# Components of Total Return for a Fully Collateralized Commodity Futures Contract

The total return on commodity futures is analyzed into the following key components:

• The price return (or spot yield).
• The roll return (or roll yield).
• The collateral return (or collateral yield).

## The Price Return

This refers to the change in commodity futures prices. Note that this price change is different from the change in the physical commodity price. This is due to the lack of standardization of the physical markets.

It is calculated using the following equation:

$$\text{Price return}=\frac{\text{Current price}-\text{Previous price}}{\text{Previous price}}$$

It is important to note that when investors move from a futures contract expiring soon to the next available futures contract, they must “roll” that exposure by selling the current contract. They must then buy the next futures contract on the assumption of a long position.

A portfolio may require an investor to buy far more contracts than the near contracts being sold if backwardation drives the shape of the commodity futures price curve. Alternatively, if the futures price curve shape is being driven by contango, with a higher futures price in the far contract, this scenario will require the purchase of fewer commodity contracts than in the near position.

## The Roll Return

The roll return is an accounting calculation used to replicate a portion of the total return for a fully collateralized (i.e., with no leverage) commodity index. It is the accounting difference (in percentage terms) between the near-term commodity futures contract price and the further-term commodity futures contract price. It is important to note that this roll return is not a return because it can be captured independently; investors cannot construct a portfolio consisting of only roll returns.

The roll return is calculated using the following equation:

$$\text{Roll return}=\frac{\text{Near-term futures contract closing price}-\text{Further-term futures contract closing price}}{\text{Near-term futures contract closing price}}\times\text{% Futures contract position being rolled}$$

## Collateral Return

This refers to the yield (e.g., interest rate) for the bonds or cash used to maintain an investor’s futures position(s). Suppose an investor has less cash than is required by the exchange to maintain the position, the broker who acts as custodian will require more funds (a margin call). Alternatively, he may close out the position by buying to cover a short position or selling to eliminate a long position. The collateral, therefore, acts as insurance for the exchange that the investor can pay for losses.

In conclusion:

$$\text{Total return on a collateralized commodity futures contract}=\text{Spot price return}+\text{Roll return}+\text{Collateral return (risk-free rate return)}$$

## Question

An investor has realized a 5% price return on a commodity futures contract position and a 2.5% roll return after all her contracts were rolled forward. She had held this position for one year with collateral equal to 100% of the position at a risk-free rate of 2% per year.  The total return on this position (annualized excluding leverage) is closest to:

1. 4.5%.
2. 7.5%.
3. 9.5%.

#### Solution

$$\text{Total return }=\text{Spot price return}+\text{Roll return}+\text{Collateral return}$$

She held the contracts for one year, so the price return of 5% is an annualized figure. In addition, the roll return is also an annual 2.5%. Her collateral return equals 2% per year × 100% initial collateral investment = 2%.

Hence her annualized total return is:

$$\text{Total annualized return}= 5\text{%}+2.5\text{%}+2\text{%} =9.5\text{%}$$

B is incorrect. The 7.5% results form summation of price return and roll return.

A is incorrect. The 7% results from the summation of roll return and collateral return.

Reading 35: Introduction to Commodities and Commodity Derivatives

LOS 35 (g) Describe, calculate and interpret the components of total return for a fully collateralized commodity futures contract.

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