The Skewness of Commodity Futures Returns

Accepted Manuscript The Skewness of Commodity Futures Returns Adrian Fernandez-Perez , Bart Frijns , Ana-Maria Fuertes , Joelle Miffre PII: DOI: Reference: S0378-4266(17)30150-4 10.1016/j.jbankfin.2017.06.015 JBF 5167 To appear in: Journal of Banking and Finance Received date: Revised date: Accepted date: 10 November 2016 21 June 2017 30 June 2017 Please cite this article as: Adrian Fernandez-Perez , Bart Frijns , Ana-Maria Fuertes , Joelle Miffre , The Skewness of Commodity Futures Returns, Journal of Banking and Finance (2017), doi: 10.1016/j.jbankfin.2017.06.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT The Skewness of Commodity Futures Returns Adrian Fernandez-Perez*, Bart Frijns**, Ana-Maria Fuertes***, Joelle Miffre**** Research Fellow, Auckland University of Technology, Private Bag 92006, 1142 Auckland, New Zealand. Phone: +64 9 921 9999; Fax: +64 9 921 9940; Email: [email protected] ** Professor of Finance, Auckland University of Technology; Email: [email protected] *** Professor of Financial Econometrics, Cass Business School, City University London, ECIY 8TZ, England; Tel: +44 (0)20 7040 0186 E-mail: [email protected]. IP T * Abstract US CR **** Professor of Finance, Audencia Business School, 8 Route de la Jonelière, 44312 Nantes, France; Tel: +33 (0)2 40 37 34 34. Corresponding author. This article studies the relation between the skewness of commodity futures returns and AN expected returns. A trading strategy that takes long positions in commodity futures with the most negative skew and shorts those with the most positive skew generates significant excess M returns that remain after controlling for exposure to well-known risk factors. A tradeable skewness factor explains the cross-section of commodity futures returns beyond exposures to PT ED standard risk premia. The impact that skewness has on future returns is explained by investors’ preferences for skewness under cumulative prospect theory and selective hedging CE practices. Keywords: Skewness; Commodities; Futures pricing; Selective hedging AC JEL classifications: G13, G14 This version: June 21, 2017 1 ACCEPTED MANUSCRIPT US CR IP T § We are thankful to two anonymous referees for their valuable comments and suggestions. We also acknowledge the comments of Guiseppe Bertola, Maik Dierkes, Fabian Hollstein, Florian Ielpo, Abraham Lioui, Florencio Lopez-de-Silanes, Rafael Molinero, Marcel Prokopczuk, Sofia Ramos, Andrea Roncoroni, Andy Vivian, Robert Webb, and conference participants at the 2015 EDHEC-Risk Institute Conference, London, the 2015 Derivative Markets Conference, Auckland, the 2015 CFE Conference, London, the 2016 New Zealand Finance Colloquium, the 2016 Commodity Markets Conference, Hannover, the 2016 Energy and Commodity Finance Conference, Cergy, the 2016 INFINITI Conference on International Finance, Dublin, the 2016 FMA, Las Vegas, and the 2016 Word Finance Conference, New York; and seminars participants at Audencia Business School, EDHEC Business School, ESSEC Business School and Leibniz University Hannover. We also acknowledge excellent technical assistance of Olaf Draeger in processing the data. 1. Introduction Recent research on equities has studied the relationship between skewness and expected returns. While theory predicts a negative relation between skewness and expected returns AN (Mitton and Vorkink, 2007; and Barberis and Huang, 2008), empirical results are mixed (e.g., M Kumar (2009), Bali et al. (2011), Amaya et al. (2015) find evidence in support of this negative relation, whereas Xiang et al. (2010), Cremers and Weinbaum (2010), and Rehman PT ED and Vilkov (2012) document a positive relation). Given these mixed results, a study that focuses on a different asset class can shed light on the relation between skewness and expected returns. In this paper, we fill this gap by focusing on commodity futures and CE examining whether the skewness of daily commodity futures returns tells us anything about expected returns on these futures. The answer to this question is of great importance to AC academics interested in developing commodity pricing models and more generally getting a better understanding about the role of skewness in the pricing of assets. It is also relevant to long-short market participants concerned with the design of practical investment solutions in commodity futures markets. Using a time-series approach, we examine the performance of a long-short portfolio sorted on skewness where the latter is estimated over the past 12 months of daily futures returns. Taking fully-collateralized long positions in the 20% of commodities with the most 2 ACCEPTED MANUSCRIPT negative skewness and short positions in those with the most positive skewness at each month-end generates an average excess return of 8.01% per annum that is statistically significant (t-statistic of 3.83). The average alpha of the long-short skewness-sorted portfolio stands at 6.21% per annum across pricing models1 and thus the excess return cannot be explained by standard pricing models documented in the literature. The time-series evidence IP T is robust to transaction costs and liquidity considerations. Cross-sectional tests show that the long-short skewness portfolio explains the pricing of US CR commodity futures. The price of skewness is statistically significant and positive with an average of 5.04% per annum across models. In comparison to other factors, the skewness factor commands the most significant and largest premium. Including the skewness factor AN increases the average explanatory power of commodity pricing models marginally (from 31.77% to 35.26% or by 3.5%) but systematically. 2 These results corroborate the time-series M evidence in showing that skewness matters to the pricing of commodity futures and that of skewness. PT ED investors demand higher compensation for exposure to commodity futures with lower levels Taken altogether, these results lend support to the theories on skewness preferences 1 CE (Mitton and Vorkink, 2007; Barberis and Huang, 2008). In these frameworks, skewness AC The literature on commodity futures pricing has established that a suitable benchmark should include a long-only commodity portfolio as well as long-short portfolios deemed to capture the phases of backwardation and contango (see Bakshi et al., 2017 or Fernandez-Perez et al., 2017 for recent references). Acknowledging that backwardation (contango) signals a likely rise (fall) in futures prices, such long-short portfolios buy backwardated commodities described by lower standardized inventories (Fama and French, 1987; Symeonidis et al., 2012; Gorton et al., 2013), downward sloping forward curves (Erb and Harvey, 2006; Gorton and Rouwenhorst, 2006; Szymanowska et al., 2014; Koijen et al., 2017), good past performance (Erb and Harvey, 2006; Miffre and Rallis, 2007; Asness et al., 2013; Gorton et al., 2013), net short hedging and net long speculation (Bessembinder, 1992; Basu and Miffre, 2013; Dewally et al., 2013); they also short contangoed commodities with opposite characteristics. Aside from these now-standard signals, the literature also documents significant spreading returns earned on portfolios sorted on liquidity, change in open interests, inflation beta, dollar beta, value or volatility (Hong and Yogo, 2012; Asness et al., 2013; Szymanowska et al., 2014). 2 The rise in explanatory power obtained when moving from a given model to the same model augmented with a skewness factor, albeit small, is similar to that obtained in the equity literature (Chang et al., 2013). 3 ACCEPTED MANUSCRIPT matters because of investors’ preference for positive skewness (lottery-type payoffs), which causes positively skewed equities to become overpriced and earn lower expected returns than equities with negative skews. This overpricing is not arbitraged away either because of shortselling restrictions (Mitton and Vorkink, 2007) or because positive skewness has a valuable impact on the utility investors derive from their investments (Barberis and Huang, 2008).3 IP T Since commodity futures markets are not subject to short-sale constraints and are dominated by speculators and hedgers, with retail investors rarely participating, our findings are more in US CR line with the cumulative prospect theory framework of Barberis and Huang (2008). An additional mechanism through which skewness could affect commodity prices relates to selective hedging, or more specifically, to hedging under skewness preferences (Stulz, AN 1996; Gilbert et al., 2006 and Lien and Wang, 2015). Selective hedging is a practice in which hedgers’ view of future price movements influences their optimal hedge ratio. In this sense, M hedgers with preferences either described by cumulative prospect theory (Barberis and Huang, 2008) or influenced by skewness (Gilbert et al., 2006) may not only want to minimize PT ED risk but also maximize skewness. Consistent with our empirical findings, these skewness preferences could increase net long hedging, and accordingly, overprice positively skewed commodities; and vice versa for negatively-skewed ones. Aligned with the selective hedging CE hypothesis, we show that commercial traders have a propensity to take relatively longer (shorter) hedges in positively (negatively) skewed commodities. AC Neither the theory of storage of Kaldor (1939), nor the hedging pressure hypothesis of Cootner (1960) explicitly state that skewness matters to commodity futures pricing. It is important to note however that in an extension of the theory of storage, Deaton and Laroque (1992) argue that scarce inventories induce positive skewness, backwardation and thus an 3 Barberis and Huang (2008) use the cumulative prospect theory framework of Tversky and Kahneman (1992) to show that overweighting the probabilities of the occurrence of tail events leads to a preference for positively skewed assets. As this preference for positive skewness is part of the utility functions of investors this is not arbitraged away by short positions. 4 ACCEPTED MANUSCRIPT expectation of rising futures prices. Stated differently, their model allows for the possibility of a positive link between skewness and expected returns. Our results highlight the presence of a strong negative relation between skewness and expected returns and thus do not support the predictions of Deaton and Laroque (1992). The rest of the article unfolds as follows. Section 2 presents the theoretical motivation of IP T why skewness matters in commodity futures markets. Section 3 presents the commodity futures data and benchmarks. Section 4 examines the performance of the skewness trading US CR strategy. Section 5 investigates the ability of a tradeable skewness factor to explain the crosssection of individual commodity returns. Finally Section 6 concludes. AN 2. Theoretical background In this section, we discuss the theoretical background for why skewness can affect the M expected returns of commodities. We focus specifically on the skewness preference literature, which argues that investor preferences affect demand for assets with certain distributional PT ED properties. In addition, we discuss the literature on selective hedging where hedgers’ view of future price movements influences the exposure that is hedged. There are two theoretical frameworks that motivate a negative relation between skewness CE and expected returns. The first framework by Mitton and Vorkink (2007) relies on the notion of two types of traders, one being the traditional mean-variance optimizer, while the other AC being a trader with an inherent preference for assets with positively skewed distributions (i.e., lottery-like assets). This framework largely builds on a behavioral bias, where investors have an intrinsic preference for positive skewness (lottery-like equities); hence, positive-skewness equities are overpriced and have lower expected returns than equities with negative skewness. Equivalently, we could say that there is a negative relationship between skewness and expected returns. The overpricing is not arbitraged away because of short-selling restrictions. 5 ACCEPTED MANUSCRIPT Empirically, Kumar (2009) shows that those investors with preferences for lottery-type equities are typically retail investors. The second framework (based on the work of Barberis and Huang, 2008) is different, in the sense that all investors have homogenous preferences, but have utility functions based on cumulative prospect theory preferences (Tversky and Kahneman, 1992). Under cumulative IP T prospect theory preferences, investors have value functions that are concave over gains, but convex over losses (this makes investors risk averse over moderate gains, but risk seeking US CR over moderate losses). In addition, investors overweigh the likelihood of events with low probabilities of occurring, and underweigh the likelihood of events with high probabilities of occurring. Barberis and Huang (2008) demonstrate that in an economy with skewed assets AN and short-selling constraints, investors overweigh the likelihood of extreme events occurring, and thus are willing to pay more for an asset with a small probability of a large positive M outcome; positively skewed assets will then become overpriced and will have low expected expected returns. PT ED returns. Stated differently, this setting predicts a negative relationship between skewness and However, as Barberis and Huang (2008) point out, even in the case where investors can short-sell, under cumulative prospect theory preferences skewed assets will be mispriced. In CE the case of a positively skewed asset, investors would not be willing to short much of that asset, as it would expose them to the possibility of a large negative return, and since these AC investors overweigh the probability of these negative events occurring, they would find short position in positively skewed asset very unattractive unless they receive a premium for exposing themselves to this risk. Likewise, investors with cumulative prospect theory preferences would not prefer to hold negatively skewed assets, but actually prefer to short those assets (as that would essentially expose them to positive skewness). This suggests that even in the case where short-selling is allowed (as in commodity futures markets), we would 6 ACCEPTED MANUSCRIPT observe that negatively skewed assets end up being underpriced, while positively skewed assets become overpriced. In our context, commodity investors may have preferences for positive skewed commodities or utility functions with cumulative prospect theory preferences that make them overprice (underprice) contracts with positive (negative) skewness. Therefore, we expect to see a negative relationship between skewness and commodity expected returns. IP T A potential mechanism through which skewness preferences could affect commodity prices is selective hedging (see Stulz, 1996). Selective hedging is a practice in which the risk US CR manager’s view of future price movements influences the percentage of the exposure that is hedged. In this case, commercial traders do not fully hedge their positions; rather their hedging strategies incorporate a speculative component that depends on their anticipation of AN forthcoming price changes. In this sense, if hedgers form preferences based on cumulative prospect theory (Barberis M and Huang, 2008) or in general have skewness-based preferences (Gilbert et al., 2006), they will favor an overall position (underlying plus hedge) that minimizes risk and at the same PT ED time maximizes skewness. For a short hedger (or producer), a positively skewed position in the commodity will result in a short futures position that falls short of her minimum variance hedge ratio (as taking a full short hedge would remove the positive skewness that the hedger CE seeks). Likewise, a long hedger (or consumer) in a positively skewed commodity will have a hedging demand that exceeds her minimum variance hedge ratio (as she then reverts the AC negative skewness she is exposed to in the underlying into a positive skewness). This implies that from a hedging demand side, we expect to see more net long hedging demand in positively skewed assets which makes them overpriced. Reversing the argument, we expect to see more net short hedging demand in negatively skewed assets which makes them underpriced. 7 ACCEPTED MANUSCRIPT Recent hedging literature highlights this potential mechanism. For instance, Gilbert et al. (2006) develop an optimal hedging model where hedgers care about mean, variance and skewness of the expected profit distribution (which include the positions in the spot and futures contracts) through a negative exponential utility function, and compare this with the optimal hedging positions under a mean-variance utility framework. Under the assumption IP T that the futures price is a biased estimate of the expected future spot price, they demonstrate that positive skewness reduces the short hedging, and likewise, a negative skewness of the US CR spot prices increases the short hedging. Lien and Wang (2015) show that under the assumption of a skewed Student t-distribution for the spot price and negative exponential utility for the producer, the producers will hedge more (less) when negative (positive) AN skewness prevails compared with a mean-variance hedger. In both papers, skewness of the PT ED 3. Data and Pricing Models M underlying has an effect on the hedgers’ hedging positions and thus the demand for futures. 3.1. Description of Commodity Futures Data Our main data for the analysis are daily settlement prices from Datastream on front-end and second-nearest futures contracts for 27 commodities from distinct sectors: agriculture (cocoa, CE coffee C, corn, cotton n°2, frozen concentrated orange juice, oats, rough rice, soybean meal, AC soybean oil, soybeans, sugar n°11, wheat), energy (electricity, gasoline, heating oil n°2, light sweet crude oil, natural gas), livestock (feeder cattle, frozen pork bellies, lean hogs, live cattle), metal (copper, gold, palladium, platinum, silver), and random length lumber. Returns are changes in log prices of the front-end contract up to one month before maturity; we then roll to the second-nearest contract. The sample period is January 1987 to November 2014. We compute the Pearson’s moment coefficient of skewness of each commodity at monthend t using the daily return history in the preceding 12-month window 8 ACCEPTED MANUSCRIPT ̂ where [ ∑ ( ̂ ) ] ̂ are the daily returns of the ith commodity, observations within the [t-11, t] window, and the parameters ̂ =[ ∑ ( (1) is the number of daily ∑ and ̂ ̂ ) ] are the mean and variance estimates of the daily return IP T distribution, respectively. The higher the absolute value of the skewness measure, the more asymmetric the distribution. US CR Figure 1 plots for illustrative commodities from each sector (corn, crude oil, gold and feeder cattle) the evolution of ̂ alongside the 95% confidence bands; the legend of the significant ̂ . Table I summarizes the distribution of skewness of and ̂ AN graph summarizes for each commodity i the percentage of sample months t=1,…,T with individual commodity futures returns by providing the mean, 25th quantile, median (50th where T are the sample months. M quantile), 75th quantile and standard deviation of ̂ [Insert Figure 1 and Table I around here] PT ED The graphs in Figure 1, along with the standard deviation and 25th versus 75th percentile statistics in Table I, show that, despite the overlapping nature of the 12-month observation windows of daily data used to compute ̂ (at a monthly rolling frequency), the CE skewness of commodity futures returns varies considerably over time, changing sign too. The percentage of months when the skewness coefficient attains a positive (negative) value ranges AC between 20% and 71% (29% and 80%) across the 27 commodities and averages 43% (57%).4 3.2. Commodity Risk Factors 4 Commodity futures prices are observationally equivalent to non-stationary process and therefore the moments may not be constant. Effectively, this means that the skewness of the price distribution is potentially problematic as it may not converge to any meaningful value as D increases. 9 ACCEPTED MANUSCRIPT To properly address the question of whether skewness matters, we place our forthcoming time-series and cross-sectional analyses in the context of a baseline and augmented commodity pricing models as outlined next in Sections 3.2.1 and 3.2.2, respectively. Section 3.2.3 discusses various summary statistics for the set of commodity risk factors employed. IP T 3.2.1. Baseline Commodity Pricing Model Bakshi et al. (2017) construct three systematic risk factors as the excess returns of an equally- US CR weighted long-only portfolio of all commodity futures (EW factor, hereafter) that they refer to as the average commodity factor, a term structure portfolio (TS) and a momentum portfolio (Mom). Basu and Miffre (2013) advocate a hedging pressure (HP) factor. Whereas the EW factor is meant to capture overall commodity market risk, the TS, Mom and HP factors proxy AN for the risks associated with the backwardation/contango cycle of commodity futures markets. The beta-expected return representation of the baseline four-factor model can be written as ) PT ED where i is a commodity futures, (2) M ( are the risk factors, collects the vector of factor risk premia, which is common to all commodities, and are the commodity-specific factor CE betas or loadings which represent scaled conditional covariances. The EW portfolio is a long-only, equally-weighted and monthly-rebalanced portfolio of AC all commodity futures. The factors, referred to as TS, Mom and HP, are the excess returns of long-short fully-collateralized portfolios of commodity futures that long (short) the most backwardated (contangoed) quintile. The TS and HP risk factors are directly motivated by the theories of storage and hedging pressure, respectively. The Mom factor can also be motivated, albeit indirectly, by the theory of storage. For most commodities, the replenishing of scarce inventories through production in backwardated markets or the depletion of abundant inventories through consumption in contangoed markets is a lengthy process during which 10 ACCEPTED MANUSCRIPT price continuation will occur. To put it differently, scarce (backwardated) commodities are likely to be momentum winners and abundant (contangoed) commodities are likely to be momentum losers (Miffre and Rallis, 2007; Gorton et al., 2013). To construct the TS, Mom and HP risk factors, we average the following signals over a prior 12-month ranking period and hold the long-short portfolios on a fully-collateralized IP T basis for a month. The signal employed in the construction of the long-short TS portfolio is the roll yield measured for each commodity as the daily difference in the logarithmic prices of US CR the front-end and second-nearest contracts; the portfolio buys (and simultaneously sells) the quintile with highest (lowest) average roll-yield over the previous 12 months. The long-short Mom portfolio is based on past performance over the past 12 months; the portfolio buys AN (sells) the quintile with highest (lowest) average return over the previous 12 months. Finally, the pertinent signal for the construction of the long-short HP portfolio is the hedgers’ and M speculators’ hedging pressure measured for each commodity as PT ED , respectively; where ( ) and and ( ) denote the open interests of long and short hedgers (speculators), respectively;5 the long-short HP portfolio buys (sells) the quintile with the lowest (highest) and highest (lowest) . The CE time span of our sample together with the choice of ranking period imply that we obtain monthly observations for the risk factors from January 1987 to November 2014. The choice AC of a “long” ranking period of 12 months is motivated by the slow evolution of the backwardation/contango cycle as suggested by the theory of storage and hedging pressure hypothesis (e.g., Gorton et al., 2013). 5 The Commodity Futures Trading Commission (CFTC) classifies traders based on the size of their positions as large (reportable) or small (non-reportable). The reportable category accounts for 76% of long open interest and 80% of short open interest on average across commodities in our sample period. Non-reportable traders are not required to specify the motives of their positions but reportable traders have to inform the CFTC as to whether they are commercial (hedgers) or non-commercial (speculators) participants. These declarations are checked, summarized in the Aggregated Commitment of Traders Report and published on the CFTC website going back to January 1986. 11 ACCEPTED MANUSCRIPT 3.2.2. Augmented Commodity Pricing Models We augment the baseline commodity pricing model (featuring the , , and factors) with a set of factors that is deemed to explain the pricing of commodity futures (Hong and Yogo, 2012; Asness et al., 2013; Szymanowska et al., 2014). This set of additional systematic factors that may price commodity futures includes i) a liquidity risk factor based IP T on (as sorting signal) the daily Amihud et al.’s (1997) dollar volume to absolute return ratio averaged over the two most recent months, ii) an open interest (∆OI) factor deemed to capture US CR future price inflation and based on the changes in the open interest of individual commodities at the time of portfolio formation, iii) an inflation factor constructed according to the slope coefficient β of prior 60-month regressions of monthly commodity futures returns on AN unexpected inflation measured as the change in one-month U.S. CPI inflation rate, iv) a currency risk factor constructed according to the slope coefficient β of prior 60-month M regressions of monthly commodity futures returns on the changes in the U.S. dollar versus a basket of foreign currencies, iv) a value factor that picks up long-run mean reversion by PT ED sorting commodities on the log of the average daily front-end futures prices from 4.5 to 5.5 years ago divided by the log of the front-end futures price at time t, and vi) a volatility factor, net of the momentum effect, constructed as the coefficient of variation (CV) of daily futures CE returns over the prior 36 months. The literature has shown that contracts with low liquidity, rising OI, high inflation betas, low dollar betas, high value and high CV outperform those at AC the other extreme (Erb and Harvey, 2006; Hong and Yogo, 2012; Asness et al., 2013; Szymanowska et al., 2014). Similar to our definition of TS, Mom and HP factors, these additional systematic factors are defined as the excess returns of long-short quintiles with the long and short positions held for one month on a fully-collateralized basis. Appendix A provides further details. 3.2.3. Descriptive Statistics for the Risk Factors 12 ACCEPTED MANUSCRIPT Table II presents descriptive statistics for the risk factors employed in the paper. Beginning with the commodity risk factors, the results confirm the importance of capturing the phases of backwardation and contango when modelling the risk premium of commodity futures. Over the period January 1987 to November 2014, the TS, Mom and HP portfolios outperform all other commodity portfolios. For example, the mean excess returns of the TS, Mom and HP- IP T sorted portfolios range from 4.63% to 8.95% p.a., all of which are significant at the 5% level or better. In sharp contrast, the other commodity portfolios earn at best 3.52% p.a. and none US CR of the mean excess returns is significant at the 10% level. The risk-adjusted performance metrics reported in Table II, Sharpe and Omega ratios, unanimously confirm the outperformance of the TS, Mom and HP portfolios among all commodity portfolios.6 Panel C AN of Table II reports summary statistics for the S&P-GSCI, the well-known equity (market portfolio, SMB, HML and UMD) risk factors and bond (Barclays) risk factor, which we M eventually employ in various robustness checks. Appendix B shows that the pairwise correlations amongst the other long-short factors are small. This motivates their joint PT ED inclusion into the various pricing models employed. [Insert Table II around here] CE 4. Time-Series Portfolio Setting 4.1. Characteristics of Skewness-Sorted Portfolios AC We conduct time-series tests of the relationship between commodity futures skewness and expected returns using a long-short portfolio approach. To do so, at the end of each month, t, 6 Additional summary statistics computed separately for the long and short portfolios confirm the stylized fact that backwardated (contangoed) contracts appreciate (depreciate) in value. For concreteness, the long TS, Mom and HP portfolios earn positive mean excess returns of 4.24% (tstatistic of 1.05), 7.41% (t-statistic of 1.61) and 2.29% (t-statistic of 0.58) p.a., respectively; while the short TS, Mom and HP portfolios earn negative mean excess returns of -5.03% (t-statistic of -1.36), 10.49% (t-statistic of -2.54) and -9.28% (t-statistic of -2.53) p.a., respectively. Since the long-short portfolios are fully collateralized their return is half that of the longs minus half that of the shorts. 13 ACCEPTED MANUSCRIPT we estimate the Pearson’s moment coefficient of skewness ( ̂ ) of the daily return distribution of commodity using the data available within the most recent month t-11 to month t window.7 Then at each month-end t, we rank the i = 1,…,N commodities in the cross-section (N = 27) according to their ̂ values and group them into five portfolios or quintiles; quintile Q1 contains the 20% of commodities with the lowest ̂ , and so forth, IP T up to quintile Q5 that contains the 20% of commodities with the highest ̂ . US CR We start by examining some of the properties of the skewness portfolios by looking at the characteristics of the different quintiles. Table III summarizes the results with Panel A focusing on the pre-ranking skewness of the quintiles. Since this is precisely the signal used to group the commodities into quintiles, it is not surprising to see that ̅̅̅ is negative for Q1 at - AN 0.73 and positive for Q5 at 0.54, and the differential ̅̅̅ ̅̅̅ is strongly significant at the column of the table. M 1% level as suggested by the Newey-West (1987) h.a.c. robust t-statistic reported in the last PT ED [Insert Table III around here] Then we turn attention to four signals – roll-yield, past performance, hedgers’ hedging pressure and speculators’ hedging pressure – that are well-known to capture the backwardation and contango cycle. The signals are measured at each month-end t over the CE same 12-month rolling observation windows as the ̂ signal, and the statistics reported are AC again averages. The main conclusion that can be gleaned from Panel B of Table III is that the constituents of Q1 present backwardated characteristics such as higher roll-yield, better performance, higher speculators’ hedging pressure and lower hedgers’ hedging pressure. Vice versa, the constituents of Q5 present contangoed characteristics such as lower roll-yield, worst 7 For expositional clarity, throughout the paper our skewness signal is obtained employing a ranking period R=12 months and a holding period H=1 month. Nevertheless, in additional unreported results, we considered different ranking and holding periods R={6, 36, 60, 96} and H={3, 6, 12}. The main empirical findings remain unchallenged. Detailed results are available upon request. 14 ACCEPTED MANUSCRIPT past performance, lower speculators’ hedging pressure and higher hedgers’ hedging pressure. The difference in roll-yield between Q1 and Q5 is highly significant at the 1% level; likewise for hedgers’ hedging pressure and speculators’ hedging pressure. For these three signals, there are clear monotonic patterns across quintiles; e.g., the speculators’ hedging pressure decreases without exception from 0.6570 for the most negative-skew commodities (Q1) to 0.5848 for IP T the most positive-skew commodities (Q5). The difference in past performance (excess return p.a.) across Q1 and Q5 is also significant albeit only at the 10% level. Hence, in assessing US CR whether skewness contains information about expected returns, we need to control for these traditional risk factors. AN 4.2. Summary Statistics for the Performance of the Skewness-Sorted Portfolios Figure 2 illustrates the cumulative logarithmic returns ( ∑ ) of each M skewness-sorted quintile. Monotonically, the end-of-period cumulative returns of the skewness quintiles are inversely related to the degree of skewness; that is, PT ED . For concreteness, the end-of-period cumulative return of the most negativelyskewed portfolio Q1 amounts to a gain of about 150% (or 5.12% p.a.) whereas that of the CE most positively-skewed portfolio Q5 amounts to a loss of about 300% (or 10.89% p.a.). [Insert Figure 2 around here] A potential concern that one could raise is that the returns of the different quintile AC portfolios could be driven by a few commodities that persistently end up in the high or low skewness portfolios. To address this concern, Figure 3 shows the frequency of portfolio formation months t = 1,…,T that each commodity enters the long (Q1) and short (Q5) portfolio per sector. None of the frequencies comes near 100% (most below 50%) which confirms that none of the commodities is perpetually part of the Q1 or Q5 portfolios; in other 15 ACCEPTED MANUSCRIPT words, different commodities enter the extreme (most positive or negative) skewness portfolios over time. [Insert Figure 3 around here] The observation that commodities in Q5 outperform those in Q1 as observed in Figure 2 motivates us to examine a commodity skewness trading strategy: a monthly-rebalanced “low- IP T minus-high skewness” portfolio (or long-short skewness portfolio, hereafter) that buys Q1 and shorts Q5. Table IV summarizes the 1-month returns accrued by the individual long-only US CR (quintiles) portfolios and by the long-short skewness portfolio. All portfolios are fullycollateralized and returns are in excess of the risk-free rate. [Insert Table IV around here] AN Panel A of Table IV shows that mean excess returns decrease monotonically from the most negatively (Q1) to the most positively skewed portfolio (Q5). The mean excess return of M Q1 is positive at 5.12% a year (Newey-West t-statistic of 1.42), and that of Q5 is negative at 10.89% a year (Newey-West t-statistic of -3.35). With regards to risk, the standard deviation PT ED of Q1 is larger than that of Q5. In terms of risk-adjusted performance, and as consistently suggested by the Sharpe, Sortino and Omega ratios, portfolio Q1 outperforms portfolio Q2, portfolio Q2 outperforms portfolio Q3, and so forth in a monotonic fashion. As the CE penultimate column of Table IV reveals, taking simultaneous fully-collateralized long positions in the most negative-skew commodities (Q1) and short positions in the most AC positive-skew commodities (Q5) at each month-end t of the sample period yields a mean excess return of 8.01% a year (Newey-West t-statistic of 3.83), a Sharpe ratio of 0.7848 and an Omega ratio of 1.8136. We should note that these performance measures are better than 16 ACCEPTED MANUSCRIPT those of the long-short TS, Mom and HP portfolios typically used as risk factors in the literature on commodity futures pricing (c.f., Table II).8 The performance of the long-short portfolios appears to be more driven by the relatively large negative return and low volatility of the shorts (Q5) than by the lesser positive return and higher volatility of the longs (Q1). The performance of the fully-collateralized long-short IP T skewness portfolio is quite alluring both relatively-speaking (i.e., compared to each of the individual, long-only Q1 to Q5 portfolios) and absolutely due to its high 8.01% excess return US CR p.a., low risk (e.g., low volatility, 99% VaR, and maximum drawdown), and high Sharpe, Sortino and Omega ratios. These results show that the skew of the distribution of daily commodity futures returns conveys information about subsequent returns; namely, there is a AN significantly negative relation between skewness and expected returns.9 Panel A of Table IV also reports the average post-ranking skewness of the quintile M returns, where the latter is measured by first calculating the skewness of each constituent using daily returns in the holding period and then averaging these skewness measures for a PT ED given quintile across constituents and over time. Relative to the pre-ranking skewness reported in Panel A of Table III, the post-ranking skewness measures do not rise monotonically from Q1 to Q5 and show little variation across quintiles (range of [-0.10, - CE 0.01] for the post-ranking skewness versus [-0.73, 0.54] for the pre-ranking skewness). Panel AC A of Table IV also reports the skewness of portfolio returns per quintile and again we do not 8 Inspired by Harvey and Siddique (2000) and other studies in the equity market literature, we sort commodities into quintiles based on their co-skewness with a market proxy M made of 90% of stocks and 10% of commodities (the co-skewness signal is the slope coefficient on the M² returns in a regression of daily commodity futures returns onto M and M² returns). The long-short systematic coskewness portfolio yields a Sharpe ratio of 0.1132, which is much lower than that reported in Table IV (0.7848). The skewness signal, Equation (1), therefore conveys more information about expected commodity futures returns than co-skewness. We filter out from Q1 (Q5) those commodities with non-negative (non-positive) ̂ . The performance measures for the resulting long-short portfolio are nearly identical to those reported in Table IV, e.g. a mean excess return of 7.93%, Sharpe ratio of 0.78 and Omega ratio of 1.80. 9 17 ACCEPTED MANUSCRIPT observe any monotonic increase in skewness going from Q1 to Q5. These results are in line with the observations in Figures 1 and 3 and show that commodity skewness is time-varying, which leads to different commodities making up the extreme quintiles over time. Overall, Table IV demonstrates that positively (negatively) skewed commodities underperform (outperform), which is in line with the skewness preference theories discussed IP T in Section 2. These results are also consistent with the notion that commercial participants engage in selective hedging and, for example, take longer hedging positions in positively US CR skewed commodities to reflect upon their preference for positive skewness. As a result these positively-skewed commodities become overpriced and subsequently underperform. AN 4.3. Alpha and Factor Decomposition Seeking to ascertain whether the profitability of the skewness portfolios is merely a M compensation for exposure to commodity risk factors, we measure the alpha of the skewness PT ED trading strategy relative to the baseline four-factor commodity pricing model where (3) denotes the month t return of either the long-short skewness portfolio or the individual long-only Q1 to Q5 portfolios. The parameter vector ( is CE estimated by Ordinary Least Squares (OLS) and inferences are based on Newey-West robust t-statistics. Table IV, Panel B, presents the results. Q1 (Q5) has positive (negative) loadings AC on the TS and HP risk factors, albeit they are only significant for the Q1 regression. The sign of these loadings suggests that the negative-skew quintile Q1 tends to display more backwardated characteristics than the positive-skew quintile Q5. Accordingly, the TS and HP risk loadings in the long-short skewness portfolio are positive but only the beta of the TS risk factor is significant as suggested by a robust t-statistic of 2.74. 18 ACCEPTED MANUSCRIPT The most important finding is that the baseline four-factor model cannot fully explain the outperformance of Q1 and the underperformance of Q5. The alphas of the five skewness quintiles decrease monotonically from 4.28% a year (t-statistic of 1.79) for Q1 to -8.89% a year (t-statistic of -3.96) for Q5. The risk-adjusted excess return of the fully-collateralized long-short skewness portfolio is a non-negligible 6.58% a year (t-statistic of 3.58). This account for the possibility of non-normality in the alpha distribution.10 IP T inference is not challenged when we employ bootstrap p-values (reported in curly brackets) to US CR The alpha of 6.58% p.a. accrued by the long-short skewness portfolio is not much smaller than its mean excess return of 8.01% p.a. (Panel A of Table IV). This suggests that the outperformance of the long-short skewness portfolio is not merely compensation for exposure AN to the backwardation and contango risk factors. This result is confirmed by the low adjustedR² of the four-factor benchmark fitted to the long-short skewness portfolio returns (5.66%) M and by the low correlations between the skewness excess returns and the TS, Mom and HP PT ED factors (in the last row of Appendix B). 4.4. Robustness Tests We now assess the robustness of the performance of the long-short skewness portfolio to CE various considerations. We begin by addressing the time-dependence issue by carrying out conditional tests in the same spirit of Lewellen and Nagel (2006). To visualize the time- AC variation in the alpha, we deploy the long-short portfolio strategy based on the ̂ signal We construct B=10,000 sequences of bootstrap residuals, { ̂ , , by concatenating random blocks (length M) drawn from the residuals of regression (3). Using these artificial residuals and the original regression parameter estimates we simulate B time-series of portfolio returns under the null hypothesis ( and then re-estimate regression (3) with each of them. The bootstrap p∑ ̂ value is ̂ ̂ ̂ ̂ where ̂ with ̂ and ̂ the original estimate and the estimates of alpha over bootstrap replications, respectively. We empirically verify that M=10 suffices to obtain B sequences of bootstrap residuals with similar autocorrelation properties (average 1st order autocorrelation 0.25) as the sequence of original residuals (1 st order autocorrelation 0.28). 10 19 ACCEPTED MANUSCRIPT over seven-year subsamples that are rolled forward monthly. Figure 4 plots the alphas together with 95% confidence bands based on Newey-West standard errors. The magnitude of the alpha changes over time as one would expect but the significance of the alpha is quite pervasive. Consistent with the preceding unconditional results, the average conditional alpha is positive and significant at 8.53% a year (Newey-West t-statistic of 21.74). IP T [Insert Figure 4 around here] Table V shows the annualized alphas of long-short skewness-sorted portfolios for various US CR additional tests, their corresponding Newey-West significance t-statistics in parentheses and bootstrap p-values in curly brackets. We begin by measuring the commodity skewness, Equation (1), at the end of each month t using filtered-returns instead of observed returns as AN until now. These filtered returns are residuals of regressions of the daily commodity futures excess returns spanned in [t-11, t] windows on an intercept and i) the baseline four systematic M risk factors, ii) business cycle indicators11 and/or iii) calendar-month dummies (deemed to capture seasonality in supply and demand). We then proceed as before and form long-short PT ED portfolios by sorting commodities according to the thus-obtained skewness ̂ . The results in Panel A of Table V indicate that the alphas of the long-short -sorted portfolios remain economically sizeable and statistically significant. Altogether, this first batch of robustness CE checks suggest that the negative skewness-expected return relation uncovered is not driven by exposure to backwardation and contango, the ups and downs of the business cycle and the AC phases of production and consumption. [Insert Table V around here] 11 Following the literature, the business cycle indicators are the default spread (yield differential between BAA and AAA bonds), TED spread (3-month LIBOR minus 3-month T-bill rate), term spread (10-year T-bond minus 3-month T-bill yield), daily change in VXO index and, given our commodity focus, the change in the Baltic Dry index (Bakshi et al., 2012). Interest rates and VXO data are obtained from the FED and CBOE websites, respectively, and Baltic Dry Index from Bloomberg. 20 ACCEPTED MANUSCRIPT In Panel B, we measure the alpha of the long-short skewness strategy with reference to i) a four-factor model that employs the long-only S&P-GSCI returns (instead of the EW portfolio returns) as proxy for the overall commodity market portfolio, and ii) augmented versions of the baseline pricing model that includes additional systematic risk factors. We add the additional factors described in Section 3.2.2, in turn, and also estimate “kitchen sink” IP T pricing models that features all systematic factors. The sign and significance of the resulting alphas are not challenged by these benchmark re-specifications. For completeness, the bottom US CR part of Panel B reports the alpha of the long-short skewness portfolio relative to traditional pricing models employed in the equity market and bond market literatures which remain sizable. AN Our next batch of robustness tests, reported in Panel C of Table V, addresses liquidity and transaction costs issues. To address concerns relating to illiquidity, we systematically M exclude at each formation point the 20% of commodities with the lowest liquidity according to the Amihud et al. (1997) measure and reconstruct the long-short skewness portfolios on the PT ED remaining cross-section. The alpha of the resulting long-short portfolio relative to the baseline four-factor model remains positive and significant. To address matters pertaining to transaction costs, we calculate the alpha of the long-short skewness portfolio after subtracting CE from traded returns twice the transaction cost estimate of Locke and Venkatesh (1997) or twice 0.033%. We also calculate the break-even transaction cost (or cost per trade that would AC be needed to wipe out all excess returns) of the skewness strategy and find it equal to 0.933%. Both of these tests show that transaction costs have a negligible effect on skewness profits. Taken altogether, the robustness tests presented in this section suggest that the effect of skewness on expected returns is robust to how skewness is measured, alternative asset pricing model and illiquidity and transaction costs. 21 ACCEPTED MANUSCRIPT 5. Cross-sectional Asset Pricing Tests The time-series evidence presented in the previous section motivates us to ask whether a tradeable skewness factor can explain the cross-section of commodity futures over and above well-known commodity risk factors. IP T 5.1. Tradeable Skewness Factor In this section we test whether the tradeable skewness factor calculated as the difference in US CR returns between Q1 and Q5 explains the cross-section of excess returns for individual commodity futures. For expositional clarity, we use the notation for the tradeable skewness factor to distinguish it from the commodity-specific skewness signal denoted . Let the AN baseline representation of the pricing model be formalized as in Equation (2). We re-specify it by adding the tradeable skewness factor as follows ) (4) M ( PT ED and estimate both models (baseline and augmented) by OLS using the Fama and MacBeth (1973) approach. Accordingly, we estimate pass-one time-series regressions month-by-month (daily data) to obtain the commodity sensitivities or monthly betas to the risk factors the number of days in month t. Then we estimate the pass-two cross-sectional CE with (5) AC regression ̂ ̂ (6) on each month (t=1,…,T) of the sample period. We report the average lambdas of the pass- two cross-sectional regression (6) which includes the skewness factor, and of the counterpart regression without the skewness factor, ̂ . We also compare the explanatory power of both pass-two regressions and test the statistical significance of the 22 ACCEPTED MANUSCRIPT price of skewness, ̅ , using Shanken’s (1992) t-statistics. We repeat these cross- sectional pricing tests by augmenting Equation (2) with the factors discussed in Section 3.2.2. Table VI presents the pass-two cross-sectional estimation results. Model A focuses on the baseline four-factor model, Models B to H consider additional systematic risk. The most striking and novel result of Table VI is the pervasive rejection of the hypothesis that the of skewness priced factor IP T tradable skewness factor is not priced at the 5% significance level or better. The average price equals 0.0042 a month or 5.02% p.a. Thus, investors demand a US CR higher compensation or premium for exposure to commodity futures with lower levels of skewness. Albeit small, we notice a systematic increase in explanatory power when switching from a given pricing model to an extended version thereof that includes the tradeable AN skewness factor. On average, explanatory power in Table VI rises from 31.77% to 35.26% or by 3.5%. This increase in adjusted R-square is similar to that obtained in equity markets M (Chang et al., 2013). [Insert Table VI around here] PT ED The conclusion that skewness is priced cross-sectionally holds within the baseline pricing model that captures the phases of backwardation and contango (Model A) and shows that skewness is not merely another proxy for the phases of backwardation and contango. The CE Mom and HP risk factors relating to the fundamentals of backwardation and contango are found to pervasively price the cross-section of commodity returns. On average and AC equal 0.0040 and 0.0035 per month which amount to annualized risk premia of 4.76% and 4.17%, respectively. This result, alongside the insignificance of the price of risk associated with the long-only EW risk factor, stresses the wisdom that the risk premia of commodity futures markets can only be captured in a long-short portfolio setting. These results align well with the summary statistics reported in Table II and with the literature (e.g., Basu and Miffre, 2013). The “kitchen sink” model (Model H) explains close to 50% of the cross-sectional 23 ACCEPTED MANUSCRIPT variation in the excess returns of individual commodities. Altogether four risk factors are found to have significant pricing power at the 10% level or better; these are based on skewness, momentum, hedging pressure, and value. In comparison to other factors, the skewness factor is found to command the most significant and largest premium.12 5.2. Robustness Checks IP T We first deploy the Fama-McBeth two-step regressions conditionally using seven-year rolling windows. The focus is on Equation (6), referred to as Model A in Table VI, and the parameter together with 95% US CR of interest is the price of the skewness factor. Figure 5 plots the ̂ confidence bands based on the Shanken (1992) standard errors. The price of skewness ̂ is not constant over time, as one would expect, but it is generally positive. AN [Insert Figure 5 around here] Table VII shows additional analyses conducted to assess the robustness of the previous M cross-sectional results. For this purpose, first we alter the signal used to construct the tradeable skewness factor in Panel A constraining the analysis to the baseline pricing model PT ED (Model A of Table VI). Second, we use the same skewness signal, Equation (1), but alter the pricing model in Panel B. The table reports the average cross-sectional price of skewness factor ̅ and the significance Shanken’s (1992) robust t-statistic. The last two columns in CE each panel are the explanatory power of the pricing model and its simpler version without the AC tradable skewness factor. [Insert Table VII around here] As shown in Panel A, when the tradeable skewness factor is constructed using the daily commodity futures returns stripped of i) the systematic and risks; ii) 12 We also consider the 29 commodity portfolios formed by sorting the commodities into quintiles using skewness, roll-yield, past performance, hedgers’ hedging pressure or speculators’ hedging pressure signals, and 4 additional sector portfolios – agriculture, energy, livestock and metal – that monthly-rebalance and equally-weight constituent commodities. The skewness factor is significantly positively priced with an average price of 0.0063 a month or 7.52% p.a.. 24 ACCEPTED MANUSCRIPT business cycle; or iii) monthly seasonality, reassuringly, the significantly positive price of skewness factor is not challenged. These cross-sectional results reinforce the evidence from the time-series portfolio analysis in Section 4 leading us to more firmly assert that the skewness signal is not simply a manifestation of (and thus it conveys information beyond) the phases of backwardation and contango. The information content of skewness is not an artifact IP T either of the ups-and-downs of the business cycle nor of seasonality in supply and demand. Panel B of Table VII shows that replacing the EW portfolio with the S&P-GSCI portfolio US CR as alternative proxy for the average commodity factor or using traditional pricing models emanating from the equity and bond literature does not qualitatively alter the findings on the skewness factor pricing. Overall, Table VII confirms the previous results (c.f., Table VI) that AN the tradable skewness factor is significantly positively priced at 0.0044 or 5.23% p.a. on average. Adding the skewness factor to a given pricing model increases explanatory power by M 4.05% on average. Finally, we run additional cross-sectional regressions that include the original PT ED characteristics instead of the factor loadings in the second step of the Fama-McBeth regressions. Taking, for example, the baseline model, this amounts to replacing the slope in (4) by lagged characteristics such as roll-yield, futures returns, hedgers’ and vector CE speculators’ hedging pressure as averaged over the previous 12 months. Table VII, Panel C reports ̅ , the average slope coefficient obtained in the second stage on the skewness signal, AC its associated Newey-West t-statistic, as well as the adjusted-R² of models that include and exclude the skewness signal. Irrespective of the specification considered, the skewness signal is negatively priced corroborating once again the presence of a negative relationship between skewness and expected returns. Its inclusion in the pricing equation raises explanatory power systematically throughout models but only slightly (by an average of 1.41%). 25 ACCEPTED MANUSCRIPT 6. Conclusions This article studies the relationship between past skewness and expected returns in commodity futures markets, providing an important out-of-sample test on this relation observed in equities. Using a time-series portfolio analysis and cross-sectional pricing tests, we demonstrate that the skewness of commodity futures returns contains information about IP T subsequent returns and, in particular, the direction suggests a negative skewness-expected returns relation. A tradeable skewness factor that buys the most negatively-skewed US CR commodities and shorts the most positively-skewed commodities commands a premium that is economically and statistically larger than the risk premiums previously identified. The long-short skewness portfolio earns a sizeable alpha relative to a battery of benchmarks AN deemed to capture commodity risk factors. Through cross-sectional pricing tests, the paper further establishes that the tradable skewness factor commands a positive premium that is M more sizeable and more significant than any of the risk factors thus far considered in the literature. PT ED We document that traditional commodity risk factors cannot explain the excess returns generated by the skewness strategy, suggesting that skewness is not another proxy for the fundamentals of backwardation and contango in commodity futures. Our findings are thus in CE line with the literature on skewness preferences, and specifically provide evidence for investors with cumulative prospect theory preferences and selective hedging practices in AC commodity markets. To gain better understanding of the reasons behind the pricing of skewness, we see it as interesting to study, in the spirit of Moskowitz et al. (2012), Asness et al. (2013) or Koijen et al. (2017), skewness profits and drawdowns across asset classes. 26 IP T ACCEPTED MANUSCRIPT This table provides definitions and data sources for the risk factors utilized in the paper. Name Definition US CR Appendix A. Description of the risk factors. AN Panel A: Baseline four-factor model EW Excess return of equally-weighted long-only monthly-rebalanced portfolio of commodity futures TS Excess return of long-short portfolio sorted by prior 12-month roll yield Mom Excess return of long-short portfolio sorted by prior 12-month excess returns HP Excess return of long-short portfolio double-sorted by prior 12-month speculators' and hedgers' hedging pressure PT ED M Panel B: Other systematic risk factors Liquidity Excess return of long-short portfolio sorted by prior 2-month dollar volume over absolute return ∆OI Excess return of long-short portfolio sorted by changes in current total open interest along entire term structure Inflation b Excess return of long-short porfolio sorted by β of 60-month regression of commodity futures returns on unexpected inflation Dollar b Excess return of long-short porfolio sorted by β of 60-month regression of commodity futures returns on effective US dollar changes versus a basket of foreign currencies Value Excess return of long-short portfolio sorted on value, defined as the ratio of the log of the average daily front-end futures prices from 4.5 to 5.5 years ago divided by the front-end log futures price at time t CV Excess return of long-short portfolio sorted by variance-over-mean of daily futures returns over prior 36 months AC CE Panel C: Traditional risk factors motivated by the equity, fixed income and commodity literature S&P-GSCI S&P-GSCI excess return index EqMkt Excess value-weighted return of all CRSP US firms listed on the NYSE, AMEX, or NASDAQ SMB Small-minus-large or size factor (difference in returns between small and large capitalization stocks) HML High-minus-low or value factor (difference in returns between high and low book-to-market stocks) UMD Up-minus-down or equity momentum factor (difference in returns between winner and loser stocks) Bond Excess returns on the Barclays US Aggregate Bond Index Data source Datastream Datastream Datastream CTFC Datastream Datastream FED FED Datastream Datastream Datastream K.R. French's website K.R. French's website K.R. French's website K.R. French's website Bloomberg 27 IP T ACCEPTED MANUSCRIPT US CR Appendix B. Pairwise correlations among monthly factors. The table reports Pearson correlation coefficients for the factors described in Table II and Table IV (Q1-Q5). Appendix A provides a detailed description of all the risk factors. Bold signifies significance at the 10% level or better. The sample observations for the estimation are monthly returns from January 1987 to November 2014. 0.05 0.00 0.19 0.16 -0.23 0.11 0.15 -0.08 0.24 0.15 -0.30 0.16 -0.02 -0.17 0.14 0.01 -0.42 0.20 -0.26 0.06 -0.08 0.13 -0.31 0.18 -0.05 0.33 0.05 -0.01 -0.01 -0.06 -0.08 0.08 0.06 S&P-GSCI EqMkt SMB HML UMD Bond Skewness 0.74 0.26 0.09 0.01 -0.05 0.01 0.07 0.23 0.08 0.14 -0.09 0.07 -0.01 0.21 0.21 0.02 0.11 0.02 0.20 0.05 0.10 -0.07 0.04 0.15 -0.06 -0.05 0.03 0.15 0.34 0.02 -0.02 -0.01 0.08 -0.10 0.09 -0.03 0.02 -0.02 -0.14 0.02 -0.06 -0.14 PT ED CE AC Augmented commodity pricing model ∆OI Inflation b Dollar β Value 0.16 -0.33 0.00 0.47 -0.02 0.04 0.09 0.15 -0.13 0.28 CV S&P-GSCI 0.09 0.02 0.02 0.02 0.03 0.07 0.06 0.17 0.11 0.06 0.07 -0.03 0.16 Traditional risk factors EqMkt SMB HML UMD Bond 0.26 -0.29 -0.25 0.11 -0.10 0.00 AN Liquidity ∆OI Inflation b Dollar b Value CV Liquidity M TS Mom HP Baseline commodity pricing model EW TS Mom HP 0.10 0.14 0.30 0.11 0.02 0.29 -0.23 -0.08 -0.20 0.29 0.15 0.15 -0.05 0.02 0.02 0.16 -0.37 -0.09 -0.15 -0.06 -0.07 -0.11 -0.16 -0.30 0.04 -0.14 0.09 -0.09 0.03 -0.01 0.05 0.12 28 ACCEPTED MANUSCRIPT References Adrian, T., and Rosenberg, J., 2008. Stock returns and volatility: pricing the short-run and long-run components of volatility risk. Journal of Finance 63, 2997-3030. Amaya, D., Christoffersen, P., Jacobs, K., and Vasquez, A., 2015. Does realized skewness predict the cross-section of equity returns? Journal of Financial Economics 118, 135-167. Amihud, Y., Mendelson, H., and Lauterbach, B., 1997. Market microstructure and securities values: evidence from the Tel Aviv stock exchange. Journal of Financial Economics 45, 365–390. IP T Asness, C., Moskowitz, T., and Pedersen, L., 2013. Value and momentum everywhere. Journal of Finance 68, 929-985. US CR Bakshi, G., Gao, X., and Rossi, A., 2017. Understanding the sources of risk underlying the cross-section of commodity returns. Management Science, Forthcoming. Bakshi, G., Panayotov, G., and Skoulakis, G., 2012. The Baltic Dry index as a predictor of global stock returns, commodity returns, and global economic activity. Unpublished working paper, University of Maryland, Hong Kong University of Science & Technology, University of British Columbia. AN Bali, T. G., Caciki, N., and Whitelaw, R. F., 2011. Maxing out: stocks as lotteries and the cross-section of expected returns. Journal of Financial Economics 99, 427–446. M Bali, T. G., and Murray, S., 2013. Does risk-neutral skewness predict the cross section of equity option portfolio returns?. Journal of Financial and Quantitative Analysis 48, 11451171. PT ED Barberis, N., and Huang, M., 2008. Stocks as lotteries: the implications of probability weighting for security prices. American Economic Review 98, 2066–2100. Basu, D., and Miffre, J., 2013. Capturing the risk premium of commodity futures: the role of hedging pressure. Journal of Banking and Finance 37, 2652-2664. CE Bessembinder, H., 1992. Systematic risk, hedging pressure, and risk premiums in futures markets. Review of Financial Studies 5, 637-667. Boyer, B., Mitton, T., and Vorkink, K., 2010. Expected Idiosyncratic Skewness. Review of Financial Studies 23, 169-202. AC Boyer, B., and Vorkink, K., 2014. Stock options as lotteries. Journal of Finance 64, 14851527. Chang, B. Y., Christoffersen, P., and Jacobs, K., 2013. Market skewness risk and the cross section of stock returns. Journal of Financial Economics 107, 46–68. Conrad, J., Dittmar, R., and Ghysels, E., 2012. Ex-ante Skewness and Expected Stock Returns. Journal of Finance 68, 85-124. Cootner, P., 1960. Returns to speculators: Telser vs. Keynes. Journal of Political Economy 68, 396–404. 29 ACCEPTED MANUSCRIPT Cremers, M., and Weinbaum, D., 2010. Deviations from put-call parity and stock return predictability. Journal of Financial and Quantitative Analysis 45, 335-367. Deaton, A., and Laroque, G., 1992. On the behaviour of commodity prices. Review of Economic Studies 59, 1-23. Dewally, M., Ederington, L., and Fernando, C., 2013. Determinants of trader profits in commodity futures markets. Review of Financial Studies 26, 2648-2683. Erb, C., and Harvey, C., 2006. The strategic and tactical value of commodity futures. Financial Analysts Journal 62, 69-97. IP T Fama, E. F., and MacBeth, J. D., 1973. Risk, returns, and equilibrium: empirical tests. Journal of Political Economy 81, 607-636. US CR Fama, E., and French, K., 1987. Commodity futures prices: some evidence on forecast power, premiums, and the theory of storage. Journal of Business 60, 55-73. Fernandez-Perez, A., Fuertes, A.-M., and Miffre, J., 2017. Commodity markets, long-horizon predictability and intertemporal pricing. Review of Finance 21, 1159-1188. Gilbert, S., Jones, S. K, Morris, G. H. 2006. The impact of skewness in the hedging decision. Journal of Futures Markets 26, 503-520. AN Gorton, G., Hayashi, F., and Rouwenhorst, G., 2013. The fundamentals of commodity futures returns. Review of Finance 17, 35-105. M Gorton, G., and Rouwenhorst, G., 2006. Facts and fantasies about commodity futures. Financial Analysts Journal 62, 47-68. PT ED Harvey, C. R., and Siddique, A., 2000. Conditional skewness in asset pricing tests. Journal of Finance 55, 1263-95. Hong, J., and Yogo, M., 2012. What does futures market interest tell us about the macroeconomy and asset prices? Journal of Financial Economics 150, 473-490. Kaldor, N., 1939. Speculation and economic stability. Review of Economic Studies 7, 1-27. CE Koijen, R., Moskowitz, T., Pedersen, L., Vrugt, E. 2017. Carry. Journal of Financial Economics, Forthcoming. Kumar, A., 2009. Who gambles in the stock market? Journal of Finance 64, 1889-1933. AC Lewellen, J., and Nagel, S., 2006. The conditional CAPM does not explain asset-pricing anomalies. Journal of Financial Economics 82, 289-314. Lien, D., Wang, Y., 2015. Effects of skewness and kurtosis on production and hedging decisions: A skewed t distribution approach. European Journal of Finance 21, 1132-1143. Locke, P., and Venkatesh, P., 1997. Futures market transaction costs. Journal of Futures Markets 17, 229-245. Miffre, J., and Rallis, G., 2007. Momentum strategies in commodity futures markets. Journal of Banking and Finance 31, 1863-1886. Mitton, T., and Vorkink, K., 2007. Equilibrium underdiversification and the preference for skewness. Review of Financial Studies 20, 1255-1288. 30 ACCEPTED MANUSCRIPT Moskowitz, T., Ooi, Y. H., Pedersen, J. 2012 Time Series Momentum. Journal of Financial Economics 104, 228-250. Newey, W. K., and West, K.D., 1987. Hypothesis testing with efficient method of moments estimation. International Economic Review 28, 777-787. Rehman, Z., and Vilkov, G., 2012. Risk-neutral skewness: Return predictability and its sources. Goethe University Working Paper. Shanken, J., 1992. On the estimation of beta-pricing models. Review of Financial Studies 5, 1–33. IP T Symeonidis, L., Prokopczuk, M., Brooks, C., and Lazar, E., 2012. Futures basis, inventory and commodity price volatility: an empirical analysis. Economic Modelling 29, 26512663. US CR Stulz, R., 1996, Rethinking risk management. Journal of Applied Corporate Finance 9, 3, 824. Szymanowska, M., De Roon, F., Nijman, T., and Van Den Goorbergh, R., 2014. An anatomy of commodity futures risk premia. Journal of Finance 69, 453-482. AN Tversky, A., Kahneman, D. 1992. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5, 297–323. AC CE PT ED M Xiang, Y., Zhang, X., and Zhao, R., 2010, What does the individual option volatility smirk tell us about future equity returns? Journal of Financial and Quantitative Analysis 45, 641-662. 31 ACCEPTED MANUSCRIPT Table I. Summary statistics for individual commodity time-series of skewness This table summarizes per commodity the sequence of Pearson coefficients of skewness, Equation (1), obtained at each month-end t using daily data over the preceding t-11 to t window. It provides the mean, 25th quintile, median (50th quantile), 75th quintile and standard deviation. The sampling period is January 1987 to November 2014. T Mean StDev 25% Median 75% 0.5245 0.673 0.3587 0.3231 0.3057 1.3526 0.3684 0.263 0.3428 0.2817 0.4004 0.279 -0.3079 -0.3098 -0.2583 -0.2489 -0.2919 -0.3171 -0.1372 -0.3605 -0.2281 -0.0406 -0.3954 -0.1064 0.1248 -0.0256 -0.0413 -0.0911 -0.1269 -0.0414 0.0290 -0.1473 -0.0058 0.1441 -0.1061 0.0941 0.3355 0.3314 0.2527 0.0502 0.1111 0.4672 0.1986 0.0112 0.2086 0.3433 0.0435 0.2606 0.8284 0.3473 0.6951 0.8497 0.4151 -0.3697 -0.1216 -0.385 -0.2984 -0.2346 -0.1297 0.1472 -0.2202 -0.1017 -0.0038 0.0828 0.299 0.0025 0.077 0.2693 0.0138 -0.0093 -0.0190 -0.0938 -0.0931 0.3687 0.0117 -0.1705 0.0011 0.1510 -0.1596 0.0677 Panel B: Energy commodities Crude oil 335 Electricity 128 Gasoline 335 Heating oil 335 Natural gas 295 -0.2461 0.0880 -0.2716 -0.2272 0.0250 Panel C: Livestock commodities Feeder cattle 335 Frozen pork bellies 303 Lean hogs 335 Live cattle 335 -0.1269 0.0915 -0.0746 -0.0500 0.2751 0.5039 0.1788 0.265 -0.2134 -0.0587 -0.2025 -0.1574 -0.1062 -0.0038 -0.0922 -0.0152 0.0295 0.1053 0.0372 0.0984 -0.1144 -0.3056 -0.1998 -0.2762 -0.4321 0.5333 1.0287 0.4487 0.4287 0.5833 -0.3018 -0.7974 -0.4991 -0.5504 -0.8362 -0.0059 -0.4286 -0.2702 -0.3338 -0.3501 0.2157 0.0532 0.0987 -0.0933 0.0115 0.0616 0.1554 -0.0337 0.0654 0.1320 Panel E: Lumber Lumber 335 US CR AN M PT ED CE AC Panel D: Metal commodities Copper 316 Gold 335 Palladium 335 Platinum 335 Silver 335 IP T Panel A: Agricultural commodities Cocoa 335 Coffee 335 Corn 335 Cotton 335 Oats 335 Orange juice 335 Rough rice 178 Soybeans 335 Soybean meal 335 Soybean oil 335 Sugar 335 Wheat 335 32 ACCEPTED MANUSCRIPT Table II. Summary statistics for the risk factors StDev Sharpe ratio Omega ratio US CR Mean IP T The table presents summary statistics for monthly risk factors over the sample January 1987 to November 2014. Panel A focuses on a baseline pricing model that includes a long-only equally-weighted portfolio of all commodities, as well as long-short portfolios based on signals that capture the backwardation and contango cycle. Panel B contains other long-short commodity-specific benchmarks that mimic systematic factors. Panel C presents traditional risk factors that emanate from the equity, bond and commodity pricing literature. Appendix A provides a detailed description of all the factors. Significance t-ratios for the annualized mean excess returns are shown in parentheses. Sharpe ratios are annualized mean excess returns (Mean) over annualized standard deviations (StDev). Omega ratios are the probability of gains divided by the probability of losses using 0% as threshold. 0.9861 1.3355 1.5979 1.4460 Panel B: Augmented commodity pricing model Liquidity 0.0114 ∆Open interest (∆OI) 0.0032 Inflation b 0.0296 Dollar b 0.0127 Value 0.0334 Coefficient of variation (CV) 0.0318 (0.52) (0.18) (1.16) (0.57) (1.44) (1.56) 0.1003 0.0946 0.1340 0.1162 0.1201 0.0993 0.1133 0.0338 0.2208 0.1093 0.2783 0.3207 1.0900 1.0255 1.1848 1.0872 1.2320 1.2944 Panel C: Traditional risk factors S&P-GSCI Equity index (EqMkt) Size (SMB) Value (HML) Equity momentum (UMD) Bond index (0.77) (2.70) (0.14) (1.23) (2.15) (4.51) 0.1989 0.1542 0.1055 0.1010 0.1621 0.0367 0.1768 0.5275 0.0236 0.2742 0.4313 0.9156 1.1481 1.4823 1.0192 1.2482 1.4667 1.9465 Panel A: Baseline pricing model Equal-weighted portfolio (EW) Term structure (TS) Momentum (Mom) Hedging pressure (HP) (-0.08) (2.07) (3.40) (2.37) 0.0352 0.0814 0.0025 0.0277 0.0699 0.0336 0.1207 0.1196 0.1455 0.1206 -0.0175 0.3873 0.6153 0.4796 AC CE PT ED M AN -0.0021 0.0463 0.0895 0.0578 33 ACCEPTED MANUSCRIPT Table III. Relationship between skewness signal and other characteristics Q2 Q3 Q4 -0.7294 -0.2596 -0.0707 0.0978 Panel B: Backwardation versus contango characteristics Roll-yield -0.0008 -0.0034 Excess return 2.91% 0.57% Hedgers' hedging pressure 0.3969 0.4295 Speculators' hedging pressure 0.6570 0.6387 -0.0060 0.78% 0.4389 0.6198 Q1-Q5 0.5407 -1.27 (-17.73) 0.01 4.77% -0.06 0.07 (5.29) (1.75) (-6.10) (5.97) -0.0094 -1.90% 0.4417 0.5974 -0.0105 -1.86% 0.4531 0.5848 AC CE PT ED M AN Panel A: Pre-ranking skewness Q5 US CR Q1 IP T The table summarizes the properties of skewness-based commodity quintiles from January 1987 to November 2014. Q1 is the quintile with the 20% lowest commodities and Q5 the quintile with the 20% highest commodities. The characteristics are measured over 12month windows that are sequentially rolled forward one month at a time. The last column shows Newey-West h.a.c. t-statistics for the null hypothesis that there is no difference in a given characteristic across the Q1 and Q5 quintiles. Panel B shows the characteristics related with backwardation and contango phases such as the roll-yield, excess return, hedgers’ hedging pressure and speculators’ hedging pressure signals. Bold font denotes significant at the 10% level or better. The sampling period is January 1987 to November 2014. 34 ACCEPTED MANUSCRIPT Table IV. Performance of skewness quintiles and long-short portfolios Excess kurtosis 0.0512 (1.42) 0.1748 -0.1006 0.0090 (0.07) 1.3891 (5.10) 0.1291 55.25% -0.4244 0.2932 0.1266 1.2547 0.0401 (0.99) 0.1755 -0.0774 -0.7888 (-5.80) 3.1699 (11.65) 0.1696 55.56% -0.6006 0.2287 0.0910 1.1985 -0.0020 (-0.06) 0.1715 -0.0102 -0.2246 (-1.65) 0.9979 (3.67) 0.1341 48.46% -0.7300 -0.0114 -0.0045 0.9915 0.0428 (1.79) {0.08} 0.9571 (13.12) 0.1951 (2.27) 0.0334 (0.47) 0.0786 (0.93) 0.0410 (1.93) {0.02} 1.0502 (15.05) 0.2375 (3.69) -0.0894 (-1.78) 0.0806 (1.65) 49.12% 56.57% PT ED 99% VaR (Cornish-Fisher) % of positive months Maximum drawdown Sharpe ratio Sortino ratio (0%) Omega ratio (0%) Q3 Q4 Q5 Q1-Q5 -0.0277 (-0.80) 0.1647 -0.0165 -0.5818 (-4.28) 2.7427 (10.08) 0.1577 50.62% -0.8205 -0.1683 -0.0632 0.8792 -0.1089 (-3.35) 0.1596 -0.0247 -0.1563 (-1.15) 1.0168 (3.74) 0.1321 41.05% -0.9731 -0.6820 -0.2375 0.5969 0.0801 (3.83) 0.1020 -0.0760 0.2874 (2.11) 1.1646 (4.28) 0.0627 59.26% -0.2973 0.7848 0.4017 1.8136 0.0134 (0.67) {0.31} 1.0427 (19.31) -0.0933 (-1.45) 0.0037 (0.07) -0.0606 (-0.98) -0.0174 (-0.80) {0.19} 1.0283 (13.80) -0.1096 (-1.66) 0.0048 (0.09) 0.0341 (0.54) -0.0889 (-3.96) {0.00} 0.8949 (14.55) -0.1645 (-2.31) 0.0293 (0.48) -0.1439 (-1.75) 0.0658 (3.58) {0.00} 0.0311 (0.66) 0.1798 (2.74) 0.0021 (0.04) 0.1113 (1.46) 52.79% 56.87% 45.21% 5.66% AN StDev Post-ranking skewness Skewness Q2 M Panel A: Summary statistics Mean Q1 US CR IP T This table summarizes the performance of the long-only portfolios containing the 20% most negative-skew commodities (Q1) to the 20% most positive-skew (Q5) commodities, and the low-minus-high fully-collateralized skewness portfolio that longs Q1 and shorts Q5. The underlying signal is the Pearson’s moment of skewness of the daily returns measured over a ranking period of 12 months. Panel A summarizes the portfolio monthly return distribution. Mean denotes annualized average excess return, StDev annualized standard deviation, Sharpe ratio is Mean divided by StDev, Sortino ratio is Mean divided by annualized downside volatility and Omega ratio measures the probability of gains over probability of losses. Panel B presents annualized alphas and beta coefficients with Newey-West t-statistics in parentheses (bootstrap p-values for alphas in brackets) from regressions of the excess returns of skewness portfolios on the average commodity factor (EW), term structure factor (TS), momentum factor (Mom) and hedging pressure factor (HP); details on the construction of the factors are provided in Section 3.2.1. Bold font denotes significant at the 10% level or better. The sample period is January 1987 to November 2014. Panel B: Regression analysis β (EW) AC β (TS) CE α β (Mom) β (HP) Adjusted R 2 35 ACCEPTED MANUSCRIPT Table V. Robustness checks for performance of long-short skewness portfolios US CR IP T The table studies the abnormal performance of various long-short skewness (Q1-Q5) portfolios. Panel A uses as signal the skewness of the residuals from time-series regressions of daily commodity futures returns on daily observations for the EW, TS, Mom and HP factors, business cycle indicators and/or calendar-month dummies. Panel B uses as alternative pricing models i) a four-factor equation comprising the excess returns of the S&P-GSCI, TS, Mom and HP portfolios, ii) the baseline four-factor equation augmented with systematic risk factors, and iii) equations motivated from the equity/bond pricing literature. Panel C excludes from the cross-section the 80% of futures contracts with lowest liquidity according to the Amihud et al. (1997) measure, and deducts transaction costs of 0.066% per trade. The abnormal performance is measured as the annualized alpha (α) modeled in reference to the baseline four-factor model, except in Panel B where alternative pricing models are used in place. Newey-West t-statistics for the alphas are reported in parentheses and bootstrap pvalues are in curly brackets. Appendix A provides a detailed description of all the factors. Bold denotes significance at the 10% level or better. The sampling period is January 1987 to November 2014. α Panel A: Signal used to construct the skewness risk factor EW, TS, HP, Mom-filtered returns 0.0673 0.0386 Business cycle-filtered returns Calendar month dummy-filtered returns 0.0518 Risk factor, business cycle and dummy-filtered 0.0383 t -stat p -value {0.00} {0.03} {0.01} {0.02} 0.0647 (3.53) {0.00} Baseline pricing model augmented with systematic risk factors Liquidity 0.0637 ∆OI 0.0681 Inflation β 0.0602 Dollar β 0.0652 Value 0.0702 CV 0.0658 All risk factors 0.0581 (3.51) (3.67) (3.36) (3.54) (3.71) (3.61) (3.20) {0.00} {0.00} {0.00} {0.00} {0.00} {0.00} {0.00} Traditional commodity, equity and fixed income pricing models Carhart (1997), Bond index 0.0873 Carhart (1997), Bond, Commodity risk factors 0.0765 (3.59) (3.52) {0.00} {0.00} Panel C: Iliquidity and transaction costs 80% most liquid contracts T-costs = 0.066% (2.80) (3.40) {0.01} {0.00} Panel B: Choice of asset pricing model AC CE PT ED S&P-GSCI, TS, Mom, HP M AN (3.92) (1.94) (2.51) (2.07) 0.0512 0.0624 36 IP T ACCEPTED MANUSCRIPT Table VI. Cross-sectional pricing ability of skewness factor EW TS Mom HP Liquidity ∆OI Model E Model F Model G Model H -0.0015 -0.0016 (-0.84) (-0.89) 0.0040 (2.48) 0.0024 0.0027 (1.20) (1.35) -0.0006 0.0000 (-0.35) (-0.02) 0.0031 0.0034 (1.47) (1.54) 0.0031 0.0031 (1.76) (1.72) 0.0012 0.0014 (0.76) (0.86) -0.0020 -0.0016 (-1.14) (-0.90) 0.0034 (2.10) 0.0029 0.0026 (1.46) (1.31) 0.0002 0.0006 (0.09) (0.35) 0.0042 0.0042 (1.97) (1.95) 0.0031 0.0031 (1.75) (1.72) -0.0028 -0.0030 (-1.57) (-1.67) 0.0043 (2.62) 0.0037 0.0041 (1.87) (2.01) 0.0001 0.0006 (0.08) (0.32) 0.0035 0.0039 (1.60) (1.72) 0.0036 0.0035 (1.96) (1.88) -0.0024 -0.0020 (-1.32) (-1.09) 0.0042 (2.57) 0.0033 0.0030 (1.64) (1.51) 0.0007 0.0008 (0.42) (0.46) 0.0044 0.0042 (2.03) (1.93) 0.0034 0.0038 (1.90) (2.06) -0.0019 -0.0020 (-0.98) (-1.04) 0.0044 (2.49) 0.0028 0.0031 (1.32) (1.49) 0.0003 0.0004 (0.16) (0.22) 0.0036 0.0034 (1.57) (1.45) 0.0034 0.0033 (1.80) (1.68) -0.0022 -0.0019 (-1.21) (-1.08) 0.0045 (2.70) 0.0031 0.0030 (1.55) (1.51) 0.0002 0.0005 (0.09) (0.26) 0.0038 0.0038 (1.75) (1.73) 0.0039 0.0040 (2.18) (2.15) 0.0023 0.0022 (1.46) (1.37) -0.0008 -0.0012 (-0.40) (-0.59) 0.0046 (2.62) 0.0024 0.0029 (1.07) (1.27) 0.0008 0.0013 (0.43) (0.67) 0.0051 0.0052 (2.16) (2.19) 0.0037 0.0037 (1.88) (1.82) 0.0017 0.0019 (0.97) (1.06) 0.0011 0.0009 (0.72) (0.57) 0.0033 0.0033 (1.57) (1.52) 0.0001 0.0004 (0.06) (0.19) 0.0038 0.0038 (1.90) (1.90) 0.0022 0.0024 (1.31) (1.38) 30.39% 33.71% 47.17% 49.80% 0.0004 0.0010 (0.31) (0.70) Inflation b Dollar b Value CV 29.82% 33.54% CE 25.82% 29.68% AC Adjusted R 2 Model D AN Skewness -0.0020 -0.0016 (-1.12) (-0.92) 0.0040 (2.42) 0.0027 0.0025 (1.34) (1.26) -0.0002 0.0003 (-0.11) (0.16) 0.0039 0.0038 (1.82) (1.76) 0.0033 0.0035 (1.86) (1.93) Model C PT ED Intercept Model B M Model A US CR The table reports average coefficients from pass-two Fama-MacBeth cross-sectional regressions of excess commodity futures returns on factor loadings or betas, where we augment the baseline four-factor model, Model A, with systematic risk factors. The test assets are the 27 individual commodities. Shanken (1992) t-statistics are reported in parentheses. Appendix A provides a detailed description of all the factors. Bold means significant at the 10% level or better. The sample period is January 1987 to November 2014. 30.32% 33.65% 0.0031 0.0028 (1.51) (1.37) 0.0005 0.0004 (0.26) (0.24) 0.0041 0.0040 (2.05) (1.98) 30.99% 34.25% 29.70% 33.26% 29.94% 34.18% 37 ACCEPTED MANUSCRIPT Table VII. Cross-sectional robustness tests Adjusted R² without with skewness skewness US CR Panel A: Signal used to construct the skewness factor EW, TS, HP, Mom-filtered returns Business cycle-filtered returns Calendar month dummy-filtered returns ̂ IP T The table tests the robustness of the cross-sectional Fama-MacBeth estimation results to the signal used for the construction of the tradeable skewness factor (Panel A), to the choice of pricing models (Panel B) and to the use of commodity characteristics in place of sensitivities to the risk factors in the cross-sectional regression (Panel C). The table reports the average skewness premium, ̂ ; t-statistic for its significance using a Shanken-adjustment in Panels A and B and Newey and West-adjustment in Panel C; the explanatory power of the pricing model at hand and of the same model without the skewness factor. The pricing model in Panel A is the baseline four-factor (EW, TS, Mom and HP) model. Appendix A provides a detailed description of all the factors. Bold font indicates significance at the 10% level or better. The sample covers the period from January 1987 to November 2014. t -statistic (2.80) (2.02) (2.04) 28.78% 29.66% 30.19% 25.82% 25.82% 25.82% 0.0039 0.0048 0.0057 (2.40) (2.64) (3.20) 29.59% 29.43% 42.21% 25.93% 23.54% 38.63% -0.0088 (-3.59) 10.19% 9.04% Baseline characteristic model augmented with systematic signals -0.0083 Liquidity ∆OI -0.0093 Inflation β -0.0085 Dollar β -0.0089 -0.0083 Value -0.0078 CV -0.0076 All systematic signals (-3.37) (-3.67) (-2.90) (-3.28) (-3.41) (-2.95) (-2.38) 8.98% 10.30% 15.26% 14.24% 15.04% 11.40% 22.05% 7.72% 9.19% 14.09% 12.48% 13.64% 10.13% 20.16% AN M Panel B: Other pricing models S&P-GSCI, TS, Mom, HP Carhart (1997), Bond index Carhart (1997), Bond, Baseline commodity factors AC CE PT ED Panel C: Pricing model based on characteristics Baseline characteristic model 0.0042 0.0035 0.0033 38 ACCEPTED MANUSCRIPT Figure 1. Skewness of daily commodity futures returns over 12-month rolling windows AC CE PT ED M AN US CR IP T This figure plots the Pearson moment of skewness of the distribution of daily commodity futures returns on each month end t using data over the preceding t-11 to t window. The two horizontal lines are the 95% confidence bands to test the hypothesis that skewness is zero. The plotted lines pertain to four representative commodities pertaining to different sectors. The legend reports the percentage of months for each commodity when the skewness is significantly positive or negative. The sampling period is January 1987 to November 2014. 39 ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T Figure 2. Cumulative log returns of skewness-based commodity portfolios The figure plots the cumulative log return of five portfolios: quintiles Q1 to Q5 formed according to the Pearson’s moment of skewness signal measured at the end of each month with the daily returns in the most recent 12-month window. Q1 contains the 20% of commodities with the lowest ̂ values and Q5 contains the 20% of commodities with the highest ̂ values. The sampling period is January 1987 to November 2014. 40 ACCEPTED MANUSCRIPT Figure 3. Frequency of commodities in long Q1 and short Q5 commodity portfolios AC CE PT ED M AN US CR IP T The graph shows the percentage of months over the entire sample period from January 1987 to November 2014 (T=324 months in total) that each commodity enters the long (mostnegatively-skew Q1) portfolio and short (most-positively-skew Q5) portfolio. For instance, cocoa is a constituent of Q1 during 66 months (20.37%), Q5 during 124 months (38.27%), and does not enter any portfolio, long or short, during the remaining 134 months (41.36%). 41 ACCEPTED MANUSCRIPT Figure 4. Conditional alpha of commodity skewness strategy AC CE PT ED M AN US CR IP T The graph shows the sequential annualized alpha of the long-short skewness strategy based on seven-year rolling regressions. The strategy buys the most negative-skew quintile Q1 and shorts the most positive-skew quintile Q5 at the end of each month each seven-year window. The discontinuous lines are the upper limit and lower limit of the 95% confidence band based on Newey-West standard errors. 42 ACCEPTED MANUSCRIPT Figure 5. Conditional price of skewness factor AC CE PT ED M AN US CR IP T The figure shows the conditional lambda of the skewness factor in Equation (6) based on seven-year rolling estimation windows for 27 individual commodities (Model A in Table VI). The discontinuous lines are the upper limit and lower limit of the 95% confidence band based on Shanken standard errors. 43