COMMENTAR Y
Deconstructing Futures Returns The role of roll yield AN ABRIDGED VERSION OF A WHITE PAPER IN THE CAMPBELL WHITE PAPER SERIES, CAMPBELL & COMPANY
Executive summary F
utures and spot returns on the same underlying asset often diverge, and the magnitude of this divergence is known as the futures “roll yield.” The cumulative impact of roll yield can be quite significant, in some cases being similar in magnitude to the entire gain or loss an
investor experiences over the lifetime of a trade. In spite of the importance of roll yield in futures markets, misconceptions abound regarding its nature, measurement, and relevance.
This paper aims to demystify roll yield by connecting it to ideas familiar to investors and addressing common misunderstandings. The roll yield is not the result of “rolling” positions from one contract to the next. We demonstrate this by walking through the life cycle of a futures trade. We also demonstrate that there is a direct relationship between roll yield and the slope of the futures term structure. Finally, we show that the decomposition of a futures return into its spot return and roll yield components provides insights that have implications for both carry and trend-following strategies. At Campbell, many of these ideas are used in the ongoing development of new trend-following strategies. They also serve as the foundation for some of the strategies included in Campbell PRISM, a quantitative trading programme which utilises a suite of non-trend-based alpha strategies to exploit structural market opportunities.
Relating roll yield to the roll transaction Futures-spot divergence is known as the futures “roll yield,” which can be defined as:
EQUATION 1: Roll Yield = Futures Return - Spot Return
A common misconception is that roll yield represents the P&L generated on the day of the contract roll.
For example, if rolling a futures position requires you to sell the current contract and buy the next one at a higher price, it may appear that the transaction will cause a loss (since you are selling low and buying high). However, this is not the case; the roll yield accumulates over the life of the trade as the futures price converges to spot at expiration.1
Fig.1 Daily P&L from long position in S&P futures On the roll day, Lois's P&L is due entirely to the change in price of ESH3. There is no P&L from the price difference between ESH3 and ESM3. $10
ESH3 (Mar-13 contract) ESM3 (Jun-13 contract)
$5 $0 Position Opened: -$5 -$10 08-Mar 11-Mar 12-Mar 13-Mar 14-Mar 15-Mar 18-Mar
ESH3: Position opened at the close, so no P&L impact ESM3: No position
Prior to the Roll:
ESH3: Position held steady. P&L from daily change in closing price
Roll Day: ESH3: Long position sold at the close, so P&L is close-to-close change
ESM3: New long position opened at the close, so no P&L impact
Following the Roll:
ESM3: Position held steady. P&L from daily change in closing price.
In order to observe the impact of the roll event, let’s follow along with an investor who is long a futures contract.
On 8 March, 2013, an investor (Lois) goes long one contract2 of the March 2013 e-Mini (ESH3) at the closing price of 1549.50.3 As the 15 March expiration approaches, Lois wants to maintain her exposure, so on 14 March she sells her position at the closing price of 1562.25, and goes long one June 2013 contract (ESM3) at the closing price of 1556.00. On 18 March, Lois closes her position at 1546.75.
There are a few questions to consider. What is Lois’s cumulative P&L? How much of it is directly
attributable to the roll? And to what extent is her P&L different from simply comparing the front futures prices on 8 March and 18 March?
Fig.1 shows the daily P&L in each contract. We see that nothing unusual happens on the roll day. There is, however, a 6.25 point difference between ESH3 and ESM3 on the roll day, which some mistakenly believe is a roll ‘cost’ (or in this case, a roll gain). The price difference does not directly impact P&L, but it does make any type of analysis involving prices problematic. Simply splicing the front contract prices together does not properly account for the P&L. To correct this, we need to shift the closing prices of the “rolled-into” contract by the difference in prices on the roll date (i.e., 6.25). This “joined” price series does not represent an actual contract, but it accurately accounts for the P&L experienced by an investor.
What drives the difference between the joined price and front price? The difference between the joined and spliced prices over time is called the cumulative roll adjustment, which is the sum of roll adjustments at each roll date.
EQUATION 2: Joined Price = Front Price + Cumulative Roll Adjustment
Since each roll adjustment is directly related to the slope of the futures term structure, we see that the cumulative roll adjustment reflects an average of the term structure on the roll dates. For example, if the next contract has a lower (/higher) price than the front contract, then the cumulative roll adjustment will be positive (/negative). This type of market is in backwardation (/contango). Suppose we assume that rolls occur an instant before expiry, where
Source: Bloomberg
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