Skewness Strategies in Commodity Futures Markets Adrian Fernandez-Perez, Auckland University of Technology Bart Frijns, Auckland University of Technology Ana-Maria Fuertes, Cass Business School Joëlle Miffre, EDHEC Business School, EDHEC-Risk Institute Investors are known to display a preference for equities with positive skews (or lottery-like payoffs) and an aversion to equities with negative skews (or those for which the probability of large losses is higher than that of similar large gains). As a result, equities with positive skews tend to be overpriced and thus offer low expected returns, while equities with negative skews tend to be underpriced and thus offer high expected returns. While the pattern is well documented in the equity market literature (see, for example, Amaya et al., 2015, for some recent evidence), the question as to whether skewness matters to the pricing of commodity futures has not yet been addressed. This article is aimed at filling that gap in the literature by designing and analyzing the performance of novel skewness strategies in commodity futures markets. Special attention is devoted to testing the robustness of our results and to the strategic role of the newly-designed skewness portfolio as inflation hedge and risk diversifier. Strategy Design and Performance Analysis Our first task is to construct long-short commodity portfolios based on skewness or the third standardized moment of the returns distribution. 1 We measure the degree of asymmetry or skewness of the daily return distribution of each of 27 commodity futures contracts 2 over a 1 We use the standard skewness coefficient measure with the daily return of the ith commodity on day d, and and the mean and standard deviation (first and second moment) of the daily returns distribution, respectively. 2 We use 12 agricultural commodities (cocoa, coffee C, corn, cotton n 2, frozen concentrated orange juice, oats, rough rice, soybean meal, soybean oil, soybeans, sugar n 11, wheat), 5 energy commodities (electricity, gasoline, heating oil n 2, light sweet crude oil, natural gas), 4 livestock commodities (feeder cattle, frozen pork bellies, lean hogs, live cattle), 5 metal commodities (copper, gold, palladium, platinum, silver), and random length lumber. The futures returns are constructed by holding the nearest-to-maturity contract up to one month before maturity and then rolling to the second nearest contract. 1
ranking period of R= {6, 12, 36, 60, 96, 120} months. The skewness portfolio buys the 20% of contracts with the lowest skewness, shorts the 20% of contracts with the highest skewness and the portfolio is held for 1 month. The ranking is then repeated over a new set of skewness signals. This portfolio formation approach is conducted sequentially over the time period from January 1987 to November 2014. The constituents of the long-short portfolios are equallyweighted and the portfolios are fully-collateralized. Figure 1 shows the skewness of the individual commodity futures returns (left axis) measured over the whole sample period; the lowest (i.e., most negative) skewness corresponds to crude oil and the highest (i.e., most positive) skewness corresponds to orange. The corresponding t-statistics (right axis) confirm that the degree of skewness is not negligible. We compare the performance of the long, short and long-short skewness portfolios to two sets of traditional portfolios. On the one hand, naively assuming that commodity futures markets are always backwardated, the first set includes the S&P-GSCI and a long-only equallyweighted monthly-rebalanced portfolio of all commodity futures (EW). On the other hand, more credibly assuming that both the backwardation and contango characteristics of commodity futures markets matter to pricing, we use long-short commodity portfolios based on the slope of the term structure (TS), hedging pressure (HP) and past performance (Mom) of commodity futures. 3 Extant studies indeed show that these portfolios can price commodity futures (Bakshi et al., 2013; Basu and Miffre, 2013; Szymanowska et al., 2014), and they also form the basis of strategies followed by indexers and CTAs (Bhardwaj et al., 2008). Performance is presented in Table 1. As expected, the commodities with the lowest (i.e., most negative) skewness coefficient values tend to surprise us positively, earning positive excess returns that average 4.25% a year across ranking periods (Panel A). As anticipated, the highest (i.e., most positive) skewness commodities underperform, earning on average -8.03% a year (Panel B). Systematically taking long positions in low-skewness commodities and short positions in the high-skewness commodities yields positive and statistically significant mean excess returns that average 6.14% a year across ranking periods (Panel C). With a mean excess return at 8.01% a year (t-statistic of 4.08) and a Sharpe ratio at 0.78, the skewness 3 The term structure portfolio buys the 20% of contracts with the most downward-sloping term structures and shorts the 20% of contracts with the most upward-sloping term structures. The hedging pressure portfolio buys the 20% of contracts for which hedgers are the shortest and speculators the longest and sells the 20% of contracts for which hedgers are the longest and speculators the shortest. Finally, the momentum portfolio buys the 20% of contracts with the best past performance and sells the 20% of contracts with the worst past performance. The ranking period over which the three signals are averaged is 12 months and the holding period is 1 month. 2
strategy with a ranking period of 12 months stands out as being the most profitable. Its performance compares very favorably to that of traditional long-only and long-short commodity portfolios (Panels D and E). To illustrate graphically the profitability of our strategy, Figure 2 plots the time evolution of $1 invested at the beginning of the sample period in the long-short skewness, TS, Mom and HP portfolios (all of them formed using a ranking period of 12 months), and in the long-only S&P-GSCI and EW strategies. The long-short skewness portfolio clearly stands out. Robustness Analysis Is the skewness signal merely another proxy for the backwardation and contango phases that are well known to play a key role in commodity futures pricing? After all, skewness could be driven by supply and demand shocks and therefore, a disguised manifestation of inventory and/or hedging pressure dynamics. To formally test this conjecture, we measure the abnormal performance of the skewness strategies after accounting for the risks present in commodity futures markets. Table 2, Panel A presents the annualized alpha of the skewness strategy measured as the intercept of an Ordinary Least Squares regression of the long-short skewness excess returns on the excess returns of the EW, TS, HP and Mom portfolios. Clearly, the resulting alphas across all ranking periods R considered are economically significant (at 5.03% on average) and often statistically significant as well, suggesting that the skewness signals capture other risks beyond those embedded in the backwardation and contango phases. As a further robustness check, we test the impact that transaction costs may have on the profitability of the strategies. Relative to Locke and Venkatesh (1997), we are conservative in setting transaction costs at 0.033% and at twice that amount at 0.066%. The results presented in Table 2, Panel B show that the skewness strategy is cheap to implement and profitable net of transaction costs. The preferred strategy with a ranking period of 12 months still earns an average net excess return of 7.66% a year (t-stat of 3.90) when transaction costs are 0.066%. Finally, we address possible concerns over lack of liquidity by redeploying the strategies, systematically excluding the 10% of commodities with the lowest average open interest over the R months preceding portfolio formation. The results reported in Table 2, Panel C highlight that the performance of the skewness strategy in commodity futures markets is clearly not a compensation for lack of liquidity of the assets included in the long-short portfolios. 3
Strategic Role of Skewness Portfolios Traditionally investors have regarded commodity portfolios as risk diversifiers and inflation hedges. It remains to be tested whether these appealing properties also apply to the long-short skewness portfolios. The correlation between US equity returns and the total returns on the skewness portfolio (with R=12 months) stands at -0.10 (t-stat of -1.84), which is much lower than that obtained with, say, the long-only EW portfolio (0.28, t-stat of 5.16). Likewise, the skewness portfolio is found to diversify fixed income risk better than known long-only alternatives. However, the correlation between the excess returns of the skewness portfolio and shocks to inflation is found to be as low as 0.07 (t-stat of 1.24), whereas that of S&P- GSCI stands at 0.33 (t-stat of 6.21). Hence, the superior performance and diversification benefits of following our long-short approach to commodity investing come at the cost of losing the inflation hedge that is naturally provided by long-only commodity positions. Conclusions This article argues that systematically buying commodities with low skewness and shorting commodities with high skewness is a profitable strategy. The performance is not merely a compensation for the inherent backwardation and contango risks present in commodity futures markets, for the transaction costs incurred in implementing the trades or for the relative lack of liquidity of the assets traded. The long-short skewness portfolio is also found to act as a good risk diversifier but not as an inflation hedge. References Amaya, D.; P., Christoffersen; K., Jacobs and A., Vasquez, 2015, Does realized skewness predict the cross-section of equity returns? Journal of Financial Economics, forthcoming. Bakshi, G., Gao, X., and Rossi, A., 2013, A better specified asset pricing model to explain the cross-section and time-series of commodity returns. Unpublished Working Paper, University of Maryland. Bhardwaj, G., G. Gorton and K. G., Rouwenhorst, 2008, You can fool some of the people all of the time: The inefficient performance of commodity trading advisors, Yale ICF Working paper N o 08-21 Basu, D., and J., Miffre, 2013, Capturing the risk premium of commodity futures: The role of hedging pressure, Journal of Banking and Finance, 37, 2652-2664. Locke, P., and P., Venkatesh, 1997, Futures market transaction costs, Journal of Futures Markets, 17, 229-245. 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. 4
Table 1. Summary Statistics of Performance The table presents summary statistics for long-only, short-only and long-short commodity portfolios. The sample spans January 1987 to November 2014. Conventional significance t-ratios are reported in parentheses. Sharpe ratios are annualized mean excess returns (Mean) divided by annualized standard deviations (StDev). Mean StDev Sharpe ratio Panel A: Low skewness commodity portfolio (long) Panel D: Traditional long-short commodity portfolio (R = 1 R = 6 0.0369 (1.09) 0.1772 0.2080 Term structure 0.0377 (1.95) 0.1017 R = 12 0.0512 (1.52) 0.1748 0.2932 Hedging pressure 0.0490 (2.66) 0.0971 R = 36 0.0263 (0.72) 0.1817 0.1447 Momentum 0.0746 (3.32) 0.1186 R = 60 0.0435 (1.09) 0.1914 0.2271 Average 0.0537 0.1058 R = 96 0.0542 (1.22) 0.1987 0.2728 R = 120 0.0427 (0.82) 0.2211 0.1931 Average 0.0425 0.1908 0.2231 Panel B: High skewness commodity portfolio (short) Panel E: Traditional long-only commodity portfolio R = 6-0.0744 (-2.37) 0.1649-0.4511 EW -0.0016 (-0.07) 0.1144 R = 12-0.1089 (-3.54) 0.1596-0.6820 S&P-GSCI 0.0034 (0.09) 0.1989 R = 36-0.0770 (-2.32) 0.1663-0.4630 Average 0.0009 0.1566 R = 60-0.0747 (-2.07) 0.1734-0.4306 R = 96-0.0757 (-1.90) 0.1777-0.4258 R = 120-0.0715 (-1.66) 0.1823-0.3921 Average -0.0803 0.1707-0.4741 Panel C: Long-short skewness commodity portfolio R = 6 0.0556 (2.94) 0.0991 0.5615 R = 12 0.0801 (4.08) 0.1020 0.7848 R = 36 0.0516 (2.48) 0.1041 0.4959 R = 60 0.0591 (2.46) 0.1149 0.5140 R = 96 0.0649 (2.52) 0.1153 0.5632 R = 120 0.0571 (2.00) 0.1212 0.4708 Average 0.0614 0.1094 0.5650 Mean StDev 5
Table 2. Robustness Analysis The table tests the performance of the skewness strategy after accounting for the risks present in commodity futures markets (Panel A), transaction costs (Panel B) and lack of liquidity (Panel C). The sample spans January 1987 to November 2014. Conventional significance t- ratios are reported in parentheses. Panel A: Abnormal Panel B: Impact of transaction costs Panel C: 90% most Ranking period performance TC=0.033% TC=0.066% liquid contracts R = 6 0.0484 (2.59) 0.0530 (2.81) 0.0505 (2.67) 0.0385 (1.99) R = 12 0.0675 (3.67) 0.0783 (3.99) 0.0766 (3.90) 0.0631 (3.30) R = 36 0.0393 (1.64) 0.0509 (2.44) 0.0501 (2.41) 0.0439 (2.26) R = 60 0.0482 (2.02) 0.0584 (2.44) 0.0578 (2.41) 0.0537 (2.30) R = 96 0.0545 (1.95) 0.0645 (2.50) 0.0641 (2.49) 0.0572 (2.35) R = 120 0.0441 (1.44) 0.0566 (1.98) 0.0562 (1.97) 0.0480 (1.86) Average 0.0503 0.0603 0.0592 0.0507 6
Figure 1. Skewness of Daily Commodity Futures Returns Sample period: January 5, 1987 to November 28, 2014. 7
Figure 2. Future Value of $1 Invested in Fully-Collateralized Long-Short and Long- Only Commodity Portfolios 8