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Journal of Financial Markets

Journal of Financial Markets 21 (2014) 25–49

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journal homepage: www.elsevier.com/locate/finmar

Macroeconomic uncertainty and the cross-sectionof option returns$

Sirio Aramonte n

Office of Financial Stability Policy and Research, Board of Governors of the Federal Reserve System,Mail Stop 155-C, 20th and C Streets NW, Washington, DC 20551, United States

a r t i c l e i n f o

Article history:Received 31 May 2013Received in revised form19 June 2014Accepted 23 June 2014Available online 2 July 2014

JEL classification:G12G13G14

Keywords:Option pricingMacroeconomic uncertaintyScheduled announcements

x.doi.org/10.1016/j.finmar.2014.06.00181/Published by Elsevier B.V.

uld like to thank Elroy Dimson, Joost Drier, Raman Uppal, and an anonymous refeted as reflecting the views of the Board ofþ1 202 912 4301.ail address: sirio.aramonte@frb.gov

a b s t r a c t

I empirically investigate whether macroeconomic uncertainty is apriced risk factor in the cross-section of equity and index optionreturns. The analysis employs a non-linear factor model, estimatedwith the Fama-MacBeth methodology, where the macroeconomicuncertainty factor is the return on a long/short portfolio of equityoptions, built on the basis of how implied volatilities changearound macroeconomic announcements. I find that macroeco-nomic uncertainty is priced in the cross-section of option returns,even after controlling for a number of relevant factors. The resultsare robust to alternative ways of measuring option returns, and tothe non-random pattern of missing returns.

Published by Elsevier B.V.

1. Introduction

In this paper, I study whether time-varying uncertainty about the current value of macroeconomicvariables is a priced risk factor in the cross-section of equity and index option returns. Building on theresults of Beber and Brandt (2009), I rely on the behavior of equity option implied volatilities aroundselected scheduled macroeconomic announcements to form a long/short factor mimicking portfolio

ssen, Vito Gala, Francisco Gomes, Oguzhan Karakas, Antonio Mele, Stephenree. This article represents the views of the author, and should not beGovernors of the Federal Reserve System or other members of its staff.

S. Aramonte / Journal of Financial Markets 21 (2014) 25–4926

that proxies for unobservable macroeconomic uncertainty. The factor peaks during periods ofeconomic turmoil, it has a large negative average return, and it explains the cross-section of optionreturns over the 1996–2010 sample. The results, which are based on the Fama and MacBeth (1973)methodology, account for the non-linearity of option returns relative to returns on the underlying,and are robust to a large set of additional relevant factors, to the non-random pattern of missingoption returns, and to alternative ways of measuring returns and building the macroeconomicuncertainty factor.

Researchers typically study the drivers of option returns by comparing the properties of option-implied and objective return distributions (e.g., Bakshi, Cao, and Chen, 1997; Bates, 2003; Broadie,Chernov, and Johannes, 2007). Reduced-form option pricing models consist of assumptions about thedistribution of the underlying asset's returns, the specification of the sources of uncertainty that carrya risk premium, and the estimation of objective/risk-neutral distributions of returns that havedifferent parameter values for the priced sources of uncertainty. Risk premia effectively act as degreesof freedom that reconcile the discrepancies between the objective and risk-neutral distributions,which means that misspecification can appear as a risk premium, and that specification tests are ofprimary importance (Broadie, Chernov, and Johannes, 2007).

A reduced-form approach to option pricing also poses questions in terms of economicinterpretation, because, first, the preferences of investors are implied by the pricing kernel thatreconciles the objective and risk-neutral distributions, and, second, the economic mechanisms thatdrive the sources of uncertainty are not fully specified. In his 2003 retrospective study of empiricaloption pricing, Bates (2003, p. 399) explicitly emphasized the desirability of a sharper focus on theeconomic fundamentals behind the differences between objective and risk-neutral distributions: “Toblithely attribute divergences between objective and risk-neutral probability measures to the free ‘riskpremium’ parameters within an affine model is to abdicate one's responsibilities as a financialeconomist.”

The literature has indeed grown along the lines suggested by Bates (2003). It now includes anumber of contributions that link stylized option pricing facts to fundamental economic mechanisms.For instance, the implied volatility skew has been explained in terms of demand pressure and theunhedgeable risks borne by market makers (Bollen and Whaley, 2004; Gârleanu, Pedersen, andPoteshman, 2009); in terms of heterogeneous beliefs (Buraschi and Jiltsov, 2006); in terms of learningabout the process that drives returns (Benzoni, Collin-Dufresne, and Goldstein, 2011); and in terms ofKnightian model uncertainty (Drechsler, 2013).

This paper focuses on the implications that the uncertainty surrounding macroeconomicannouncements has for the cross-section of returns on equity and index options. The macroeconomicuncertainty factor is the return on a long/short portfolio of equity options, which are bought and soldaccording to the ranking, during the preceding quarter, of their implied volatility changes aroundmacroeconomic announcements. The sorting builds upon studies showing that the implied volatilitiesof bond options react strongly to macroeconomic announcements (Ederington and Lee, 1996; Beberand Brandt, 2006), and that the reduction in bond implied volatilities after a scheduledannouncement is proportional to the level of macroeconomic uncertainty, as measured by theimplied volatilities of “Economic Derivatives,” a type of options on macroeconomic variables that weremarketed between 2002 and 2007 (Beber and Brandt, 2009). By narrowing the focus on events thatare associated with larger changes in uncertainty, the ranking based on changes in implied volatilityprovides a cleaner proxy for the sensitivity of each option to the unobserved macroeconomicuncertainty factor. Savor and Wilson (2014), for instance, find that market betas, as estimated onannouncement days, have a stronger relation with asset returns than market betas estimated on dayswithout announcements.

The literature provides ample evidence that the price impact of scheduled releases is not limited tobond options, but can be found in stocks (Jain, 1988; McQueen and Roley, 1993; Flannery andProtopapadakis, 2002; Lee, 2012), bonds (Ederington and Lee, 1993, 1995; Fleming and Remolona,1999; Balduzzi, Elton, and Green, 2001; De Goeij and Marquering, 2006), exchange rates (Andersenand Bollerslev, 1998; Andersen, Bollerslev, Diebold, and Vega, 2003, 2007; Faust, Rogers, Wang, andWright, 2007), and co-movements across asset classes (Brenner, Pasquariello, and Subrahmanyam,2009).

S. Aramonte / Journal of Financial Markets 21 (2014) 25–49 27

Consistent with the hypothesis that uncertainty about the state of the economy is higher justbefore scheduled announcements, and that investors are compensated for holding securities sensitiveto such uncertainty, Jones, Lamont, and Lumsdaine (1998) find that most of the excess returns onTreasury bonds are earned on days with employment or Producer Price Index announcements.Similarly, Savor and Wilson (2013) show that equities and long-term Treasury bonds earn higherreturns on announcement days, while, consistent with an increased demand for precautionarysavings, short maturity T-Bills have lower returns. Beber and Brandt (2006) also find that riskaversion, obtained from the comparison of objective and risk-neutral distributions of bond returns,decreases after positive macroeconomic announcements.

Researchers that study the asset pricing implications of uncertainty and investor disagreement often relyon survey data in their empirical implementations. For instance, Anderson, Ghysels, and Juergens (2009)derive market uncertainty from variables in the Survey of Professional Forecasters, and find that it is pricedin the cross-section of stock returns. Yu (2011) uses earnings forecasts to build a bottom-up measure ofdisagreement, and shows that disagreement correlates with changes in the discount rate, and the valuepremium is higher for stocks with high disagreement. Buraschi and Whelan (2012) find that the commoncomponent in the disagreement about the forecasts of several macroeconomic variables explains futurebond returns, while Buraschi, Trojani, and Vedolin (2014a,b) show that the common component indisagreement about future firm-level earnings helps explain credit spreads, the correlation risk premiumimplied in index option prices, and the cross-section of returns on selected option strategies. In this paper, Irely on options rather than on survey data because options are likely to be especially informative aboutmacroeconomic uncertainty. The reason is that informed traders are active in the option market (Easley,O'Hara, and Srinivas,1998; Pan and Poteshman, 2006; Ni, Pan, and Poteshman, 2008; Xing, Zhang, and Zhao,2010; An, Ang, Bali, and Cakici, 2014), and that options are well suited for trading on the non-linearities thatsome macroeconomic releases induce in stock returns (Lee, 2012).

I interpret the implied volatility of options aroundmacroeconomic announcements as a manifestation ofuncertainty about economic fundamentals. It is important to note, however, that the primitive driver ofimplied volatility, and of the results presented in the paper, could be risk rather than uncertainty. Risk isdefined as the dispersion of fundamentals in a model with an unequivocal probabilistic representation,while uncertainty better characterizes an imperfect knowledge of the probability distribution offundamentals [as discussed, for instance, in Kogan and Wang, 2003]. While I stop short of attributing myresults to uncertainty rather than risk, the literature has shown how they both have asset pricingimplications through separate channels.1 A variance premium,2 for instance, can be generated by sources ofrisk like time-varying jumps in the first and secondmoments of consumption growth (Drechsler and Yaron,2011), stochastic volatility-of-volatility in consumption growth (Bollerslev, Tauchen, and Zhou, 2009; Zhou,2011), or rare disasters with time-varying severity that greatly reduce consumption (Gabaix, 2012).3 On theother hand, ambiguity aversion (Miao, Wei, and Zhou, 2012) and time-varying Knightian uncertainty aboutthe true dynamics of economic fundamentals (Drechsler, 2013) can increase the variance premium abovethe level attributable to sources of risk. Similarly, the slope of the volatility smile, which reflects the highprices of out-of-the-money index put options, can be interpreted as compensation for jump risk, as theproduct of aversion to ambiguity about rare events (Liu, Pan, and Wang, 2005), or as the result of Knightianuncertainty (Drechsler, 2013).

1 See, among others, Kogan and Wang (2003), Anderson, Ghysels, and Juergens (2009), Drechsler (2013), and referencestherein.

2 The variance premium is the difference between an index option implied variance and statistical estimates of expectedvariance. Bollerslev, Gibson, and Zhou (2011) relate the variance risk premium to several macroeconomic variables, includingsome of those used in this paper, like housing starts, the producer price index, and nonfarm employment. In related work,Bakshi, Panayotov, and Skoulakis (2011) find that option-implied forward variances can predict stock and bond returns, as wellas measures of growth in real economic activity. The variance risk premium can also be interpreted as a manifestation ofcorrelation risk, as in Driessen, Maenhout, and Vilkov (2009). While the variance premium is typically calculated from indexoptions, Bali and Hovakimian (2009), for instance, find that the realized-implied volatility spread, measured at the individualstock level, can also predict stock returns.

3 Stochastic volatility-of-volatility and time variation in the intensity of relatively frequent jumps can be the manifestationof the dynamics of economic primitives like the technological process, as in Bloom, Floetotto, Jaimovich, Saporta-Eksten, andTerry (2012). In Gabaix (2012), rare disasters have the scale and frequency of wars and economic depressions.

S. Aramonte / Journal of Financial Markets 21 (2014) 25–4928

2. Data and empirical implementation

The daily data on options, interest rates, and closing stock prices are provided by OptionMetrics,which covers U.S. exchange traded index and equity options, and it includes January 1996 to October2010. The Fama and French (1993), momentum, and Pastor and Stambaugh (2003) liquidity factors,together with stock returns, are from the Center for Research in Security Prices (CRSP) throughWharton Research Data Services (WRDS). Data on the S&P 500 implied volatility index (VIX)maintained by the Chicago Board Options Exchange (CBOE), is also from WRDS. The release dates aregenerally from the Archival Federal Reserve Economic Data (ALFRED) website of the Federal ReserveBank of St. Louis; where needed, I integrate the ALFRED data with information from the actual releasesavailable on the Census Bureau's website (for New Home Sales and Durable Good Orders), and withthe description of the release schedule available on the website of the Institute for SupplyManagement (ISM) for the Manufacturing ISM Report on Business.

The analysis presented below builds on scheduled announcements for seven macroeconomicvariables,4 which I select on the basis of the price impact that announcement surprises have on U.S.30-year bonds, as reported by Balduzzi, Elton, and Green (2001). Specifically, the standardizedannouncement surprises associated with the seven variables have the largest statistically significanteffect on bond price changes from 5 minutes before to 30 minutes after the announcement.5

As is customary with option prices (e.g., Goyal and Saretto, 2009), I apply a series of filters toeliminate illiquid prices and recording errors. I exclude options with the following characteristics:zero trading volume, non-standard settlement, the option's bid price is greater than the ask price, theoption's bid or ask price is equal to zero or negative, the underlying security is not a common stock,and the underlying security pays more than 200 dividends in the sample period. While equity optionshave American exercise, I discard those with a missing exercise style flag because additional datafields may be incorrectly recorded. The remaining sample contains approximately 87 millionobservations, or about 15% of the size of the initial database; most of the reduction is due to requiringnon-zero trading volume. I further restrict the focus to options with a maturity between 15 and 365days, with a moneyness between �1 and 1,6 and whose bid, ask, and bid–ask spread are above theminimum tick size (0.05 for options with a price below 3, and 0.1 otherwise).

In the empirical analysis I study how macroeconomic uncertainty, together with a set of assetpricing and option pricing factors, affects the cross-section of equity and index option returns. I do sowith the Fama and MacBeth (1973) methodology, which estimates factor risk premia in two stages.The first stage obtains the sensitivity of the test assets' returns to a set of factors, using time-seriesregressions:

rkt �rft ¼ αkþ ∑n

i ¼ 1βi;kf i;tþεk;t ; 8k; ð1Þ

where rtk is the weekly return on asset k, rft the riskless rate, and f i;t is one of the n factors. The test

assets are portfolios of index and equity options (see Section 4), whose returns are arithmetic returns

4 The seven variables are: Nonfarm Payroll, Durable Goods Orders, New Home Sales, Producer Price Index, Consumer PriceIndex, ISM Manufacturing PMI Index (formerly, NAPM Index), Housing Starts.

5 The coefficients are reported in the second to last column of Table 2, p. 530, in Balduzzi, Elton, and Green (2001). At thetime their article was published, the Institute for Supply Management was known as the National Association of PurchasingManagers (NAPM).

6 Moneyness is defined as: m¼ðlnðS=KÞþðrþ0:5σ2Þ � tÞ=ðσ � ffiffit

p Þ, where S is the stock price, K the strike price, r theannualized riskless rate, σ the annualized one-year trailing stock volatility, and t is the time to maturity as a fraction of a year.Options are assigned to a moneyness category (1¼out-of-the-money, 5¼ in-the-money) according to the following schedule:

Moneynesst ¼

Put Call5 1 �1:00rmo�0:604 2 �0:60rmo�0:253 3 �0:25rmo0:252 4 0:25rmo0:601 5 0:60rmo1:00

8>>>>>>>><>>>>>>>>:

S. Aramonte / Journal of Financial Markets 21 (2014) 25–49 29

based on the midpoint of the bid–ask spread, and, unless specified otherwise, are calculated onWednesdays. Returns on individual options (rather than portfolios) are winsorized at 0.5% and 99.5%. Ialso require that test assets have at least 400 non-missing returns, and that, in a given week, there areat least 35 test assets with non-missing returns.

The second stage uses cross-sectional regressions to determine the extent to which differences inthe estimated factor sensitivities explain excess returns:

rkt �rft ¼ λ0;tþ ∑n

i ¼ 1λi;t β̂ i;kþϵk; 8t: ð2Þ

The risk premium on factor f is estimated as the time-series average of the coefficients from the Tcross-sectional regressions:

λ̂f ¼1T

∑T

t ¼ 1λ̂f ;t : ð3Þ

Broadie, Chernov, and Johannes (2009) discuss the limitations of linear factor models applied toindex option returns, including how the potentially extreme statistical nature of out-of-the-moneyindex option returns, driven by the non-linearity of option payoffs, makes standard inference aboutaverage returns problematic. The use of CAPM alphas or Sharpe ratios is also difficult to justify in lightof the return distribution of out-of-the-money index options. They suggest that market-neutralpositions, like straddles, are more informative about the asset pricing properties of index options.

Besides conducting robustness checks that evaluate how the results are affected by large returns,I account for the concerns raised by Broadie, Chernov, and Johannes (2009) by designing the analysisin a way that mitigates the inference issues highlighted in their study. The factor model on whichI base my conclusions is non-linear [see Jones, 2006 for an application of non-linear factor models toS&P 500 index option returns], and it accounts for convexity and for jump risk – two of the factors aresquared market returns and out-of-the-money index option returns. In addition, I use weekly holdingreturns, halving return volatility and making large returns less likely, although parts of the robustnesschecks in Section 5 are based on monthly hold-to-maturity returns.7 The sample includes the 2008financial crisis, but the results hold in sub-periods that exclude 2008 to 2010. Finally, my analysis islargely based on equity options, rather than index options. In this case, the non-linear relation betweenmarket returns and option returns is less stark. The reason is that the sensitivity of equity optionreturns to the market depends on the elasticity of option returns to returns on the underlying stock, aswell as on the sensitivity of stock returns to market returns.

3. The macroeconomic uncertainty factor

The macroeconomic uncertainty factor (MU) is the weekly return on a long/short option strategybased on the pattern of implied volatility changes around scheduled announcements, and it is built inthree steps. First, I calculate an option's relative change in implied volatility from day t�1 to day t(ΔIV), where t is the day of a scheduled release. Fig. 1 shows that scheduled releases take place mostfrequently on Thursdays and Fridays, with Tuesdays and Wednesdays following closely. Second, I formoption portfolios on the basis of several characteristics, like moneyness and put/call type, andcalculate the portfolios' median implied volatility change during every quarter. Third, I sort the option

7 Broadie, Chernov, and Johannes (2009) note that calculating weekly returns for options with different maturities createsan “apples and oranges” problem. For example, a one-week return on a five-week option is theoretically different from a one-week return on a one-week option. In order to preserve the density of observations in each portfolio, maturity is not acharacteristic I use to form portfolios in the main analysis, although the results in Section 5.2 indicate that maturity does notplay a crucial role. Broadie, Chernov, and Johannes (2009) also note that trading can become thin, and bid–ask spreads large, atcertain moneyness/maturity combinations, with the consequence that the analysis can be affected by less liquid prices. One ofthe robustness checks in Section 5 entails discarding equity options with high bid–ask spreads. Finally, using market-neutralstraddles would significantly reduce the sample, because I would need put/call pairs with similar characteristics on twoconsecutive weeks; delta-hedging establishes market-neutral positions without reducing the sample, but hedge ratios aremodel dependent.

0

50

100

150

200

250

Num

ber o

f sch

edul

ed a

nnou

ncem

ents

1) Mon 2) Tue 3) Wed 4) Thu 5) Fri

Fig. 1. The histogram shows the number of scheduled macroeconomic announcements, by weekday, from January 1996 toOctober 2010.

S. Aramonte / Journal of Financial Markets 21 (2014) 25–4930

portfolios on the basis of the distribution of the median ΔIV during the previous quarter, so that the20% with the largest drop is the long leg of MU, and the 20% with the smallest drop (possibly anincrease) is the short leg; the quintiles are recalculated every quarter.

The MU factor is based on a sorting of option portfolios, rather than individual options, because the pricetime series of individual options typically have gaps, a fact that constrains the ability to reliably measurefactor sensitivities. The option portfolios used in building MU are the intersection of four characteristicswhich, ex ante, can be expected to create dispersion in how options react to macroeconomic uncertainty:(1) five moneyness categories, (2) put/call type, and tertiles of lagged sensitivity of the underlying stock tothe (3) size and (4) book-to-market factors of Fama and French (1993) (denoted by, respectively, SMB andHML). The rationale behind using the sensitivities to SMB and HML is that the value effect is related to thereal option nature of growth stocks (Barinov, 2013), and that the size and value effects have been linked tothe sensitivity of stocks to news about macroeconomic variables (Vassalou, 2003) and to innovations inproxies for investment opportunities (Petkova, 2006). These findings imply that the sensitivities to SMB andHMLmay be a source of dispersion to macroeconomic uncertainty. I sort options along the sensitivity of theunderlying to SMB and HML, rather than along the underlying's size and book-to-market, because thecompanies covered by OptionMetrics are not a representative sample of CRSP, especially in terms of firmsize. The sensitivities are computed by regressing daily stock excess returns on the Fama and French (1993)factors every year from 1995 to 2009. Stocks are then sorted into three tertiles based on their SMB betas, andinto three tertiles based on their HML betas. The year t sorting applies to year tþ1, and it is based on the setof stocks with listed options.

Finally, I should emphasize that the MU factor is built from individual equity options, rather thanindex options. The reason is that the prices of index options, but not those of individual options, arestrongly affected by jump risk [see Bakshi, Kapadia, and Madan (2003) for a comparison of index andindividual volatility smiles]. By focusing on individual options, I can better identify the distinctcontributions of jump risk and macroeconomic uncertainty to option returns.

3.1. Empirical properties

In this section I discuss the time-series properties of the MU factor, the characteristics of its longand short legs, and how it relates to the measure of economic activity of Aruoba, Diebold, and Scotti(2009). TheMU factor is long assets that have a higher price during periods of heightened uncertainty,and, to the extent that macroeconomic uncertainty negatively affects the utility of investors, itsexpected return should be negative. Indeed, as reported in Table 1, the average return on MU issubstantially negative at �20.27% per week, with a median of �18.62%. While such returns are large,

Table 1Factor summary statistics.

μ tB t tNW p50

MKT 0.0006 0.65 0.65 0.66 0.0025SMB 0.0005 0.92 0.93 0.80 0.0005HML 0.0006 1.02 0.98 0.89 0.0010UMD 0.0011 1.12 1.10 0.97 0.0025Liq �0.0002 �0.42 �0.41 �0.28 �0.0001

GV 0.0550 15.63nnn 15.99nnn 12.48nnn 0.0423Vix �0.0001 �0.07 �0.07 �0.08 �0.0010Vixv �0.0000 �0.12 �0.12 �0.21 �0.0003Vixs �0.0065 �0.20 �0.20 �0.45 �0.0079Put �0.0908 �4.71nnn �4.67nnn �4.47nnn �0.2304Putv 0.0001 0.01 0.01 0.02 �0.0058

MU �0.2027 �22.61nnn �23.43nnn �15.90nnn �0.1862

MUB �0.4391 �46.98nnn �48.24nnn �31.46nnn �0.4092

MUBM �0.3090 �42.17nnn �44.23nnn �28.27nnn �0.3019

MU? �0.1636 �15.01nnn �15.98nnn �11.96nnn 0.0086

MUB? �0.3962 �33.89nnn �35.90nnn �25.76nnn 0.0207

MUBM? �0.2733 �29.34nnn �32.49nnn �22.53nnn 0.0006

μ is the factor mean, tB, t, and tNW are t-statistics from testing the null that the mean is zero (based, respectively, on 1,000bootstrap replications with replacement, asymptotic standard errors, and 4-lag Newey-West standard errors). p50 is themedian. MKT, SMB, HML, and UMD are the Fama-French and momentum factors. The liquidity factor Liq is the weekly return ona portfolio which mimics the Pastor and Stambaugh (2003) traded liquidity factor. The long/short legs of the Liq factor includeCRSP stocks (with share code 10 and 11, and exchange code 1 to 3) in the top/bottom liquidity beta quintiles. Liquidity betas arecalculated with regressions of monthly excess stock returns on the Fama-French, momentum and Pastor-Stambaugh liquidityfactors, from 1996 to 2010. GV is the average excess return on the five equity option portfolios with the highest average gammaand the five equity option portfolios with the highest average vega in week t�1. Vix, Vixv, Vixs are weekly changes in VIX, andchanges in the weekly volatility and skewness of daily VIX changes. Put and Putv are average weekly returns on out-of-the-money S&P 500 put options and changes in the weekly volatility of daily returns on out-of-the-money S&P 500 put options.MUis the macroeconomic uncertainty factor calculated using the bid–ask midpoint. MUB is the macroeconomic uncertainty factorcalculated using bid and ask prices. MUBM is the macroeconomic uncertainty factor calculated using bid and ask prices, andbased on positions funded according to margin requirements. MU? , MUB

? , and MUBM? are the residuals from regressions of MU,

MUB, and MUBM on the following factors: MKT, SMB, HML, UMD, Liq (and corresponding squared factors), GV, Vix, Vixv, Vixs, Put,and Putv. For the orthogonalized macroeconomic uncertainty factors, the mean and t-stat columns report the intercepts of theregressions and the corresponding bootstrapped, robust, and 4-lag Newey-West t-statistics, because the means are zero byconstruction. The sample period is January 1996 to October 2010. n, nn, and nnn denote statistical significance at the 10%, 5%, and1% levels, respectively.

S. Aramonte / Journal of Financial Markets 21 (2014) 25–49 31

they are comparable to returns on other types of options, in particular index puts [see, for instance,Table 1 in Bondarenko, 2003]. Goyal and Saretto (2009) also find that a strategy that buys (sells)straddles on stocks for which implied volatility is high (low) in relation to historical volatility earnsabout �23% per month.

The intercept from a regression of MU on a large set of relevant asset pricing and option pricingfactors (see Section 4 for details) is �16.36%; the residuals of such regression define theorthogonalized MU factor (MU? ). Fig. 2 shows that MU? stays below its sample average for mostof the late 1990s, and it clearly shows level shifts and volatility clusters during the recent financialcrisis and in its aftermath. The vertical lines indicate the bankruptcy of Lehman Brothers Holdings Inc.,and three policy actions around the financial crisis [from the list in Carlson, Lewis, and Nelson, 2014].The MU? factor increases noticeably in late 2007/early 2008 to one of the then-highest levels, and itdrops rapidly after the purchase of The Bear Stearns Companies Inc. by JPMorgan Chase & Co. withpublic assistance (March 16, 2008, shown by the first vertical line). The collapse of Lehman BrothersHoldings Inc. (they filed for Chapter 11 bankruptcy protection on September 15, 2008, second verticalline) ushers in a period of higher volatility until March 2009 (the third vertical line corresponds to theannouncement of the Public–Private Investment Program for Legacy Assets on March 23, 2009). Aftera relatively short period of lower volatility, both the factor's volatility and its level pick up again in late

−0.5

0

1

Orth

ogon

aliz

ed M

U fa

ctor

19971998

19992000

20012002

20032004

20052006

20072008

20092010

Date

0.5

Fig. 2. The solid line is the MU factor, orthogonalized with respect to the following factors: MKT, SMB, HML, UMD, Liq (andcorresponding squared factors), GV, Vix, Vixv, Vixs, Put, and Putv. See Table 1 for factor definitions. The four vertical lines indicate:(a) the purchase of The Bear Stearns Companies Inc. by JPMorgan Chase & Co., as facilitated by the Federal Reserve (March 16,2008), (b) the day Lehman Brothers Holdings Inc. filed for bankruptcy (September 15, 2008), (c) the day the Public–PrivateInvestment Program for Legacy Assets was announced (March 23, 2009), and (d) the day the Federal Reserve re-establisheddollar swap lines with certain foreign central banks (May 11, 2010). The sample period is January 1996 to October 2010.

−5

0

5

Orth

. MU

fact

or (s

td.)

and

AD

S In

dex

(std

.)

19971998

19992000

20012002

20032004

20052006

20072008

20092010

Date

Orthogonalized MU factor (std.) ADS Index (std.)

Fig. 3. The solid line is the MU factor, orthogonalized with respect to the following factors: MKT, SMB, HML, UMD, Liq (andcorresponding squared factors), GV, Vix, Vixv, Vixs, Put, and Putv. See Table 1 for factor definitions. The dashed line is the Aruoba,Diebold, and Scotti (2009) Business Conditions Index. Both the factor and the index are standardized, to facilitate the visualcomparison. The sample period is January 1996 to October 2010.

S. Aramonte / Journal of Financial Markets 21 (2014) 25–4932

2009. There is a clear drop after May 2010, which corresponds to the re-establishment of dollar swaplines among central banks (May 11, 2010).

In Figs. 3 and 4, I show the relation between the MU? factor and the Aruoba-Diebold-ScottiBusiness Conditions Index [ADS Index, see Aruoba, Diebold, and Scotti, 2009]. In the time series(Fig. 3), the MU? factor is consistently lower than average when, in the early part of the sample anduntil 2000, business conditions are consistently better than average. MU? is quite volatile in thedepths of the 2007–2009 recession, but it still experiences high levels and volatility when businessconditions begin to improve in late 2009. Fig. 4 shows a scatter plot of MU? and of the ADS Index.

−0.5

0

0.5

1

Orth

ogon

aliz

ed M

U fa

ctor

−4 −2 0 2ADS Index

Fig. 4. The y-axis shows the MU factor, orthogonalized with respect to the following factors: MKT, SMB, HML, UMD, Liq (andcorresponding squared factors), GV, Vix, Vixv, Vixs, Put, and Putv. See Table 1 for factor definitions. The x-axis shows the Aruoba,Diebold, and Scotti (2009) Business Conditions Index. The solid and dashed lines are linear and quadratic fitted values. Thesample period is January 1996 to October 2010.

Table 2Composition of the high/low macroeconomic uncertainty quintiles.

First quintile Fifth quintile

Call/Put Mon. βSMB βHML # #/59 (%) Call/Put Mon. βSMB βHML # #/59 (%)

C 1 1 3 46 78 C 5 2 3 29 49C 1 2 1 40 68 C 5 3 3 28 47C 1 2 2 39 66 C 5 3 1 28 47C 1 2 3 38 64 C 5 2 2 28 47C 1 3 3 37 63 C 5 2 1 28 47C 1 1 2 37 63 C 5 1 3 27 46C 1 1 1 37 63 P 5 3 2 27 46C 1 3 1 36 61 P 5 2 2 26 44C 1 3 2 35 59 C 5 3 2 26 44P 5 1 1 28 47 P 5 3 3 25 42P 5 2 3 27 46 P 4 3 2 24 41P 5 1 3 26 44 P 5 3 1 24 41P 5 2 1 26 44 C 5 1 2 23 39P 5 2 2 25 42 C 4 3 3 22 37P 5 3 1 25 42 C 5 1 1 21 36

The table shows the 15 portfolios that are more often included in the high and low macroeconomic uncertainty quintiles.Option portfolios are defined by the exercise style and moneyness of the options, and by the sensitivity of the underlying stocksto SMB and HML. The column # shows the number of times a portfolio is assigned to the indicated quintile. Every quarter,option portfolios are assigned to each of the macroeconomic uncertainty quintiles on the basis of implied volatility changesaround scheduled macroeconomic announcements during the previous quarter. As a result, a given portfolio can be assigned tothe high/low macroeconomic uncertainty quintile between 0 and 59 times. The sample period is January 1996 to October 2010.

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As indicated by the linear and quadratic fitted values, the nature of the relation appears to differ basedon the level of the ADS Index: for “normal” levels of the ADS Index, better business conditions areassociated with lower uncertainty, while, in conditions seen during the financial crisis, the scatter plotis flat.

Table 3Average returns and four-factor intercepts for the uncertainty portfolios.

Panel A: 1996–2010

IV drop after macro announcementsLarge Small Large – Small

Average return �0.0652 0.0067 0.0346 0.0422 0.1375 �0.2027�10.42nnn 1.29 7.53nnn 7.30nnn 14.95nnn �15.90nnn

Four-factor alpha �0.0671 0.0041 0.0343 0.0460 0.1392 �0.2063�11.75nnn 0.93 7.32nnn 8.10nnn 14.91nnn �16.51nnn

Panel B: 2008–2010

IV drop after macro announcementsLarge Small Large – Small

Average return �0.0468 0.0073 0.0380 0.0334 0.0684 �0.1153�3.13nnn 0.62 3.53nnn 2.32nn 3.42nnn �4.12nnn

Four-factor alpha �0.0418 0.0138 0.0378 0.0234 0.0584 �0.1002�3.17nnn 1.43 3.74 2.55nn 3.50nnn �4.42nnn

TheMU uncertainty factor is built by buying the portfolio with the largest implied volatility (IV) drop following macroeconomicannouncements (shown under the “Large” header), and by shorting the portfolio with the smallest drop. The table shows theaverage returns and the four-factor intercepts, with 4-lag Newey-West t-statistics below the averages and intercepts.The sample period is January 1996 to October 2010, unless specified otherwise. See Table 1 for details on the statisticalsignificance levels.

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With the aim of shedding light on the composition of the long and short legs of the MU factor,Table 2 shows the portfolios that are most often included in the first and fifth MU quintiles. The nineportfolios based on out-of-the-money calls are each in the first MU quintile more than half the time,with in-the-money put portfolios also contributing to the first MU quintile quite often. In-the-moneycall portfolios, and some of the in-the-money put portfolios, are the most frequent components of thefifth quintile. The sensitivities of the underlying to the SMB and HML factors do not generate a clearpattern, neither for the first nor the fifth MU quintile. The fact that out-of-the-money call options aremore sensitive to scheduled announcements is consistent with the finding in Savor and Wilson (2013)that most of the equity premium is earned around announcement days, and also with the result in Lee(2012) that macroeconomic announcements induce jumps in stock returns: out-of-the-money calloptions are well suited to both trading on jumps and to leveraging predictably positive returns.

Table 3 shows the average returns of the five portfolios sorted on implied volatility changes aroundmacroeconomic announcements. The returns decline monotonically with the sensitivity tomacroeconomic uncertainty. The returns on the top and bottom portfolios have opposite signs andare strongly statistically significant, which suggests that the MU factor is driven by both the long legand the short leg of the mimicking portfolio.8 The intercepts from regressions of portfolio returns onthe Fama-French and momentum factors are very similar to the average returns. Panel B of Table 3reports the average returns and Fama-French/momentum intercepts over the 2008–2010 period.While the patterns identified in the full sample carry over, the average return on the portfolio with

8 The difference between the average returns of the “Large” and “Small” portfolios shown in Table 3 is the average returnon the MU factor, and it matches the value reported in Table 1. The average returns on the macroeconomic uncertaintyportfolios shown in the first panel of Table 4 are slightly different from those in Table 3, for two reasons. First, Table 3 is basedon weeks for which all the risk factors described in Section 4 are available, and in a limited number of instances there aremissing factors. For instance, the implied volatility index VIX is not available on November 26, 1997. Second, when building theMU factor I drop options with available returns but for which the corresponding change in implied volatility is missing – inorder to reduce the effect of noisy prices on the factor – but I do not apply this filter when calculating the returns of the testassets, to avoid the censoring bias discussed in Duarte and Jones (2007). A comparison of Tables 3 and 4 shows that excludingreturns with missing volatility changes when forming the factor has an immaterial effect on the results.

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high sensitivity is about two-thirds the return over the full sample; the return on the low sensitivityportfolio is about half the return calculated using the full sample.

4. Additional risk factors and test assets

In order to isolate the risk premium associated with the MU factor, the estimation includes anumber of additional factors that account for sources of risk that are important for option returns, inparticular volatility and jumps (Bates, 2003; Broadie, Chernov, and Johannes, 2007).

A first set of factors affect option returns by driving returns on the underlying stocks. Weekly log-returns for the market (MKT), size (SMB), book-to-market (HML), and momentum (UMD) factors aregenerated by compounding daily returns, while I proxy for liquidity risk with a long/short portfolio(Liq) that mimics the Pastor and Stambaugh (2003) traded liquidity factor, which is available fromWRDS at a monthly frequency. The mimicking portfolio is based on CRSP common stocks that trade onAMEX, NASDAQ or NYSE, with its long (short) leg including stocks in the top (bottom) liquidity betaquintile. The quintiles are based on regressions of monthly excess stock returns on the Fama-French,momentum, and Pastor and Stambaugh (2003) traded liquidity factors from 1996 to 2010.9

A second set of factors includes proxies for higher moment risks, like volatility and jump risk. Thevolatility factor (Vix) is the series of weekly changes in the VIX, while the volatility-of-volatility (Vixv)and skewness of volatility (Vixs) are changes in the weekly volatility and skewness of daily VIXchanges. The jump factor (Put) is the average weekly return on S&P 500 put options with moneynessm between 1 and 4. The volatility of jumps (Putv) is the change in the weekly volatility of daily returnson S&P 500 put options with moneyness between 1 and 4.

The gamma-vega factor (GV), which is meant to capture the hedging risk borne by market makers,is the excess return on a portfolio consisting of the five equity option portfolios with the largestaverage gamma in week t�1, and of the five equity option portfolios with the largest average vega inweek t�1 (both sensitivities are provided by OptionMetrics). As discussed in Gârleanu, Pedersen, andPoteshman (2009), gamma and vega are proxies for hedging risk originating from, respectively,discrete trading and stochastic volatility. Gârleanu, Pedersen, and Poteshman (2009) also report thatinvestors are net short options on individual stocks, which implies that market makers pay a lowerprice when they want to buy less hard-to-hedge inventory. Other things equal, GV is negative whenthe marginal utility of investors that are long equity options is higher. The risk premium on GV shouldthen be positive, as the results in Section 5 confirm.

Table 1 shows that the equity pricing factors have statistically insignificant average returns overthe 1996–2010 sample. Put, which is the only mimicking portfolio among the proxies for highermoment risk, has a statistically significant average return of about �9% per week, and, with a medianof about �24%, it exhibits a noticeable skewness. The average return is comparable to that reported bySanta-Clara and Saretto (2009), although it is less negative than in Bondarenko (2003).10 Factorcorrelations tend to be moderate to low, with the exception of those between MKT and Vix (�79%),MKT and Put (�80%), Put and Vix (79%), and Vixv and Putv (70%). TheMU factor has a correlation of 34%with MKT, and of about �35% with both Vix and Put.

Factor risk premia are estimated on a set of test assets that includes the traded factors (MKT, SMB,HML, UMD, Liq, GV, Put, and MU), in addition to ten portfolios of index options (puts and calls sortedinto five moneyness categories), and portfolios of equity options derived from those described inSection 3. Given that the sensitivity of the portfolios of equity options to macroeconomic uncertainty

9 Stocks with a liquidity beta outside the 0.1th and 99.9th percentiles are discarded. The sample correlation between thePastor and Stambaugh (2003) traded liquidity factor and monthly values of the Liq proxy is 79.71%.

10 The compounded four-week average return on the Put factor is about �32%. Santa-Clara and Saretto (2009) report anearly �46% return from buying put options on index futures that are 5% out-of-the-money (the sample includes 1985–2001).Options with the same moneyness, but on the S&P 500 cash index studied in this paper, also have an average return of about�46% (the sample is from 1996 to 2006). The sample of Bondarenko (2003) covers 1985 to 2001, and puts on index futures thatare 6% out-of-the-money have a �95% average monthly return. Both papers focus on options that have a maturity of about onemonth. With such maturity, put options with a strike-to-underlying price ratio of 94% or 95% would normally be included in thePut factor.

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is mainly driven by put/call type and moneyness (Table 2), I combine the portfolios of equity optionsinto a smaller set of portfolios formed on the basis of sensitivity to macroeconomic uncertainty (fivequintiles), and sensitivity of the underlying to SMB and to HML (three tertiles each). The set of testassets requires traded factors to price themselves (Lewellen, Nagel, and Shanken, 2010), and it allowsfor dispersion in the sensitivities to market returns (index puts and calls), to the SMB and HML factors(portfolios of equity options based on sensitivity of the underlying to SMB and HML), to the jumpfactor (index puts with different moneyness), and to the MU factor. The test assets are not sortedacross option maturity, which could make the identification of the risk premium on diffusive volatilitymore difficult (Broadie, Chernov, and Johannes, 2007). However, an unreported analysis of first-stagebetas shows that there is dispersion in the sensitivities to Vix, especially along the moneyness ofindex calls.

Table 4 reports a number of statistics for the weekly time series of individual option returnsaveraged across the characteristics used to form the test assets based on equity options. Averagereturns are decreasing in the sensitivity to macroeconomic uncertainty, and are significant for all butone of the quintile portfolios. The t-statistics based on 1,000 bootstrap replications are quite similar tothose derived from asymptotic standard errors, while the Newey-West t-statistics indicate thepresence of autocorrelation, especially for the fifth quintile portfolio. Autoregressions confirm thatreturns on the fifth quintile portfolio are autocorrelated, although a sub-period analysis reveals thatthe autocorrelation is mostly driven by the first half of the sample, which includes the bull market ofthe late 1990s. Indeed, in Fig. 2 one can see that the MU? factor is persistently low until about 2000.

Table 4 also shows that equity option returns are monotonically decreasing in moneyness, beinglarge and positive for out-of-the-money options, and large and negative for in-the-money options;such patterns are consistent with the results in Duarte and Jones (2007). Equity call options also havea positive return of about 3.5% per week, while put options have a statistically insignificant return. Thesensitivity of the underlying stock to the SMB and HML factors does not produce variation in averagereturns.

As discussed in Section 2, Broadie, Chernov, and Johannes (2009) highlight the importantimplications that the non-linearity of option returns has for inference based on linear factor models. Ievaluate which factors should be included non-linearly in the Fama-MacBeth analysis by running aforward (backward) selection algorithm. Starting with an intercept-only model (a model with MU, allthe factors in this section, and selected squared factors), the algorithm iteratively includes (excludes)factors that are (are not) statistically significant. I consider the squared versions of the five assetpricing factors (MKT, SMB, HML, UMD, and Liq), and Vix, Put, and MU. The algorithms are run on eachoption test asset, and I collect the percentage of portfolios for which a given squared factor survivesthe selection. The results, which are available upon request, show that the squared MKT and MUfactors are included in, respectively, about 50% and 40% of the cases. The remaining candidate squaredfactors are included less often, hence the Fama-MacBeth analysis will only incorporateMKT2 andMU2.

5. Results

A first set of risk premia estimates is reported in Table 5. Both the first- and second-stageregressions are based on ordinary least squares (OLS), and factor sensitivities are estimated over thefull 1996–2010 sample. This and subsequent tables also include average second-stage adjusted R-squared coefficients, as a measure of cross-sectional goodness-of-fit; the reported t-statistics arebased on Shanken (1992)-adjusted standard errors. As discussed in Section 4, the test assets are equityoption portfolios formed according to MU quintiles and the sensitivity of the underlying to the SMBand HML factors, in addition to index option portfolios formed on the basis of moneyness and put/calltype, and in addition to the traded factors (GV, Put, MU, and the equity pricing factors).

A comparison of Table 1 with specification (1) of Table 5 indicates that the risk premia on thetraded factors are close to the corresponding factor averages: the equity pricing factors have astatistically insignificant risk premium, while GV, Put, and MU have risk premia equal to, respectively,7.04%, �9.49%, and �20.61%; the averages of the equity factors are statistically insignificant, whilethose of GV, Put, and MU are 5.50%, �9.08%, and �20.27%, respectively. As for the non-traded factors,

Table 4Return statistics for equity options, by characteristic.

Characteristic % μ tB t tNW p50 ρ1 ρ2 ρ3 ρ4 R2

Macro unc. 1 13 �0.0641 �13.51nnn �13.26nnn �8.00nnn �0.0718 0.090n 0.038 0.172n1 0.150n1 0.07r3=2001 0.108 �0.182n 0.132 0.124

43=2001 0.027 0.070 0.135n1 0.0842 24 0.0076 1.57 1.54 1.46 �0.0132 0.025 �0.044 0.100n �0.003 0.013 27 0.0354 9.40nnn 9.15nnn 6.87nnn 0.0192 0.078n 0.018 0.105n1 0.103n 0.034 24 0.0433 9.22nnn 9.07nnn 6.09nnn 0.0238 0.098 0.078 0.096n 0.041 0.035 12 0.1384 23.54nnn 23.30nnn 10.90nnn 0.1153 0.217n1 0.127n 0.210n1 0.075 0.19

r3=2001 0.142n1 0.134n 0.174n1 0.169n1

43=2001 0.130n 0.015 0.118n �0.057

Moneyness 1 13 0.2329 36.68nnn 37.63nnn 23.96nnn 0.2086 0.134n1 0.102n 0.063 0.103n1 0.052 24 0.0736 19.75nnn 19.73nnn 14.74nnn 0.0592 0.094n1 0.032 0.043 0.068 0.013 39 0.0006 0.19 0.19 0.17 �0.0096 0.030 �0.026 0.094n 0.026 0.014 16 �0.0579 �16.63nnn �16.60nnn �12.92nnn �0.0541 0.057 0.017 0.130n1 0.048 0.025 7 �0.1433 �48.03nnn �49.04nnn �29.60nnn �0.1343 0.125n1 0.059 0.163n1 0.152n1 0.09

Call/Put C 66 0.0342 4.94nnn 4.88nnn 4.96nnn 0.0294 �0.041 �0.015 0.058 �0.011 0.00P 34 0.0035 0.48 0.48 0.45 �0.0321 �0.006 0.025 0.073n 0.006 0.00

βSMB 1 53 0.0244 8.85nnn 8.90nnn 8.11nnn 0.0149 0.020 �0.048 0.032 0.049 0.002 27 0.0328 9.46nnn 9.30nnn 8.76nnn 0.0167 0.018 �0.022 0.042 0.020 0.003 20 0.0325 7.61nnn 7.32nnn 7.00nnn 0.0167 0.039 �0.013 0.086n �0.014 0.00

βHML 1 49 0.0225 6.76nnn 6.71nnn 6.23nnn 0.0094 0.055 �0.064 0.066 �0.004 0.002 26 0.0313 10.33nnn 10.06nnn 9.21nnn 0.0178 �0.034 0.002 0.058 0.073n 0.003 26 0.0359 10.33nnn 10.15nnn 9.80nnn 0.0208 0.000 �0.008 0.028 0.039 0.00

% is the percentage of individual equity options for which a characteristic takes the specified value. The rest of the table shows time-series statistics for the weekly average of returns onequity options with the indicated characteristic. μ is the mean, tB, t, and tNW are t-statistics from testing the null that the mean is zero (based, respectively, on 1,000 bootstrap replicationswith replacement, asymptotic standard errors, and 12-lag Newey-West standard errors). p50 is the median. ρ1 to ρ4 are coefficients from autoregressions of returns on four lags. R

2is the

adjusted R-squared from such autoregressions. The subscripts r3=2001 and 43=2001 indicate autoregressions run on samples including data up to March 31, 2001, and data from April 1,2001 onwards. March 2001 is the NBER peak after the bull market of the late 1990s. The sample period is January 1996 to October 2010. 1 indicates that an autocorrelation coefficient issignificant at 10% after a Bonferroni adjustment for four hypotheses (e.g., that any one of the lags is significant while the remaining three are not). See Table 1 for additional details on thestatistical significance levels.

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Table 5Risk premia.

λ̂0 MKT SMB HML UMD Liq GV MKT2 Vix Vixv Vixs Put Putv MU MU2R22

(1) 0.0060 0.0022 0.0029 �0.0046 �0.0030 0.0058 0.0704 0.0005 �0.0100 �0.0157 0.8976 -0.0949 �0.0569 �0.2061 0.0947 0.5201.32 0.86 0.62 �1.28 �0.36 0.82 3.53nnn 0.96 �1.74n �2.21nn 1.38 �3.59nnn �0.59 �6.88nnn 1.93n

(2) 0.0050 0.0018 0.0024 �0.0043 �0.0021 0.0072 0.0712 0.0006 �0.0110 �0.0150 0.9650 �0.0971 �0.0546 �0.2047 0.5121.17 0.73 0.50 �1.15 �0.27 1.06 3.61nnn 1.15 �1.94n �2.05nn 1.52 �3.66nnn �0.57 �6.78nnn

(3) �0.0249 �0.0046 �0.0108 �0.0028 �0.0151 �0.0086 0.1340 0.0013 �0.0099 �0.0124 �1.7355 �0.0633 �0.0628 0.471�3.06nnn �1.37 �1.63 �0.58 �1.42 �0.92 4.48nnn 2.05nn �1.29 �1.26 �1.70n �1.95n �0.50

(4) 0.0035 0.0001 0.0036 �0.0026 0.0700 0.0004 �0.0096 �0.0063 �0.0906 �0.2026 0.4831.10 0.08 1.13 �0.94 4.88nnn 1.15 �2.54nn �1.29 �3.96nnn �8.97nnn

(5) �0.0301 �0.0103 �0.0098 �0.0047 0.1490 0.0015 0.0016 �0.0069 �0.0370 0.435�4.54nnn �4.78nnn �1.96nn �1.20 6.17nnn 3.12nnn 0.31 �1.01 �1.37

(6) 0.0039 0.0004 0.0039 �0.0024 0.0698 �0.0101 �0.0059 �0.0909 �0.2036 0.4751.23 0.29 1.23 �0.88 5.06nnn �2.79nnn �1.19 �3.91nnn �9.02nnn

(7) 0.0222 0.0023 0.0094 �0.0022 �0.0093 �0.0086 �0.1102 �0.2083 0.4676.72nnn 1.57 3.07nnn �0.40 �2.55nn �1.69n �4.88nnn �9.04nnn

The table shows second-stage coefficients (λ̂) and t-stats below the coefficients. The standard errors are adjusted according to Shanken (1992) (with Σ̂n

F in Theorem 2 being a 4-lag Newey-West covariance matrix). R

22 is the average second-stage adjusted R-squared. MKT2 and MU2 are the squared MKT and MU factors. See Table 1 for factor definitions. The parameters are

estimated with OLS in the first and second stages. Weekly returns, measured on Wednesdays. The sample period is January 1996 to October 2010. See Table 1 for details on the statisticalsignificance levels.

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Vix and Vixv have a statistically significant risk premium of about �1%. The premium on MU2 is 9.47%,which is statistically significant. In addition, the second-stage intercept is not statistically significant,and the average cross-sectional adjusted R-squared is 52%.

Table 5 also shows a number of other specifications. In the two cases in which MU is removed, theintercept is statistically significant and equal to 2.5–3.0%, but it remains insignificant otherwise.Without MU, the premia on MKT and MKT2 in specification (5) are statistically significant, and the oneon GV roughly doubles, while the premium on Put is not significant. The premium on Vix is alsosignificant only in the presence of MU, and is always about �1%.

Table 6 shows the first set of robustness checks. The sub-period analysis reveals that the premiumon MU is much larger between 1996 and 2002 than in the remaining years of the sample, at nearly�28% versus about �10% from 2003 to 2010. The premium on Put is also statistically insignificantbetween 1996 and 2002. During the 2008 financial crisis and its immediate aftermath (2008–2010),the risk premium on MU is about �11%, while that on Put is statistically insignificant. The averagecross-sectional adjusted R-squared is also noticeably higher in 2008–2010 than in the rest of thesample. The factor Put carries a statistically insignificant risk premium in the two periods that includethe 2000–2002 and 2007–2009 market downturns.

As discussed in Section 2, Broadie, Chernov, and Johannes (2009) point out that linear factormodels suffer from important limitations when applied to index option returns, mainly because thekinked structure of option payoffs causes non-linearity in the relation between option returns andreturns on the underlying, or between option returns and returns on assets correlated with theunderlying. Non-linearity, in turn, can be the source of extreme properties for the distribution ofoption returns, especially in the case of out-of-the-money options, and such properties can invalidatestandard statistical inference. In Section 2, I discuss the aspects of the research design that mitigatethe issues raised in Broadie, Chernov, and Johannes (2009), while, in the remainder of Table 6,I present the relevant empirical evidence.

Table 6Risk premia: sub-period analysis and the effect of return non-linearity.

λ̂0 MKT SMB HML GV MKT2 Vix Vixv Put MU R22

Sub-period analysis: 1996–2002(1) �0.0100 0.0010 0.0061 �0.0032 0.1236 0.0008 �0.0114 �0.0048 �0.0374 �0.2754 0.475

�1.40 0.49 1.19 �0.59 4.11nnn 2.13nn �1.79n �1.12 �1.14 �7.37nnn

Sub-period analysis: 2003–2010(2) 0.0040 �0.0019 �0.0033 �0.0018 0.0510 0.0003 �0.0073 �0.0160 �0.1182 �0.1043 0.516

0.78 �0.88 �1.08 �0.46 3.07nnn 0.61 �1.18 �2.52nn �3.13nnn �4.97nnn

Sub-period analysis: 2008–2010(3) 0.0036 �0.0021 0.0008 �0.0029 0.0408 0.0004 �0.0114 �0.0167 �0.0851 �0.1137 0.608

0.54 �0.70 0.17 �0.62 1.88n 0.45 �1.34 �3.31nnn �1.08 �3.34nnn

Exclude observations if MKT is in the top/bottom 5% of the historical distribution(4) 0.0096 0.0011 0.0045 �0.0015 0.0455 �0.0001 �0.0066 �0.0059 �0.1724 �0.1784 0.474

2.65nnn 0.60 1.44 �0.46 2.85nnn �0.90 �1.66n �1.16 �7.82nnn �6.56nnn

Index puts not in test assets, and exclude if MKT in top/bottom 5%(5) 0.0092 �0.0002 0.0047 �0.0014 0.0398 �0.0001 0.0010 �0.0054 �0.0693 �0.1784 0.361

2.41nn �0.08 1.69n �0.50 2.68nnn �0.82 0.22 �1.17 �1.68n �7.15nnn

Index calls not in test assets, and exclude if MKT in top/bottom 5%(6) 0.0058 0.0033 0.0000 �0.0028 0.0394 0.0002 0.0005 �0.0068 �0.1511 �0.1798 0.396

1.31 1.61 0.00 �0.79 2.16nn 1.38 0.09 �1.21 -7.01nnn �6.08nnn

The table shows second-stage coefficients (λ̂) and t-stats below the coefficients. The standard errors are adjusted according toShanken (1992) (with Σ̂

n

F in Theorem 2 being a 4-lag Newey-West covariance matrix). R22 is the average second-stage adjusted

R-squared. MKT2 is the squared MKT factor. See Table 1 for factor definitions. In specifications (4) to (6), the sample excludesobservations for which the MKT factor is either in the top or bottom 5% of its historical distribution. Weekly returns, measuredon Wednesdays. The sample period is January 1996 to October 2010, unless specified otherwise. See Table 1 for details on thestatistical significance levels.

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Specification (4) in Table 6 shows the results of the Fama-MacBeth procedure when the top andbottom 5% of MKT returns are excluded from the sample. The premium onMU, at nearly �18%, is aboutthe same as in Table 5, while the one on Put is much larger, at about �17%. The reason is that out-of-the-money put options have high positive returns when the broader stock market experiences largedeclines, and excluding the bottom 5% of MKT returns eliminates many positive returns for Put. Theremaining risk premia are about the same as discussed so far, but the intercept is now equal to about 1%and statistically significant. The statistical significance of the intercept is driven by index call options, asshown by specifications (5) and (6), where the test assets do not include, respectively, index put andindex call portfolios. The risk premium onMU is unaffected by whether index puts or calls are excluded,but the Put premium is much smaller and weakly statistically significant in specification (5). The reasonis that, with the exclusion of index put options, the test assets do not span the Put factor.

Additional robustness checks are presented in Table 7. In specification (1) equity option returns arecalculated using the actual bid and ask prices, rather than the midpoint, and in specification (2) equityoption returns are calculated using bid/ask prices and the CBOE option margin requirements.11 In bothcases, the intercepts reflect the presence of transaction costs, and become negative and statisticallysignificant. The premium on Put is insignificant, while the one on GV negative but only weaklystatistically significant. When returns are measured on Thursdays (specification (3)), the interceptbecomes statistically significant and positive, at 61 basis points, and the premium on SMB is alsosignificant. In order to address the measurement error concerns raised in Duarte and Jones (2007), inspecification (4) I exclude equity option portfolios whose average relative bid–ask spread is in the top10% of each week's cross-sectional distribution, which increases the risk premium on GV to nearly 10%.

In specification (5) in Table 7, second-stage regressions include the risk-neutral skew and volatilityspread measures of, respectively, Xing, Zhang, and Zhao (2010) and Bali and Hovakimian (2009). Xing,Zhang, and Zhao (2010) find that the slope of the volatility smile, defined as the difference between theimplied volatility of out-of-the-money put options and at-the-money call options, can explain the cross-section of future stock returns [also see Bali and Murray, 2013 for the effect of risk-neutral skewness onoption returns]. Bali and Hovakimian (2009) show that the spread between realized and implied volatilityalso has cross-sectional implications for equity returns, while Goyal and Saretto (2009) find that thevolatility spread has cross-sectional implications for the returns on straddles and delta-hedged options. Thetwo measures12 are included as characteristics that may proxy for exposure to omitted risk factors.The results, however, indicate that they do not command a statistically significant risk premium in thecontext of option returns, although the premium onMU appears slightly smaller in absolute value at nearly�18%, and the average cross-sectional adjusted R-squared is now considerably higher at about 78%.

As noted in Section 2, the requirement that options have non-zero trading volume eliminates alarge amount of observations from the database; this and additional filters, for instance in terms ofmaturity and moneyness, contribute to the presence of missing option returns. The pattern of missingreturns may not be random, which could bias the estimated risk premia. In an unreported analysis,which is available upon request, I find that the probability of missing returns is affected by Vix, MU,and the logarithm of the average relative bid–ask spread of very out-of-the-money index put options.In specification (6) in Table 7, these three variables are included as covariates in the selection equationof Heckman regressions that I use to estimate first-stage factor loadings [note that the selection

11 See CBOE (2000). The margins are calculated for individual options only, and do not account for portfolio margins rules.12 Bali and Hovakimian (2009) calculate volatility spreads using the last monthly observation of each option. I do the same

when replicating their measure in the monthly analysis described later in the paper, but in the weekly analysis I use the lastweekly observation for each option. Xing, Zhang, and Zhao (2010) compute their weekly skew measure by averaging the dailyskew within a week. I do the same in the weekly analysis, but in the monthly analysis I take the average in a given month. For agiven option portfolio, I calculate the average of the volatility skews and of the volatility spreads for all stocks that underlieoptions in the portfolio. By construction, portfolios of S&P 500 options are all assigned the same volatility skew and volatilityspread. The equity factors that are included as test assets are assigned the volatility skew and the volatility spread of theportfolios of S&P 500 options. The skew measure is based on selecting one put option and one call option with moneynessclosest to 0.95 and 1 [see the discussion in Xing, Zhang, and Zhao, 2010]. Note that, when building the volatility skew, I onlyretain options with at least 15 days to expiration, rather than 10 as in Xing, Zhang, and Zhao (2010), for consistency with therest of the analysis (see Section 2). Also note that period t cross-sectional regressions include volatility skews and volatilityspreads measured at the end of period t�1.

Table 7Risk premia: additional robustness checks.

λ̂0 Vol:Spread Skew MKT SMB HML GV MKT2 Vix Vixv Put MU R22

Equity option returns and MU calculated using bid/ask prices(1) �0.0546 0.0012 �0.0022 0.0082 �0.0242 �0.0001 0.0000 0.0031 �0.0207 �0.3073 0.475

�15.19nnn 0.65 �0.57 2.43nn �1.46 �0.37 0.01 0.54 �0.88 �11.67nnn

Equity option returns and MU calculated with bid/ask prices and reflecting margin requirements(2) �0.0475 �0.0005 �0.0014 0.0095 �0.0305 �0.0003 0.0065 0.0056 �0.0267 �0.2295 0.464

�11.94nnn �0.29 �0.34 2.65nnn �1.74n �0.81 1.42 0.94 �1.14 �10.37nnn

Returns measured on Thursdays(3) 0.0061 �0.0001 0.0078 �0.0006 0.0616 0.0007 �0.0094 �0.0068 �0.0798 �0.2033 0.485

1.90n �0.05 2.18nn �0.18 5.13nnn 1.80n �1.76n �1.66n �2.88nnn �8.54nnn

High-spread option portfolios are excluded(4) 0.0036 �0.0004 0.0047 �0.0037 0.0959 0.0002 �0.0068 �0.0052 �0.0950 �0.1899 0.512

1.25 �0.23 1.34 �1.33 6.81nnn 0.50 �1.82n �1.15 �4.13nnn �8.11nnn

Risk-neutral skews and volatility spreads included in the second stage(5) 0.0053 0.0541 0.1559 0.0013 0.0033 �0.0007 0.0580 0.0009 �0.0190 �0.0140 �0.0964 �0.1780 0.783

0.48 0.36 0.67 0.68 0.90 �0.18 4.06nnn 2.28nn �3.44nnn �2.57nn �3.68nnn �7.54nnn

Heckman first stage(6) 0.0097 �0.0005 0.0045 �0.0020 0.0592 0.0003 �0.0067 �0.0042 �0.0985 �0.2015 0.387

1.63 �0.29 1.31 �0.69 2.59nnn 0.90 �1.67n �0.87 �4.29nnn �9.41nnn

The table shows second-stage coefficients (λ̂) and t-stats below the coefficients. The standard errors are adjusted according to Shanken (1992) (with Σ̂n

F in Theorem 2 being a 4-lag Newey-West covariance matrix). R

22 is the average second-stage adjusted R-squared. MKT2 is the squared MKT factor. See Table 1 for factor definitions. In specification (4), equity option portfolios

whose average relative bid–ask spread is in the top 10% of the weekly distribution are excluded. In specification (5), second-stage regressions include t�1 values for the risk-neutral skewmeasure of Xing, Zhang, and Zhao (2010) and the volatility spreads of Bali and Hovakimian (2009). In specification (6), first-stage factor loadings are calculated with Heckman regressions, inwhich the occurrence of missing returns is a function of Vix, MU, and the natural logarithm of the average spread of very out-of-the-money S&P 500 options. Weekly returns, measured onWednesdays, unless specified otherwise. The sample period is January 1996 to October 2010. See Table 1 for details on the statistical significance levels.

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equation contains one variable not included in the outcome equation, which is important foridentification purposes; see for instance, Sartori, 2003]. The risk premia are quite similar to thosediscussed so far, although the average cross-sectional adjusted R-squared is noticeably lower.

5.1. Monthly analysis: setup

I now discuss a set of robustness checks that significantly alter four aspects of the analysispresented so far. This additional set of results is in line with those described above.

First, I measure returns at a monthly frequency, using monthly option expiration dates to identifynon-overlapping intervals. Options expire on the Saturday after the third Friday of each month andsettle on the basis of Friday stock prices; I calculate returns from the third Friday of month t�1 to thethird Friday of month t. As a consequence, the “monthly” interval is actually four or five weeks long,depending on the month. Monthly factors are identified with the same notation used so far, with theaddition of a superscript m.

Second, in month t�1 I only consider options that expire in month t. I calculate returns on thebasis of the payoff at expiration in t and the bid–ask midpoint in month t�1. This change makesthe options homogeneous in terms of maturity, a characteristic that is not taken into account in theweekly analysis discussed above. The use of settlement values at expiration to calculate returns is inline with Broadie, Chernov, and Johannes (2009), and it allows me to maximize the number of optionsavailable, because it does not require an option to have two valid prices one month apart. However,dividing settlement payoffs by potentially much smaller prices one month prior can generate extremepositive returns. As a consequence, I will directly evaluate the sensitivity of the results to large positivereturns.

Third, option portfolios are built on the basis of fully observable characteristics. In the weeklyanalysis, I first calculate the sensitivity to a latent macroeconomic uncertainty factor for optionportfolios sorted on moneyness, put/call type, and loadings of the underlying stocks on the SMB andHML factors. Then, I build the test assets by absorbing moneyness and put/call type into the estimatedsensitivity to macroeconomic uncertainty, so that the equity option test assets are portfolios ofoptions sorted according to the sensitivity to SMB, HML, and macroeconomic uncertainty. With thenew sorting method, equity option portfolios are simply based on three observable characteristics,and no characteristic is absorbed after estimating the sensitivity to macroeconomic uncertainty. Thethree characteristics are: moneyness (see Section 2 for a definition of the five moneyness categories),put/call type, and the durability of the output produced by the company referenced by an option,using the SIC code-to-durability mapping of Gomes, Kogan, and Yogo (2009). Investors in companiesproducing durable goods are more exposed to demand cyclicality, which should make options onthese companies more sensitive to macroeconomic uncertainty. The five durability categoriesidentified by Gomes, Kogan, and Yogo (2009) are: durables, investment, nondurables, services, other.

Fourth, the MUm factor is built as the mimicking portfolio of a fully observable macroeconomicuncertainty proxy – the monthly change in the volatility of the Aruoba-Diebold-Scotti (ADS) BusinessConditions Index (Aruoba, Diebold, and Scotti, 2009). The sensitivity is calculated by regressing optionportfolio excess returns on a set of risk factors13 and on changes in the volatility of the ADS Index. Thisapproach is similar to the way Bali, Brown, and Caglayan (2014) calculate the sensitivity of hedge-fundreturns to a set of proxies for macroeconomic uncertainty. The factor is the return on a strategy thatbuys option portfolios with loadings on the ADS Index in the top quintile, and sells those withloadings in the bottom quintile. The regression coefficients are calculated using the full 1996–2010sample, because the use of rolling regressions with 3-, 4-, and 5-year windows produces mimickingportfolios whose returns are poorly correlated with changes in the volatility of the ADS Index (usingthe full sample, the correlation is about 37%).

As noted above, the returns on equity options are calculated using the bid–ask midpoint in t�1and the settlement value in t; however, the returns on the out-of-the-money index put options used

13 The set includes the following risk factors: MKTm, SMBm, HMLm, UMDm (and their squared values), Vixm, Vixvm, GVm, andPutm. See Section 5.2 for details on the choice of factors.

Table 8Summary statistics for the monthly factors.

μ tB t tNW p50

MKTm 0.0049 1.14 1.15 1.14 0.0113SMBm 0.0029 1.20 1.25 1.19 0.0021HMLm 0.0024 0.88 0.86 0.80 0.0009UMDm 0.0072 1.64 1.62 1.57 0.0095

GVm 0.8491 21.63nnn 21.32nnn 21.05nnn 0.7629Vixm 0.0011 0.23 0.23 0.24 �0.0022Vixmv 0.0001 0.14 0.15 0.15 �0.0004

Putm �0.1607 �1.68n �1.71n �1.65n �0.4820Putm? �0.3428 �6.06nnn �6.02nnn �5.96nnn �0.0535

MUm �0.5607 �9.47nnn �9.73nnn �9.72nnn �0.5688MUm

? �0.5275 �4.60nnn �5.31nnn �5.05nnn �0.0224

Monthly returns are measured over the four or five week periods between monthly option expiration dates. Options expire onthe Saturday after the third Friday of each month, and returns are calculated from the Friday before the expiration date inmonth t�1 to the Friday before the expiration date in month t. Option returns are calculated using the settlement value atexpiration in t and the option bid–ask midpoint in t�1, while equity returns are calculated by compounding daily returns.Option characteristics, like moneyness, are calculated on the third Friday of month t�1. μ is the factor mean, tB, t, and tNW are t-statistics from testing the null that the mean is zero (based, respectively, on 1,000 bootstrap replications with replacement,asymptotic standard errors, and 1-lag Newey-West standard errors). p50 is the median. MKTm, SMBm, HMLm, and UMDm are theFama-French and momentum factors. GVm is the average excess return on the five equity option portfolios with the highestaverage gamma and the five equity option portfolios with the highest average vega in month t�1. Vixm and Vixmv are monthlychanges in VIX, and changes in the monthly volatility of daily VIX changes. Putm is the average return on out-of-the-money S&P500 put options with prices available in month t�1 and t. Note that, to reduce the impact of returns equal to �100%, Putm isbased on returns calculated using the bid–ask midpoint in both t�1 and t, rather than the midpoint in t�1 and the settlementvalue in t; as a result, Putm is based on options with longer maturity than the options used in building the equity option testassets and the GVm andMUm factors. Putm? is the residual from a regression of Putm on the following factors:MKTm, SMBm, HMLm,UMDm (and corresponding squared factors), GVm, Vixm, Vixmv , and MUm. MUm is the macroeconomic uncertainty factor. SeeSection 5.1 for details on its construction. MUm

? is the residual from a regression of MUm on the following factors: MKTm, SMBm,HMLm, UMDm (and corresponding squared factors), GVm, Vixm, Vixmv , and Putm. For Putm? and MUm

? , the mean and t-stat columnsreport the intercepts of the regressions and the corresponding bootstrapped, robust, and 1-lag Newey-West t-statistics, becausethe means are zero by construction. The sample period is January 1996 to October 2010, unless specified otherwise. SeeTable 1 for details on the statistical significance levels.

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to build the Putm factor – and, for consistency, the returns on all index options – are calculated withthe bid–ask midpoint in both time t�1 and t. The reason for this difference is that investors routinelypurchase tail-risk protection by buying far out-of-the-money index put options that typically expirewith zero value, and the jump factor would have had a large number of returns equal to �100%. Usingreturns to maturity for index options does not alter the conclusions, and results are available uponrequest.

The set of test assets includes the option portfolios built on the basis of moneyness, put/call type,and durability of the output of the underlying companies. As in the weekly analysis, the set alsoincludes portfolios of index options (puts and calls sorted into five moneyness categories, for a total often portfolios), all the equity factors shown in Table 1, the hedging risk factor GVm, the jump risk factorPutm, and the macroeconomic uncertainty factor, MUm. Unless noted otherwise above, the factors arebuilt in the same way as their weekly counterparts; see Table 8 for additional details.

5.2. Monthly analysis: results

The Fama-MacBeth regressions are based on the factors used in most of the weekly specifications(Tables 6 and 7), plus momentum and the squared values of the equity factors. I include the squaredvalues of all the equity factors, rather than just MKT as in the weekly analysis, to better capture thehigher convexity of hold-to-maturity returns on options with one month to maturity.

Table 9Average returns and four-factor intercepts for the monthly uncertainty portfolios.

Panel A: 1996–2010

Sensitivity to ADS volatility changesHigh Low High – Low

Average return 0.9602 0.7941 0.2449 1.0756 1.5208 �0.560718.73nnn 21.42nnn 17.57nnn 30.76nnn 33.16nnn �9.72nnn

Four-factor alpha 1.0058 0.7894 0.2477 1.0800 1.5034 �0.497617.51nnn 21.89nnn 16.76nnn 27.50nnn 34.11nnn �9.95nnn

Panel B: 2008–2010

Sensitivity to ADS volatility changesHigh Low High – Low

Average return 1.1890 0.7023 0.2085 1.0771 1.5626 �0.37366.91nnn 10.27nnn 5.22nnn 9.17nnn 13.38nnn �2.18nn

Four-factor alpha 1.1334 0.6389 0.1830 1.0087 1.5365 �0.40317.30nnn 8.21nnn 7.45nnn 11.67nnn 13.20nnn �3.54nnn

The High/Low uncertainty portfolios underlie a factor-mimicking strategy that replicates changes in the monthly volatility ofthe ADS Index. The portfolios are built by sorting individual option portfolios according to their betas on changes in thevolatility of the ADS Index, calculated from regressions that also include the following factors: MKTm, SMBm, HMLm, UMDm (andtheir squared values), GVm, Vixm, Vixmv , and Putm. The high-sensitivity uncertainty portfolio includes the option portfolios withADS betas in the top quintile, while the low-sensitivity portfolio includes the option portfolios with ADS betas in the bottomquintile (the intermediate uncertainty portfolios are based on the intermediate quintiles of the distribution of ADS betas). Thebetas are calculated using full-sample regressions. The table shows the average returns and the four-factor intercepts, with1-lag Newey-West statistics below the averages and intercepts. See Table 3 for a comparison with weekly uncertainty portfoliosbased on implied volatility drops after macroeconomic announcements. The sample period is January 1996 to October 2010,unless specified otherwise. See Table 1 for details on the statistical significance levels.

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Summary statistics for these factors are shown in Table 8. The average MUm is �56.07%, which isclose to the weekly average in Table 1 compounded for four weeks (�59.59%). The average Putm is�16.07% and is weakly statistically significant; however, orthogonalizing Putm with respect to theother factors and squared values of the equity factors yields an intercept of �34.28%, which is close tothe weekly average compounded for four weeks (�31.67%). The only factor for which the monthly andweekly averages are hard to reconcile is GVm, whose averages are 84.91% (monthly) and 23.87%(weekly compounded four times).

A possible explanation is that the monthly analysis focuses on options that expire in one month,and near-the-money options (whose gamma, in particular, is higher than the gamma of in-the-moneyand out-of-the-money options, hence they are more likely to be included in the GVm factor) areespecially difficult to hedge as they get close to maturity, because the effect of small changes in thevalue of the underlying is magnified by the kink in the option payoff function. Hence, hedging riskmay be of much greater significance when studying options with a relatively short maturity (as in themonthly analysis) than when studying options with a maturity of up to one year (as in the weeklyanalysis), which would make the average GVm larger than the appropriately compounded GV average.

Table 9 shows the average returns and the Fama-French/momentum intercepts for the five MUm

portfolios, formed by sorting the option portfolios into quintiles on the basis of their loading onchanges in the volatility of the ADS Index. As in the case of the weekly analysis (see Table 3), the factoris driven by both the long and short legs, and the dispersion across the five portfolios remains afterorthogonalizing the returns with respect to the Fama-French/momentum factors. As in the case of theweekly analysis, focusing on the 2008–2010 period makes the average of the factor less negative,although in this case the reduction comes from larger returns on the high-sensitivity portfolio. Notethat the returns on the five portfolios are positive and quite large; the reason is that negative returnsare at most �100%, while positive returns can be larger than 100%. This effect is expected in a lowerfrequency analysis that focuses on returns to maturity. Below I directly address the impact of largepositive returns on the estimation of risk premia.

Table 10Risk premia, monthly analysis.

λ̂0 Vol:Spread Skew MKTm SMBm HMLm UMDm GVm Vixm Vixmv Putm MUmR22

For consistency with the weekly analysis, UMDm is not included but the (unreported) squared value of MKTm is(1) 0.0512 �0.0132 0.0275 0.0444 1.4824 0.1591 0.0122 0.5074 �0.6830 0.663

1.09 �1.16 1.30 1.42 5.25nnn 5.42nnn 1.65n 2.09nn �3.93nnn

The squared value of GVm is not included(2) 0.0570 �0.0152 0.0443 0.0678 0.0437 1.2512 0.1452 0.0140 0.5511 �0.6712 0.708

0.93 �1.56 1.70n 2.09nn 0.72 4.00nnn 4.89nnn 1.69n 2.41nn �3.60nnn

(3) 0.0324 �0.0172 0.0386 0.0615 0.0641 1.3830 0.1333 0.0177 0.4295 �0.6433 0.7270.53 �2.02nn 1.45 1.87n 1.04 4.71nnn 4.35nnn 2.09nn 2.19nn �3.06nnn

High-spread option portfolios are excluded(4) 0.0133 �0.0007 0.0191 0.0345 0.0805 1.3148 0.0817 0.0251 0.1867 �0.6475 0.703

0.26 �0.05 0.82 1.00 1.38 6.64nnn 2.75nnn 2.32nn 0.83 �3.03nnn

High-spread option portfolios are excluded, and the sample ends in 2007(5) 0.0812 0.0024 0.0028 �0.0539 0.1151 1.4790 0.0228 0.0048 �0.3068 �0.6152 0.628

1.48 0.24 0.15 �1.73n 2.04nn 6.64nnn 0.83 0.78 �1.84n �3.15nnn

Risk-neutral skews and volatility spreads included in the second stage(6) �0.0084 �0.4812 �0.5133 �0.0162 0.0386 0.0666 0.0735 1.2974 0.1339 0.0157 0.3812 �0.6207 0.751

�0.04 �0.30 �0.13 �3.00nnn 1.45 1.92n 1.26 4.70nnn 4.28nnn 1.81n 3.98nnn �2.92nnn

Risk-neutral skews and volatility spreads included in the second stage, high-spread option portfolios are excluded, and the sample ends in 2007(7) 0.0159 �0.3872 �0.1220 0.0008 0.0041 �0.0481 0.1355 1.4360 0.0259 0.0051 �0.2331 �0.5596 0.662

0.09 �0.25 �0.03 0.12 0.19 �1.37 2.39nn 7.25nnn 0.93 0.79 �1.22 �2.27nn

The table shows second-stage coefficients (λ̂) and t-stats below the coefficients. The standard errors are adjusted according to Shanken (1992) (with Σ̂n

F in Theorem 2 being a 1-lag Newey-West covariance matrix). R

22 is the average second-stage adjusted R-squared. The parameters are estimated with OLS in the first and second stages. See Table 8 for details on return

calculation and factor definitions. All specifications other than (1) include the squared values of MKTm, SMBm, HMLm, and UMDm, whose risk premia are unreported. Given the high riskpremium on GVm, all specifications starting from (3) also include the squared value of GVm, whose risk premium is unreported. Specification (1) includes the same factors as the weeklyspecifications reported in Tables 6 and 7. “High-spread” means that the equity option portfolio is in the top 10% of the distribution of relative bid–ask spreads in month t�1. Vol:Spread andSkew are the measures of Bali and Hovakimian (2009) and of Xing, Zhang, and Zhao (2010). The sample period is January 1996 to October 2010, unless specified otherwise. See Table 1 fordetails on the statistical significance levels.

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Table 11Risk premia, monthly analysis: winsorizing the right tail of option returns at 97.5%.

λ̂0 Vol:Spread Skew MKTm SMBm HMLm UMDm GVm Vixm Vixmv Putm MUmR22

(1) 0.0490 �0.0234 0.0620 0.0846 0.0997 1.1071 0.1662 0.0142 0.1325 �0.5093 0.6950.71 �1.61 2.10nn 2.29nn 1.46 4.74nnn 4.49nnn 1.55 0.66 �2.38nn

High-spread option portfolios are excluded, and the sample ends in 2007(2) 0.0973 �0.0003 �0.0013 �0.0320 0.0929 1.2439 0.0450 0.0047 �0.3425 �0.5207 0.624

1.70n �0.03 �0.07 �1.04 1.83n 6.23nnn 1.62 0.74 �2.77nnn �3.05nnn

Risk-neutral skews and volatility spreads included in the second stage(3) 0.0319 �0.6270 �0.7008 �0.0226 0.0627 0.0852 0.1059 1.0762 0.1629 0.0124 0.1188 �0.4876 0.728

0.16 �0.40 �0.17 �1.96nn 2.07nn 2.15nn 1.69n 5.17nnn 4.30nnn 1.25 0.66 �2.32nn

Risk-neutral skews and volatility spreads included in the second stage, high-spread option portfolios are excluded, and the sample ends in 2007(4) 0.0363 �0.6071 �0.2463 �0.0014 �0.0018 �0.0314 0.1119 1.2423 0.0480 0.0048 �0.2829 �0.4355 0.663

0.21 �0.39 �0.06 �0.19 �0.08 �0.88 2.04nn 6.29nnn 1.79n 0.72 �1.73n �1.83n

The table shows second-stage coefficients (λ̂) and t-stats below the coefficients. The standard errors are adjusted according to Shanken (1992) (with Σ̂n

F in Theorem 2 being a 1-lag Newey-West covariance matrix). R

22 is the average second-stage adjusted R-squared. The parameters are estimated with OLS in the first and second stages. See Table 8 for details on return

calculation and factor definitions. The results in this table are based on option returns winsorized at 0.5% on the left tail, and 97.5% on the right tail. All the specifications include the squaredvalues of MKTm, SMBm, HMLm, UMDm, and GVm, whose risk premia are unreported. “High-spread” means that the equity option portfolio is in the top 10% of the distribution of relative bid–ask spreads in month t�1. Vol.Spread and Skew are the measures of Bali and Hovakimian (2009) and of Xing, Zhang, and Zhao (2010). The sample period is January 1996 to October 2010,unless specified otherwise. See Table 1 for details on the statistical significance levels.

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The first set of monthly Fama-MacBeth results is shown in Table 10, where specification(1) includes the same factors used in most of the weekly specifications, and it should be comparedwith line (4) in Table 5. In all specifications, I require that test assets have at least 100 non-missingreturns, and that, in a given month, there are at least 35 test assets with non-missing returns (thethresholds are 400 and 35 in the weekly case, see Section 2). The risk premium on GVm is much largerthan that on GV, which is line with the difference between the averages of the monthly and weeklyversions of the hedging risk factor, and, as discussed above, it could arise because of the focus onshorter maturity options, which are more difficult to hedge.

The premia on Vixm and Putm are positive and statistically significant, a notable difference relativeto the results in the weekly analysis; in the case of Putm, the estimated risk premium is alsoinconsistent with the average return shown in Table 8. The risk premium on MUm is �68.30%, whichis in line with the average return and the compounded weekly risk premium (�56.07% and �59.59%,respectively). Including UMDm and the squared equity factors in specification (2) in Table 10 does notchange the results, with the exception of the risk premia on SMBm and HMLm, which are now positiveand statistically significant; however, as shown in the remainder of Table 10 and in Table 11, this resultis not robust to changing various aspects of the specification. The risk premium on GVm is quite large,and, starting from specification (3), its squared value is included as a factor, although with limitedeffects.

One possible explanation for the positive sign of the risk premia on Vixm and Putm in Table 10 isthat the use of settlement payoffs in the numerator generates extreme returns, especially during therecent financial crisis. These extreme returns may exert an unduly strong leverage on the risk premiaassociated with the higher moments of the return distribution. In order to explore this possibility, inspecification (4) in Table 10 I exclude equity option portfolios whose average bid–ask spreads,standardized by the bid–ask midpoint, are in the top decile of the cross-sectional distribution in t�1.In specification (5), I further exclude 2008 to 2010 to limit the impact of the large returns during thefinancial crisis. The first filter makes the risk premium on Putm statistically insignificant, while the twofilters combined render the risk premium on Vixm statistically insignificant, and the one on Putm

negative and in line with the factor's abnormal return (�30.68% vs. �34.28%). The average second-stage adjusted R-squared also decreases by about 10%, suggesting that the excluded observations didexert a noticeable influence. Note that the risk premium on MUm remains about the same across thespecifications discussed so far, at around �60% to �65%.

In specifications (6) and (7) of Table 10, the second-stage regressions include the lagged volatilityspreads and risk-neutral skews of Bali and Hovakimian (2009) and Xing, Zhang, and Zhao (2010). As inthe weekly analysis, the two measures do not have a statistically significant risk premium, althoughthey have an impact on the risk premia on MUm and in particular Putm, which is of the appropriatesign but statistically insignificant in specification (7).

As already noted, focusing on returns to maturity, and increasing the horizon from weekly tomonthly, can generate very large returns. Given that negative returns are limited to �100%, whilepositive returns can be larger than 100%, in the last set of results I evaluate the impact of very largepositive returns on the estimated risk premia. I do so by winsorizing the right tail of the distribution ofindividual option returns (by year) at 97.5% rather than 99.5%, while keeping the winsorizationthreshold for the left tail at 0.5%.

Table 11 shows that the results remain largely unchanged, even when including volatility spreadsand risk-neutral skews in the second Fama-MacBeth stage. The risk premium on the MUm factor isabout 10–15% less negative than in the corresponding specifications of Table 10. The reason is thatout-of-the money options are typically those with higher sensitivity to macroeconomic uncertainty(see Table 2), and these options tend to have higher spreads and larger returns, hence excluding theformer and winsorizing the latter attenuates the estimated risk premium.

6. Conclusions

I study whether macroeconomic uncertainty is a priced risk factor in the cross-section of optionreturns. The analysis is based on a non-linear factor model that includes both equity factors and

S. Aramonte / Journal of Financial Markets 21 (2014) 25–4948

option pricing factors, like proxies for stochastic volatility and jump risk. The model is estimated usingthe Fama-MacBeth methodology. The macroeconomic uncertainty factor is a long/short tradingstrategy based on how the implied volatilities of option portfolios change around a set ofmacroeconomic announcements.

The analysis shows that macroeconomic uncertainty commands a large negative risk premium.The results are robust to accounting for hedging risk, in the sense of Gârleanu, Pedersen, andPoteshman (2009), for non-randomly missing option returns, the non-linearity of option returns inreturns on the underlying, transaction costs in the form of the bid–ask spread, and marginrequirements. The results are also robust to calculating returns with the settlement payoffs of optionsheld until maturity, and to building the macroeconomic uncertainty factor with loadings on thechanges in the volatility of the Aruoba, Diebold, and Scotti (2009) Business Conditions Index.

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