess returns toidiosyncratic volatility sorted long-short portfolios of international stocksdisappear after controlling for exposure to the idiosyncratic volatility of U.S. firms.While the negative price of idiosyncratic volatility risk we find is similar toAHXZ, our results do not suggest a similarly high level of co-movement betweenREIT and non-REIT idiosyncratic volatility.

Overall, this study contributes to the literature on REITs and volatility risk inseveral ways. First, we demonstrate that REITs are not sensitive to innovations inaggregate volatility in the cross-section of expected equity REIT returns usingmultiple proxies for aggregate volatility risk. This stands in stark contrast to bothasset pricing theory and established empirical results for non-REIT stocks. Second,using empirical methods free from look-ahead bias, we find that equity REITidiosyncratic volatility is negatively related to expected returns in the cross-


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section. Third, we show that REITs are not sensitive to aggregate skewness noridiosyncratic skewness, while in both cases there is opposing theory and non-REIT evidence. Fourth, we find that non-REIT idiosyncratic volatility cannotexplain REIT idiosyncratic volatility. Finally, we provide additional support forthe idea that idiosyncratic volatility risk dominates systematic risk in REIT pricingby showing this to be the case using aggregate volatility measures rather thanmarket beta.

The remainder of this study is developed in the following sections. In the nextsection, we describe the data and variable creation. In the third section, we outlinethe analysis and discuss the results. We present concluding remarks in the lastsection concludes.

� D a t a a n d Va r i a b l e C r e a t i o n

Our sample is comprised of the universe of equity REIT firms as identified inFeng, Price, and Sirmans (2011), which includes all equity REITs that are publiclytraded on the three major exchanges (NYSE, AMEX, and NASDAQ). We examinethe 1996–2010 period due to options data availability starting in 1996, with dailyprices for options on the S&P 500 and Russell 2000 indices obtained fromOptionMetrics IvyDB. VIX index levels are from the CBOE website.6 Daily andmonthly returns data, stock prices, number of shares outstanding, and the numberof shares traded are from the Center for Research in Security Prices (CRSP).Excess market returns (MKT), the risk-free rate, and the Fama and French (1993)size (SMB) and book-to-market (HML) factors are from Ken French’s website.7

Book equity is from Standard & Poor’s Compustat database and the number ofshares owned by institutions is from the Thomson-Reuters Institutional Holdings(13F) Database. In accordance with extant literature, only observations withpositive book equity and data available in CRSP for at least one year are kept inthe sample.

We employ empirical methods in the spirit of AHXZ (2006) with a fewmodifications to render them more appropriate for our sample and allow for theincorporation of additional, important control variables. While AHXZ rely on thechange in VIX to proxy for innovations in systematic volatility risk, we recognizethat VIX is somewhat limited in its ability to adequately capture overall expectedmarket volatility. Unlike the VIX computation,8 by following the procedure ofBKM (2003) we are able to estimate the implied aggregate volatility of the risk-neutral probability distributions [VOL(SP500) and VOL(R2000)] constructed fromall non-zero bid European calls and puts on the S&P 500 and Russell 2000indices.9 Exhibit 1 shows daily implied market volatility over the sample periodusing VIX, VOL(SP500), and VOL(R2000). There are significant differencesbetween these three volatility measures even though they unmistakably follow asimilar path. Although not shown, VIX and VOL(SP500) are correlated at 98.9%,while VIX and VOL(R2000) are correlated at 86.8%, and VOL(SP500) and

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Exhibi t 1 � Daily Implied Market Volatility as Measured by VIX and Annualized VOL for the S&P500 (SP500) and Russell 2000 (R2000)

Notes: VIX is the CBOE market volatility index shown on a daily basis over the 1996–2010 sample period. Following BKM (2003), VOL(SP500) is calculated as thestandard deviation of the risk-neutral density using a continuum of European call and put options on the S&P 500 Index and represents estimated implied market volatility.VOL(R2000) is calculated in the same manner using a options on the Russell 2000 index.


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VOL(R2000) are correlated at 87.7%. Each measure renders a slightly differentdepiction of option-implied aggregate volatility.

The BKM (2003) procedure also enables us to estimate implied market skewness(SKEW). This is important when working with implied market volatility becausethe Black and Scholes (1973) model tends to misprice deep in-the-money anddeep out-of-the-money options (Black, 1975; Merton, 1976). Furthermore, option-implied volatility and skewness are related (Corrado and Su, 1996, 1997; BKM,2003). Without controlling for expected skewness, the asymmetry, or fat tails ofa returns distribution, may be incorrectly interpreted as additional volatility. Thisis a potentially critical distinction as studies have shown that investors desirepositive skewness in their portfolio, but dislike volatility (Kraus and Litzenberger,1976; Barberis and Huang, 2008). Additionally, Chabi-Yo (2012) demonstratesthe mechanism by which expected aggregate skewness is priced. Chang,Christoffersen, and Jacobs (2013) empirically confirm the predictions aboutskewness pricing from Chabi-Yo’s model. Thus, incorporating the third moment(skewness) into the analysis allows us to better isolate the cross-sectional effectsof the second moment (variance).

While AHXZ (2006) use simple first differences to capture the changes in theVIX, we estimate the actual time series innovations using an autoregressivemoving average (ARMA) model with two lags for each component.10 TheARMA(2,2) innovations are denoted �VIX, �VOL(SP500), and �VOL(R2000) forthe three measures of implied market volatility. Similarly, ARMA(2,2) innovationsfor the BKM (2003) estimated skewness control variables are represented as�SKEW(SP500) and �SKEW(R2000).

DS (2011) note that there is a certain degree of arbitrariness in stock index choicewhen deriving volatility proxies, which can be affected by time-varying portfolioweights and correlations. Theory merely suggests that the index used in a CAPMtype of asset pricing framework should be broad-based and, preferably, value-weighted. In order to circumvent this lack of guidance and any potentialarbitrariness, DS construct a ‘‘non-parametric’’ volatility proxy by analyzing thecross-section of realized monthly volatility innovations for all U.S. equities.Specifically, they extract the first principal component (F1), each month, of theone-period-ahead ARMA(1,1) innovations in the (log) realized volatilities of eachstock in the CRSP value-weighted index. They show the F1 factor to be a statevariable, which consistently prices volatility risk in stocks, options, and bonds.We incorporate F1 into our analysis as an additional measure of systematicvolatility.11

With estimates for �VIX, �VOL(SP500), �SKEW(SP500), �VOL(R2000), and�SKEW(R2000) we then obtain factor loadings by regressing daily excess returns(RET) on MKT and each market volatility measure, over the most recent month,� � 1, as follows:


RET � � � � MKT � � Volatilityi,t i MKT,i t �Volatility,i t

� � Skewness � � , (1)�Skewness,i t i,t

where RETi,t and MKTt are as defined above for each firm i on day t. For Volatilityt,we substitute �VIXt, �VOL(SP500)t, and �VOL(R2000)t to obtain factor loadingsfor each implied volatility measure. Skewnesst is only included in the case of�VOL(SP500)t and �VOL(R2000)t, where the corresponding skewness measures,�SKEW(SP500) and �SKEW(R2000), are substituted in. For F1, we obtain factorloadings using monthly excess returns.

The loading ��VIX represents firm sensitivity to innovations in implied marketvolatility computed using the AHXZ (2006) method. ��VOL(SP500) and ��VOL(R2000)

signify firm sensitivity to innovations in implied aggregate volatility following theBKM (2003) method with options on the S&P 500 and Russell 2000 indices,respectively. �F1 is the loading on the DS (2011) market volatility factor. Positive(negative) loadings indicate that firms with high positive (negative) sensitivities to�VIX, �VOL(SP500), �VOL(R2000), or F1 have positive (negative) returns whenthe expected market volatility increases.

Following AHXZ (2006, 2009), idiosyncratic volatility (IVOL) is computedrelative to the Fama and French (1993) three-factor model estimated over the mostrecent month, � � 1:

RET � � � � MKT � � SMBi,t i MKT,i t SMB,i t

� � HML � � , (2)HML,i t i,t

where RETi,t, MKTt, SMBt, and HMLt are as discussed previously and IVOL isequal to the standard deviation of the residuals:

1/21 2IVOL � � , (3)�� i,� i,tN t�1,N

where N is the number of days in the regression and �i,t are the residuals fromthe regression in equation (2). This technique avoids introducing a look-ahead biasin the calculation of idiosyncratic volatility (Fink, Fink, and He, 2012; Guo, Kassa,and Ferguson, 2013). We compute idiosyncratic skewness (ISKEW) as a controlvariable because Boyer, Mitton, and Vorkink (2010) find that idiosyncraticskewness helps explain cross-sectional pricing variation in idiosyncratic volatility.


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ISKEW is calculated as the third central moment of the residuals from the sameregression as in Boyer, Mitton, and Vorkink:

31 � �t�1,N i,tISKEW � . (4)i,� 3N (IVOL )i,�

We also incorporate several additional control variables. A number of firmcharacteristics are shown to be priced in the cross-section of returns, and, thus,we wish to control for these variables. For example, literature shows that size(Banz, 1981; Fama and French, 1992) and the ratio of book-to-market equity(Stattman, 1980; Fama and French, 1992) explain much of the variation in thecross-section of stock returns. Jegadeesh and Titman (1993) demonstrate that stockprice momentum has the power to predict future stock returns. Lee andSwaminathan (2000) find liquidity (as measured by share turnover) is related tofuture returns. Institutional ownership has also been shown to be correlated withfuture returns [see Sias, Starks, and Titman (2006) for an extensive literaturereview]. We define the nomenclature of these variables as follows: SIZE is thenatural log of firm market capitalization. BM is the ratio of book-to-market equity.MOM12 represents returns momentum over the most recent 12-month period(non-inclusive of month t � �1) computed as summed excess returns. TURN isthe number of shares traded divided by the number of shares outstanding. Lastly,IO is the proportion of shares outstanding held by institutional owners. Exhibit 2provides sample means and standard deviations for the variables. Note that, whilethe means of all the aggregate volatility measures are close to zero (due to themean-reverting nature of market volatility), they exhibit a considerable amountof variation, which is reflected by their standard deviation. Additionally, thesensitivities to the aggregate volatility measures are far less correlated than themeasures themselves. Exhibit 3 shows that ��VIX and ��VOL(SP500) have a correlationcoefficient of 0.76, while ��VOL(R2000) is only correlated with ��VIX and ��VOL(SP500)

at 0.36. The highest correlation between �F1 and any of the other measures is�0.04. Thus, each measure provides a different representation of systematicvolatility. As expected, IVOL is not highly correlated with any of the loadings onthe systematic factors.

� A n a l y s i s a n d R e s u l t s

At the beginning of each month we separately rank stocks by sensitivity toinnovations in implied market volatility, for each of the three measures (��VIX,��VOL(SP500), and ��VOL(R2000)), as well as by idiosyncratic volatility (IVOL). Quintileportfolios are then independently formed each month using the rankings of thesecharacteristics. Next, we create long-short portfolios where we take a long positionin equity REITs in the highest quintile (5) of the portfolio formation attribute and


Exhibi t 2 � Descriptive Statistics

Variable Obs. Mean Std. Dev. Median

RET 26,451 0.012 0.105 0.011

�VIX 3,772 0.013 1.636 �0.126

�VOL(SP500) 3,774 0.004 1.880 �0.144

�SKEW(SP500) 3,774 0.001 0.358 0.024

�VOL(R2000) 3,678 0.002 1.569 �0.093

�SKEW(R2000) 3,678 0.000 0.287 �0.004

F1 480 �0.000 0.134 0.025

IVOL 26,451 1.571 1.597 1.153

ISKEW 26,451 0.087 0.694 0.070

SIZE 26,451 6.131 1.704 6.381

BM 26,451 0.821 1.197 0.648

MOM12 26,451 0.126 0.320 0.145

IO 26,451 0.467 0.341 0.481

TURN 26,451 1.040 1.322 0.650

Notes: RET is the daily excess return for each firm. �VIX denotes ARMA(2,2) innovations in theChicago Board Options Exchange’s market volatility index (VIX). �VOL(SP500) represents ARMA(2,2) innovations in estimated implied market volatility (VOL) using options data on the S&P 500Index. �SKEW(SP500) are the ARMA(2,2) innovations in estimated implied market skewness(SKEW). VOL and SKEW are computed, following BKM (2003), as the second and third centralmoments of the risk-neutral density using a continuum of European call and put options on theS&P 500 Index, respectively. �VOL(R2000) and �SKEW(R2000) are calculated in the samemanner using options data on the Russell 2000 index. F1 is the DS (2011) monthly marketvolatility innovation factor, which is calculated as the first principal component from the monthlycross-section of individual stock volatility ARMA (1,1) innovations. IVOL is the standard deviationof the residuals from a Fama and French (1993) three-factor model regression estimated over themost recent month, � � 1. ISKEW is the skewness of the residuals from the same regression. SIZEis the natural log of firm market capitalization. BM is the ratio of book-to-market equity. MOM12is the returns momentum over the most recent twelve month period computed as summed excessreturns. IO is the percentage of outstanding shares held by institutional owners. TURN is a proxyfor liquidity computed as the average daily number of shares traded divided by the number ofshares outstanding. No variables have been scaled to be different than the underlying data asfound in their original sources. For example, percentages are expressed in decimal form.

a short position in equity REITs in the lowest quintile (1). The long-shortportfolios represent a zero-investment strategy based on the attribute of interest.Value-weighted portfolio returns are then examined for the following month. Thismethod of portfolio formation is similar to how an investor would use historicalinformation to construct a portfolio, and realize the portfolio returns over the nextmonth. The investor would then rebalance her portfolio based on new information


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acquired over the past month. To further examine the long-short portfolio returns,we regress the 5-1 portfolio returns on the Fama and French (1993) three-factormodel and report the alphas.12 In the idiosyncratic volatility case, following AHXZ(2009), we also augment the model with long-short IVOL returns to the portfolioof all non-REIT U.S. firms. This allows us to check for co-movement betweenREIT IVOL and aggregate IVOL. AHXZ (2009) find large and significant co-movements between idiosyncratic volatility portfolio returns in internationalmarkets and the U.S. market; where alphas to international IVOL portfolio returnsare statistically insignificant when aggregate U.S. IVOL portfolio returns areincluded in the regression.

Exhibit 4 shows value-weighted post-portfolio-formation monthly returns. For theIVOL-based portfolios, we find mixed initial results. While the long-short (5-1)monthly returns are negative but not significant, when risk-adjusting the returnsby controlling for market returns, size, and book-to-market equity in the Famaand French (1993) three-factor model, the alpha becomes a highly significant�1.14% per month. This negative return is consistent with the idiosyncraticvolatility-based portfolio returns for non-REIT equities in AHXZ (2006, 2009),but is contrary to the positive relation between REIT idiosyncratic volatility andreturns in OWW (2009). The alpha remains large and significant at �0.89% permonth (p-value of 0.059) when controlling for the returns to a portfolio long allnon-REIT U.S. stocks in the highest IVOL quintile and short all non-REIT U.S.stocks in the lowest IVOL quintile as in AHXZ (2009).13 Thus, REIT idiosyncraticvolatility appears to be largely independent of aggregate idiosyncratic volatility,yet appears to be priced by investors in a similar manner.

For the three implied market volatility measures (��VIX, ��VOL(SP500), and��VOL(R2000)), the 5-1 strategy yields monthly returns that are not significantlydifferent from zero. The Fama and French (1993) alphas are insignificant as well.The lack of significant differences stands in stark contrast to the highly significantportfolio returns differences for non-REIT equities in AHXZ (2006). This isparticularly interesting in the case of ��VOL(R2000), which represents the sensitivityto aggregate implied volatility for a large group of small stocks, a segment of themarket with which REITs are commonly compared. While some REITs areconsidered large capitalization stocks, with a few included in the S&P 500 Indexstarting in the fall of 2001, most REITs are relatively small.

To disentangle a potential size effect, we break the sample into size and volatilityterciles and sequentially sort the sample at the end of each month, first by sizeand then by volatility.14 For each volatility measure, the monthly long-short (3-1)value-weighted returns differences are shown for small, medium, and large firmsin Exhibit 5. With IVOL, the statistical significance increases as size increases andall long-short returns differences are negative. Similar to the one-dimensional sortreturns in Exhibit 4, the IVOL long-short returns in Exhibit 5 are insignificant forsmall- and medium-sized firms and only weakly significant for large firms.However, the Fama and French (1993) alphas are significant at close to the 5%level for small firms and are strongly significant at the 1% level for medium and

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Exhibi t 3 � Correlations

RET �MKT ��VIX ��VOL(SP500) ��SKEW(SP500) ��VOL(R2000) ��SKEW(R2000) �F1 IVOL ISKEW

RET 1

�MKT �0.01 1

��VIX 0.01 0.47 1

��VOL(SP500) 0.00 0.57 0.76 1

��SKEW(SP500) �0.02 0.29 0.13 0.05 1

��VOL(R2000) 0.01 0.19 0.36 0.36 �0.01 1

��SKEW(R2000) 0.02 �0.03 �0.04 0.01 0.15 �0.03 1

�F1 0.05 �0.01 0.01 0.01 0.01 �0.04 �0.01 1

IVOL 0.01 0.09 0.01 �0.02 0.08 �0.10 0.02 �0.05 1

ISKEW �0.01 �0.04 �0.03 �0.02 0.01 �0.02 0.01 �0.15 0.12 1

SIZE �0.03 0.26 0.03 0.05 0.00 0.00 �0.06 0.14 �0.36 �0.07

BM 0.02 �0.06 0.01 0.00 �0.03 �0.01 0.03 0.06 0.09 0.03

MOM12 0.02 �0.06 0.00 0.03 �0.04 0.00 0.03 0.09 �0.28 �0.04

IO 0.01 0.31 0.03 0.04 0.02 �0.03 �0.09 0.27 �0.15 �0.06

TURN 0.03 0.36 0.02 0.01 0.06 �0.02 �0.10 0.23 0.27 0.00

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Exhibi t 3 � (continued)

Correlations

SIZE BM MOM12 IO TURN

SIZE 1

BM �0.24 1

MOM12 0.10 0.11 1

IO 0.64 �0.16 0.02 1

TURN 0.32 �0.10 �0.18 0.45 1

Notes: For each firm, RET is regressed on MKT and �VIX on a daily basis in month � � 1, to obtain the factor loadings, ��MKT and ��VIX. RET is the dailyexcess return for each firm, MKT is the daily excess market returns, and �VIX is the ARMA (2,2) innovations in the Chicago Board Options Exchange’smarket volatility index (VIX). Similarly, for each firm, RET is regressed on MKT and the other aggregate market volatility and skewness measures[�VOL(SP500), �SKEW(SP500), �VOL(R2000), �SKEW(R2000), and F1] over the same window to obtain their respective factor loadings [��VOL(SP500),��SKEW(SP500), ��VOL(R2000), ��SKEW(R2000), and �F1]. �VOL(SP500) represents ARMA (2,2) innovations in estimated implied market volatility (VOL) using optionsdata on the S&P 500 Index. �SKEW(SP500) are the ARMA(2,2) innovations in estimated implied market skewness (SKEW). VOL and SKEW are computed,following BKM (2003), as the second and third central moments of the risk-neutral density using a continuum of European call and put options on the S&P500 Index, respectively. �VOL(R2000) and �SKEW(R2000) are calculated in the same manner using options data on the Russell 2000 Index. F1 is the DS(2011) market volatility innovation factor, which is calculated as the first principal component from the cross-section of individual stock volatility ARMA (1,1)innovations. IVOL is the standard deviation of the residuals from a Fama and French (1993) three-factor model regression estimated over the most recentmonth, � � 1. ISKEW is the skewness of the residuals from the same regression. SIZE is the natural log of firm market capitalization. BM is the ratio ofbook-to-market equity. MOM12 is the returns momentum over the most recent twelve month period computed as summed excess returns. IO is thepercentage of outstanding shares held by institutional owners. TURN is a proxy for liquidity computed as the average daily number of shares traded dividedby the number of shares outstanding.

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Exhibi t 4 � Value-Weighted Monthly Portfolio Returns Sorted by Sensitivity to Volatility Measures

��VIX ��VOL(SP500) ��VOL(R2000) IVOL

Pre-formation Post-formation Pre-formation Post-formation Pre-formation Post-formation Pre-formation Post-formationQuintiles Mean Returns % Mean Returns % Mean Returns % Mean Returns %

1 (Low) �0.85 1.16 �0.75 0.83 �0.75 0.77 0.77 1.26

2 �0.19 1.28 �0.17 1.32 �0.22 1.38 1.04 1.06

3 0.05 1.13 0.05 0.96 �0.02 1.15 1.25 1.09

4 0.30 1.09 0.26 1.26 0.17 1.11 1.57 0.99

5 (High) 0.94 0.90 0.81 1.13 0.69 0.85 3.20 0.87

5-1 �0.27 0.30 0.08 �0.49(�0.98) (0.86) (0.27) (�0.88)

FF3 � �0.22 0.46 0.15 �1.14**(�0.70) (1.23) (0.43) (�2.69)

FF3 �� 0.89*(�1.90)

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Value-Weighted Monthly Portfolio Returns Sorted by Sensitivity to Volatility Measures

Notes: For each firm, RET is regressed on MKT and �VIX on a daily basis in month � � 1, to obtain the factor loading, ��VIX. RET is the daily excess returnfor each firm, MKT is the daily excess market returns, and �VIX is the ARMA (2,2) innovations in the Chicago Board Options Exchange’s market volatilityindex (VIX). Similarly, for each firm, RET is regressed on MKT and other aggregate market volatility measures [�VOL(SP500) and �VOL(R2000)] over thesame window to obtain their respective factor loadings [��VOL(SP500) and ��VOL(R2000)]. �VOL(SP500) represents ARMA (2,2) innovations in estimated impliedmarket volatility (VOL) using options data on the S&P 500 Index; where VOL is computed, following BKM (2003), as the standard deviation of the risk-neutral density using a continuum of European call and put options on the S&P 500 Index. �VOL(R2000) is calculated in the same manner using optionsdata on the Russell 2000 Index. IVOL is the standard deviation of the residuals from a Fama and French (1993) three-factor model regression estimated overthe most recent month, � � 1. In this table, firms are sorted at the end of each month � � 1 into quintiles based on their respective aggregate marketvolatility sensitivities, ��VIX, ��VOL(SP500), and ��VOL(R2000), as well as IVOL. Post-portfolio-formation monthly returns are then computed as value-weightedaverages in each quintile portfolio for every month �. 5-1 monthly returns are the return differences between the high and low quintile portfolios for themonth following the pre-formation period. FF3 � is the alpha from regressing the 5-1 portfolio returns on the Fama and French (1993) three-factor model.FF3 �� is the alpha from regressing the 5-1 portfolio returns on the Fama and French (1993) three-factor model augmented with returns to the IVOL long-short portfolio of all non-REIT U.S. firms. The pre-formation means are averages of the loadings [��VIX, ��VOL(SP500), and ��VOL(R2000)] of each firm within therespective portfolios. Similarly, the pre-formation IVOL means are averages of the IVOL of each firm within the respective portfolios. Robust t-statistics areshown in parentheses.*p � 0.10.**p � 0.05.***p � 0.01.

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Exhibi t 5 � Value-Weighted Monthly Portfolio Returns Sorted by Sensitivity to Volatility Measures and Firm Size

��VIX ��VOL(SP500) ��VOL(R2000) IVOL

Small Med Large Small Med Large Small Med Large Small Med Large

1 (Low) 0.95 1.25 1.10 1.03 1.15 0.94 0.76 1.27 0.97 1.2 1.33 1.11

2 1.29 1.04 1.11 1.16 1.21 0.95 1.55 1.27 1.12 1.22 1.23 1.1

3 (High) 1.49 1.37 1.03 1.32 1.26 1.02 1.24 1.1 0.82 1.05 1.01 0.72

3-1 0.54 0.12 �0.06 0.29 0.11 0.08 0.48 0.17 0.15 0.15 0.32 0.39*(1.46) (0.38) (�0.31) (0.94) (0.40) (0.42) (1.59) (�0.69) (�0.86) (�0.23) (�0.77) (�1.73)

FF3 � 0.64* 0.26 0.01 0.37 0.24 0.17 0.44 �0.03 �0.13 �0.82* �0.81*** �0.61***(1.68) (1.06) (0.04) (1.20) (0.96) (0.80) (1.43) (�0.13) (�0.69) (�1.84) (�2.61) (�3.09)

FF3 �� 0.29 �0.65** �0.48**(�0.47) (�2.04) (�2.24)

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Value-Weighted Monthly Portfolio Returns Sorted by Sensitivity to Volatility Measures and Firm Size

Notes: For each firm, RET is regressed on MKT and �VIX on a daily basis in month � � 1, to obtain the factor loading, ��VIX. RET is the daily excess returnfor each firm, MKT is the daily excess market returns, and �VIX is the ARMA (2,2) innovations in the Chicago Board Options Exchange’s market volatilityindex (VIX). Similarly, for each firm, RET is regressed on MKT and other aggregate market volatility measures [�VOL(SP500) and �VOL(R2000)] over thesame window to obtain their respective factor loadings [��VOL(SP500) and ��VOL(R2000)]. �VOL(SP500) represents ARMA (2,2) innovations in estimated impliedmarket volatility (VOL) using options data on the S&P 500 Index, where VOL is computed, following BKM (2003), as the standard deviation of the riskneutral density using a continuum of European call and put options on the S&P 500 Index. �VOL(R2000) is calculated in the same manner using optionsdata on the Russell 2000 Index. IVOL is the standard deviation of the residuals from a Fama and French (1993) three-factor model regression estimated overthe most recent month, � � 1. In this table, firms are sequentially sorted at the end of each month � � 1 into terciles first based on firm size and then bytheir respective aggregate market volatility sensitivities, ��VIX, ��VOL(SP500), and ��VOL(R2000), as well as IVOL. Post-portfolio-formation monthly returns are thencomputed as value-weighted averages in each portfolio for every month �. 3-1 monthly returns are the return differences between the high and low tercileportfolios for the month following the pre-formation period. FF3 � is the alpha from regressing the 3-1 portfolio returns on the Fama and French (1993)three-factor model. FF3 �� is the alpha from regressing the 5-1 portfolio returns on the Fama and French (1993) three-factor model augmented with returnsto the IVOL long-short portfolio of all non-REIT U.S. firms. Robust t-statistics are shown in parentheses.*p � 0.10.**p � 0.05.***p � 0.01.


large REITs. When controlling for the returns to a portfolio long all non-REITU.S. stocks in the highest IVOL quintile and short all non-REIT U.S. stocks inthe lowest IVOL quintile, the alphas are slightly reduced, but remain economicallylarge, �0.65% and �0.48% per month, and statistically significant at the 5% levelfor medium and large REITs, respectively. The size sorts confirm the earlier resultsthan any co-movement between REIT idiosyncratic volatility and aggregateidiosyncratic volatility is, at best, only modest.

For ��VIX, ��VOL(SP500), and ��VOL(R2000), only one portfolio difference out of the 18tested shows up even weakly statistically significant. Across all three aggregateimplied volatility measures, the return differences tend to be positive, althoughdecreasing monotonically as size increases. Taken together, the two-way sorts inExhibit 5 suggest that size is an important characteristic that should be controlledfor when pricing volatility risk in REITs.

While informative, the relatively small number of firms in the equity REITuniverse renders portfolios formed on multiple dimensions more susceptible tothe influence of outlier observations. Moreover, portfolio-level analysis is limitedin the extent to which additional potential influences can be controlled. At thefirm-level, we are able to add numerous control variables simultaneously andincorporate the F1 monthly market volatility measure of DS (2011) into theanalysis. We use Fama and MacBeth (1973) regressions with Newey and West(1987) standard errors to determine the price of risk. Excess returns are regressedon the variables of interest (IVOL, ��VIX, ��VOL(SP500), ��VOL(R2000), and �F1), alongwith various controls each month.15 The time series of estimated coefficients onthese variables are then used to construct the respective prices of risk and thecorresponding test statistics.

The results are presented in Exhibit 6. In Panel A, excess returns are regressedon IVOL and firm-level sensitivity to each aggregate volatility measureindividually. The negative and significant (at the 1% level) coefficient on IVOL inregression (1) confirms the portfolio level finding of a negative relation betweenREIT returns and idiosyncratic volatility. In other words, REITs with lowidiosyncratic volatility outperform those with high idiosyncratic volatility. Thissuggests that the EGARCH look-ahead bias (Fink, Fink, and He, 2012; Guo,Kassa, and Ferguson, 2013) may have affected the positive price manifest inOWW (2009).

None of the systematic volatility measures are significantly different from zero inExhibit 6, Panel A, including firm-level sensitivity to the new F1 volatility factor.While the insignificant coefficients on the sensitivities to aggregate impliedvolatility measures are consistent with the portfolio-level sorts in Exhibits 4 and5, the insignificant coefficient on the sensitivity to the F1 factor is curious. DS(2011) find F1 to be priced across multiple asset classes including stocks, bonds,and various derivative securities.16 In an ICAPM framework (such as Chabi-Yo,2012), if market volatility is a state variable then it should be priced consistentlyacross asset classes, including REITs. Yet, we do not find evidence of aggregate

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Exhibi t 6 � Fama-MacBeth Regressions of Excess Equity REIT Returns on Volatility Measures and Controls

[1] [2] [3] [4] [5]

Coeff. t-stat. Coeff. t-stat. Coeff. t-stat. Coeff. t-stat. Coeff. t-stat.

Panel A: Regressions of RET on the various volatility measures

IVOL �0.35*** (�3.43)

��VIX 0.04 (0.28)

��VOL(SP500) �0.06 (�0.36)

��VOL(R2000) �0.12 (�0.81)

�F1 0.02 (1.31)

Constant 1.28*** (3.48) 0.81** (2.03) 0.79** (1.97) 0.79** (2.00) 1.00*** (3.31)

Panel B: Regressions of RET on the various volatility measures with controls

�MKT �0.03 (�0.33) �0.03 (�0.26) 0.07 (0.43) 0.06 (0.39) �0.76** (�2.38)

��VIX 0.11 (0.92)

��VOL(SP500) �0.08 (�0.35)

��SKEW(SP500) �0.05 (�1.09)

��VOL(R2000) �0.12 (�0.60)

��SKEW(R2000) 0.09 (1.58)

�F1 0.01 (1.04)

IVOL �0.40*** (�3.85) �0.39*** (�3.74) �0.37*** (�3.59) �0.38*** (�3.82) �0.23** (�2.15)

ISKEW �0.03 (�0.36) �0.02 (�0.21) �0.03 (�0.39) �0.03 (�0.32) 0.00 (0.03)

SIZE �0.18** (�2.48) �0.16** (�2.31) �0.17*** (�2.61) �0.19*** (�2.72) �0.05 (�1.04)

BM 0.06 (0.48) 0.08 (0.62) 0.08 (0.56) 0.02 (0.12) 0.06 (0.42)

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Fama-MacBeth Regressions of Excess Equity REIT Returns on Volatility Measures and Controls

[1] [2] [3] [4] [5]

Coeff. t-stat. Coeff. t-stat. Coeff. t-stat. Coeff. t-stat. Coeff. t-stat.

MOM12 1.33*** (2.96) 1.36*** (3.05) 1.38*** (3.02) 1.33*** (3.10) 0.86* (1.93)

IO 0.42 (1.59) 0.38 (1.45) 0.53* (1.97) 0.47* (1.75) 0.49* (1.96)

TURN 0.16 (1.47) 0.18 (1.65) 0.21** (1.99) 0.18 (1.63) 0.24 (1.38)

Constant 1.77*** (3.56) 1.69*** (3.40) 1.56*** (3.46) 1.81*** (3.83) 1.28*** (3.43)

Notes: The table provides estimated coefficients for Fama and MacBeth (1973) regressions of RET on the various volatility measures individually (Panel A)and with controls (Panel B). RET is the daily excess return for each firm. �MKT, ��VIX, ��VOL(SP500), ��SKEW(SP500), ��VOL(R2000), ��SKEW(R2000), and �F1, are thefactor loadings obtained by regressing daily RET on MKT, �VIX, �VOL(SP500), �SKEW(SP500), �VOL(R2000), �SKEW(R2000), and F1 over the previousmonth, � � 1. MKT is the daily excess market returns. �VIX is ARMA(2,2) innovations in the Chicago Board Options Exchange’s market volatility index(VIX). �VOL(SP500) represents ARMA (2,2) innovations in estimated implied market volatility (VOL) using options data on the S&P 500 Index.�SKEW(SP500) are the ARMA(2,2) innovations in estimated implied market skewness (SKEW). VOL and SKEW are computed, following BKM (2003), asthe second and third central moments of the risk-neutral density using a continuum of European call and put options on the S&P 500 Index, respectively.�VOL(R2000) and �SKEW(R2000) are calculated in the same manner using options data on the Russell 2000 Index. F1 is the DS (2011) market volatilityinnovation factor, which is calculated as the first principal component from the cross-section of monthly individual stock volatility ARMA (1,1) innovations.IVOL is the standard deviation of the residuals from a Fama and French (1993) three-factor model regression estimated over the most recent month, � � 1.ISKEW is the skewness of the residuals from the same regression. SIZE is the natural log of firm market capitalization. BM is the ratio of book-to-marketequity. MOM12 is the returns momentum over the most recent 12-period computed as summed excess returns. IO is the percentage of outstanding sharesheld by institutional owners. TURN is a proxy for liquidity computed as the average daily number of shares traded divided by the number of sharesoutstanding. Robust Newey and West (1987) t-statistics are in parentheses.*p � 0.10.**p � 0.05.***p � 0.01.


J R E R � V o l . 3 5 � N o . 2 – 2 0 1 3

volatility risk pricing in a REIT setting using numerous measures of firm-levelsensitivity to systematic volatility (��VIX, ��VOL(SP500), ��VOL(R2000), and �F1). Withrespect to exposure to aggregate volatility risk, REITs appear to be substantiallydifferent than other financial assets, such as industrial equities and bonds.

In Exhibit 6, Panel B, we repeat the same regressions and include firm sensitivityto a standard market factor, �MKT, as well as additional firm-level controls(��SKEW(SP500), ��SKEW(R2000), ISKEW, SIZE, BM, MOM12, IO, and TURN).17

Consistent with prior results, the negative and strongly significant coefficient forIVOL shows that idiosyncratic volatility is priced in the same manner as AHXZ(2006) find for non-REIT equities. Furthermore, like AHXZ (2006, 2009) andOWW (2009), the pricing of idiosyncratic volatility is not explained by exposureto systematic risk. IVOL dominates ��VIX, ��VOL(SP500), ��VOL(R2000), and �F1.However, it is interesting to note that when �F1 is included in the regression, �MKT

becomes significant. That is, controlling for market volatility using the DS (2011)F1 measure, individual REIT sensitivity to market returns is negatively priced.This result is consistent with the negative market premium DS find to beassociated with non-REIT equities.

To better understand the magnitude of the effect of IVOL on returns in the presenceof these controls, we compare the results from Exhibit 6, Panel B, with the value-weighted long-short monthly portfolio returns in Exhibit 4. Using the IVOLcoefficient from regression [1], a one unit increase in idiosyncratic volatility hasa price of a negative 40 bps per month during the 1996 to 2010 sample period,holding all else constant. The mean IVOL in Exhibit 4 of the long-short portfoliois (3.20 � 0.77 �) 2.43. Evaluating the IVOL risk premium coefficient of �0.40at the mean of 2.43 results in an equal-weighted return of (�0.40 � 2.43 �)�0.972, or about �97 bps per month. When compared to the long-short portfolioFama and French (1993) alpha of �1.14% per month from Exhibit 4, the equal-weighting and additional controls included in the Fama and MacBeth (1973)regressions result in a long-short returns magnitude that is remarkably similar.Likewise, similar results are obtained using the IVOL coefficients from Panel B,regressions [2], [3], and [4], where aggregate implied volatility is controlled forusing ��VIX, ��VOL(SP500) and ��SKEW(SP500), and ��VOL(R2000) and ��SKEW(R2000),respectively. When controlling for firm sensitivity to market volatility using �F1

in regression [5], the magnitude of the IVOL risk premium is reduced by a littleless than half. However, while the IVOL risk premium is lowered, it remainsstatistically significant at the 5% level.

� C o n c l u s i o n

We investigate whether volatility risk, both aggregate (systematic) and firm-specific (idiosyncratic), is priced in the cross-section of expected equity REITreturns. For aggregate volatility risk, we use several distinct measures that drawupon either options data or innovations in the broad cross-section of individualfirm returns. By incorporating empirical methods in the spirit of AHXZ (2006),


we model equity REIT sensitivity to implied systematic volatility risk using theChicago Board Options Exchange’s VIX index. We also utilize the techniques ofBKM (2003) to derive two additional implied aggregate volatility measures usingthe full-spectrum of options available on the S&P 500 and Russell 2000 indices.The BKM (2003) methods allow us to calculate the higher moments of the returnsdistribution in order to control for, and determine the price of, implied aggregateskewness. We also incorporate the market volatility factor of DS (2011), which isderived using the first principal component of the innovations in realizedvolatilities of all available firms in the cross-section. For firm-specific volatilityrisk, we follow AHXZ (2006, 2009) and estimate idiosyncratic volatility withoutthe unintentional look-ahead bias introduced by EGARCH models (Fink, Fink,and He, 2012; Guo, Kassa, and Ferguson, 2013). Employing these methodsenables us to avoid the limitations of relying on market beta to proxy forsystematic risk and biased estimates of idiosyncratic risk.

We find that systematic volatility risk is not priced in equity REIT stocks. Thisresult holds across all four measures of aggregate volatility in portfolio- and firm-level tests, and both univariate and multivariate analyses. The lack of aggregatevolatility risk pricing is in sharp contrast to that which is observed by AHXZ(2006) and DS (2011) for typical non-REIT equities. This robust result suggeststhat REITs are distinctively different from non-REIT equities, with portfolioformation implications. This finding has important portfolio implications, asinvestors should be able to use REITs to hedge their portfolios against innovationsin aggregate market volatility. Using REITs to hedge aggregate volatility shouldalso be particularly attractive to size-style investors, since REITs are not sensitiveto aggregate volatility in neither large stocks (S&P 500), nor small stocks (Russell2000). Similarly, REITs diverge from both theory and non-REIT empirical resultsin that aggregate skewness is not priced (Chabi-Yo, 2012; Chang, Christoffersen,and Jacobs, 2013), and its inclusion does not change aggregate volatility pricing.

We find that idiosyncratic volatility risk is priced in the cross-section of equityREIT returns and that the price is negative. REITs with low idiosyncratic volatilityoutperform those with high idiosyncratic volatility. While this is consistent withthe negative price for non-REIT stocks (AHXZ 2006, 2009), we do not observesignificant co-movement between REIT idiosyncratic volatility and non-REITidiosyncratic volatility. These results add to the recent mixed evidence in the REITliterature where three papers reach three separate conclusions. Chiang, Jiang, andLee (2009) find a negative time series relation between idiosyncratic volatility andREIT returns; Sun and Young (2009) do not find robust support for idiosyncraticvolatility pricing; and, most prominently, OWW (2009) find a positive price. Weattribute the sign difference between our results and OWW to the inadvertent look-ahead bias that is introduced into the estimation of idiosyncratic volatility usingEGARCH techniques (Fink, Fink, and He, 2012; Guo, Kassa, and Ferguson,2013). We find the method used in this study convincing as it uses onlyinformation available to investors at the time of portfolio formation.

The negative price of equity REIT idiosyncratic volatility risk documented here,for U.S. non-REIT equities in AHXZ (2006) and for international non-REIT


J R E R � V o l . 3 5 � N o . 2 – 2 0 1 3

equities in AHXZ (2009) is puzzling. Since the market should only rewardinvestors for bearing that portion of volatility risk that cannot be diversified away,we are left to conjecture that market frictions and incomplete information createan environment where investors are unable to fully diversify away firm-specificrisk (Merton, 1987). However, in such a case, we would expect the price ofidiosyncratic volatility risk to be positive. Nonetheless, AHXZ (2006, 2009) ruleout several possible explanations for the negative price including the potential foridiosyncratic volatility to proxy for transactions costs, analyst coverage, and pricedelay. Moreover, other possible economic explanations for the negative price couldinclude the potential for idiosyncratic volatility to proxy for the overpricing ofpositive skewness, the presence of uninformed traders, or liquidity risk. We controlfor each of these possibilities by including measures of skewness, institutionalownership, and share turnover, and still find a strongly negative price in the cross-section. Despite the puzzling sign, we find that REIT idiosyncratic volatility riskpricing is also robust to the inclusion of various controls for aggregate volatilityrisk. In short, aggregate volatility risk is dominated by firm-specific volatility riskin the cross-section of REIT pricing. Thus, in the context of portfolio formation,investors should consider the negative pricing of idiosyncratic volatility whenchoosing equity REIT stocks to hedge aggregate volatility risk.

� E n d n o t e s1 Market beta is widely found to be an insignificant variable in the presence of other

factors, and papers with this finding are too numerous to be referenced completely.However, Fama and French (1992, 1993) provide convincing evidence of theinadequacies of market beta.

2 See Whaley (2000) for a complete description of VIX.3 The precision of EGARCH estimates is another concern. EGARCH is a data-hungry

process that often does not converge in small samples and short windows (Cumby,Figlewski, and Hasbrouk, 1993; Fink, Fink, and He, 2012; Guo, Kassa, and Ferguson,2013).

4 Chiang, Jiang, and Lee (2009) also find a negative relation in time series tests of REITreturns, but do not determine an actual price.

5 AHXZ (2009) find this difference to be even more pronounced internationally at�1.31%.

6 http: / /www.cboe.com/micro/vix/historical.aspx.7 http: / /mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html.8 As explained in the CBOE white paper located at http: / /www.cboe.com/micro/vix/

vixwhite.pdf, if options with two consecutive strike prices both have zero-bids, alloptions beyond those strike prices are disregarded, even if there are options with non-zero bids.

9 Essentially, risk-neutral probabilities represent the only arbitrage-free price for a givenredundant security in a complete market. We refer interested readers to Gisiger (2010)for a primer on risk-neutral probabilities.

10 The optimal lags were determined to be (2,2) using Bayesian Information Criteria.

http://www.cboe.com/micro/vix/historical.aspx

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

http://www.cboe.com/micro/vix/vixwhite.pdf

http://www.cboe.com/micro/vix/vixwhite.pdf


11 We thank Ernst Schaumburg for providing the F1 market volatility factor time-series,which runs through December, 2006.

12 Although not shown, we repeat the analysis while controlling for skewness, momentum,and using equal-weighted returns and obtain consistent results with each.

13 AHXZ (2009) find highly significant coefficients on aggregate IVOL long-short portfolioreturns, whereas the aggregate IVOL long-short portfolio returns coefficient in ourregression (not shown) is nowhere near significant at any conventional level (p-value of0.225).

14 Given the relatively small number of firms in the REIT industry, we use terciles for thetwo-dimensional sorts to increase the number of observations in each portfolio.

15 Brennan, Chordia, and Subrahmanyam (1998) find firm-level characteristics to havemore explanatory power than the sensitivity to the Fama and French (1993) factorsthemselves, thus we use the actual firm characteristics when possible.

16 We note that DS (2011) examine the pricing of the market wide measure, F1, onportfolios of assets, whereas we examine the pricing of individual firm sensitivity to F1.

17 We control for outliers by Winsorizing all variables at the 1% and 99% levels.

� R e f e r e n c e s

Ang, A., R.J. Hodrick, Y. Xing, and X. Zhang. The Cross-Section of Volatility and ExpectedReturns. Journal of Finance, 2006, 51:1, 259–99.

——. High Idiosyncratic Volatility and Low Returns: International and Further U.S.Evidence. Journal of Financial Economics, 2009, 91:1, 1–23.

Bakshi, G., N. Kapadia, and D. Madan. Stock Return Characteristics, Skew Laws, and theDifferential Pricing of Individual Equity Options. Review of Financial Studies, 2003, 16:1, 101–43.

Banz, R.W. The Relationship between Returns and Market Value of Common Stocks.Journal of Financial Economics, 1981, 9, 3–18.

Barberis, N. and M. Huang. Stocks as Lotteries: The Implications of Probability Weightingfor Security Prices. American Economic Review, 2008, 98:5, 2066–2100.

Black, F. Fact and Fantasy in the Use of Options. Financial Analysts Journal, 1975, 31:4,36–41 and 61–72.

Black, F. and M. Scholes. The Pricing of Options and Corporate Liabilities. Journal ofPolitical Economy, 1973, 81:3, 637–54.

Boyer, B., T. Mitton, and K. Vorkink. Expected Idiosyncratic Skewness. Review ofFinancial Studies, 2010, 23:1, 169–202.

Brennan, M., T. Chordia, and A. Subrahmanyam. Alternative Factor Specifications, SecurityCharacteristics and the Cross-Section of Expected Stock Returns. Journal of FinancialEconomics, 1998, 49, 345–73.

Chabi-Yo, F. Pricing Kernels with Stochastic Skewness and Volatility Risk. ManagementScience, 2012, 58:3, 624–40.

Chaudhry, M.K., S. Maheshwari, and J.R. Webb. REITs and Idiosyncratic Risk. Journal ofReal Estate Research, 2004, 26:2, 207–22.

Chan, S.H., J. Erickson, and K. Wang. Real Estate Investment Trusts: Structure,Performance, and Investment Opportunities. New York: Oxford University Press, 2003.


J R E R � V o l . 3 5 � N o . 2 – 2 0 1 3

Chang, B.Y., P. Christoffersen, and K. Jacobs. Market Skewness Risk and the Cross-Sectionof Stock Returns. Journal of Financial Economics, 2013, 107:1, 46–68.

Chiang, K.C.H., X. Jiang, and M.L. Lee. REIT Idiosyncratic Risk. Journal of PropertyResearch, 2009, 26:4, 349–66.

Chiang, K.C.H., M.L. Lee, and C.H. Wisen. On the Time-Series Properties of Real EstateInvestment Trust Betas. Real Estate Economics, 2005, 33:2, 381–96.

Corrado, C.J. and T. Su. Skewness and Kurtosis in S&P 500 Index Returns Implied byOption Prices. Journal of Financial Research, 1996, 19:2, 175–92.

Corrado, C.J. and T. Su. Implied Volatility Skews and Stock Index Skewness and KurtosisImplied by S&P 500 Index Option Prices. Journal of Derivatives, 1997, 4:4, 8–19.

Cumby, R., S. Figlewski, and J. Hasbrouk. Forecasting Volatilities and Correlations withEGARCH Models. Journal of Derivatives, 1993, 1:2, 51–63.

Da, Z. and E. Schaumburg. The Pricing of Volatility Risk across Asset Classes. FederalReserve Bank of New York Working Paper, 2011.

DeLisle, R.J., J.S. Doran, and D.R. Peterson. The Pricing of Risk-Neutral SystematicMoments in the Cross-Section of Expected Returns. Washington State University WorkingPaper, 2011.

Fama, E.F. and K.R. French. The Cross-section of Expected Stock Returns. Journal ofFinance, 1992, 47:2, 427–65.

——. Common Risk Factors in the Returns on Stocks and Bonds. Journal of FinancialEconomics, 1993, 33:1, 3–56.

Fama, E.F. and J.D. MacBeth. Risk, Return, and Equilibrium: Empirical Tests. Journal ofPolitical Economy, 1973, 81:3, 607–36.

Fei, P., L. Ding, and Y. Deng. Correlation and Volatility Dynamics in REIT Returns:Performance and Portfolio Considerations. Journal of Portfolio Management, 2010, 36:2,113–25.

Feng, Z., S.M. Price, and C.F. Sirmans. An Overview of Equity Real Estate InvestmentTrusts (REITs): 1993–2009. Journal of Real Estate Literature, 2011, 19:2, 307–43.

Fink, J.D., K.E. Fink, and H. He. Expected Idiosyncratic Volatility Measures and ExpectedReturn. Financial Management, 2012, 41:3, 719–67.

Fu, F. Idiosyncratic Risk and the Cross-section of Expected Stock Returns. Journal ofFinancial Economics, 2009, 91:1, 24–37.

Ghosh, C., M. Miles, and C.F. Sirmans. Are REITs Stocks? Real Estate Finance, 1996,13, 46–53.

Gisiger, N. Risk-Neutral Probabilities Explained. ETH Zurich Working Paper, 2010.

Glascock, J.L., C. Lu, and R.W. So. Further Evidence on the Integration of REIT, Bond,and Stock Returns. Journal of Real Estate Finance and Economics, 2000, 20:2, 177–94.

Guo, H., H. Kassa, and M.F. Ferguson. On the Relation between EGARCH IdiosyncraticVolatility and Expected Stock Returns. Journal of Financial and Quantitative Analysis,2013, Forthcoming.

Jegadeesh, N. and S. Titman, Returns to Buying Winners and Selling Losers: Implicationsfor Stock Market Efficiency. Journal of Finance, 1993, 48, 65–91.

Kraus, A. and R. Litzenberger. Skewness Preference and the Valuation of Risk Assets.Journal of Finance, 1976, 31:4, 1085–1100.


Lee, C.M.C. and B. Swaminathan. Price Momentum and Trading Volume. Journal ofFinance, 2000, 55, 2017–70.

Ling, D.C. and A. Naranjo. The Integration of Commercial Real Estate Markets and StockMarkets. Real Estate Economics, 1999, 27:3, 483–515.

Liow, K.H. and K. Addae-Dapaah. Idiosyncratic Risk, Market Risk and CorrelationDynamics in the U.S. Real Estate Investment Trusts. Journal of Housing Economics, 2010,19, 205–18.

Malkiel, B.G. and Y. Xu. Idiosyncratic Risk and Security Returns. University of Texas atDallas Working Paper, 2002.

Merton, R.C. Option Pricing When Underlying Stock Returns are Discontinuous. Journalof Financial Economics, 1976, 3:1&2, 125–44.

——. Presidential Address: A Simple Model of Capital Market Equilibrium withIncomplete Information. Journal of Finance, 1987, 42:3, 483–510.

Newey, W.K. and K.D. West. A Simple Positive-definite Heteroskedasticity andAutocorrelation Consistent Covariance Matrix. Econometrica, 1987, 55:3, 703–08.

Ooi, J.T.L., J. Wang, and J.R. Webb. Idiosyncratic Risk and REIT Returns. Journal of RealEstate Finance and Economics, 2009, 38:4, 420–42.

Sias, R., L. Starks, and S. Titman, Changes in Institutional Ownership and Stock Returns:Assessment and Methodology. Journal of Business, 2006, 79:6, 2869–2910.

Stattman, D. Book Values and Stock Returns. The Chicago MBA: A Journal of SelectedPapers, 1980, 4, 25–45.

Sun, Q.S. and K. Yung. Idiosyncratic Risk and Expected Returns of Equity Real EstateInvestment Trusts. Journal of Real Estate Portfolio Management, 2010, 15:1, 45–57.

Wang, K., J. Erickson, and S.H. Chan. Does the REIT Stock Market Resemble the GeneralStock Market? Journal of Real Estate Research, 1995, 10, 445–60.

Whaley, R.E. The Investor Fear Gauge. Journal of Portfolio Management, 2000, 26:3,12–17.

The authors acknowledge the helpful comments and suggestions of Ko Wang (theeditor), three anonymous referees, Chia Chien, Haim Kassa, and seminar participantsat University of Georgia, Pennsylvania State University, 2011 AsRES & AREUEAJoint International Conference, and the 2012 ARES Conference. We thank ErnstSchaumburg for providing the F1 market volatility factor time-series data.

R. Jared DeLisle, Washington State University, Vancouver, WA 98686 or [email protected].

S. McKay Price, Lehigh University, Bethlehem, PA 18015 or [email protected].

C.F. Sirmans, Florida State University, Tallahassee, FL 32306-1110 or [email protected].

pricing of volatility risk in reitsidiosyncratic volatility sorted long-short portfolios of...

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