Carry on commodity futures contains information on implicit subsidies, such as convenience yields and hedging premia. Its precision as a trading signal improves when incorporating adjustments for inflation, seasonal effects, and volatility. There is strong evidence for the predictive power of various metrics of real carry with respect to subsequent future returns for a broad panel of 23 commodities from 2000 to 2023. Furthermore, stylized naïve PnLs based on real carry point to material economic value, either independently or through managing commodity long exposure. The predictive power and value generation of relative carry signals seem to be even more potent than that of directional signals.

The below post is based on proprietary research of Macrosynergy. It follows on from the “Commodity carry as a trading signal – part 1”.

A **Jupyter notebook for audit and replication** of the research results can be downloaded here. The notebook operation requires access to J.P. Morgan DataQuery to download data from JPMaQS, a premium service of quantamental indicators. J.P. Morgan offers free trials for institutional clients. Also, there is an academic research support program that sponsors data sets for relevant projects.

The post ties in with this site’s summary of implicit subsidies, particularly the section on commodity futures.

## Carry factors and adjustments

Commodity carry is the return on a long futures position that would accrue if all prices along the curve remained unchanged. A futures curve in backwardation implies positive carry. A curve in contango implies negative carry. __The shape of the curve is partially influenced by non-standard risk premia (implied subsidies), such as those that arise from convenience yields, i.e., benefits from holding physical stocks, and hedging pressure__, i.e., the willingness of consumers or producers to pay extra for locking in a future price. However, the commodity futures curve also prices expected demand and supply imbalances in conjunction with storage costs. These lead to intertemporal market segmentation and do not imply premia but rather reflect rational predictions of cash prices (view post here).

Since carry partially reflects premia, it is a valid building block for trading factors. But since expected cash price dynamics also influence it, it is a noisy signal. Several types of adjustments reduce the noise:

**Inflation adjustment**produces “real carry,” accounting for price drifts related to macroeconomic price drifts.**Adjustment for futures price volatility**scales the carry in terms of statistical risk and makes the carry more comparable across commodities and periods.**Seasonal adjustment**of commodities with storage costs and regular supply or demand patterns over the year removes a component of commodity carry that is unrelated to premia.**Normalization and winsorization**(containment of values at a threshold) adjust carry for its own volatility and discount large data outliers that are typically related to short-term distortions.

For details of these adjustments and consequences for the statistical properties of carry, see a previous post here. In this post, we investigate whether various versions of adjusted carry have displayed significant predictive power for commodity futures returns and if related naïve strategies would have generated material excess returns. The metrics considered are:

- vol-targeted normalized and winsorized real carry (seasonally adjusted and non-adjusted)
- vol-targeted real carry (seasonally adjusted and non-adjusted)
- normalized and winsorized real carry (seasonally adjusted and non-adjusted)
- real carry (seasonally adjusted and non-adjusted)

Where a single metric is shown in a graph or used as the main reference, the “fully adjusted carry” is chosen, i.e., the normalized and winsorized seasonally adjusted and volatility-targeted real carry.

__Tests are run on a panel of 23 commodities for the period 2000 to 2023 (November).__ The commodity groups considered here are fuels, base metals, precious metals, and agricultural commodities. For a complete list of the commodity futures contracts and the acronyms used in the charts below, see the annex below. Since return variation across commodities has been sizeable, the target for all below analysis is vol-targeted returns, i.e., commodity futures returns for positions that are scaled to 10% annualized standard deviations based on an exponential moving average of returns with a half-life of 11 days. Positions are rebalanced at the end of each month.

## Commodity carry as a directional signal

There is pervasive and convincing evidence that real commodity carry has been a predictor of futures returns. The Macrosynergy panel correlation test (view post here) suggests that __fully adjusted carry has been a predictor of subsequent commodity futures returns at a weekly, monthly, or quarterly frequency with less than 0.1% chance that these relations have been accidental__. Indeed, all real carry metrics that adjust for outliers post highly significant positive forward linear correlation, according to the standard Pearson measure. Moreover, all real carry versions, without exception, show highly significant non-parametric positive forward correlation according to the Kendall measure.

Also, balanced accuracy, i.e., the average ratio of correct positive and negative month-ahead predictions of the sign of returns, has been well above 50%. Balanced accuracy ratios have been at 52.8-52.9% for all seasonally adjusted carry metrics. For the non-adjusted versions, they have been 51.8-51.9%. Generally, __seasonally adjusted carry metrics have outperformed non-adjusted carry for all performance metrics and all carry versions__.

Correct sign predictions have been prevalent over time. Balanced accuracy of the fully adjusted carry has been above 50% in 83% of all calendar years since 2000.

Across different commodities, fully adjusted carry has recorded above 50% monthly balanced accuracy for 74% of all markets. Simple accuracy has been above 50% in 87% of all markets. Indeed, __there have only been two markets where both accuracy and balanced accuracy of monthly return predictions have been below 50%: gold and zinc__.

We have calculated __naïve profit and loss series (PnLs) based on the various real carry metrics for signals across all 23 markets and by standard rules used in previous posts__. These PnLs take monthly volatility-adjusted positions in each market in accordance with the carry metric, contained at two standard deviations, as a realistic risk and concentration limit. Positions are updated at the beginning of each month based on the carry signal at the end of the previous month and allowing for a 1-day implementation delay for trading. The naïve PnL does not consider transaction costs or compounding because those depend on assets under management and institutional rules. PnLs are scaled to an annualized volatility of 10% for representation in charts. PnL correlation with global market risk is measured based on the returns of a global directional risk basket, a volatility-weighted composite of equity index futures, credit default swap indices, and FX forwards published by JPMaQS (view documentation here).

__A fully adjusted carry signal would have produced a PnL with a naïve Sharpe ratio of 0.45, a Sortino ratio of 0.64, and a near-zero correlation with returns of a global directional risk basket__. Thus, it is a plausible diversifier of a long-risk cross-asset portfolio. For comparison, a simple long-only risk parity portfolio, giving equal vol-adjusted weight to all 23 commodity futures, would have earned a long-term Sharpe of 0.35 but with an above 40% correlation with the returns of a global directional risk basket.

Performance differences across different real carry versions have been modest, with long-term PnL Sharpe ratios all between 0.30 and 0.54 and Sortino ratios between 0.42 and 0.76 since 2000. Also, global risk correlation has been near zero for all types of carry.

__All carry signals have had a modest short bias since 2000, and none displayed a systematic correlation with the long commodity book__. Hence, carry is a valid complement to a long-only risk parity strategy, managing the long exposure across time and across markets. For assessing the value of such “managed long exposure,” we add one standard deviation to the normalized carry signals of the naïve PnL generator, which means that the ratio of long positions is expected to be above 84%.

__All versions of adjusted commodity carry would have enhanced the performance of such long biased commodity market exposure relative to the risk parity approach__, lifting the long-term Sharpe ratio from 0.36 to a range of 0.45 to 0.57 and the long-term Sortino ratio from 0.49 for the risk parity book to a 0.61-0.78 range.

## Commodity carry as a global relative signal

__Relative here means taking positions in one commodity futures versus an equal risk-adjusted opposite in a basket of all commodity futures__. A relative strategy of this type ensures that the book never intentionally holds an aggregate net long exposure to commodities and, thereby, mitigates the many directional commodity market disturbances that affect PnLs but have no relation to carry. The flip side is the need for enhanced leverage and the increase in basis risk, i.e., unexpected exposure to market directional forces that arise from the mis-prediction of volatilities.

For relative signals, we can reasonably only consider vol-targeted carry for the sake of making cross-commodity positions comparable. As for directional carry, the predictive power of relative carry signals for subsequent relative returns has been positive and highly significant across different frequencies. __The positive forward correlation of fully adjusted relative carry with subsequent relative vol-adjusted returns has been higher than for the directional case__. Also, the positive correlation at a monthly frequency has prevailed in commodity futures panels in 21 of 24 years since 2000 and was often highly significant despite the small size of annual datasets.

Balanced monthly accuracy has been a bit higher in the relative case than the directional case, at 53.5-53.7% for seasonally adjusted metrics and 52.1-52.8% for unadjusted carry measures. Above-50% balanced accuracy has been recorded in 20 of 24 recorded years.

Naïve PnL value generation was spectacular in 2000-2013 but flattened thereafter, particularly for signals without seasonal adjustment. This is an __example of strong seasonality, which is a characteristic of many single-concept macro trading signals__.

Overall performance ratios of the relative value carry signal have been materially higher than for directional strategies, with __Sharpe ratios in a range of 0.48 to 0.78 and Sortino ratios between 0.69 and 1.11__. Correlation coefficients of all relative carry strategies with the global directional risk basket return have been low (3-7%).

## Commodity carry as an intra-group relative signal

__An alternative to global relative positioning is intra-group relative positioning__. As distinct groups, we choose here precious metals (gold, silver, palladium, and platinum), base metals (aluminum, copper, lead, nickel, tin, and zinc), fuels (Brent, WTI, natural gas, gasoline, and heating oil), U.S. corn belt crops (cotton, corn, soy, and wheat), and other agricultural commodities (coffee, sugar, orange juice, and lumber).

Groupwise relative positioning and signaling filter out more non-carry-related return factors from the strategy PnL and, hence, should increase the carry influence. However, it further enhances required leverage, trading costs, and increases basis risk.

__The predictive correlation of fully adjusted carry with subsequent returns has been stronger for intra-group relative signals and positions__ than for global relative variables for all carry metrics and both parametric and non-parametric correlation measures. Also, the significance of predictive correlation has been higher and a bit more consistent across the years.

However, the balanced accuracy of the prediction of monthly return direction was in a range of 52-53%, a bit lower than for the global relative signals.

__Naïve PnLs based on intra-group relative carry signals have been more consistent value generators than those based on “global” relative PnLs__. The seasonally adjusted carry metrics have produced __long-term Sharpe ratios of 0.71-0.84 and Sortino ratios of 1.07-1.24__, with 5-10% correlation to the global directional risk basket. Relative carry without seasonal adjustment would have produced significantly lower performance ratios, with Sharpe ratios just above 0.5 and Sortino ratios around 0.75.

## Annex: commodity contracts and acronyms

For this post, we looked at five commodity groups: energy, base metals, precious metals, and agricultural commodities.

The energy commodity group contains:

- BRT: ICE Brent crude
- WTI: NYMEX WTI light crude
- NGS: NYMEX natural gas, Henry Hub
- GSO: NYMEX RBOB Gasoline
- HOL: NYMEX Heating oil, New York Harbor ULSD

The base metals group contains:

- ALM: London Metal Exchange aluminium
- CPR: Comex copper
- LED: London Metal Exchange Lead
- NIC: London Metal Exchange Nickel
- TIN: London Metal Exchange Tin
- ZNC: London Metal Exchange Zinc

The precious metals group contains:

- GLD: COMEX gold 100 Ounce
- SIV: COMEX silver 5000 Ounce
- PAL: NYMEX palladium
- PLT: NYMEX platinum

The agricultural commodity group contains:

- COR: Chicago Board of Trade corn composite
- WHT: Chicago Board of Trade wheat composite
- SOY: Chicago Board of Trade soybeans composite
- CTN: NYBOT / ICE cotton #2
- CFE: NYBOT / ICE coffee ‘C’ Arabica
- SGR: NYBOT / ICE raw cane sugar #11
- NJO: NYBOT / NYCE FCOJ frozen orange juice concentrate
- CLB: Chicago Mercantile Exchange random-length lumber