PRICING COMMODITY FORWARDS & FUTURES #
For a given commodity on any trading day, several futures contracts will exist with varying maturity dates. The prices of the commodity futures contracts will differ with the different contract expiration dates. The set of futures prices for a given commodity is known as a forward curve or a forward strip on that particular day.
Commodity forward price :
F0,T = E (ST)e (r – α) T
Where E (ST )= expected spot price of the commodity at time T
α = discount rate for the ST cashflow at time T.
Forward price today is the bilateral estimate of the expected commodity spot price at time T.
COMMODITY ARBITRAGE #
Cash– and– carry arbitrage:
At the initiation:
- Borrow money to market interest rate.
- Buy underlying commodity at the spot price.
- Sell a futures contract at the current futures price.
At contract expiration:
- Deliver the commodity & receive futures contract price.
- Repay the loan plus interest
If the futures contract is overpriced, above steps will generate a riskless profit
If futures price is too low-
Reverse cash– and– carry arbitrage: (opposite of above mentioned steps should be exercised).
LEASE RATE #
Amount of return the investor requires to buy and then lend a commodity. From the borrower’s perspective, the lease rate represents the cost of borrowing the commodity.
Commodity forward price with time T with an active lease market is expressed as :
F0,T = S0e(r – δ )T
Where, S0 = Commodity current spot price
r- δ = Risk free rate less the lease rate
CONTANGO & BACKWARDATION:
Contango– Upward sloping forward curve. Lease rate is less than the risk free rate. Forward price must be greater than the spot price.
Backwardation – Downward sloping forward curve. Lease rate is greater than the risk free rate. Forward price must be less than the spot price.
LEASE RATE #
The forward price must be greater than the spot price to compensate physical storage costs & financial storage cost.
- If the commodity is sold at forward price— Cash & Carry
- Market in which commodity is stored— Carry market.
The commodity will only be stored if the forward price is greater than or equal to the expected spot price plus storage cost.
F0,T = S0 e (r + λ) T
λ = Continuous annual storage cost proportional to the value of the commodity.
COMMODITY ARBITRAGE #
Holding an excess amount of a commodity for a non-monetary return is referred to as convenience yield.
F0,T ≥ S0 e( r + λ – c) T
c = continuously compounded convenience yield, proportional to the value of the commodity.
COMMODITY CHARACTERSTICS #
- GOLD FORWARD PRICE FACTORS : Strategies for holding synthetic gold offer a higher return than holding just the physical gold without lending it out. The present value of gold received in the future is the present value of the forward price computed at the risk free rate of return.
- CORN FORWARD PRICE FACTOR: Commodity with a seasonal production & constant demand. Interest & storage cost need to be considered in determination of forward price. Forward curve is increasing until harvest time & it drops sharply and slopes upward again after harvest time is over.
- ELECTRICITYPRICE FACTORS : Electricity is not storable & demand is not constant. Due to non-stability, price is set by demand & supply.
- NATURAL GAS FORWARD PRICE FACTORS: Constant production but seasonal demand. Forward curve rises steadily when the demand is low due to storage cost.
- OIL FORWARD PRICE FACTORS: Long run forward price is more stable due to constant demand. In the short run, supply & demand shocks cause more volatile prices because supply is fixed.
COMMODITY SPREAD #
Commodity spread results from a commodity that is an input in the production process of other commodities. Example:
Soyabean – Product
Long position in soyabean & short in soyabean meal & oil is crush spread.
Difference between the price of crude oil & petroleum products extracted from it is crack spread.
BASIS RISK #
Basis = Futures price used to hedge – Spot price.
Basis Risk: Risk that the value of a future contract will not move in lines with that of the underlying exposure.
STRIP HEDGE VS. STACK HEDGE #
Suppose a firm faces a series of dates during which it faces price risk. That is, it has a year (or longer) of production. It can:
- Use a strip hedge futures contracts, each with a different delivery date.
- Use a Stack hedge , in which the most nearby and liquid contract is used, and is rolled over to the next-to-nearest contract as time passes.
CROSS HEDGE #
A cross hedge happens when there is risk due to market factors that need to be mitigated but there are no futures on the underlying commodities that are available for trading in the market.
Three factors are relevant when trading a cross hedge decision :
- Liquidity of the futures contracts ( Since delivery may not be an option).
- The correalation between the underlying for the futures contract and the asset(s) being hedged.
- The maturity of the futures contract.