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Strategic and Tactical Roles of Enhanced-Commodity Indices

July 2010

Ana-Maria FuertesProfessor of Financial Econometrics, Cass Business School

Joëlle MiffreAssociate Professor of Finance, EDHEC Business School

Georgio RallisResearch Fellow, Cass Business School

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AbstractThis article compares the risk and performance of two traditional commodity indices with enhanced long-only versions that exploit signals based on momentum, term structure and the time-to-maturity of the contracts. Regarding risk diversification and inflation hedging properties, the enhanced indices are as effective tools for strategic asset allocation as the traditional ones. In addition, with alphas ranging from 0.49% to 6.18% a year, the enhanced indices improve upon the performance of their traditional counterparts, both statistically and economically, suggesting that they can also be utilized for tactical asset allocation. Among those considered, the leadingenhanced index targets maturities far away from the present.

Keywords: Long-only commodity indices; Momentum; Term structure; Time-to-maturityJEL classification codes: G13, G14

We thank Amir Alizadeh, Andros Gregoriou and Jerry Coakley for helpful comments and suggestions.

EDHEC is one of the top five business schools in France. Its reputation is built on the high quality of its faculty and the privileged relationship with professionals that the school has cultivated since its establishment in 1906. EDHEC Business School has decided to draw on its extensive knowledge of the professional environment and has therefore focused its research on themes that satisfy the needs of professionals.

EDHEC pursues an active research policy in the field of finance. EDHEC-Risk Institute carriesout numerous research programmes in the areas of asset allocation and risk management in both the traditional and alternative investment universes. Copyright © 2010 EDHEC

1. IntroductionIndices are regarded as the simplest and most cost-efficient way to acquire exposure to underlying markets. In commodity markets the first index goes back to 1957 and was created by the Commodity Research Bureau (CRB) as a broad indicator of commodity price movements. Many other indices followed such as the Standard & Poor’s Goldman Sachs Commodity Index (S&P-GSCI) or the Dow Jones-UBS Commodity Index (DJ-UBSCI, formerly known as DJAIGCI). The traditional or first-generation indices tend to hold the most active contracts and promise a passive, long-only exposure to commodities. These indices have often been cast as sub-optimal precisely because they are long-only, rebalance infrequently and fail to take into account the term structure of commodity prices. To remedy these problems, a plethora of enhanced or second-generation indices has emerged with novel features such as exploiting market signals influential to commodities, changing allocation more frequently or explicitly accounting for the propensity of commodity markets to be either contangoed or backwardated.1

Given today’s proliferation of customized indices, it has become important and yet increasingly challenging for investors to discriminate between them; this is largely because their risk profile lies behind complex technical specifications and also because their characteristics vary greatly from one index to another, making comparisons difficult.2 To assist investors in this endeavor, the present paper provides a rigorous comparative analysis of two popular firstgeneration indices (S&P-GSCI and DJ-UBSCI) and their second-generation counterparts that exploit signals based on: 1) momentum, 2) term structure, 3) a combination of the latter two, or 4) the time-to-maturity of the contracts. In so doing, the implicit goal is to test whether the second-generation indices meet the twofold objective, often claimed by index providers, of providing similar risk exposure to commodity markets as traditional indices while also exhibiting better performance. The analysis is conducted in a long-only framework in order to accommodate the asset allocation constraints of managers with long-only mandates and also to differentiate our paper from extant studies.3 This choice is also dictated by the fact that most of the second-generation indices that are available to investors involve long-only positions. To preview our key results, we demonstrate empirically that the enhanced S&P-GSCI and DJ-UBSCI can be useful for both strategic and tactical asset allocations. The strategic benefits come from successfully replicating the baseline indices and thus providing investors with as good an indicator of commodity price movements as the traditional indices themselves.4 To put it differently, our findings show that the enhanced S&P-GSCI and DJ-UBSCI are as suitable as the baseline S&P-GSCI and DJ-UBSCI when it comes to risk diversification and inflation hedging (Bodie & Rosansky, 1980; Bodie, 1983; Erb & Harvey, 2006). Moreover, the enhanced indices add value relative to the traditional ones in the form of alpha generation, suggesting that they can also be exploited for tactical asset allocation; with alphas ranging from 0.49% to 6.18% a year, the enhanced indices outperform, both statistically and economically, the baseline S&P-GSCI and DJ-UBSCI. In particular, the enhanced index with leading performance targets maturities that are far away from the present up to 12 months. This indicates that, among the four signals considered, the time-to-maturity of the contract is a decisive factor driving the outperformance.

The remainder of this article is organized as follows. The dataset is described in the next section. The baseline S&P-GSCI and DJ-UBSCI replication methodology and corresponding empirical findings are presented afterwards. The subsequent sections discuss the methodology and empirical findings pertaining to enhanced indices based on momentum, term structure, a combination of these signals and the time-to-maturity of the contracts. We then study the strategic roles of the baseline and enhanced indices in more detail, focusing on their ability to diversify risk and hedge inflation shocks. Finally, the last section concludes.

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1. To cite only a few, the following enhanced indices are open to investment at the time of writing this paper: Bache Commodity Index, Barclays Commodity Index, Credit Suisse Commodity Benchmark Index, Deutsche Bank Liquid Commodity Index, Diapason Commodity Index, DCI BNP Paribas Enhanced Index, JPMorgan Commodity Index, Merrill Lynch Commodity Index, MorningStar Commodity Index, UBS Bloomberg Constant Maturity Commodity Index. For detailed information on some of these indices, see Kazemi, Schneeweis and Spurgin (2007).2. Comparing performance is challenging because commodity indices differ in terms of constituents, allocations, rolling techniques, diversification constraints and weighting schemes (Akey, 2005; Erb & Harvey, 2006).3. Erb and Harvey (2006), Gorton and Rouwenhorst (2006), Miffre and Rallis (2007), Shen, Szakmary and Sharma (2007), Fuertes, Miffre and Rallis (2010) and Szakmary, Shen and Sharma (2010) study the performance of long-short strategies based on momentum, roll-returns or a combination of the two signals, showing that they are useful at generating abnormal returns. Other contributions such as Jensen, Johnson and Mercer (2002) and Vrugt, Bauer, Molenaar and Steenkamp (2007) highlight the role of fundamental information in forecasting commodity returns.4. Investors in index trackers are first and foremost interested in the ability of the tracker to mimic the ups and downs of the index. The closer the tracker’s beta (relative to the index) is to unity and the lower the tracking error, the better the ability of the tracker to passively mimic the index; see Elton, Gruber and Busse (2004) for index funds or Elton, Gruber, Comer and Li (2002) for exchange traded funds.

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2. DataThe S&P-GSCI and DJ-UBSCI were officially created in 1991 and 1998, respectively, but their performance has been backfilled by index providers. The sample spans the period October 24, 1988, to November 20, 2008, for the S&P-GSCI and the period January, 4 1991 to November, 20 2008 for the DJ-UBSCI. The dataset from Bloomberg consists primarily of: i) the daily (dead andlive) futures prices for all maturities of the 30 commodities that form the S&P-GSCI and the DJUBSCI, and ii) the daily prices of the two indices.5 For each index, the constituents list alongside the time of inclusion of each commodity can be found in Table I. We use closing prices of the contracts traded on the London Mercantile Exchange (i.e., aluminum, copper, lead, nickel, tin and zinc) expiring on the third Wednesday of each month. Before December 2000 most of the LME futures did not exist, thus in order to replicate the indices we use daily forward contracts with fixed maturities available from Bloomberg.

Table I. Commodities and active contracts included in the S&P-GSCI and the DJ-UBSCI

Note. The table contains the futures months included in the S&P-GSCI and DJ-UBSCI at the beginning of each calendar month, starting with January. The letter codes are F (January), G (February), H (March), J (April), K (May), M (June), N (July), Q (August), U (September), V (October), X (November) and Z (December).

For each commodity index, we collect data on the constituent indices from Bloomberg, including the futures returns and the rolling procedure. The crude oil DJ-UBSCI index, for example, is a constituent index that follows the exact rolling procedure of the DJ-UBSCI but focusing exclusively on crude oil. Using the returns of these constituent indices and the annual weighting allocation of the DJ-UBSCI, we calculate the daily weighting of each constituent index over the sample period. The idea is to mimic the portfolio allocation on a daily basis based on the constituents of the DJ-UBSCI and the yearly weights allocated to each constituent. Likewise for the S&P-GSCI.

3. Baseline Commodity Indices3.1S&P-GSCI Methodology and ReplicationWe follow the methodology in the Standard & Poor’s GSCI manual (2007) to replicate the S&PGSCI Excess Return Index. The S&P-GSCI is a production-weighted index of the prices of exchange-traded, liquid physical commodity futures contracts. Figure 1 presents the time evolution of the index weightings and illustrates the historical heavy skew towards the petroleum sector. At the start of the expiration month, futures contracts that are expiring are rolled (exchanged) for contracts with the next applicable expiration month. Details on the roll schedule are provided in Table I, column 5. Certain commodities (e.g. energy and industrial metals) roll more frequently

5 - The indexes are available on both an excess return and total return basis. The excess return indexes reflect the return of underlying commodity futures price movements only, whereas the total return indexes reflect the theoretical return on fully-collateralized futures positions. In line with previous research we have not included the return of the collateral in our analysis. Henceforth when referring to the S&P-GSCI, DJ-UBSCI and enhanced versions thereof the term “returns” refers to the excess returns of the indices.

than others (e.g. agricultural and livestock), with the least frequent rollers having contracts with longer average life expectancy. The roll-period lasts five days and occurs on the fifth through the ninth business day of the month at a rate of 20% per day dollar-weighted.

Figure 1. S&P-GSCI weightings

Note. The ticker definition can be found in Table 1.

The second and third columns of Table II present summary statistics for the S&P-GSCI and our replicating portfolio. Overall, the S&P-GSCI replication exercise is successful in terms of both performance and risk. First, the S&P-GSCI and the replicating portfolio have identical annualized geometric means and the difference between their annualized arithmetic means is negligible (as suggested by a t-statistic of 1.17). Although statistically significant at the 10% level, the alpha of our replicating portfolio relative to the S&P-GSCI is economically small at 0.22% a year. The reward-to-risk ratios of the S&P-GSCI and of the replicating portfolio are also of the same magnitude. Second, the annualized volatility of the replicating portfolio is undistinguishable from that of the S&P-GSCI (21.26%) and likewise for the rest of the risk measures. The correlation between the replicating portfolio and the S&P-GSCI stands at 0.9992 and is not significantly different from unity (t-statistic = -0.30). The tracking error is very small at 0.83% a year.6 The beta of the replicating portfolio relative to the S&P-GSCI at 0.9987 is insignificantly different from unity (t-statistic = -0.65).

Table II. Replication of S&P-GSCI and DJ-UBSCI

Note. The t-statistics in parentheses are for the null hypothesis that alpha is 0 and beta is 1. Significance at the 10% level denoted in bold.

56. Following the literature, tracking errors are measured as the annualized standard deviation of the residuals from a regression of our replicating portfolio on the S&P-GSCI; see Pope and Yadav (1994).

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The effectiveness of the S&P-GSCI replication constituent-by-constituent is documented in Appendix A, columns 3 (“GSCI”) and 4 (“GSCI replicated”). Most constituents are mimicked with highly precise accuracy. The largest discrepancy in annualized mean returns between the index and the replicating portfolio is found for lean hogs but it stands at merely 0.4% a year.

3.2 DJ-UBSCI Methodology and ReplicationIn order to replicate the DJ-UBSCI Excess Return Index (formerly known as DJ-AIGCI) we follow the DJ-AIGCI Index Handbook (2006). The DJ-UBSCI is both a liquidity- and production-weighted index of the prices of exchange-traded, physical commodity futures contracts. Contrary to the S&P-GSCI, the index was designed to achieve better diversification and less concentration into specific commodities. No commodity sector can have more than 33% allocation to the index and no individual commodity more than 15%.

The DJ-UBSCI historical weightings are depicted in Figure 2.

Figure 2. DJ-UBSCI weightings


Each month the index replaces the contracts that have near-term expirations with contracts that have more-distant expirations following a specific designated contracts table (see Table I, column 6). Some differences can be observed in the latter for the S&P-GSCI and the DJ-UBSCI. The energy sector rolls less frequently in the DJ-UBSCI, meaning that its energy contracts expire further away from the present. The roll-period of the DJ-UBSCI lasts 5 days and occurs on the 6th through the 10th business day of the month at a rate of 20% per day dollar-weighted.

The last two columns of Table II present summary statistics for the DJ-UBSCI and our replicating portfolio. The results suggest that the replication of the DJ-UBSCI is at least as good as that of the S&P-GSCI. The difference between the annualized mean returns of the DJ-UBSCI and the replicating portfolio is indeed very small at 0.1% a year and statistically insignificant at the 10% level. The alpha of the replicating portfolio against the DJ-UBSCI merely equals 0.1% a year which is borderline significant at the 10% level. The risk measures of the two portfolios are almost identical. The tracking error of the replicating portfolio is very small at 0.26%. The beta of the replicating portfolio relative to the DJ-UBSCI at 1.0003 is statistically not different from unity (t-statistic = 0.21). The correlation of the replicating portfolio with the DJ-UBSCI stands at 0.9998 and is not significantly different from unity either (t-statistic = -0.13). Appendix B documents the accuracy of the replicating exercise commodity by commodity. The largest discrepancy between the mean returns of the replicated and actual DJ-UBSCI constituents is observed for zinc, although it is no more than 0.55% a year.

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With this satisfactory replication exercise in place for the traditional S&P-GSCI and DJUBSCI, their methodology is next modified in “search” of alpha regarding when/where to roll, which designated contracts table to use, and/or which weighting scheme to follow. We first turn our attention to enhanced versions of the baseline indices that exploit momentum signals.

4. Momentum-Enhanced Indices4.1 MethodologyFollowing recent literature that documents momentum effects in commodity futures markets (Erb and Harvey, 2006; Miffre and Rallis, 2007; Shen, Szakmary and Sharma, 2007; Szakmary, Shen and Sharma, 2010), we design enhanced versions of the baseline S&P-GSCI and DJ-UBSCI that are based on price continuation. The presence of momentum implies that if a specific constituent performed well (or poorly) relative to its peers in the recent past, it is expected that it will continue to do so in the near future. To capture this pattern, the weightings of the best performers (called winners) over the preceding month are adjusted upwards and the weighting of the worst performers (called losers) over the preceding month are adjusted downwards. At the start of every roll-period (fifth business day of the maturity month for the S&P-GSCI or sixth business day for the DJ-UBSCI), we calculate the return of each constituent over the preceding month. We then rebalance the index to the original index weightings (S&P-GSCI or DJ-UBSCI) with the weighting adjusted upwards for a given constituent if its previous month’s performance was above the cross-sectional median performance and downwards if it was below the median. The long-only portfolio7 that over-weights winners and under-weights losers is held for one month. At the end of that holding period, we first reset the weights of the constituents of the momentumenhanced index back to the weights of the baseline index and, second, we recalculate the new weights adjusting the index weights upwards for the commodities with good past performance and downward for the commodities with poor past performance.

It is important to stress that the methodology assigns a higher or lower weight to a commodity depending on its past one-month performance, so that the percentage increase in the weighting of the commodity with the best past performance is higher than the percentage increase in the weighting of the commodity with the second highest performance and so forth. We use two different weighting schemes which are explained in turn below.

The first weighting scheme is based on the real relative performance of the constituents of the index. Hereafter, we refer to the index enhanced by this real momentum effect as Mom (real). The weights of the i=1,..,m constituents with previous month mean returns that are below or equal to the median are adjusted downwards as follows:

(1)

We measure all the new weightings for the commodities with mean returns below the median in order to calculate the maximum allowed increase in the weights for the contracts with above-themedian mean returns. The weights of the j=1,…,N-m constituents that have exhibited mean returns above the median over the preceding month are then adjusted as follows:

(2)

77 - The downward adjustment of each component’s weight is naturally limited since in our setting short-selling an index constituent is not possible.

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where the subscript i(=1 to m) refers to the constituents that have exhibited mean returns below-or-equal-to-median in the previous month, N is the total number of constituents for each index, t is the roll-date (5th or 6th business day according to the index), wreali,t is the real weighting of the i constituent after the adjustment on the t roll-date (wreali,t ≥ 0), woi,t is the original index weighting for the commodity at that roll-date, p is the percentage by which we want the weighting of the below-the-median commodities as a whole to fall. We adopt p= 50% so that if, say, the woi,t of the below-the-median commodities aggregated as a group is 50% (namely,

, we target to reduce it by 50% making . The mean return of constituent i over the preceding month in the below-or-equal-to-median group is denoted ri,t; hence, is the maximum of these mean returns and is the minimum.

Between roll-dates, the constituents’ weights evolve naturally according to performance as:

(3)

The weighting of the constituents in the real momentum-enhanced indices can be significantly influenced by past outliers (i.e., extreme performance). To mitigate this potential problem and to test the sensitivity of the results to the weight-adjustment method employed, we design a second approach where the weights are changing more gradually. This is accomplished by taking into account the relative performance of the index constituents instead of their absolute performance. We refer to indices enhanced by this gradual momentum approach, which is explained next, asMom (gradual) S&P-GSCI and Mom (gradual) DJ-UBSCI.

The weights of constituents with below-or-equal-to-median mean returns are adjusted using:

(4)

and we measure the new weightings for all the constituents of the below-the-median group in order to calculate the maximum allowed increase in the weights for the contracts with above-the-median mean returns. Second, the weights for the constituents with above-the-median mean returns are adjusted accordingly as follows:

(5)

where t, woj,t and p are as described above after equation (2); wgradi,t is the gradual weighting of constituent i after the adjustment on the t roll-date (wgradi,t ≥ 0), position is the ranking of the constituent. If the constituent is in the below-or-equal-to-median group, position takes the value of 1 for the asset with the worst performance, 2 for the second-worst performance asset and so forth. If the constituent is in the above-the-median group, position takes the value of 1 for the asset with the best performance, 2 for the asset with the second-best performance and so forth. Between roll-dates, weights evolve naturally according to their performance as in equation (3).

4.2 Performance and Risk Profile of Momentum-Enhanced IndicesTable III reports summary statistics for the momentum-enhanced S&P-GSCI and DJ-UBSCI using both weighting schemes (that is, real and gradual). To ease the exposition, the performance of the baseline S&P-GSCI and DJ-UBSCI (as in Table II) is also reported. Panel A presents summary statistics for the baseline and enhanced commodity indices. Panel B focuses on the spread between

the enhanced and baseline indices and thus it illustrates the performance of a long position in the enhanced portfolio combined with a short position in the baseline index.

Table III. Momentum-enhanced S&P-GSCI and DJ-UBSCI

Note. The t-statistics in parentheses are for the null that alpha is 0 (panel A), beta is 1 (panel A) and the arithmetic mean is 0 (panel B), significance at the 10% level denoted in bold.

Irrespective of the commodity index and weighting scheme considered, the enhanced indices perform better than the traditional ones; on a yearly basis the average outperformance amounts to 1.64% relative to S&P-GSCI and 1.75% relative to DJ-UBSCI. Similarly, the reward-to-risk ratios of the enhanced indices (at 0.2463 on average) are 60% higher than the baseline ones (at 0.1543 on average).8 The annualized alphas relative to the baseline indices range from 1.38% to 2.11%; two out of four alphas are significant at the 5% level. This confirms that the enhanced indices generate better mean returns than the traditional indices.

While outperformance is of interest, the main purpose of an index is to enable investors to get exposure to the ups and downs of a market. In order for this to be achieved, the risk profile of the enhanced indices should not be too dissimilar from that of the baseline indices. The small tracking errors of the enhanced indices relative to the baseline ones (ranging from 3.73% to 4.54% a year with an average at 4.17%) and their close-to-unity betas relative to the baseline indices bear this out. This is confirmed also by the correlations between the returns of the enhanced and baseline indices, ranging from 0.9575 to 0.9843, that are statistically not different from unity. In terms of volatility, kurtosis and 99% Cornish-Fisher Value-at-Risk (VaR), the probability distributions of the baseline and enhanced indices are virtually identical, while the skewness of the enhanced portfolios appears less negative than that of the baseline indices.

We should note that the enhanced indices tracking errors, although small, are higher than those reported for the baseline replication (0.54% on average; Table II). Similarly, the betas of the enhanced indices are less close to unity than those of the replicating portfolios in Table II. This is to be expected as the price to pay for enhanced performance. Yet the betas are close enough to

98 - Further increases in the reward-to-risk ratios can be achieved by taking long positions in the enhanced indices and shorting the baseline indices. Accordingly, the reward-to-risk ratios ofthe long-short portfolios in Table III, Panel B range from 0.3437 to 0.4472 with an average at 0.40.

109 - The roll-return is calculated as Rt={ln(Pt,1)- ln(Pt,2)}×( nt, 2- nt,1), where Pt,1 is the time t price of the nearest-to-maturity contract, Pt,2 is the price of the second-nearest contract, nt,1 (nt, 2) is the number of days between time t and the maturity of the nearby contract (second-nearby contract).

unity and the tracking errors sufficiently small to safely conclude that the enhanced portfolios mimic well the ups and downs of commodity markets.

Overall, the results presented in Table III show that the momentum-enhanced indices enable investors to obtain similar exposure to commodity markets as the one typically achieved via the baseline indices themselves and, in addition, they offer better performance. The ensuing sectionoutlines and assesses a novel enhancement approach that exploits the shape of the term structure of commodity futures prices.

5. Term, Structure-Enhanced Indices5.1 MethodologyFollowing Erb and Harvey (2006) and Gorton and Rouwenhorst (2006), who show that commodities with high roll-returns outperform commodities with low roll-returns, we examine the performance of the S&P-GSCI and DJ-UBSCI enhanced by signals taken from the term structure (TS) of commodity futures prices. Accordingly, if a constituent is in relative backwardation (namely, its roll-return9 is higher than that of its peers), it is expected to perform well in the future, so its weighting is adjusted upwards. Conversely, if a constituent is in relative contango (namely, its roll-return is lower than that of its peers), it is expected to perform poorly in the future, so its weighting is adjusted downwards. At the start of every rolling period (fifth or sixth business day according to the index), we measure the roll-return of the index constituents. We then rebalance each of the index constituents’ weightings upwards (downwards) if its roll-return is above (less than or equal to) the median roll-return. The long-only portfolio that over-weights high-roll commodities and under-weights low-roll commodities is held for one month. At the end of that holding period, we first reset the weights of the constituents of the TS-enhanced index back to the weights of the baseline index and then recalculate the new weights adjusting the index weights upwards for the commodities with above-the-median roll-returns and downward for the commodities with below-the-median roll-returns. As with the momentum-enhanced indices, we consider two different weighting schemes, one based on actual roll-returns and one that allows for a more gradual adjustment of the weights.

The first weighting scheme is based on the real roll-returns of the index constituents; hence, we refer to the resulting index as TS (real) hereafter. The weights of the constituents with below-or-equal-to-median roll-return are adjusted as follows:

(6)

and these new weightings enable us to calculate the maximum allowed increase in the weightsfor the contracts with above-the-median roll-returns. The weights of the j=1,…,N-m constituents with roll-returns above the median are then adjusted as follows:

(7)

where i (=1 to m) are the constituents that exhibit roll-returns below or equal to the median, N is the total number of constituents for each index; t, wreal, wo and p are as described after equation (2); rolli,t is the roll-return of the constituent i at the roll-date t, therefore and are, respectively, the maximum and minimum roll-return of the below-or-equal-to-median group constituents. Between roll-dates, weights evolve naturally according to (3).

To lessen the effect of outliers (i.e., extreme roll-returns) and to make the results robust to the weighting method, a second scheme is adopted that gradually adjusts the weights according toequations (4) and (5). This gradual weighting scheme resembles the momentum adjustment implemented above but the distinctive factor is now the roll-return on the roll-date instead of the mean return over the previous month. Hereafter, we refer to the resulting index as TS (gradual).

5.2 Performance and Risk Profile of Term Structure-Enhanced IndicesSummary statistics for the baseline and TS-enhanced S&P-GSCI and DJ-UBSCI are presented in Table IV. Regarding both performance and risk, the findings are broadly similar to those presented in Table III for the momentum-enhanced indices. For concreteness, the TS indices outperform the traditional ones by an average of 2.09% against the S&P-GSCI and 1.27% against the DJ-UBSCI; the spreads are statistically significant at the 5% level in three out of four cases. With a 2.45% annualized difference in mean returns against the S&P-GSCI, the TS (gradual) S&P-GSCI is ranking top (t-statistic = 2.62). In terms of risk-adjusted performance, the TS (gradual) S&P-GSCI is also leading with an annualized alpha of 2.66% (t-statistic = 3.33) and a reward-to-risk ratio of 0.3105 (versus 0.1730 for the baseline S&P-GSCI). The other TS-enhanced indices also present higher reward-to-risk ratios than their baseline counterparts alongside with positive alphas. A closer look at the statistics for the spread confirms the superiority of TS (gradual) S&P-GSCI which offers a reward-to-risk ratio of 0.5931. It is worth noting also that, in contrast with the momentum-enhanced indices, the gradual adjustment of weights has a more favorable effect on performance than the real adjustment.

Table IV. Term structure-enhanced S&P-GSCI and DJ-UBSCI


As in Table III for the momentum-enhanced indices, the TS-enhanced indices present higher tracking errors than those reported in Table II for the baseline replicating portfolios. The TS-enhanced index tracking error is 4.03% on average (Table IV), which is above the baseline index

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tracking error average at 0.54% in Table II. Similarly, the betas of the TS-enhanced indices depart more from unity, with an absolute deviation equal to 0.0338 on average, than the betas of the replicating portfolios in Table II with an average absolute deviation at 0.0008. This is to be expected since slightly worse tracking is the “flip side” for improved performance. Yet the betas of the TS-enhanced portfolios relative to the baseline indices range from 0.9445 to 1.0272, suggesting that these enhanced indices still follow quite well the ups and downs of commodity markets and are therefore suitable tools for strategic asset allocation. Similarly, the correlations between the baseline and TS-enhanced indices range from 0.9662 to 0.981110,10 suggesting also that the TS-enhanced indices mimic the baseline commodity indices with a high level of accuracy. This conclusion is reinforced by the virtually identical risk measures of the baseline and TS-enhanced indices, e.g., volatility, kurtosis, maximum drawdown and so forth.

So far the empirical analysis suggests that the momentum-enhanced and TS-enhanced commodity indices are useful tools for both strategic and tactical asset allocations. In other words, the enhanced indices offer investors superior performance relative to the baseline indices but a similar risk profile. Building on Fuertes, Miffre and Rallis (2010), we develop next a third novel type of index-enhancement that jointly exploits momentum and term structure signals.

6. Momentum and Term Structure-Enhanced indices6.1 MethodologyIf a specific index constituent presents higher roll-returns (term structure) and better past performance (momentum) than its peers, it is expected to keep on performing well in the near future, so its weight is adjusted upwards. On the contrary, if a constituent presents lower roll-returns and worse past performance than its peers, it is expected to keep on performing poorly in the near future, so its weight is adjusted downwards. Accordingly, the long-only portfolio that over(under)-weights high roll commodities with good (poor) past performance is held for one month. At the end of that holding period, the weights of the enhanced index constituents are reset back to the baseline index weights and then these weights are upward/downward adjusted.

In the weighting scheme based, first, on momentum and, second, on term structure (hereafter, Mom/TS), we first sort the constituents according to their previous month’s mean returns and calculate the median mean return. Accordingly, the commodities are then allocated into two groups (above and below the median) and the weightings of the winners (losers) are adjusted upwards (downwards). In this scheme, however, instead of relying on past performance as in equations (1) and (2), we calculate the new weighting relative to the roll-returns of the commodities within the group as in equations (6) and (7). Therefore, we weight the commodities according to both their roll-returns and one-month past performance. For example, if the S&P-GSCI allocates x% to corn and corn pertains to the winner portfolio, our enhanced strategy will allocate more than x% to corn with the exact weighting calculated as in equation (6). On the contrary, if the S&P-GSCI allocates y% to wheat and wheat belongs to the loser portfolio, our enhanced strategy will allocate less than y% to wheat, with the exact weighting calculated as in equation (7). As with the momentum-only and TS-only enhanced indices beforehand, we consider two types of weight adjustments. The terminology Mom/TS (real) and Mom/TS (gradual) refers to indices based on the real and gradual weighting schemes, respectively.

There is no reason, a priori, for sorting, first, on past performance and, second, on rollreturns. Hence, we also implement the above double-signal strategy in reverse order. In the TS/Mom case, we first sort the index constituents relative to their roll-returns and calculate the median roll-return. We divide the cross-section into two groups based on this median and adjust the baseline weightings inside each group according to the previous month’s mean returns of the commodities as in equations (1) and (2). The empirical results presented below are for both the TS/Mom (real) and TS/Mom (gradual) commodity indices.

10. The t-statistic was systematically unable to reject the hypothesis that these correlations equal 1 at the 5% level.

6.2 Performance and Risk Profile of Momentum and Term Structure-Enhanced IndicesSummary statistics for the commodity indices enhanced jointly by momentum and TS signals are set out in Table V. Thus far these strategies generate the best performance measures. The enhanced indices outperform the baseline indices by an average of 2.09% a year (versus 1.69% for the momentum-only indices and 1.68% for the TS-only indices). The alphas of the enhancedindices that combine momentum and term structure signals (at 2.13% on average) are also higher than those of the momentum-only and TS-only indices (at 1.71% and 1.76% a year, respectively). Of these eight alphas, four are strongly significant at the 1% level and two more are significant at the 5% or 10% level. Similarly, the reward-to-risk ratios of the momentum and TS-enhanced indices (at 0.2755 on average) are higher than those of the enhanced indices that exploit either of the two signals individually (at 0.2463 for momentum-only and 0.2540 for TS-only) and are also notably superior to those of the baseline indices (at 0.1543). The leading enhanced index is TS/Mom (real) S&P-GSCI with a mean spread at 3.27% (t-statistic = 3.45) and an annualized alpha at 3.43% (t-statistic = 3.75). Investors prepared to take short as well as long positions in commodity futures markets can reap a maximum reward-to-risk ratio of 0.7863 for the spread (Panel B), considerably higher than that for the index at 0.1730 (Panel A).

Table V. Momentum and term structure-enhanced S&P-GSCI and DJ-UBSCI


Regarding the risk profile of the double-signal enhanced indices, we observe higher tracking errors than for the baseline replication. Nevertheless, at 3.77% on average these tracking errorsare still relatively small. A noteworthy feature is that they are slightly lower than those reported in Tables III and IV when either of the two signals is individually exploited (4.17% for momentum-only and 4.03% for TS-only). The absolute departure from unity of the betas of the combined enhanced indices averages out at 0.0295 (versus 0.0311 for the momentum-only indices in Table III and 0.0338 for the TS-only indices in Table IV). This suggests that the enhanced indices based on the combined (momentum and term structure) signals follow the ups and downs of the baseline indices better than the indices based on the individual signals.

Similarly, the correlations between the baseline and enhanced indices remain high, ranging from 0.9690 to 0.9849. At 0.9767 on average, these correlations are slightly above those in Tables III and IV for the momentum-only indices at 0.9716 and for the TS-only indices at 0.9734.

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Figures 3 to 5 illustrate the time evolution of the weights allocated to the commodity futures included in the best momentum-enhanced and TS-enhanced S&P-GSCI.11 The weights of these enhanced indices are clearly more volatile than those of the baseline index (see Figure 1), warning that part of the incremental performance of the former may be a compensation for an increase in transaction costs while replicating the indices. We are reasonably confident, however, that the additional trading required in order to mimic the momentum and/or TS-enhanced indices will not wipe out their incremental mean returns and alphas. As highlighted in Fuertes, Miffre and Rallis (2010), the cost of trading commodity futures is indeed negligible (less than 0.033%), the cross-section on which the strategies are implemented is small (up to thirty commodities) and the assets that are being traded are in the front-end of the curve, thus very liquid. All these aspects support our contention that the alphas should not fade away net of transaction costs.12

Figure 3. Momentum-enhanced S&P-GSCI weightings (top performing strategy)


Figure 4. TS-enhanced S&P-GSCI weightings (top performing strategy)


11 - To preserve space, the weights of the enhanced versions of the DJ-UBSCI are not plotted but the information is available upon request. The qualitative conclusion we draw for the S&PGSCIcan be extended to the DJ-UBSCI.12 - The difference between the gross and net mean returns in Fuertes, Miffre and Rallis (2010) equals 0.65% across the momentum and/or term structure-sorted portfolios with ranking and holding periods of 1 month. The cost of tracking the adopted benchmark equals 0.21% a year. Thus the average incremental cost of tracking the enhanced indices as opposed to the mainstream benchmark can be approximated to the difference between these two costs at 0.44%. If this transaction cost estimate is applied in the present context, the average annualized alphas net of transaction costs are still high at 1.26% for the momentum-enhanced indices, 1.32% for the TS-enhanced indices and 1.69% for the momentum and TS-enhanced indices.

Figure 5. Momentum and TS-enhanced S&P-GSCI weightings (top performing strategy)


Overall, this comprehensive comparison provides relevant evidence for passive portfolio managers that are contemplating the use of enhanced indices for strategic asset allocation. Momentum- and TS-enhanced indices are successful at mimicking the ups/downs of commodity markets and are therefore as appropriate for risk diversification and inflation hedging as the baseline indices. In addition, the enhanced indices perform better than the baseline ones on a risk-adjusted basis and as such can also be useful tools for tactical asset allocation. Last but not least, in the subsequent section we investigate the absolute and relative merit of exploiting the time-to-maturity of the contracts as another enhancing signal.

7. Maturity-Enhanced Indices7.1 MethodologyProviders of first-generation indices typically roll positions from the front to the second contract on pre-defined schedules. This methodology, however, does not take into account the shape of the term structure of commodity prices nor the fact that the volatility of forward prices rises as contracts approach maturity (Samuelson, 1965; Daal, Farhat & Wei, 2006). Consequently, traditional indices can exhibit significant roll-losses, extreme volatility and returns that can be quite different from commodity spot returns. This section takes our analysis one step further by investigating the role of the maturity of the contracts on the performance of the S&P-GSCI and DJ-UBSCI. Our objective here is to assess whether maturity signals can enhance index performance and yet produce enhanced indices that are still sufficiently correlated with the baseline indices so as to provide comparable diversification benefits.

More specifically, instead of rolling the constituents as in the traditional S&P-GSCI and DJ-UBSCI methodologies, the idea is to roll into the specific contracts in the term structure of each constituent that give us an three maturity (expiry) of either three, six, nine or twelve months. Taking aluminum as an example, the three-month maturity S&P-GSCI spends on average over the whole sample 69% of the time on the third contract and 31% of the time on the fourth. As a result, its average time-to-maturity is 2.83 months. Similarly, the six-month S&P-GSCI targets six-month maturity contracts. In the case of aluminum, this implies holding an investment with an average time-to-maturity of 5.82 months, holding the sixth month contract 69% of the time

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and the seventh month contract 31% of the time. Details on the target maturities and time spent in each contract can be found in Appendices 1 and 2, columns 5 to 8. For some commodities it is simply feasible to hold contracts very far inside the term structure either because these contracts do not exist at all or because they did not exist at some point in the sample period; in this setting, it is typical to ignore commodities that lack contracts on the far end of the curve (e.g., five-year UBS Bloomberg Constant Maturity Commodity Index). Seeking to achieve good diversification properties and maintain high correlations with the baseline indices, we take a different route and include all commodities by focusing on the contracts that are the closest to the target maturity.

Finally, it is important to note that the weightings for each commodity in the maturity-enhanced indices are identical to those used by the index providers themselves given that our purpose here is to isolate the impact of time-to-maturity on index performance.

7.2 The Performance and Risk Profile of Maturity-Enhanced IndicesThe performance of the baseline and maturity-enhanced commodity indices is summarized in Table VI. It turns out that the further away from the present the maturity of the contract is, the better the performance of the enhanced indices. The annualized mean return is 3.68% for the S&P-GSCI and ranges between 8.66% (three-month) and 8.83% (twelve-month) for the maturity-enhanced S&P-GSCI; likewise, the annualized mean return at 1.97% for the DJ-UBSCI is improved monotonically by the maturity-enhanced counterpart indices from 4.97% (three-month) to 6.29% (twelve-month). All the spreads between the maturity-enhanced indices and their baseline counterpart are strongly significant at the 1% (six cases) or 5% level (two cases). Similarly, the annualized alphas tend to rise as the contracts get further inside into the curve; they range from 5.15% (three-month) to 6.18% (twelve-month) for the maturity-enhanced S&P-GSCI and from 2.99% (three-month) to 4.72% (twelve-month) for the maturity-enhanced DJ-UBSCI. All eight alphas are strongly significant at the 1% level. The reward-to-risk ratios also rise with the contract time-to-maturity, ranging from 0.3595 to 0.5753, and compare favorably to those of the baseline indices (0.1730 and 0.1356 for the S&P-GSCI and DJ-UBSCI, respectively). The best performing maturity-enhanced index is the twelve-month S&P-GSCI: its reward-to-risk ratio is 3.33 times that of the baseline S&P-GSCI and its alpha is economically and statistically significant at 6.18% a year (t-statistic= 3.35). Concerning the spreads (Table VI, Panel B), investors willing to take long positions in the maturity-enhanced indices as well as short positions in the baseline ones may want to consider the three-month enhanced S&P-GSCI or the three-month DJ-UBSCI (which offer the highest reward-to-risk ratios of 0.9838 and 1.3479, respectively, in Panel B).

Table VI. Maturity-enhanced S&P-GSCI and DJ-UBSCI


Noticeably, out of the four distinct commodity index-enhancing approaches we have developed, the one based on the time-to-maturity signals stands out by offering the best performance. The annualized alphas in Tables III to VI average out at 1.71% for the momentum-enhanced indices, 1.76% for the TS-enhanced indices, 2.13% for the combined momentum and TS-enhanced indices and 4.93% for the maturity-enhanced indices. Hence, the time-to-maturity of the contract emerges as a key factor to enhance performance.

Given that their performance is visibly better, it is not surprising to see that the average tracking error of the maturity-enhanced indices is also higher than that documented in Table III to Table V (4.50% a year versus 3.93% on average for the momentum and/or TS-enhanced indices). Similarly, the average beta of the maturity-enhanced indices departs more from unity in absolute terms than the average beta of the momentum and/or TS-enhanced indices (0.2162 in Table VI versus 0.0309 on average in Tables III to V). Higher tracking errors and higher absolute deviation of the betas from unity are indeed the price to pay for improved performance. Nevertheless, the pairwise correlations between the returns of the maturity-enhanced indices and the baseline indices remain reasonably high (ranging from 0.9130 to 0.9898 with an average of 0.9467). These findings indicate that the maturity-enhanced indices still mimic reasonably well the commodity markets, despite worse readings on tracking errors and betas, and thus are appropriate tools for strategic asset allocation (i.e., risk diversification and inflation hedging). This point is formally revisited in the next section.

Table VI (Panel A) shows that the further away from the present the maturity of the contract is, the lower the volatility of the maturity-enhanced index. For example, the annualized standard deviation of the baseline S&P-GSCI stands at 21.26%, while those of the three-month, six-month, nine-month and twelve-month S&P-GSCI stand at 19.11%, 16.91%, 15.78% and 15.35%, respectively. Similarly, the maturity-enhanced indices present lower 99% VaR and higher minimum twelve-month rolling returns. These results are consistent with Samuelson’s (1965) maturity effect suggesting that the volatility of futures prices increases as contracts approach maturity. While in terms of volatility (i.e., second moment of the returns distribution) the maturity-enhanced indices are less risky than their traditional counterparts, this is not the case in terms of third and fourth moments: their negative skewness and their kurtosis are more salient than those of the baseline indices.

Appendices A and B, columns 5 to 8, present summary statistics for the constituents of the maturity-enhanced S&P-GCSI and DJ-UBSCI. A common thread of the two indices is that the mean return of the constituents tends to increase and the volatility to decrease as the maturity of the contracts rises. The most outstanding constituent (in terms of both higher mean return and lower volatility) is natural gas with an annualized difference in mean returns of 24.77% between the twelve-month S&P-GSCI and the baseline S&P-GSCI or 11.57% between the twelve-month DJUBSCI and the baseline DJ-UBSCI. As the maturity of the contracts increases, the volatility of the natural gas contracts decreases (from 45.4% for the baseline DJ-UBSCI to 22% for the twelve- month DJ-UBSCI) in line with Samuelson’s (1965) maturity hypothesis. For both the S&P-GSCI and the DJ-UBSCI, the contracts on Brent crude, lean hogs, wheat, live cattle, corn and gasoline follow in showing better performance over the medium to the longer end of the term structure. Precious metals do not present much differentiation in mean returns along the curve.

8. Risk Diversification and Inflation HedgingThe empirical analysis in the preceding sections has documented that the enhanced indices havebetas close to unity and very high correlations with the traditional benchmarks. Hence, a tentative conclusion is that the enhanced indices are as useful as the baseline indices for strategic asset allocation (i.e., risk diversification and inflation hedging). In order to make this conclusion robust,

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we collect monthly observations from Datastream on thirteen traditional asset classes (as proxied by six J.P.Morgan fixed income indices with different durations or countries of issuance and seven international equity indices with different styles) and quarterly observations on inflation.

Table VII reports the pairwise return correlations between the baseline and enhanced commodity indices and the aforementioned 13 traditional asset classes. The average correlations between the baseline indices and the traditional asset classes equal 8.14% for the S&P-GSCI (in Panel A) and 17.15% for the DJ-UBSCI (in Panel B). At first sight, these averages are very close to those reported for the enhanced indices (8.11% and 16.38%, respectively). Formal tests indicate that the degree of correlation observed between the baseline indices and the traditional asset classes remains virtually unchanged when the enhanced indices are used instead.13 This formally reinforces our first impression that the enhanced indices are as useful for risk diversification as their baseline counterparts.

Table VII. Diversification and inflation hedging properties

Note. βUI is the slope coefficient of a regression of each index on unexpected inflation; t(βUI) is the t-statistic; R² is the regression goodness-of-fit statistic.

Another crucial strategic role that commodity indices play is as inflation hedging tools; e.g., see Bodie (1983). Indeed, the results reported on the right-hand side of Table VII indicate that the correlations between unexpected inflation and the traditional benchmarks are high (0.47 and 0.43 for the baseline S&P-GSCI and DJ-UBSCI, respectively) and that their inflation betas are positive and significant at the 1% level.14 Interestingly, the average correlations between unexpected inflation and the enhanced indices are equally high (0.48 for the S&P-GSCI and 0.43 for the DJ-UBSCI) and the inflation betas are very close to those reported for the baseline indices. This confirms our first intuition that the enhanced indices are as good a hedge against inflation shocks as their baseline counterparts.

9. ConclusionsUntil relatively recently, investors interested in passively holding commodities as part of their strategic asset allocation have invested in first-generation commodity indices such as the S&P-GSCI or the DJ-UBSCI (formerly called DJ-AIGCI). However, these indices are currently regarded as sub-optimal for several reasons. For example, they rebalance too infrequently, they consider only the front end of the term structure of commodity futures prices and they fail to take into account

13 - In each case, we tested the null hypothesis that the correlation between a baseline index and a traditional asset class is identical to that between an enhanced index and the same traditional asset class. The unreported t-statistics are very small ranging from -0.92 to 0.62 and systematically fail to reject the null hypothesis.14 - Unexpected inflation is measured quarterly as the spread between the percentage change in the consumer price index (CPI) and the one-year moving average of the percentage CPI change. The choice of a quarterly frequency follows from Bodie and Rosansky (1980) and Gorton and Rouwenhorst (2006).

features such as past performance and roll-returns that have been shown to be important drivers of commodity futures prices (Erb & Harvey, 2006; Gorton & Rouwenhorst, 2006; Miffre & Rallis, 2007). Since the inception of the Deutsche Bank Liquid Commodity Index in 2003, a plethora of second-generation indices has emerged, each of them attempting to offer investors both a faithful exposure to commodity markets and enhanced performance. As a result of this index proliferation, it has become increasingly bewildering for investors to formally choose among competing indices. The purpose of this article is to contribute to the literature by presenting a comprehensive study of the performance and risk of the baseline S&P-GSCI and DJ-UBSCI and four enhanced versions thereof that exploit signals based on 1) momentum, 2) term structure, 3) a combination of the two, or 4) the time-to-maturity of the contracts.

The main conclusions we can draw are threefold. First, regarding risk diversification and inflation hedging, the enhanced S&P-GSCI and DJ-UBSCI are as good tools for strategic asset allocation as the baseline indices themselves. Second, with alphas ranging from 0.49% to 6.18% a year, the enhanced indices outperform the baseline S&P-GSCI and DJ-UBSCI and therefore they can also be utilized for tactical asset allocation. Third, the leading enhanced index in terms of outperformance relative to its baseline index is characterized by targeting maturities far away from the present up to twelve months, suggesting that the time-to-maturity of the contracts is the most promising signal to exploit, among the ones here considered, for tactical asset allocation.

Possible extensions of this study for future research include the design of long-only maturity-enhanced indices that assign higher weights to commodities with high past performance and above-average roll-returns and lower weights to commodities with low past performance and below-average roll-returns. The combination of the three signals might prove profitable. Moreover, digging deeper into the financial mechanisms as to why the maturity-enhanced indices perform so well is warranted. The outperformance could be due in part to a lack of liquidity of the contracts located on the mid- and back-end of the term structure and thus to higher transaction costs. A rigorous analysis of the net performance of the enhanced indices is no doubt an interesting avenue for further research.

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References• Akey, R. (2005). Commodities: A case for active management. Journal of Alternative Investments, 8, 2, 8-29.

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Appendix A. Analysis of the S&P-GSCI constituent-by-constituent

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Note. An.Ret denotes the annualized arithmetic mean, Real Ret denotes the annualized geometric mean, SD is the annualized standard deviation, Min R/Max R are the minimum return /maximum return

Appendix B. Analysis of the DJ-UBSCI constituent-by-constituent

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Note. An.Ret denotes the annualized arithmetic mean, Real Ret denotes the annualized geometric mean, SD is the annualized standard deviation, Min R/Max R are the minimum return/maximum return.

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