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.
Cash– and– carry arbitrage:
At the initiation:
At contract expiration:
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).
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.
The forward price must be greater than the spot price to compensate physical storage costs & financial storage cost.
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.
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 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 = 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.
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:
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 :
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