READING 45 : COMMODITY FORWARDS AND FUTURES

Commodity Concepts

        When holding a commodity requires storage costs, the forward price must be greater than the spot price to compensate for the financial and physical storage costs.
         The market in which a commodity is stored is referred to as a carry market.
         A lease rate is the amount of rent a lender of a commodity requires.
         Convenience yield is the non-monetary benefit earned from holding an excess inventory of a commodity.

Forward Pricing

        The commodity forward price today is defined as a biased estimate of the expected spot commodity price at time T as follows:
                                 F_0,T = E(S_T)e^{(risk-free rate − discount rate)T}

        A synthetic commodity forward price can be derived by combining a long position on a commodity forward, F0,T , and a long zero-coupon bond that pays F0,T at time T.

Commodity Arbitrage

        The steps in a cash-and-carry arbitrage are as follows:
                 At the initiation of the contract:
                          Step 1: Borrow money for the term of the contract at market interest rates.
                          Step 2: Buy the underlying commodity at the spot price.
                          Step 3: Sell a futures contract at the current futures price.
                At contract expiration:
                          Step 1: Deliver the commodity and receive the futures contract price.
                          Step 2: Repay the loan plus interest.

Lease Rates

        The lease rate is defined as the amount of return the investor requires to buy and then lend a commodity. If an active lease market exists for a commodity, a commodity lender can earn the lease rate by buying a commodity and immediately selling it forward.

Contango and Backwardation

        Markets characterized by upward-sloping forward curves (i.e., contango) occur when the lease rate is less than the risk-free rate. When lease rates exceed the risk-free rate, backwardation occurs.

Storage Costs and Convenience Yields

        Convenience yield is the non-monetary benefit enjoyed by producers who hold excess inventory of raw material inputs. This excess inventory precludes disruptions in the production process caused by temporary shortages of the input in the market. Accounting for existence of a convenience yield, the forward price is calculated as:
                                                                      F_0,T ≥ S₀e^{(r + λ − c)T}
        Accordingly, the arbitrage-free range of the forward price is:
                                                            S₀e^{(r + λ − c)T} ≤ F_0,T ≤ S₀e^{(r + λ)T}
        A commodity owner will only store the commodity if the forward price is greater than or equal to the spot price plus the future storage costs as follows:
                                                                   F_0,T ≥ S₀e^rT + λ(0,T)
        where λ(0,T) represents the future value of storage costs.
         If storage costs are continuously compounded, the no-arbitrage forward price becomes:
                                                                   F_0,T = S₀e^{(r + λ)T}

Comparing Lease Rates, Storage Costs, and Convenience Yields

        Arbitrage-free conditions dictate that continuous lease rates should be equal to either:

• The risk-adjusted required rate of return on commodity investment minus the expected price appreciation of the commodity:or
  
• The risk-free rate minus the forward premium on the commodity:
  

        Lease rates and convenience yields both reduce the futures price. The lease rate is the monetary benefit that the holder of a commodity can earn by lending the commodity. The convenience yield is the non-monetary benefit enjoyed by the user of the commodity by having an excess inventory of the commodity, reducing potential production disruptions caused by temporary shortages of that input.

Commodity Characteristics

        Since gold can earn a return by being loaned out, strategies for holding synthetic gold offer a higher return than holding just the physical gold without lending it out.
         Corn is an example of a commodity with seasonal production and constant demand.
         Electricity is not a storable commodity. In addition, demand for electricity is not constant and will vary with time of day, day of the week, and season.
         Natural gas is an example of a commodity with constant production but seasonal demand.
         Oil is easier to transport than natural gas. Therefore, the price of oil is comparable worldwide. Supply and demand adjust to price changes in the long run.

Commodity Spread

        A commodity spread results from a commodity that is an input in the production process of other commodities. For example, a 7-4-3 crack spread refers to the profit from holding four gasoline futures plus three heating oil futures less seven crude oil futures.

Basis Risk

        Basis risk results from the inability to create a perfect hedge due to differences in commodities with respect to timing, grade, storage costs, and/or transportation costs.

Strip Hedge vs. Stack Hedge

        A strip hedge is created by buying futures contracts that match the maturity and quantity for every month of the obligation. A stack hedge is created by buying a futures contract with a single maturity based on the present value of the future obligations. Advantages of the stack hedge are the availability and liquidity of near-term contracts and narrower bid-ask spreads for near-term contracts.

Cross Hedging

        There are no contracts for jet fuel futures in the United States. Therefore, hedging jet fuel costs requires a cross hedge (e.g., hedge with crude oil futures). A cross hedge is also applied when firms use weather derivatives.