In the context of declining commodity prices following the global financial crisis, inverse indices became popular for market participants looking to profit from negative returns. As the oil war unfolded and drove commodity prices further down, market participants took a renewed interest in using inverse indices to bet against the market. When commodities rebounded last year, market participants remained opportunistic, demanding leveraged indices for the potential to earn extra in the comeback by doubling down. However, there have been some questions and observations about the performance of inverse and leveraged indices as their popularity has increased.

**Why is the performance of the inverse indices not exactly opposite from the standard, long-only versions? **The inverse performance is exactly opposite the standard, long-only indices, but only for the stated period. For example, most of the inverse indices have a daily rebalance, which means the daily return of the inverse excess return index will be opposite from the standard excess return. However, when these returns are compounded, a performance difference arises that is beneficial in trending markets. Exhibit 1 shows a simple example of the performance impact of two daily consecutive positive moves and two daily consecutive negative moves. Note that there is an arbitrage opportunity for market participants if they pursue both strategies during trending times; when there are two consecutive negative moves, the inverse index gains more than the standard index loses, and if there are two consecutive positive moves, the standard index gains more than the inverse index loses. The magnitude of the consecutive losses and gains does not matter for this relationship to hold.**What happens to the cumulative returns when the daily returns move in opposite directions? **In this case, the magnitude of the returns matters, but not the order. If a market participant were to pursue both strategies, it would likely be a losing proposition in a choppy market. The only way to profit is by picking whether the larger absolute return will be positive or negative and using the standard long index for the larger absolute positive return and the inverse index, which is like a short position, for the larger absolute negative return. If the magnitudes of the opposite consecutive returns are the same, the directional order makes no difference, as shown in the first column of Exhibit 2, and there is a certain loss for both the standard and inverse indices. However, there is a chance to win if opting for only one strategy with a correct bet on the bigger absolute return, regardless of order.**What conclusions can be drawn for 2x leveraged indices when daily returns are compounded? **Similar results are observed when comparing the standard indices to the 2x leveraged indices, which double the daily return. The compounded returns when there are two days of consecutive losses or gains show that the 2x leveraged version has a better payoff profile, since it loses less than double the standard index return but gains more than double. If a market participant is sure about commodity trends over time, then the 2x leveraged index may be a winning bet, even if the direction is uncertain.

However, if the daily returns move in opposite directions, then the magnitude matters. For returns of the same magnitude moving in opposite directions, the 2x leveraged version magnifies the loss by more than a factor of two, as shown in Exhibit 3. Also, the gain in the 2x leveraged index is less than double when the magnitude of the positive return is larger than the magnitude of the negative return, while the loss is more than double when the magnitude of the negative return is bigger than the magnitude of the positive return. Again, unless a market participant picks the direction of the big move, the standard index may be the better choice in a choppy market.**Are there some commodities that trend more than others, and might be advantageous in a 2x leveraged or inverse version? **The most popular commodities used in 2x leveraged and inverse indices for products are Brent crude, copper, corn, WTI crude oil, gold, natural gas, silver, and soybeans.

From Jan. 2, 2007, to March 24, 2017, each of these commodities trended nearly 50% of the time. Corn trended the most, exactly 50% of the time, while copper and silver trended the least, around 46% of the time. During trending days, silver and gold posted the highest percentage of consecutive positive returns, 55% and 53%, respectively, while natural gas posted the highest percentage of consecutive negative returns, spending 54% of its trending time with consecutive losses.

Most of the commodities had larger positive returns than negative returns on opposite consecutive days, with gold and soybeans each recording 54% of consecutive opposite direction days with a larger gain than loss. Corn, the most-trending commodity, showed 52% of its non-trending days with a bigger gain than loss. Copper, one of the least-trending commodities, had 51% of non-trending consecutive days with bigger losses than gains, as did natural gas.

Given that **corn** trended the most and had relatively large gains to losses on opposite days during the period studied, it may be the best overall commodity choice for 2x leveraged and inverse indices. **Natural gas** may be a strong choice for an inverse index, based on its high consecutive negative returns and high losses in opposite consecutive daily returns. **Copper** also had more losses on opposite days, which may be beneficial in its inverse version. Lastly, **gold **and **silver **may be good choices for the 2x leveraged indices, based on their high positive consecutive return rates, even though silver was more choppy than trending.

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