Analyzing Returns and Index Construction

An investor who desires long exposure to a commodity price will typically achieve this exposure through a derivative investment in forwards or futures. Some physical commodities cannot be effectively purchased and stored long term, and for others, such as precious metals, derivative positions may be a more efficient means of gaining long exposure than purchasing the commodities outright and storing them long term.

The return on a derivatives position is not the same as the return on a commodity itself. The total return on a fully collateralized long futures position has three components: collateral return, price return, and roll return.

To take a position in futures, an investor must post collateral. When a futures portfolio is fully collateralized, the investor has posted cash or acceptable securities with a value equal to the notional value (price multiplied by contract size) of the futures contracts in the portfolio. If U.S. Treasury bills are deposited as collateral, the collateral return or collateral yield is simply the holding period yield on the T bills.

The price return or spot yield on an investment in commodity futures is the change in spot prices (which can be proxied by futures prices on near month contracts).

Since commodity derivative contracts expire, an investor who wants to maintain a position over time must close out the expiring futures position and reestablish a new position with a settlement date further in the future. This process is referred to as rolling over the position and leads to gains or losses which are termed the roll return or roll yield. The roll return can be positive if the futures price curve is in backwardation or negative if the futures price curve is in contango.

To hold the value of a long position constant, an investor must buy more contracts if the new longer dated futures are trading at a lower price (market in backwardation) and buy fewer contracts if the new longer dated futures are trading at a higher price (market in contango). In any event, the roll return on the contracts traded can be calculated as:

Roll return is modest over multiple periods but can be a significant portion of total return in a single period.

Consider a situation where the manager of a portfolio of commodity futures contracts is rolling over July corn futures trading at 397 (cents per bushel) into November corn futures trading at 406. The roll return is:

With the corn futures market in contango, the roll return is negative.

Now consider a situation where the manager is rolling over July natural gas futures trading at 2.35 (dollars per million cubic feet) into August futures trading at 2.22. In this case the roll return is:

Suppose we wanted a specific dollar exposure to natural gas, say $10,000. We would have originally gone long 10,000 / 2.35, or approximately 4,255 contracts. To maintain the dollar exposure upon rolling over into new contracts, we would have gone long 10,000 / 2.22, or approximately 4,504 contracts.

Hence, when the contract is in backwardation, the roll return is positive and results in a larger number of long contracts upon rolling over.

If natural gas exposure is 8.5% of the manager’s portfolio, we can calculate the net roll return for the portfolio as 0.085 × 5.53% = 0.47%.

Swaps can be used to increase or decrease exposure to commodities risk. Swaps are customized instruments created and sold by dealers, who may take on the risk of their swap exposure or hedge their exposure by entering into an offsetting swap contract (in which they have the opposite exposure to the risk factor) or by holding the physical commodity.

Swaps are created for which the payments between the two parties are based on various risk factors such as the excess returns on a commodity, the total return on the commodity, or a measure of price volatility.

In a total return swap the swap buyer (the long) will receive periodic payments based on the change in the futures price of a commodity plus the return on the collateral, in return for a series of fixed payments. Each period, the long will receive the total return on holding the commodity times a notional principal amount, net of the payment promised to the short. If the total return is negative, the long makes the promised fixed payment percentage plus the negative return percentage on the commodity over the period, times the notional amount.

For example, consider a total return swap on oil with a notional value of $10 million, in which for two years the long must pay 25 basis points monthly and will receive the total return on West Texas Intermediate (WTI) crude oil. If over the first month the price of WTI increases from 41.50 bbl to 42.10 bbl (+1.45%), the long will receive a net payment of (0.0145 − 0.0025) × $10 million = $120,000.

If over the second month the price of WTI decreases from 42.10 to 41.20 (−2.14%), the long must make a payment of (−0.0214 − 0.0025) × $10 million = $239,000 to the short.

Total return swaps are often used by institutions to gain exposure to the price risk of the underlying commodity, avoiding either holding the commodity or managing a long position in futures contracts over time.

In an excess return swap, a party may make a single payment at the initiation of the swap and then receive periodic payments of any percentage by which the commodity price exceeds some fixed or benchmark value, times the notional value of the swap. In months in which the commodity price does not exceed the fixed value, no payments are made.

In a basis swap, the variable payments are based on the difference between the prices of two commodities. Often the two commodities are one that has liquid traded futures available for hedging and the other (the one the swap buyer actually uses in production) with no liquid futures contracts available. Because the price changes of the two commodities are less than perfectly correlated, the difference between them (the basis) changes over time.

By combining a hedge using the liquid futures with a basis swap, the swap buyer can hedge the price risk he faces from the input that does not have a liquid futures market.

In a commodity volatility swap, the underlying factor is the volatility of the commodity’s price. If the volatility of the commodity’s price is higher than the expected level of volatility specified in the swap, the volatility buyer receives a payment. When actual volatility is lower than the specified level, the volatility seller receives a payment.

A similar swap settles based on variance in price levels of a commodity, with a swap buyer receiving a payment if the actual variance exceeds the fixed variance established at the onset of the swap. If the actual variance is lower, the variance seller receives a payment.

There are several published commodity indexes. To be most useful, an index should be investable, in that an investor should be able to replicate the index with available liquid futures contracts.

The available commodity indexes differ in the following dimensions:

Which commodities are included

The weighting of the commodities in the index

The method of rolling contracts over as they near expiration

The method of rebalancing portfolio weights

While no index methodology will consistently outperform another index methodology, differences in methodology do result in returns differences, at least over shorter periods. Over long periods, differences between the mix and weights of constituent commodities in individual indexes will result in differences between returns, as some commodities outperform others.

Indexes may be equal weighted or weighted on some factor, such as the value of global production of an individual commodity or commodity sector. A production value weighted index will have more exposure to energy than to livestock or softs, for example.

With regard to roll methodology, a passive strategy may be to simply roll the expiring futures contracts into the near month contract each month. A more active strategy would be to maximize roll return by selecting the further out contracts with the greatest backwardation or smallest contango.

The frequency of rebalancing will also affect commodity index returns. Rebalancing portfolio weights will decrease returns when prices are trending but increase returns when price changes are choppy and mean reverting. For this reason, price behavior across rebalancing periods will influence returns.

If the prices of a commodity are choppy over short horizons but trending on a longer term basis, frequent rebalancing may capture gains from mean reversion over the shorter periods but give up some of the gains from the trend of the commodity’s price over the longer term.

While differences in index construction methodology will lead to differences among index returns over relatively shorter periods, no one methodology is necessarily superior over longer periods. Correlations between returns on different indexes have been relatively high, while correlations between commodity indexes and returns on stocks and bonds have been low.