Futures Contracts
A derivative is a product whose value is derived from the value of one or more basic variables called bases. These underlying assets or reference rates can include Equity, Forex, and Commodity. Futures contracts are a significant type of financial derivative.
Definition and Nature
A Futures Contract is an agreement between two parties that commits one party to buy an underlying financial instrument (bond, stock, or currency) or commodity (gold, soybean, or natural gas) and one party to sell a financial instrument or commodity at a specific price at a future date. This agreement is completed at a specified expiration date.
Futures contracts are described as special types of forward contracts. However, they differ from forward contracts in key ways. Unlike forwards which are customized bilateral contracts, futures contracts are standardized and exchange-traded contracts. This standardization covers aspects like the asset type, quality, and contract size. A significant difference is that the counterparty to a futures contract is typically the clearing corporation on the appropriate exchange, unlike forward contracts where the counterparty is the other original party to the agreement.
To initiate trading in futures contracts, both the buyer and seller must put up “good faith money” in a margin account. The margin levels are determined by regulators, commodity exchanges, and brokers.
The agreement under a futures contract can be completed at or before the expiration date by physical delivery, cash settlement, or offsetting the position.
Markets and Underlying Assets
There is a significant market for futures contracts. These contracts can be either commodity futures or financial futures. Financial futures are further classified as Stock index futures, Interest rate futures, and Currency futures. The underlying assets can include bonds, stocks, currencies, commodities like gold or natural gas, or indices.
Terminology
Key terms associated with futures contracts include:
- Spot price: The price at which an underlying asset is traded in the spot market.
- Futures price: The price agreed upon at the time of the contract for the delivery of an asset at a specific future date. This can also be referred to as the delivery price. The actual futures price today is sometimes denoted as AFP (Actual Forward or Future Price).
- Contract cycle: The period over which a contract is traded.
- Expiry date: The date on which the final settlement of the contract takes place.
- Contract size / Lot size: The amount of the underlying asset that must be delivered for one contract.
An investor who has agreed to buy the underlying asset is said to have a long futures position, while the party who agrees to sell holds a short futures position.
Pricing / Valuation
The theoretical forward or future price (F*) today can be determined using pricing models. The carry pricing model stipulates how this price is determined. A fundamental relationship, assuming continuous compounding and no dividends/storage costs, is F* = S0 * e^(r*t), where S0 is the current spot price, r is the risk-free interest rate, and t is the time to expiration.
Modifications to this formula are needed for assets with yields (like dividends) or carrying costs:
- For an asset that provides a known yield (y), the theoretical price is F* = S0 * e^((r – y) t).
- For assets like stocks paying discrete dividends, the theoretical future price (TFP) can be calculated as the adjusted spot price (Spot Price – Present Value of Dividend) compounded at the risk-free rate: TFP = [S0 – I] × e^(r×t), where I is the present value of dividends expected before expiry. An example calculates the present value of a dividend using the formula (Dividend Amount) × e^(-r×t).
- For commodities with storage costs (c), the theoretical forward price (TFPx) can be calculated as TFPx = Sx × e^((r+c)×t), where Sx is the spot price and c is the storage cost rate. An example shows this calculation for a commodity priced per kg with a storage cost rate and interest rate.
If the actual futures price deviates from the theoretical price calculated using these models, an arbitrage opportunity may exist. An arbitrage strategy described involves comparing the actual futures price to the theoretical price. If the futures contract is selling for more than its theoretical value, one could borrow money, buy the underlying asset, and simultaneously sell the futures contract. At expiration, the underlying asset (plus any yield, less costs) is delivered against the futures contract. The profit arises from the difference between the actual and theoretical futures price, adjusted for borrowing costs and any yield/costs of the underlying. An example shows borrowing 300, buying a share, selling a futures contract for312, and resulting in a riskless profit of `4.74 after accounting for borrowing costs.
It is noted that while current spot and forward rates are known, the future spot rates are not known; they will be revealed as the future unfolds.
Execution and Settlement
The agreement is completed at the specified expiration date. Completion methods include physical delivery or cash settlement. Positions can also be offset (closed out) prior to the expiration date. Example calculations show variations in receipts under a forward contract versus futures, including the calculation of a “Variation Margin” for futures. Profit or loss on a futures position is calculated based on the change in the futures price between the opening and closing (squaring off) transaction.
Applications: Hedging
A primary economic function of the futures market is to provide an opportunity for market participants to hedge against the risk of adverse price movements. Buyers use futures to obtain protection against rising prices, and sellers to protect against declining prices. Hedging can involve different strategies and target different levels of risk.
Examples of hedging with futures include:
- Hedging a portfolio’s beta risk using index futures. The number of index future contracts needed to hedge a portfolio can be computed using the formula: (Portfolio Value × Beta of Portfolio w.r.t Index) ÷ Value per Index futures Contract. Examples demonstrate calculating portfolio beta and then the number of contracts required to hedge based on desired beta (e.g., hedging to a desired beta of 1 or 0).
- Hedging against changes in commodity prices. A company needing a commodity in the future can compare the spot price plus carrying cost compounded at the interest rate (theoretical forward price) with the available futures contract rate to decide whether to use the futures market for hedging.
- Interest rate risk can be hedged using instruments like interest rate futures.
Comparison with Forward Contracts
As mentioned, futures are specialized forward contracts. Key differences noted in the sources and previous discussion include:
- Standardization vs. Customization: Futures are standardized exchange-traded, while forwards are customized bilateral contracts (as discussed previously).
- Counterparty Risk: For futures, the counterparty is the clearing corporation, significantly reducing counterparty risk. For forwards, counterparty risk is present because the contract is directly between two parties (as discussed previously).
- Trading: Futures trade on organized exchanges, while forwards are typically traded over-the-counter.
- Margin: Futures require margin accounts.
An example calculation compares net receipts from hedging a foreign currency amount using a forward contract versus futures, showing slightly different outcomes.
Future Value (Time Value of Money)
Separate from futures contracts, the term “Future Value” relates to the Time Value of Money concept. Future value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate.
- Future value in the case of simple interest is calculated as P0 + SI, where SI = P0 * (i) * (n).
- For compound interest, the future value (S) of a single amount (p) invested today is calculated as S = p * (1+i)^n, where i is the interest rate per period and n is the number of periods.
- The future value of an annuity (a series of equal payments) involves summing the future values of each payment.
This concept of Future Value is distinct from futures contracts, although calculating the present or future value of cash flows is fundamental in financial management, including valuation related to future contract pricing. Terminal Value, for example, is the value of an asset at some point of time in the future.