Amortized roll yield

What Is Amortized Roll Yield?

Amortized roll yield refers to the continuous and gradual accrual or decay of the return derived from the difference between a futures contract's price and the underlying asset's spot price as the contract approaches its expiration. In the realm of derivatives investing, particularly within commodity markets, roll yield is a crucial component of the total return for investors holding futures contracts. While "roll yield" often implies the profit or loss realized when an expiring futures contract is replaced with a new, longer-dated one, the "amortized" aspect emphasizes the daily or continuous nature of this gain or loss as the futures price converges towards the spot price over time. This ongoing adjustment occurs whether a market is in contango or backwardation.

History and Origin

The concept of roll yield is inherently tied to the evolution of futures contracts themselves, which arose from the need to manage price risk in commodity markets. Early forms of futures trading can be traced back to the Dojima Rice Market in 18th-century Japan, while organized futures exchanges in the U.S. began in the mid-1800s with the Chicago Board of Trade (CBOT) listing the first standardized commodity futures contract in 1864¹⁵, ¹⁶.

As futures markets matured, participants recognized that the return from holding a futures position wasn't solely dependent on changes in the underlying asset's spot price. It also included a component related to the structure of futures prices across different maturities. This component, later termed "roll yield," became an important consideration for investors maintaining continuous exposure to a commodity or financial instrument through rolling contracts. Academic research began to formally deconstruct futures returns into various components, including the roll yield, further solidifying its recognition as a distinct element of futures investment performance¹⁴. For instance, the National Bureau of Economic Research has published extensive work on the fundamentals of commodity futures returns, examining factors such as inventory levels and their relationship to the term structure of prices, which directly influence roll yield¹³.

Key Takeaways

• Amortized roll yield represents the continuous accrual or decay of return as a futures contract's price converges to its spot price over time.
• It is a significant component of the total return from holding futures contracts, alongside the change in the underlying asset's spot price.
• The nature of amortized roll yield (positive or negative) depends on whether the market is in backwardation or contango.
• Understanding amortized roll yield is vital for investors in commodity futures and other derivatives to accurately assess expected returns and manage risk.
• While often misunderstood as a discrete event during rolling, its "amortized" nature highlights its ongoing impact throughout the contract's life.

Formula and Calculation

The amortized roll yield reflects the convergence of the futures price towards the spot price as the contract approaches its expiration. While there isn't a single, universally defined "amortized roll yield" formula distinct from the broader concept of roll yield, its calculation as a rate or daily accrual highlights the amortization aspect.

The periodic roll yield (e.g., monthly) can be understood as:

However, to conceptualize it as amortized, one considers the daily or continuous price convergence. Over a given period, the amortized roll yield can be viewed as the portion of the futures return attributable to the change in the futures price relative to the spot price, not due to the spot price movement itself.

More generally, for a long futures position, the expected roll yield (or "carry return") over a period is often expressed in terms of the futures curve:

Where:

• (F_0) = Current futures price (e.g., for the nearest contract)
• (F_T) = Futures price for a contract expiring at time (T) (e.g., the next-nearest contract)
• (T) = Time to maturity difference between the two contracts (in years or a fraction of a year)

This simple representation captures the daily "roll down" or "roll up" as contracts age and their prices converge towards the spot price. In practice, calculating the precise amortized daily yield involves tracking the daily change in the basis (futures price minus spot price) and attributing that change over the remaining life of the contract.

Interpreting the Amortized Roll Yield

Interpreting amortized roll yield requires an understanding of the relationship between spot and futures prices, particularly the concepts of contango and backwardation.

In a market in contango, longer-dated futures contracts trade at a premium to near-term contracts, meaning (F_T > F_0). This typically happens when carrying costs (like storage, insurance, and financing) are positive, and the market expects the spot price to rise over time. In this scenario, as a futures contract approaches expiration, its price is expected to "roll down" towards the lower spot price. For a long futures position, this convergence results in a negative amortized roll yield. Investors holding positions through multiple roll periods will experience a drag on their returns due to this negative yield, effectively "paying" for the privilege of holding the futures position¹².

Conversely, in a market in backwardation, longer-dated futures contracts trade at a discount to near-term contracts, meaning (F_T < F_0). This often occurs when there is high current demand or limited supply of the physical commodity, leading to a higher spot price¹¹. As a futures contract approaches expiration, its price is expected to "roll up" towards the higher spot price. For a long futures position, this convergence generates a positive amortized roll yield. Investors benefit as their existing contract gains value relative to the further-out contracts, potentially enhancing overall returns¹⁰.

The amortized roll yield, therefore, provides insight into the profitability of maintaining a continuous exposure to a futures market. A consistently positive amortized roll yield (due to backwardation) can be a significant source of return for commodity investors, while a consistently negative amortized roll yield (due to contango) can erode returns. It reflects the cost or benefit of holding futures relative to the immediate physical asset, influencing long-term investment strategy in commodity markets.

Hypothetical Example

Consider an investor holding a long position in a crude oil futures contract.

Scenario: Contango Market

• Today's spot price of crude oil: $80.00 per barrel
• Price of the crude oil futures contract expiring in 1 month (F1): $81.00 per barrel
• Price of the crude oil futures contract expiring in 2 months (F2): $82.00 per barrel

The market is in contango because longer-dated contracts are more expensive than near-term ones. The price difference between F1 and F2 is $1.00.

Suppose the investor holds the F1 contract. As time passes and the F1 contract approaches its expiration, its price is expected to gradually converge toward the spot price. If, over the month, the spot price remains relatively stable at $80.00, and the F1 futures price moves from $81.00 down to $80.00 by expiration, the investor would experience a price depreciation of $1.00 from the futures contract itself. This $1.00 decline, amortized over the month, represents a negative amortized roll yield.

If the investor wishes to maintain continuous exposure, they would "roll" their position by selling the expiring F1 contract and buying the F2 contract. At the time of the roll, they would sell F1 at $80.00 and buy F2 at $82.00 (assuming the curve structure persists). The immediate $2.00 difference ($80.00 - $82.00 = -$2.00) is the negative roll yield experienced at that point. The amortized roll yield perspective emphasizes that this "cost" was actually being incurred incrementally as the F1 contract price decayed towards the spot price over the preceding month.

Practical Applications

Amortized roll yield is a crucial metric for investors and analysts engaged in derivatives markets, particularly in commodity investing. Its practical applications span several areas:

• Commodity Investment Strategies: For investors in commodity index funds or exchange-traded funds (ETFs) that track commodity prices by rolling futures contracts, understanding amortized roll yield is paramount. A positive amortized roll yield (from backwardation) can significantly enhance portfolio returns, while a negative amortized roll yield (from contango) can be a substantial drag⁸, ⁹. Investment managers often build strategies that seek to capture positive roll yield or mitigate negative roll yield, influencing decisions on which commodities to overweight or underweight in a portfolio⁷.
• Performance Attribution: Amortized roll yield helps in dissecting the total return of a futures-based investment. The overall return can be broken down into the change in the underlying spot price and the contribution from roll yield. This attribution allows investors to understand what factors are driving their profits or losses, distinguishing between pure price exposure and the effects of the yield curve structure⁶.
• Risk Management and Hedging: For producers and consumers using futures for hedging purposes, the amortized roll yield affects the cost or benefit of their hedge. For example, a producer hedging against falling prices in a contango market might find their hedge more expensive due to the negative roll yield, while a consumer in a backwardated market might benefit from a positive roll yield on their long futures positions. This understanding helps in optimizing hedging strategies and managing expected cash flows.
• Market Analysis and Forecasting: The presence and magnitude of amortized roll yield can offer insights into market expectations regarding supply and demand dynamics, inventory levels, and carrying costs for commodities. For instance, persistent backwardation may signal tight supply conditions, as market participants are willing to pay a premium for immediate delivery⁵. Analysts can use this information to gauge market sentiment and potential future price movements. Research Affiliates, for example, discusses how roll returns provide a glimpse into the expected price movement of a commodity futures contract⁴.

Limitations and Criticisms

While amortized roll yield is a critical concept in derivatives investing, particularly for commodity futures contracts, it is not without its limitations and criticisms.

One significant point of contention revolves around its definition and whether it represents an actual cash flow or a theoretical component of return. Some critics argue that the "roll yield" is a "myth" in the sense that no discrete cash payment occurs at the time of a roll trade; rather, it reflects the difference between the futures price and the spot price, or the cost of carry, which implicitly affects the total return², ³. This perspective highlights that the "gain" or "loss" from roll yield is embedded in the price changes of the futures contract itself as it moves towards maturity, rather than being a separate, distributable yield like a dividend or coupon payment. This can lead to misconceptions about its impact on an investor's purchasing power¹.

Furthermore, the relationship between roll yield and actual realized returns can be complex. While positive amortized roll yield (from backwardation) is generally seen as beneficial, and negative roll yield (from contango) as detrimental, these effects are not guaranteed. Unexpected shifts in the spot price or the shape of the yield curve can significantly alter the actual return experienced by an investor. For example, a market in contango might still yield positive returns if the underlying spot price rises sufficiently to offset the negative roll yield. Conversely, a backwardated market might still result in losses if the spot price falls sharply.

The calculation and interpretation of amortized roll yield can also be sensitive to the specific futures contracts used, their maturities, and the frequency of rebalancing in an investment strategy. Different methodologies can lead to varying assessments of its impact, making direct comparisons challenging. Additionally, factors like market efficiency and the presence of arbitrage opportunities can influence how closely the theoretical amortized roll yield aligns with observable market behavior.

Amortized Roll Yield vs. Roll Yield

While often used interchangeably or with subtle distinctions, "amortized roll yield" and "roll yield" emphasize different aspects of the same underlying phenomenon in futures contracts.

Essentially, "roll yield" is the broader concept of the return gained or lost from price differences across maturities when rolling a futures position. "Amortized roll yield" hones in on how that gain or loss is effectively accrued or diminished over the life of the contract as it naturally converges to the spot price, rather than being solely concentrated at the moment of the roll transaction. It highlights the ongoing nature of this yield component, impacting an investor's effective return continuously.

FAQs

What causes amortized roll yield?

Amortized roll yield is caused by the convergence of a futures contract's price to the underlying spot price as the contract approaches its expiration. This convergence generates a gain or loss that is effectively "amortized" or accrued over the life of the contract. The direction (positive or negative) depends on the shape of the futures yield curve, specifically whether the market is in contango or backwardation.

Is amortized roll yield always positive?

No, amortized roll yield is not always positive. It is positive when a market is in backwardation, meaning nearer-term futures contracts are more expensive than longer-term ones. Conversely, it is negative when a market is in contango, where longer-term contracts are more expensive than nearer-term ones. In a contango market, investors holding long positions experience a drag on returns due to the negative amortized roll yield.

How does amortized roll yield affect commodity investments?

Amortized roll yield significantly impacts returns for investors holding commodity futures contracts, especially those maintaining continuous exposure through rolling positions. In a backwardated market, positive amortized roll yield can enhance returns, contributing to the total return. In a contango market, negative amortized roll yield can erode potential profits, even if the underlying spot price remains stable or rises modestly. Understanding this component is crucial for proper portfolio diversification and investment strategy.