Adjusted future price index: Meaning, Criticisms & Real-World Uses

What Is Adjusted Future Price Index?

An Adjusted Future Price Index refers to the calculated value of a futures contract that incorporates various additional costs and factors beyond the simple quoted price. This adjustment aims to provide a more comprehensive and accurate representation of the true cost or value of acquiring and holding the underlying asset until the contract's expiration. This concept is particularly relevant in the field of financial market analysis, especially within the derivatives market. The Adjusted Future Price Index often considers elements such as carrying costs (e.g., storage, insurance, financing) and any applicable conversion factor for bond futures, which account for the different deliverable bonds. It provides a "cash version" of the futures contract, helping market participants understand the full economic implications of the trade³⁰.

History and Origin

The concept of adjusting futures prices has evolved alongside the increasing complexity of futures markets. Historically, early futures contracts, such as those for agricultural commodities in the 19th century through exchanges like the Chicago Board of Trade (CBOT), primarily involved physical delivery and simpler cost structures²⁸, ²⁹. As financial futures emerged in the 1970s, including those on interest rates and stock indices, the need for more sophisticated pricing models became apparent²⁷. These financial instruments introduced new complexities, such as cash settlement and the influence of interest rates and dividends, which necessitated adjustments to the basic futures price. For instance, the introduction of stock index futures in the early 1980s by exchanges like the Kansas City Board of Trade and the Chicago Mercantile Exchange (CME Group) marked a significant expansion, bringing more intricate pricing considerations into play²⁶. The ongoing evolution of these markets, overseen by regulatory bodies like the Commodity Futures Trading Commission (CFTC), continually refines the methods by which these prices are calculated and adjusted to reflect all economic realities²⁴, ²⁵.

Key Takeaways

An Adjusted Future Price Index is a refined futures contract price, incorporating additional costs and factors.
It provides a more complete economic picture of a futures position by including elements like carrying costs and conversion factors.
Adjusted futures prices are crucial for accurate valuation, risk assessment, and arbitrage strategies in the derivatives market.
They are essential for financial models, back-testing trading strategies, and long-term financial planning.
The adjustments reflect market expectations of various costs and yields associated with the underlying asset.

Formula and Calculation

The calculation of an Adjusted Future Price Index involves starting with the nominal futures price and then incorporating specific cost or yield components. While the precise formula can vary depending on the underlying asset and the specific adjustments being made, a general representation often includes the spot price plus various carrying costs and minus any income generated by the asset.

For a simple storable commodity future, the theoretical futures price (F) can be approximated as:

F = S \times e^{(r + c)T} - I

Where:

(F) = Adjusted Future Price (or theoretical futures price)
(S) = Current Spot price of the underlying asset
(e) = The base of the natural logarithm (approximately 2.71828)
(r) = Risk-free interest rates (annualized)
(c) = Storage costs as a percentage of the asset's value (annualized)
(T) = Time to expiration (in years)
(I) = Present value of any income (e.g., dividends for equities, or convenience yield for commodities) expected from the underlying asset until expiration.

In more complex scenarios, such as bond futures, a conversion factor is applied to account for the deliverability of various bonds. The adjusted futures price for a bond futures contract would then be:

\text{Adjusted Futures Price} = \text{Quoted Futures Price} \times \text{Conversion Factor}

These formulas ensure that the futures price accurately reflects the cost of holding the physical asset (or the equivalent financial position) until the futures contract matures²³.

Interpreting the Adjusted Future Price Index

Interpreting the Adjusted Future Price Index involves understanding that it represents the market's expectation of the underlying asset's price at expiration, factoring in the cost of holding or financing that asset. A higher Adjusted Future Price Index relative to the current spot price for a commodity generally indicates positive carrying costs (contango), suggesting that it costs money to store and finance the commodity over time. Conversely, a lower Adjusted Future Price Index could indicate backwardation, where the immediate demand for the asset is higher than future demand, leading to a discount for future delivery²².

For financial instruments, the Adjusted Future Price Index will reflect prevailing interest rates and any expected income streams. For instance, higher interest rates typically lead to a higher adjusted futures price for financial assets, as financing costs increase. Investors and analysts use this adjusted price to gauge market sentiment, perform price discovery, and identify potential arbitrage opportunities between the cash market and the futures market.

Hypothetical Example

Consider a crude oil futures contract with three months until expiration.

Current Spot price of crude oil: $80.00 per barrel
Risk-free interest rates: 5% per annum (0.05)
Storage and insurance costs: $0.10 per barrel per month, or $0.30 for three months. This is 0.30 / 80 = 0.00375 as a percentage of the spot price for three months.
Time to expiration (T): 3 months, or 0.25 years

To calculate the Adjusted Future Price Index (assuming no convenience yield for simplicity):

First, calculate the total carrying cost rate: (r + c = 0.05 + (0.00375 / 0.25) = 0.05 + 0.015 = 0.065) per annum, or (0.065 \times 0.25 = 0.01625) for three months.

F = S \times e^{(r + c)T}

F = 80 \times e^{(0.065 \times 0.25)}

F = 80 \times e^{0.01625}

F \approx 80 \times 1.01638

F \approx 81.31

The Adjusted Future Price Index for this crude oil contract would be approximately $81.31 per barrel. This price reflects that, in three months, holding the physical oil would incur storage and financing costs, making the future delivery price higher than the current spot price, a situation known as contango.

Practical Applications

The Adjusted Future Price Index is a critical tool across various financial sectors. In risk management, it allows companies to more accurately hedge against future price fluctuations by understanding the true cost of their futures positions, whether they are producers looking to lock in selling prices or consumers aiming to secure purchasing costs. For example, airlines use fuel futures to manage future expenses, with the adjusted price reflecting the comprehensive cost of future fuel delivery.

In investment analysis, fund managers utilize the Adjusted Future Price Index for asset allocation strategies, particularly when incorporating commodity futures into diversified portfolios²⁰, ²¹. By considering all carrying costs and conversion factors, they can better assess the expected return and risk of these derivative instruments. Furthermore, traders involved in speculation and arbitrage rely on the Adjusted Future Price Index to identify mispricings between the spot market and futures market, seeking to profit from discrepancies after accounting for all relevant costs. Regulatory bodies, such as the Commodity Futures Trading Commission (CFTC), also monitor these adjusted prices to ensure market integrity and prevent manipulative practices¹⁸, ¹⁹. Research Affiliates, an institutional asset management firm, utilizes refined forecasts and methodology that consider various factors for over 130 asset classes, including commodity futures, underscoring the importance of such detailed analysis in capital market expectations¹⁶, ¹⁷.

Limitations and Criticisms

While the Adjusted Future Price Index offers a more comprehensive view of futures contracts, it comes with certain limitations and criticisms. One significant challenge lies in accurately forecasting all components of the adjustment, especially carrying costs and future inflation and interest rates ¹⁴, ¹⁵. Unforeseen changes in these variables can lead to discrepancies between the projected and actual adjusted prices. For instance, shifts in monetary policy by central banks can alter interest rate expectations, impacting the financing component of the adjusted price¹², ¹³.

Another criticism arises in its application for back-testing trading strategies. Various methods for creating continuous futures data series (e.g., back-adjusted, proportionally adjusted) can introduce distortions, with some potentially producing negative price values in deflationary environments¹¹. These distortions can limit the accuracy of technical analysis and historical performance evaluation. Furthermore, the theoretical models used to derive the Adjusted Future Price Index often assume perfect or frictionless financial markets and complete arbitrage mechanisms, which may not hold true in reality due to factors like transaction costs, liquidity issues, and asymmetric information¹⁰. Consequently, real-world prices may deviate from theoretically adjusted prices, posing challenges for precise valuation and strategy execution.

Adjusted Future Price Index vs. Futures Price

The primary distinction between the Adjusted Future Price Index and a simple Futures Price lies in the comprehensiveness of their valuation. The nominal "Futures Price" is the publicly quoted price for a futures contract, representing the agreed-upon price for delivery of the underlying asset at a specified future date⁸, ⁹. It is the most direct and easily observable value in the derivatives market.

In contrast, the Adjusted Future Price Index takes this nominal futures price and refines it by incorporating various factors that influence the true economic cost or value of holding the contract. These adjustments typically include carrying costs such as storage, insurance, and the cost of financing (reflected by interest rates), as well as any income or benefits derived from the underlying asset (like dividends for stocks or a convenience yield for commodities)⁷. For bond futures, a conversion factor is also applied to standardize the value across different deliverable bonds. While the Futures Price is what traders see on their screens, the Adjusted Future Price Index is a more nuanced, "cash-equivalent" value that helps investors and analysts understand the full economic implications and compare the futures contract's value more accurately against other investments or the spot price of the underlying asset⁶. Confusion often arises because the quoted futures price is what is commonly discussed, but for in-depth analysis and fair valuation, the adjusted price provides a more complete picture.

FAQs

Why is an Adjusted Future Price Index necessary?

An Adjusted Future Price Index is necessary because the raw futures price often doesn't capture all the real-world costs and benefits associated with holding the underlying asset until the futures contract expires. By including factors like carrying costs and income, it provides a more accurate and economically sound valuation, crucial for informed trading, hedging, and risk management ⁵.

What factors typically influence the adjustment?

Key factors influencing the adjustment include the spot price of the underlying asset, prevailing interest rates (financing costs), storage costs (for physical commodities), insurance, and any income generated by the asset (e.g., dividends for stocks or a convenience yield for commodities). For bond futures, a conversion factor is also a significant adjustment⁴.

How does inflation affect the Adjusted Future Price Index?

Inflation can significantly impact the Adjusted Future Price Index, primarily through its effect on interest rates and the cost of holding goods. Higher inflation expectations often lead to higher nominal interest rates, which increases the financing component of carrying costs and thus generally raises the adjusted futures price. Additionally, inflation directly erodes the purchasing power of future cash flows, which futures prices aim to account for³.

Is the Adjusted Future Price Index the same as the forward price?

While often used interchangeably in some contexts, there can be subtle differences. Both futures and forward contracts specify a price for a future transaction. However, futures contracts are standardized and traded on exchanges with daily marking-to-market, whereas forward contracts are typically customized over-the-counter agreements. The Adjusted Future Price Index specifically refers to the exchange-traded futures price after accounting for various adjustments, while a forward price might not have the same standardized adjustment conventions.

Who uses the Adjusted Future Price Index?

The Adjusted Future Price Index is primarily used by professional traders, institutional investors, commodity producers and consumers, and financial analysts. These parties use it for accurate valuation, hedging against price risks, speculation, arbitrage strategies, and developing quantitative models for back-testing and forecasting¹, ².